The FutureSchool mathematics and English programmes have been fully aligned to the National Certificate of Educational Achievement (NCEA). For those schools that offer the International Baccalaureate or Cambridge International Examinations curricula, these are also available within FutureSchool as part of its standard curriculum library.

To see more detail about lessons covered within our subjects, just click on the year group titles below:







Mathematics

PYP Kindergarten Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – PYP Kindergarten
Objective: Assessment
2Using and applying numberThe numbers 1 to 5
Objective: On completion of the lesson the student will be able to read, write and identify the words and numerals for the numbers 1 to 5
3Using and applying numberThe numbers 6 to 9
Objective: On completion of the lesson the student will be able to match cardinal words and numbers with groups of 6-9 objects.
4The number systemOrdinal numbers 1 to 9
Objective: On completion of the lesson the student will be able to match ordinal words and numbers with groups of 1-9 objects.
5Using and applying numberZero and counting numbers 1 to 9
Objective: On completion of the lesson the student will be able to recognise, write and match the numeral and word for the number zero.
6Using and applying numberThe number 10
Objective: On completion of the lesson the student will be able to write the numeral and word for the number 10, count up to 10 objects and to match a group of objects to the correct number.
7Using and applying numberNumbers 11 to 20
Objective: On completion of the lesson the student will be able to write the numeral and word for the numbers 11 to 20, count up to 20 and match a group of objects to the correct number.
8Time, days of weekDays of the week
Objective: On completion of the lesson the student will be able to: name the days of the week in order, recognise them in a written form, be able to answer questions about the days of the week, and have an understanding of a diary.
9Time, durationDuration
Objective: On completion of the lesson the student will be able to estimate and measure the duration of an event using informal units, and compare and order the duration of an event using informal units.
10Time, monthsMonths and seasons of the year
Objective: On completion of the lesson the student will be able to: name and order the months of the year, know the number of days in each month, name the seasons in order, and know the number of months in each season.
11ReasoningSimple addition up to the number 10
Objective: On completion of the lesson the student will be able to write simple number sentences that show numbers adding up to another number.
12Weight/massIntroducing the concept of mass
Objective: On completion of the lesson the student will understand the concepts of mass.
13ExamExam – PYP Kindergarten
Objective: Exam
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PYP Grade 1 Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – PYP Grade 1
Objective: Assessment
2Using and applying numberThe numbers 1 to 5
Objective: On completion of the lesson the student will be able to read, write and identify the words and numerals for the numbers 1 to 5
3Using and applying numberThe numbers 6 to 9
Objective: On completion of the lesson the student will be able to match cardinal words and numbers with groups of 6-9 objects.
4The number systemOrdinal numbers 1 to 9
Objective: On completion of the lesson the student will be able to match ordinal words and numbers with groups of 1-9 objects.
5Using and applying numberZero and counting numbers 1 to 9
Objective: On completion of the lesson the student will be able to recognise, write and match the numeral and word for the number zero.
6Using and applying numberThe number 10
Objective: On completion of the lesson the student will be able to write the numeral and word for the number 10, count up to 10 objects and to match a group of objects to the correct number.
7Using and applying numberNumbers 11 to 20
Objective: On completion of the lesson the student will be able to write the numeral and word for the numbers 11 to 20, count up to 20 and match a group of objects to the correct number.
8CalculationsThe numbers 20 to 99
Objective: On completion of the lesson the student will be able to identify, name and add groups of ten, counting to ninety-nine.
9Calculation-multiplesMultiples of 10 up to 100
Objective: On completion of the lesson the student will be able to read, write, rename and add multiples of ten.
10Using and applying numberUsing place value to order numbers up to 20
Objective: On completion of the lesson the student will be able to use place value to order numbers up to the value of 20.
11ReasoningSimple addition up to the number 10
Objective: On completion of the lesson the student will be able to write simple number sentences that show numbers adding up to another number.
12ReasoningSimple addition up to the number 20
Objective: On completion of the lesson the student will be able to write simple number sentences and also write addition in a vertical format using numbers up to 20.
13CalculationsSubtraction up to the number 10
Objective: On completion of the lesson the student will be able to calculate the answer to take away or subtraction number sentences up to the number 10.
14CalculationsSubtraction by Comparison
Objective: On completion of the lesson the student will be able to calculate take away or subtraction number sentences by comparison methods.
15CalculationsSubtraction up to the number 20 and beyond
Objective: On completion of the lesson the student will be capable of subtraction using tens and units and calculating the answer to take away or subtraction number sentences.
16LengthCompare length by using informal units of measurement
Objective: On completion of the lesson the student will be able to measure objects around the student’s home and compare their length to each other. The student will also be able to compare the different ways the student measured the same object.
17LengthUsing the metre as a formal unit to measure perimeter
Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.
18LengthUsing the formal unit of the centimetre to measure length and perimeter
Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.
19Weight/massIntroducing the concept of mass
Objective: On completion of the lesson the student will understand the concepts of mass.
20Time, days of weekDays of the week
Objective: On completion of the lesson the student will be able to: name the days of the week in order, recognise them in a written form, be able to answer questions about the days of the week, and have an understanding of a diary.
21Time, durationDuration
Objective: On completion of the lesson the student will be able to estimate and measure the duration of an event using informal units, and compare and order the duration of an event using informal units.
22Time, monthsMonths and seasons of the year
Objective: On completion of the lesson the student will be able to: name and order the months of the year, know the number of days in each month, name the seasons in order, and know the number of months in each season.
23Time, digitalO’clock and half past using digital time
Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on a digital clock.
24Time, analogueO’clock and half past on the analogue clock
Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock.
25FractionsUsing fractions 1/2, 1/4, 1/8 to describe part of a whole
Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole.
26FractionsUsing fractions 1/2, 1/4, 1/8 to describe parts of a group or collection
Objective: On completion of the lesson the student will be able to use the fractions to describe equal parts of a collection of objects.
27ExamExam – PYP Grade 1
Objective: Exam
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PYP Grade 2 Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – PYP Grade 2
Objective: Assessment
2CalculationsThe numbers 20 to 99
Objective: On completion of the lesson the student will be able to identify, name and add groups of ten, counting to ninety-nine.
3Calculation-larger numbersThe numbers 100 to 999
Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999.
4Calculation 10-100Counting by 1, 2, 5, and 10 to 100
Objective: On completion of the lesson the student will be able to skip count to one hundred and show that one hundred equals ten times ten.
5AdditionAddition to 99
Objective: On completion of the lesson the student will be able to use place value to add two 2-digit numbers together up to a total of 99.
6AdditionAddition up to the number 999
Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers.
7CalculationsSubtraction up to the number 20 and beyond
Objective: On completion of the lesson the student will be capable of subtraction using tens and units and calculating the answer to take away or subtraction number sentences.
8SubtractionSubtraction of two-digit numbers Involving comparison.
Objective: On completion of the lesson the student will know how to solve and record the answer to word problems and will understand how estimation helps to find out if an answer is correct.
9SubtractionSubtraction up to the number 99
Objective: On completion of the lesson the student will know how to find the answer to take away number sentences with bigger numbers and will also know how to write these number sentences.
10SubtractionSubtraction with borrowing
Objective: On completion of the lesson the student will be able to record subtraction number sentences and will understand the need to trade between place value columns using the renaming method
11SubtractionSubtraction up to the number 999 using the renaming method
Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers.
12Time, durationDuration
Objective: On completion of the lesson the student will be able to estimate and measure the duration of an event using informal units, and compare and order the duration of an event using informal units.
13Time, digitalO’clock and half past using digital time
Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on a digital clock.
14Time, analogueO’clock and half past on the analogue clock
Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock.
15Time, minutesAnalogue – Telling time – minutes in the hour
Objective: On completion of the lesson the student will be able to recognize the coordinated movements of the hands on an analogue clock.
16Time, quarter to, pastQuarter past and quarter to
Objective: On completion of the lesson the student will be able to associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes, and use the terms ‘quarter to’ and ‘quarter past’.
17Time, unitsUnits of time
Objective: On completion of the lesson the student will be able to convert units of time and read and interpret simple timetables, timelines and calendars.
18Calculation-groupingMultiplication using equal groups
Objective: On completion of the lesson the student will be able to write about equal groups and rows and will understand how to count them.
19Calculation-groupingMultiplication using repeated addition
Objective: On completion of the lesson the student will be able to write about equal groups and rows using another method and also learn different ways to count them.
20Calculation-multiplicationThe multiplication sign
Objective: on completion of the lesson the student will be able to multiply single numbers to solve multiplication problems.
21MultiplicationMultiplication – important facts.
Objective: On completion of the lesson the student will know the connection between multiplication and division and recognise the strategies to help solve multiplication number sentences.
22LengthCompare length by using informal units of measurement
Objective: On completion of the lesson the student will be able to measure objects around the student’s home and compare their length to each other. The student will also be able to compare the different ways the student measured the same object.
23LengthUsing the metre as a formal unit to measure perimeter
Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.
24LengthUsing the formal unit of the centimetre to measure length and perimeter
Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.
25AreaComparing and ordering areas.
Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area.
26CapacityThe relationship between the common units of capacity, the litre and the millilitre
Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre.
27CapacityEstimate, measure and compare the capacity of containers
Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it.
28Weight/massIntroducing the concept of mass
Objective: On completion of the lesson the student will understand the concepts of mass.
29FractionsUsing fractions 1/2, 1/4, 1/8 to describe part of a whole
Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole.
30FractionsUsing fractions 1/2, 1/4, 1/8 to describe parts of a group or collection
Objective: On completion of the lesson the student will be able to use the fractions to describe equal parts of a collection of objects.
31DataPictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
32ExamExam – PYP Grade 2
Objective: Exam
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PYP Grade 3 Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – PYP Grade 3
Objective: Assessment
2Calculation-larger numbersThe numbers 100 to 999
Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999.
3AdditionAddition to 99
Objective: On completion of the lesson the student will be able to use place value to add two 2-digit numbers together up to a total of 99.
4Place valueThe numbers 1000 to 9999
Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999.
5AdditionAddition up to the number 999
Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers.
6SubtractionSubtraction up to the number 99
Objective: On completion of the lesson the student will know how to find the answer to take away number sentences with bigger numbers and will also know how to write these number sentences.
7SubtractionSubtraction with borrowing
Objective: On completion of the lesson the student will be able to record subtraction number sentences and will understand the need to trade between place value columns using the renaming method
8SubtractionSubtraction of two-digit numbers Involving comparison.
Objective: On completion of the lesson the student will know how to solve and record the answer to word problems and will understand how estimation helps to find out if an answer is correct.
9SubtractionSubtraction up to the number 999 using the renaming method
Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers.
10DataPictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
11DataBar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
12DataLine graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
13Calculation-groupingMultiplication using equal groups
Objective: On completion of the lesson the student will be able to write about equal groups and rows and will understand how to count them.
14Calculation-groupingMultiplication using repeated addition
Objective: On completion of the lesson the student will be able to write about equal groups and rows using another method and also learn different ways to count them.
15Calculation-multiplicationThe multiplication sign
Objective: on completion of the lesson the student will be able to multiply single numbers to solve multiplication problems.
16Calculation-multiplesMultiples of 10 up to 100
Objective: On completion of the lesson the student will be able to read, write, rename and add multiples of ten.
17MultiplicationMultiplication – important facts.
Objective: On completion of the lesson the student will know the connection between multiplication and division and recognise the strategies to help solve multiplication number sentences.
18MultiplicationMultiplying 2-digit numbers by multiple of 10
Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication.
19Calculation sharing/divisionStrategies for division
Objective: On completion of the lesson the student will be able to share objects equally and will also learn how to write about them.
20ProblemsSolve and record division using known facts and sharing
Objective: On completion of the lesson the student will be able to use sharing concepts to solve and record division problems.
21AnglesMeasure and classify angles
Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle.
222-D shapesUsing the prefix to determine polygons
Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides.
232-D shapesSpatial properties of quadrilaterals
Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals.
24Tessellating 2-D shapesUse grids to enlarge/reduce 2D shapes
Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate.
253-D shapesRecognise and name prisms according to spatial properties
Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties.
263-D shapesViewing 3-D shapes.
Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles.
27Lines and anglesDescribing position.
Objective: On completion of the lesson the student will be able to use and understand conventional location language to describe position.
28Lines and anglesMapping and grid references
Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places.
29Lines and anglesInformal coordinate system
Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper.
30FractionsUsing fractions 1/2, 1/4, 1/8 to describe part of a whole
Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole.
31FractionsUsing fractions 1/2, 1/4, 1/8 to describe parts of a group or collection
Objective: On completion of the lesson the student will be able to use the fractions to describe equal parts of a collection of objects.
32FractionsFractions 1/5, 1/10, 1/100
Objective: On completion of the lesson the student will be able to: compare fractions with the denominators 5, 10, 100, and represent fractions with the denominator 5, 10, 100.
33FractionsComparing and ordering fractions
Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts.
34Fractionsmixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one.
35FractionsImproper fractions
Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.
36FractionsFinding equivalent fractions
Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.
37FractionsSubtracting fractions from whole numbers
Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from
38FractionsAdding and subtracting fractions with the same denominator
Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator.
39LengthCompare length by using informal units of measurement
Objective: On completion of the lesson the student will be able to measure objects around the student’s home and compare their length to each other. The student will also be able to compare the different ways the student measured the same object.
40LengthUsing the metre as a formal unit to measure perimeter
Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.
41LengthUsing the formal unit of the centimetre to measure length and perimeter
Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.
42AreaComparing and ordering areas.
Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area.
43AreaIntroduction to the square centimetre.
Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly.
44Weight/massIntroducing the concept of mass
Objective: On completion of the lesson the student will understand the concepts of mass.
45Weight/massThe kilogram
Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales.
46Weight/massThe gram and net mass
Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams.
47CapacityUsing the cubic cm and displacement to measure volume and capacity
Objective: On completion of the lesson the student will know a way to find volume and capacity.
48CapacityUsing the cubic cm as a standard unit of measurement for volume and capacity
Objective: On completion of the lesson the student will understand what a cubic centimetre is and how it can be used to find out the volume and capacity of a three dimensional shape.
49CapacityThe relationship between the common units of capacity, the litre and the millilitre
Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre.
50CapacityEstimate, measure and compare the capacity of containers
Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it.
51Time, digitalO’clock and half past using digital time
Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on a digital clock.
52Time, analogueO’clock and half past on the analogue clock
Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock.
53Time, minutesAnalogue – Telling time – minutes in the hour
Objective: On completion of the lesson the student will be able to recognize the coordinated movements of the hands on an analogue clock.
54Time, quarter to, pastQuarter past and quarter to
Objective: On completion of the lesson the student will be able to associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes, and use the terms ‘quarter to’ and ‘quarter past’.
55Time, unitsUnits of time
Objective: On completion of the lesson the student will be able to convert units of time and read and interpret simple timetables, timelines and calendars.
56Time, minutes past the hourMinutes past
Objective: On completion of the lesson the student will be able to understand and read the minutes past the hour on an analogue clock.
57Time, minutes to the hourMinutes to
Objective: On completion of the lesson the student will be able to understand and read the minutes to the hour on an analogue clock.
58Time, digital, analogueComparing analogue and digital time
Objective: On completion of the lesson the student will be able to: read analogue and digital clocks to the minute, be familiar with the recording of digital time, and tell the same time using both analogue and digital clocks.
59DecimalsIntroduction to decimals
Objective: On completion of the lesson the student will be able to represent decimals to two decimal places.
60DecimalsComparing and ordering decimals to two decimal places
Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places.
61DecimalsDecimals with whole numbers 10th and 100th
Objective: On completion of the lesson the student will be able to use and understand place value to show whole numbers, tenths and hundredths as decimals.
62MultiplicationMultiplying 3 and 4-digit numbers by multiples of 100
Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication.
63MultiplicationMultiplying 2-digit numbers by 2-digit numbers
Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number.
64MultiplicationMultiples and factors of whole numbers
Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers.
65DivisionDivision with and without a remainder.
Objective: On completion of the lesson the student will understand division with and without a Remainder.
66DivisionDividing two and three digit numbers by a single digit number.
Objective: On completion of the lesson the student will understand dividing two and three digit numbers by a single digit number.
67ExamExam – PYP Grade 3
Objective: Exam
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PYP Grade 4 Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – PYP Grade 4
Objective: Assessment
2Place valueThe numbers 1000 to 9999
Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999.
3Counting and numerationThe numbers 10 000 to 99 999
Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers.
4AdditionAddition up to the number 999
Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers.
5Counting and numerationAddition to 9999 and beyond
Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems.
6Counting and numerationSeven digit numbers
Objective: On completion of the lesson the student will be able to use place value knowledge to read and write seven digit whole numbers.
7SubtractionSubtraction of two-digit numbers Involving comparison.
Objective: On completion of the lesson the student will know how to solve and record the answer to word problems and will understand how estimation helps to find out if an answer is correct.
8SubtractionSubtraction up to the number 999 using the renaming method
Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers.
9AnglesMeasure and classify angles
Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle.
102-D shapesUsing the prefix to determine polygons
Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides.
112-D shapesSpatial properties of quadrilaterals
Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals.
122-D shapesRecognise and name triangles
Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties.
13Tessellating 2-D shapesUse grids to enlarge/reduce 2D shapes
Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate.
143-D shapesRecognise and name prisms according to spatial properties
Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties.
153-D shapesRecognise nets for prisms, pyramids, cubes and cones
Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones.
163-D shapesViewing 3-D shapes.
Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles.
17Lines and anglesDescribing position.
Objective: On completion of the lesson the student will be able to use and understand conventional location language to describe position.
18Lines and anglesMapping and grid references
Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places.
19Lines and anglesInformal coordinate system
Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper.
20DataPictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
21DataBar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
22DataLine graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
23Statistic-probabilityProbability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
24Calculation-groupingMultiplication using equal groups
Objective: On completion of the lesson the student will be able to write about equal groups and rows and will understand how to count them.
25Calculation-groupingMultiplication using repeated addition
Objective: On completion of the lesson the student will be able to write about equal groups and rows using another method and also learn different ways to count them.
26Calculation-multiplicationThe multiplication sign
Objective: on completion of the lesson the student will be able to multiply single numbers to solve multiplication problems.
27Calculation-multiplesMultiples of 10 up to 100
Objective: On completion of the lesson the student will be able to read, write, rename and add multiples of ten.
28MultiplicationMultiplication – important facts.
Objective: On completion of the lesson the student will know the connection between multiplication and division and recognise the strategies to help solve multiplication number sentences.
29MultiplicationMultiplying 2-digit numbers by multiple of 10
Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication.
30MultiplicationMultiplying 3 and 4-digit numbers by multiples of 100
Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication.
31Calculation sharing/divisionStrategies for division
Objective: On completion of the lesson the student will be able to share objects equally and will also learn how to write about them.
32ProblemsSolve and record division using known facts and sharing
Objective: On completion of the lesson the student will be able to use sharing concepts to solve and record division problems.
33DivisionDivision with and without a remainder.
Objective: On completion of the lesson the student will understand division with and without a Remainder.
34DivisionDividing two and three digit numbers by a single digit number.
Objective: On completion of the lesson the student will understand dividing two and three digit numbers by a single digit number.
35Sign word problemsSolving Word Problems by recognising Sign Words
Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division.
36EquationsProblem solving strategies
Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems.
37FractionsFractions 1/5, 1/10, 1/100
Objective: On completion of the lesson the student will be able to: compare fractions with the denominators 5, 10, 100, and represent fractions with the denominator 5, 10, 100.
38FractionsComparing and ordering fractions
Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts.
39Fractionsmixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one.
40FractionsImproper fractions
Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.
41FractionsFinding equivalent fractions
Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.
42FractionsMultiplying and dividing to obtain equivalent fractions
Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.
43FractionsReducing fractions to lowest equivalent form
Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.
44FractionsComparing and ordering fractions greater than (>) 1
Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one.
45FractionsSubtracting fractions from whole numbers
Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from
46FractionsAdding and subtracting fractions with the same denominator
Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator.
47FractionsAdding and subtracting fractions with different denominators
Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.
48FractionsMultiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
49FractionsFractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
50FractionsMultiplying fractions
Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form.
51FractionsMultiplying mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.
52FractionsFinding reciprocals of fractions and mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).
53FractionsDividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
54DecimalsIntroduction to decimals
Objective: On completion of the lesson the student will be able to represent decimals to two decimal places.
55DecimalsComparing and ordering decimals to two decimal places
Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places.
56DecimalsDecimals with whole numbers 10th and 100th
Objective: On completion of the lesson the student will be able to use and understand place value to show whole numbers, tenths and hundredths as decimals.
57DecimalsAdding decimals to two decimal places
Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places)
58DecimalsSubtracting decimals to two decimal places
Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places)
59DecimalsUsing decimals – shopping problems
Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money.
60DecimalsUsing decimals to record length
Objective: On completion of the lesson the student will be able to interpret the everyday use of fractions and decimals and use their knowledge of decimals to record measurements.
61DecimalsRounding decimals
Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.
62DecimalsDecimals to three decimal places
Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths.
63PercentagesChanging percentages to fractions and decimals
Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.
64LengthUsing the metre as a formal unit to measure perimeter
Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.
65LengthUsing the formal unit of the centimetre to measure length and perimeter
Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.
66LengthRead and calculate distances on a map using the formal unit kilometre
Objective: On completion of the lesson the student will be able to read distances in kilometres and calculate total distances between different locations on a map.
67LengthCompare and convert formal units of measurement
Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert.
68AreaComparing and ordering areas.
Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area.
69AreaIntroduction to the square centimetre.
Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly.
70VolumeIntroduction to volume. using the cubic centimetre as a standard unit
Objective: On completion of the lesson the student will be able to: recognise the need for a formal unit to measure volume, use the abbreviation for cubic centimetre, construct three dimensional objects using cubic centimetre blocks, and use counting to determine vo
713-D shapesConstructing models.
Objective: On completion of the lesson the student will be able to: Construct rectangular prisms using cubic centimetre blocks and counting to determine volume. Explain the advantages of using a cube to measure volume. Construct different rectangular prisms.
72VolumeUsing the cubic centimetre to measure volume.
Objective: On completion of the lesson the student will be able to: recognise the relationship between the length, breadth, height and volume of a rectangular prism, calculate the volume of rectangular prisms, and find the volume of rectangular prisms by counting.
73VolumeIntroducing the formula for volume.
Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula.
74VolumeUsing the cubic metre to measure volume.
Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat
75CapacityUsing the cubic cm and displacement to measure volume and capacity
Objective: On completion of the lesson the student will know a way to find volume and capacity.
76CapacityUsing the cubic cm as a standard unit of measurement for volume and capacity
Objective: On completion of the lesson the student will understand what a cubic centimetre is and how it can be used to find out the volume and capacity of a three dimensional shape.
77CapacityThe relationship between the common units of capacity, the litre and the millilitre
Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre.
78CapacityConverting between volume and capacity using millilitres and litres
Objective: On completion of the lesson the student will be able to convert between units of capacity.
79Weight/massThe kilogram
Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales.
80Weight/massThe gram and net mass
Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams.
81CapacityEstimate, measure and compare the capacity of containers
Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it.
82Time, unitsUnits of time
Objective: On completion of the lesson the student will be able to convert units of time and read and interpret simple timetables, timelines and calendars.
83Time, minutes past the hourMinutes past
Objective: On completion of the lesson the student will be able to understand and read the minutes past the hour on an analogue clock.
84Time, minutes to the hourMinutes to
Objective: On completion of the lesson the student will be able to understand and read the minutes to the hour on an analogue clock.
85Time, digital, analogueComparing analogue and digital time
Objective: On completion of the lesson the student will be able to: read analogue and digital clocks to the minute, be familiar with the recording of digital time, and tell the same time using both analogue and digital clocks.
86MultiplicationMultiplying 2-digit numbers by 2-digit numbers
Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number.
87MultiplicationMultiples and factors of whole numbers
Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers.
88MultiplicationMultiplication using extended algorithms.
Objective: On completion of the lesson the student will have understood multiplication using extended algorithms.
89MultiplicationMultiplication by 2 and 3 digits
Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form.
90DivisionDivide whole numbers by a 2 digit divisor
Objective: On completion of the lesson the student will be able to solve and record division problems with whole numbers using a two-digit divisor and show any remainders as a fraction.
91ExamExam – PYP Grade 4
Objective: Exam
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PYP Grade 5 Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – PYP Grade 5
Objective: Assessment
2Counting and numerationThe numbers 10 000 to 99 999
Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers.
3Counting and numerationSeven digit numbers
Objective: On completion of the lesson the student will be able to use place value knowledge to read and write seven digit whole numbers.
4AdditionAddition up to the number 999
Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers.
5Counting and numerationAddition to 9999 and beyond
Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems.
6SubtractionSubtraction of two-digit numbers Involving comparison.
Objective: On completion of the lesson the student will know how to solve and record the answer to word problems and will understand how estimation helps to find out if an answer is correct.
7SubtractionSubtraction up to the number 999 using the renaming method
Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers.
8DecimalsIntroduction to decimals
Objective: On completion of the lesson the student will be able to represent decimals to two decimal places.
9DecimalsComparing and ordering decimals to two decimal places
Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places.
10DecimalsDecimals with whole numbers 10th and 100th
Objective: On completion of the lesson the student will be able to use and understand place value to show whole numbers, tenths and hundredths as decimals.
11DecimalsAdding decimals to two decimal places
Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places)
12DecimalsSubtracting decimals to two decimal places
Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places)
13DecimalsUsing decimals – shopping problems
Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money.
14DecimalsUsing decimals to record length
Objective: On completion of the lesson the student will be able to interpret the everyday use of fractions and decimals and use their knowledge of decimals to record measurements.
15DecimalsRounding decimals
Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.
16DecimalsDecimals to three decimal places
Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths.
17DecimalsMultiplying decimals by 10, 100 and 1000
Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.
18DecimalsMultiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
19DecimalsMultiplication of decimals by decimals to two decimal places
Objective: On completion of the lesson the student will be able to multiply decimals to two digits.
20DecimalsDividing decimals by 10, 100 and 1000
Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.
21DecimalsDividing decimal fractions by whole numbers
Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers.
22DecimalsDividing numbers by a decimal fraction
Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction.
23MultiplicationMultiplying 2-digit numbers by multiple of 10
Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication.
24MultiplicationMultiplying 3 and 4-digit numbers by multiples of 100
Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication.
25MultiplicationMultiplying 2-digit numbers by 2-digit numbers
Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number.
26MultiplicationMultiples and factors of whole numbers
Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers.
27MultiplicationMultiplication using extended algorithms.
Objective: On completion of the lesson the student will have understood multiplication using extended algorithms.
28MultiplicationMultiplication by 2 and 3 digits
Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form.
29DivisionDivision with and without a remainder.
Objective: On completion of the lesson the student will understand division with and without a Remainder.
30DivisionDividing two and three digit numbers by a single digit number.
Objective: On completion of the lesson the student will understand dividing two and three digit numbers by a single digit number.
31DivisionDivide whole numbers by a 2 digit divisor
Objective: On completion of the lesson the student will be able to solve and record division problems with whole numbers using a two-digit divisor and show any remainders as a fraction.
32Lines and anglesMapping and grid references
Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places.
33Lines and anglesInformal coordinate system
Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper.
34DataPictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
35DataBar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
36DataLine graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
37LengthUsing the metre as a formal unit to measure perimeter
Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.
38LengthUsing the formal unit of the centimetre to measure length and perimeter
Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.
39LengthRead and calculate distances on a map using the formal unit kilometre
Objective: On completion of the lesson the student will be able to read distances in kilometres and calculate total distances between different locations on a map.
40LengthCompare and convert formal units of measurement
Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert.
41AreaComparing and ordering areas.
Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area.
42AreaIntroduction to the square centimetre.
Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly.
43AnglesMeasure and classify angles
Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle.
442-D shapesRecognise and name triangles
Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties.
45Fractionsmixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one.
46FractionsImproper fractions
Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.
47FractionsFinding equivalent fractions
Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.
48FractionsMultiplying and dividing to obtain equivalent fractions
Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.
49FractionsReducing fractions to lowest equivalent form
Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.
50FractionsComparing and ordering fractions greater than (>) 1
Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one.
51FractionsSubtracting fractions from whole numbers
Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from
52FractionsAdding and subtracting fractions with the same denominator
Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator.
53FractionsAdding and subtracting fractions with different denominators
Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.
54FractionsMultiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
55FractionsFractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
56FractionsMultiplying fractions
Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form.
57FractionsMultiplying mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.
58FractionsFinding reciprocals of fractions and mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).
59FractionsDividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
60FractionsDividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
61Rules propertiesUsing Order of Operation procedures (BIDMAS) with Fractions
Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions.
62PercentagesChanging percentages to fractions and decimals
Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.
63PercentagesOne quantity as a percentage of another
Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.
64PercentagesCalculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
65VolumeUsing the cubic centimetre to measure volume.
Objective: On completion of the lesson the student will be able to: recognise the relationship between the length, breadth, height and volume of a rectangular prism, calculate the volume of rectangular prisms, and find the volume of rectangular prisms by counting.
66VolumeIntroducing the formula for volume.
Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula.
67VolumeUsing the cubic metre to measure volume.
Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat
68VolumeSolving Problems about Volume – Part 1.
Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms.
69VolumeSolving Problems about Volume – Part 2.
Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit.
70CapacityUsing the cubic cm and displacement to measure volume and capacity
Objective: On completion of the lesson the student will know a way to find volume and capacity.
71CapacityUsing the cubic cm as a standard unit of measurement for volume and capacity
Objective: On completion of the lesson the student will understand what a cubic centimetre is and how it can be used to find out the volume and capacity of a three dimensional shape.
72CapacityThe relationship between the common units of capacity, the litre and the millilitre
Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre.
73CapacityConverting between volume and capacity using millilitres and litres
Objective: On completion of the lesson the student will be able to convert between units of capacity.
74Weight/massThe kilogram
Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales.
75Weight/massThe gram and net mass
Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams.
76CapacityEstimate, measure and compare the capacity of containers
Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it.
77Sign word problemsSolving Word Problems by recognising Sign Words
Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division.
78EquationsProblem solving strategies
Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems.
79Number problemsProblems with numbers.
Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy.
80MoneyProblems involving money
Objective: On completion of the lesson the student will be able to solve problems with money.
81LengthProblems with length.
Objective: On completion of the lesson the student will be able to solve problems with length.
82AreaProblems with area.
Objective: On completion of the lesson the student will be able to solve problems with area.
83ExamExam – PYP Grade 5
Objective: Exam
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PYP Grade 6 Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – MYP Grade 6
Objective: Assessment
2Counting and numerationThe numbers 10 000 to 99 999
Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers.
3Counting and numerationSeven digit numbers
Objective: On completion of the lesson the student will be able to use place value knowledge to read and write seven digit whole numbers.
4Counting and numerationAddition to 9999 and beyond
Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems.
5SubtractionSubtraction up to the number 999 using the renaming method
Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers.
6DecimalsComparing and ordering decimals to two decimal places
Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places.
7DecimalsDecimals with whole numbers 10th and 100th
Objective: On completion of the lesson the student will be able to use and understand place value to show whole numbers, tenths and hundredths as decimals.
8DecimalsAdding decimals to two decimal places
Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places)
9DecimalsSubtracting decimals to two decimal places
Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places)
10DecimalsUsing decimals – shopping problems
Objective: On completion of the lesson the student will be able to: read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money.
11DecimalsUsing decimals to record length
Objective: On completion of the lesson the student will be able to interpret the everyday use of fractions and decimals and use their knowledge of decimals to record measurements.
12DecimalsRounding decimals
Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.
13DecimalsDecimals to three decimal places
Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths.
14DecimalsMultiplying decimals by 10, 100 and 1000
Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.
15DecimalsMultiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
16DecimalsMultiplication of decimals by decimals to two decimal places
Objective: On completion of the lesson the student will be able to multiply decimals to two digits.
17DecimalsDividing decimals by 10, 100 and 1000
Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.
18DecimalsDividing decimal fractions by whole numbers
Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers.
19DecimalsDividing numbers by a decimal fraction
Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction.
20MultiplicationMultiplying 3 and 4-digit numbers by multiples of 100
Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication.
21MultiplicationMultiplying 2-digit numbers by 2-digit numbers
Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number.
22MultiplicationMultiples and factors of whole numbers
Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers.
23MultiplicationMultiplication using extended algorithms.
Objective: On completion of the lesson the student will have understood multiplication using extended algorithms.
24MultiplicationMultiplication by 2 and 3 digits
Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form.
25DivisionDividing two and three digit numbers by a single digit number.
Objective: On completion of the lesson the student will understand dividing two and three digit numbers by a single digit number.
26DivisionDivide whole numbers by a 2 digit divisor
Objective: On completion of the lesson the student will be able to solve and record division problems with whole numbers using a two-digit divisor and show any remainders as a fraction.
27Fractionsmixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one.
28FractionsImproper fractions
Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.
29FractionsFinding equivalent fractions
Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.
30FractionsMultiplying and dividing to obtain equivalent fractions
Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.
31FractionsReducing fractions to lowest equivalent form
Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.
32FractionsComparing and ordering fractions greater than (>) 1
Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one.
33FractionsSubtracting fractions from whole numbers
Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from
34FractionsAdding and subtracting fractions with the same denominator
Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator.
35FractionsAdding and subtracting fractions with different denominators
Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.
36FractionsMultiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
37FractionsFractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
38FractionsMultiplying fractions
Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form.
39FractionsMultiplying mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.
40FractionsFinding reciprocals of fractions and mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).
41FractionsDividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
42FractionsDividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
43Rules propertiesUsing Order of Operation procedures (BIDMAS) with Fractions
Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions.
44StatisticsFrequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.
45StatisticsFrequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
46StatisticsRelative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
47StatisticsThe range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
48Statistic-probabilityThe mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
49Statistic-probabilityThe mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
50Statistic-probabilityThe median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
51DataPictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
52DataBar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
53DataLine graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
54DataPie and bar graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs.
55LengthUsing the metre as a formal unit to measure perimeter
Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.
56LengthUsing the formal unit of the centimetre to measure length and perimeter
Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.
57LengthRead and calculate distances on a map using the formal unit kilometre
Objective: On completion of the lesson the student will be able to read distances in kilometres and calculate total distances between different locations on a map.
58LengthCompare and convert formal units of measurement
Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert.
59AreaComparing and ordering areas.
Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area.
60AreaIntroduction to the square centimetre.
Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly.
61VolumeUsing the cubic centimetre to measure volume.
Objective: On completion of the lesson the student will be able to: recognise the relationship between the length, breadth, height and volume of a rectangular prism, calculate the volume of rectangular prisms, and find the volume of rectangular prisms by counting.
62VolumeIntroducing the formula for volume.
Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula.
63VolumeUsing the cubic metre to measure volume.
Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat
64VolumeSolving Problems about Volume – Part 1.
Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms.
65VolumeSolving Problems about Volume – Part 2.
Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit.
66CapacityUsing the cubic cm and displacement to measure volume and capacity
Objective: On completion of the lesson the student will know a way to find volume and capacity.
67CapacityUsing the cubic cm as a standard unit of measurement for volume and capacity
Objective: On completion of the lesson the student will understand what a cubic centimetre is and how it can be used to find out the volume and capacity of a three dimensional shape.
68CapacityThe relationship between the common units of capacity, the litre and the millilitre
Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre.
69CapacityConverting between volume and capacity using millilitres and litres
Objective: On completion of the lesson the student will be able to convert between units of capacity.
70Weight/massThe kilogram
Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales.
71Weight/massThe gram and net mass
Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams.
72CapacityEstimate, measure and compare the capacity of containers
Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it.
73Time, minutes past the hourMinutes past
Objective: On completion of the lesson the student will be able to understand and read the minutes past the hour on an analogue clock.
74Time, minutes to the hourMinutes to
Objective: On completion of the lesson the student will be able to understand and read the minutes to the hour on an analogue clock.
75Time, digital, analogueComparing analogue and digital time
Objective: On completion of the lesson the student will be able to: read analogue and digital clocks to the minute, be familiar with the recording of digital time, and tell the same time using both analogue and digital clocks.
76Time, 24-hour24 hour time
Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time.
772-D shapesUsing the prefix to determine polygons
Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides.
782-D shapesSpatial properties of quadrilaterals
Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals.
79AnglesMeasure and classify angles
Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle.
80Geometry-anglesMeasuring angles
Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.
812-D shapesRecognise and name triangles
Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties.
82Tessellating 2-D shapesUse grids to enlarge/reduce 2D shapes
Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate.
83Lines and anglesMapping and grid references
Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places.
84Lines and anglesInformal coordinate system
Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper.
85PercentagesChanging percentages to fractions and decimals
Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.
86PercentagesOne quantity as a percentage of another
Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.
87PercentagesCalculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
883-D shapesRecognise and name prisms according to spatial properties
Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties.
893-D shapesRecognise and name pyramids according to spatial properties
Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties.
903-D shapesRecognise nets for prisms, pyramids, cubes and cones
Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones.
913-D shapesViewing 3-D shapes.
Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles.
92Algebraic expressionsAlgebraic expressions.
Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.
93Algebraic expressionsSubstitution into algebraic expressions.
Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.
94Algebraic expressionsSimplifying algebraic expressions: adding like terms.
Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.
95Algebraic expressionsSimplifying algebraic Expressions: subtracting like terms.
Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.
96Algebraic expressionsSimplifying Algebraic expressions: combining addition and subtraction.
Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.
97Algebraic equationsSolving equations containing addition and subtraction
Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.
98Algebraic expressionsDirected numbers: addition and subtraction.
Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.
99Algebraic expressionsDirected numbers: multiplication and division.
Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.
100Statistic-probabilityProbability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
101Sign word problemsSolving Word Problems by recognising Sign Words
Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division.
102EquationsProblem solving strategies
Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems.
103Number problemsProblems with numbers.
Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy.
104MoneyProblems involving money
Objective: On completion of the lesson the student will be able to solve problems with money.
105LengthProblems with length.
Objective: On completion of the lesson the student will be able to solve problems with length.
106AreaProblems with area.
Objective: On completion of the lesson the student will be able to solve problems with area.
107Volume/capacityProblems with volume/capacity.
Objective: Problem Solving: problems involving volume/capacity
108ExamExam – MYP Grade 6
Objective: Exam
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MYP Grade 7 Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – MYP Grade 7
Objective: Assessment
2Algebraic expressionsAlgebraic expressions.
Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.
3Algebraic expressionsSubstitution into algebraic expressions.
Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.
4Algebraic expressionsDirected numbers: addition and subtraction.
Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.
5Algebraic expressionsDirected numbers: multiplication and division.
Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.
6Algebraic expressionsSimplifying algebraic expressions: adding like terms.
Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.
7Algebraic expressionsSimplifying algebraic Expressions: subtracting like terms.
Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.
8Algebraic expressionsSimplifying Algebraic expressions: combining addition and subtraction.
Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.
9Algebraic expressionsSimplifying algebraic expressions: multiplication
Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form.
10Algebraic expressionsSimplifying algebraic expressions: division
Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions.
11Algebraic expressionsExpanding algebraic expressions: multiplication
Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.
12Algebraic expressionsExpanding algebraic expressions: negative multiplier
Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier.
13Algebraic expressionsExpanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
14Algebraic equationsSolving equations containing addition and subtraction
Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.
15Algebraic equationsSolving equations containing multiplication and division
Objective: On completion of the lesson the student will be able to solve simple equations involving all operations.
16DecimalsRounding decimals
Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.
17DecimalsMultiplying decimals by 10, 100 and 1000
Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.
18DecimalsMultiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
19DecimalsMultiplication of decimals by decimals to two decimal places
Objective: On completion of the lesson the student will be able to multiply decimals to two digits.
20DecimalsDividing decimals by 10, 100 and 1000
Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.
21DecimalsDividing decimal fractions by whole numbers
Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers.
22DecimalsDividing numbers by a decimal fraction
Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction.
23Rules propertiesUsing Order of Operation procedures (BIDMAS) with Fractions
Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions.
24Algebraic equationsSolving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
25Algebraic equationsSolving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
26Algebraic equationsEquations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
27Algebraic equationsEquations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
28Algebra- formulaeEquations resulting from substitution into formulae.
Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations.
29Sign word problemsSolving Word Problems by recognising Sign Words
Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division.
30EquationsProblem solving strategies
Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems.
31Number problemsProblems with numbers.
Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy.
32MoneyProblems involving money
Objective: On completion of the lesson the student will be able to solve problems with money.
33LengthProblems with length.
Objective: On completion of the lesson the student will be able to solve problems with length.
34AreaProblems with area.
Objective: On completion of the lesson the student will be able to solve problems with area.
35Volume/capacityProblems with volume/capacity.
Objective: Problem Solving: problems involving volume/capacity
36Absolute value or modulusSimplifying absolute values
Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.
37Scientific notationScientific notation with larger numbers
Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation.
38Scientific notationScientific notation with small numbers
Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.
39Scientific notationChanging scientific notation to numerals
Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation.
40Fractionsmixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one.
41FractionsImproper fractions
Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.
42FractionsFinding equivalent fractions
Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.
43FractionsMultiplying and dividing to obtain equivalent fractions
Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.
44FractionsReducing fractions to lowest equivalent form
Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.
45PercentagesChanging percentages to fractions and decimals
Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.
46PercentagesOne quantity as a percentage of another
Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.
47PercentagesCalculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
48Lines and anglesInformal coordinate system
Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper.
49Algebra-inequalitiesSolving Inequalities.
Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.
50Absolute value or modulusSolving and graphing inequalities
Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.
51Statistic-probabilityProbability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
52Statistic-probabilityRolling a pair of dice
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.
53StatisticsFrequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.
54StatisticsFrequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
55StatisticsRelative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
56StatisticsThe range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
57Statistic-probabilityThe mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
58Statistic-probabilityThe mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
59Statistic-probabilityThe median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
60AnglesMeasure and classify angles
Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle.
612-D shapesRecognise and name triangles
Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties.
62Geometry-anglesMeasuring angles
Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.
63Geometry-anglesAdjacent angles
Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.
64Geometry-anglesComplementary and supplementary angles
Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.
65Geometry-anglesVertically opposite angles
Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.
66Geometry-anglesAngles at a Point.
Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.
67Geometry-anglesParallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
68Geometry-problemsAdditional questions involving parallel lines
Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.
69Geometry-trianglesAngle sum of a triangle
Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.
70LengthCompare and convert formal units of measurement
Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert.
71AreaIntroducing the rules for finding the area of a rectangle and a parallelogram.
Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides.
72AreaFinding the area of a triangle and other composite shapes.
Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas.
73AreaArea of a circle.
Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.
74AreaArea of regular polygons and composite figures.
Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula.
75VolumeIntroducing the formula for volume.
Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula.
76VolumeUsing the cubic metre to measure volume.
Objective: On completion of the lesson the student will be able to: recognise the need for a unit larger than the cubic centimetre, use the cubic metre as a formal unit for measuring large volumes, and explain why volume is measured in cubic metres in certain situat
77VolumeSolving Problems about Volume – Part 1.
Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms.
78VolumeSolving Problems about Volume – Part 2.
Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit.
79VolumeFinding the volume of prisms
Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.
80VolumeVolume of a cylinder and sphere.
Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.
81ExamExam – MYP Grade 7
Objective: Exam
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MYP Grade 8 Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – MYP Grade 8
Objective: Assessment
2Algebraic expressionsAlgebraic expressions.
Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.
3Algebraic expressionsSubstitution into algebraic expressions.
Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.
4Algebraic expressionsDirected numbers: addition and subtraction.
Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.
5Algebraic expressionsDirected numbers: multiplication and division.
Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.
6Algebraic expressionsSimplifying algebraic expressions: adding like terms.
Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.
7Algebraic expressionsSimplifying algebraic Expressions: subtracting like terms.
Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.
8Algebraic expressionsSimplifying Algebraic expressions: combining addition and subtraction.
Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.
9Algebraic expressionsSimplifying algebraic expressions: multiplication
Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form.
10Algebraic expressionsSimplifying algebraic expressions: division
Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions.
11Algebraic expressionsExpanding algebraic expressions: multiplication
Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.
12Algebraic expressionsExpanding algebraic expressions: negative multiplier
Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier.
13Algebraic expressionsExpanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
14Algebraic equationsSolving equations containing addition and subtraction
Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.
15Algebraic equationsSolving equations containing multiplication and division
Objective: On completion of the lesson the student will be able to solve simple equations involving all operations.
16Algebraic equationsSolving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
17Algebraic equationsSolving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
18Algebraic equationsEquations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
19Algebraic equationsEquations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
20Algebra- formulaeEquations resulting from substitution into formulae.
Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations.
21Algebra- formulaeChanging the subject of the formula.
Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously.
22Algebra-factorisingSimplifying easy algebraic fractions.
Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising.
23Algebraic fractionsSimplifying algebraic fractions using the index laws.
Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.
24Algebra-negative indicesAlgebraic fractions resulting in negative indices.
Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.
25FactorisationFactorisation of algebraic fractions including binomials.
Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods.
26Algebraic fractions-binomialCancelling binomial factors in algebraic fractions.
Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions.
27DataLine graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
28Coordinate Geometry-gradientGradient
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.
29Coordinate Geometry-gradientGradient formula.
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.
30Coordinate Geometry-straight lineThe straight line.
Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists.
31Coordinate Geometry-slope, etc.Lines through the origin.
Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.
32Coordinate Geometry-equation of lineGeneral form of a line and the x and y Intercepts.
Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.
33Coordinate Geometry-interceptSlope intercept form of a line.
Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.
34Algebra-inequalitiesSolving Inequalities.
Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.
35Absolute value or modulusSolving and graphing inequalities
Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.
36Absolute value or modulusSimplifying absolute values
Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.
37Simultaneous equnsSimultaneous equations
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method.
38Simultaneous equnsElimination method
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method.
39Simultaneous equnsElimination method part 2
Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method.
40Simultaneous equnsApplications of simultaneous equations
Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations.
41Rules for indices/exponentsAdding indices when multiplying terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.
42Rules for indices/exponentsSubtracting indices when dividing terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base.
43Rules for indices/exponentsMultiplying indices when raising a power to a power
Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.
44Rules for indices/exponentsMultiplying indices when raising to more than one term
Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.
45Rules for indices/exponentsTerms raised to the power of zero
Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.
46Rules for indices/exponentsNegative Indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices.
47Fractional indices/exponentsFractional indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.
48Fractional indices/exponentsComplex fractions as indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices.
49Scientific notationScientific notation with larger numbers
Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation.
50Scientific notationScientific notation with small numbers
Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.
51Scientific notationChanging scientific notation to numerals
Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation.
52Exponential functionThe exponential function.
Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1.
53StatisticsFrequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.
54StatisticsFrequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
55StatisticsRelative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
56StatisticsThe range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
57Statistic-probabilityThe mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
58Statistic-probabilityThe mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
59Statistic-probabilityThe median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
60Statistics – grouped dataCalculating mean, mode and median from grouped data
Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.
61StatisticsStem and Leaf Plots along with Box and Whisker Plots
Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.
62StatisticsScatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
63Graphing binomialsBinomial products.
Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression.
64Graphing binomialsBinomial products with negative multiplier
Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products.
65Graphing binomialsBinomial products [non-monic].
Objective: On completion of the lesson, the student will have examined more complex examples with binomial products.
66Squaring binomialSquaring a binomial. [monic]
Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial.
67Squaring binomialSquaring a binomial [non-monic].
Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials.
68FactorisingExpansions leading to the difference of two squares
Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares.
69Algebraic expressions-productsProducts in simplification of algebraic expressions
Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing.
70Algebraic expressions-larger expansionsAlgebraic Expressions – Larger expansions.
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.
71Algebra-highest common factorHighest common factor.
Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.
72Factors by groupingFactors by grouping.
Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.
73Difference of 2 squaresDifference of two squares
Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors.
74Common fact and diffCommon factor and the difference of two squares
Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.
75Quadratic trinomialsQuadratic trinomials [monic] – Case 1.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
76Factorising quadsFactorising quadratic trinomials [monic] – Case 2.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
77Factorising quadsFactorising quadratic trinomials [monic] – Case 3.
Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.
78Factorising quadsFactorising quadratic trinomials [monic] – Case 4.
Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.
79Factorising quadsFactorisation of non-monic quadratic trinomials
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
80Factorising quadsFactorisation of non-monic quadratic trinomials – moon method
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.
81Quadratic equationsIntroduction to quadratic equations.
Objective: On completion of the lesson the student will understand simple quadratic equations.
82Quadratic equationsQuadratic equations with factorisation.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.
83Quadratic equationsSolving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
84Quadratic equationsCompleting the square
Objective: On completion of the lesson the student will understand the process of completing the square.
85Quadratic equationsSolving quadratic equations by completing the square
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.
86Quadratic equationsThe quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
87Quadratic equationsProblem solving with quadratic equations
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.
88Quadratic equationsSolving simultaneous quadratic equations graphically
Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..
89PercentagesChanging percentages to fractions and decimals
Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.
90PercentagesOne quantity as a percentage of another
Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.
91PercentagesCalculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
92SurdsIntroducing surds
Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.
93SurdsSome rules for the operations with surds
Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds.
94SurdsSimplifying surds
Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication.
95SurdsCreating entire surds
Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds
96SurdsAdding and subtracting like surds
Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.
97SurdsExpanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
98SurdsBinomial expansions
Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.
99SurdsConjugate binomials with surds
Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds.
100SurdsRationalising the denominator
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds.
101SurdsRationalising binomial denominators
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions.
102PythagorasFind the hypotenuse
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse.
103PythagorasPythagorean triples
Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple.
104PythagorasFind the hypotenuse Part 2
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds.
105PythagorasCalculating a leg of a right-angled triangle
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.
106PythagorasProofs of Pythagoras theorem
Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem
107ExamExam – MYP Grade 8
Objective: Exam
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MYP Grade 9 Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – MYP Grade 9
Objective: Assessment
2LogicInductive and deductive reasoning
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.
3LogicDefinition and use of counter examples
Objective: On completion of this lesson the student will be able to create counter examples to statements.
4LogicIndirect proofs
Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved.
5LogicMathematical induction
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.
6LogicConditional statements (converse, inverse and contrapositive) (Stage 2)
Objective: On completion of the lesson the student will be able to form related conditional statements.
7AnglesMeasure and classify angles
Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle.
8Geometry-anglesMeasuring angles
Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.
9Coordinate Geometry-the planeDistance formula.
Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results.
10Coordinate Geometry-midpoint, slopeMid-point formula
Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically.
11PythagorasFind the hypotenuse
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse.
12PythagorasPythagorean triples
Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple.
13PythagorasFind the hypotenuse Part 2
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds.
14PythagorasCalculating a leg of a right-angled triangle
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.
15PythagorasProofs of Pythagoras theorem
Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem
16Geometry-anglesAdjacent angles
Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.
17Geometry-anglesComplementary and supplementary angles
Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.
18Geometry-anglesVertically opposite angles
Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.
19Geometry-anglesAngles at a Point.
Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.
20Geometry-anglesParallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
21Geometry-problemsAdditional questions involving parallel lines
Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.
22Geometry-trianglesAngle sum of a triangle
Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.
23Geometry-trianglesExterior angle theorem
Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.
24Special trianglesSpecial triangles
Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.
25Coordinate Geometry-gradientGradient
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.
26Coordinate Geometry-gradientGradient formula.
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.
27Coordinate Geometry-straight lineThe straight line.
Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists.
28Coordinate Geometry-slope, etc.Lines through the origin.
Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.
29Coordinate Geometry-equation of lineGeneral form of a line and the x and y Intercepts.
Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.
30Coordinate Geometry-interceptSlope intercept form of a line.
Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.
31Coordinate Geometry-point slopePoint slope form of a line
Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line.
32Co-ordinate Geometry-Two point formulaTwo point formula: equation of a line which joins a pair of points.
Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.
33Co-ordinate Geometry-Intercept formIntercept form of a straight line: find the equation when given x and y
Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.
34Co-ordinate Geometry-Parallel lines equationsParallel lines: identify equation of a line parallel to another
Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.
35Geometry problemsMore difficult exercises involving parallel lines
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log
36Geometry-reasoningFurther difficult exercises involving formal reasoning
Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.
37Geometry-polygonsAngles of regular polygons
Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees.
38Geometry-congruenceCongruent triangles, Test 1 and 2
Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent.
39Geometry-congruenceCongruent triangles, Test 3 and 4
Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.
40Geometry-congruenceProofs and congruent triangles.
Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent.
41Algebraic equationsSolving equations containing addition and subtraction
Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.
42Algebraic equationsSolving equations containing multiplication and division
Objective: On completion of the lesson the student will be able to solve simple equations involving all operations.
43Algebraic equationsSolving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
44Algebraic equationsSolving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
45Algebraic equationsEquations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
46Algebraic equationsEquations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
47Algebra-inequalitiesSolving Inequalities.
Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.
48Absolute value or modulusSolving and graphing inequalities
Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.
49Absolute value or modulusSimplifying absolute values
Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.
50Geometry-constructionsGeometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
51GeometryTo identify collinear points, coplanar lines and points in 2 and 3 dimensions
Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays.
52Geometry – anglesTo determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra
Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles.
53Geometry-constructionsAngle bisector construction and its properties (Stage 2)
Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge.
54Geometry-constructionsCircumcentre and incentre (Stage 2)
Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values.
55Geometry-constructionsOrthocentre and centroids (Stage 2)
Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values.
56Geometry-quadrilateralsMidsegments of Triangles
Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.
57Geometry – trianglesTriangle inequality theorem
Objective: On completion of the lesson the student will understand and use the triangle inequality theorem.
582-D shapesUsing the prefix to determine polygons
Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides.
592-D shapesSpatial properties of quadrilaterals
Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals.
60Geometry-quadrilateralsQuadrilaterals
Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.
61Geometry-quadrilateralsClassifying Quadrilaterals
Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals.
62Geometry-quadrilateralsUsing the Properties of a Parallelogram
Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram.
63Geometry-quadrilateralsProving a Shape is a Parallelogram
Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram.
64Geometry-quadrilateralsProperties of the Rectangle, Square and Rhombus
Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values.
65Geometry-quadrilateralsProperties of the Trapezium and Kite
Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values.
66Geometry-quadrilateralsThe quadrilateral family and coordinate methods in geometry
Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties.
67AreaIntroducing the rules for finding the area of a rectangle and a parallelogram.
Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides.
68AreaFinding the area of a triangle and other composite shapes.
Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas.
69AreaArea of a trapezium.
Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula.
70AreaArea of a rhombus.
Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems.
71AreaArea of a circle.
Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.
72AreaArea of regular polygons and composite figures.
Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula.
73Similar trianglesSimilar triangles
Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar.
74Similar trianglesUsing similar triangles to calculate lengths
Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles.
75Overlapping trianglesExamples involving overlapping triangles
Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles.
76Quadratic equationsIntroduction to quadratic equations.
Objective: On completion of the lesson the student will understand simple quadratic equations.
77Quadratic equationsQuadratic equations with factorisation.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.
78Quadratic equationsSolving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
79Quadratic equationsCompleting the square
Objective: On completion of the lesson the student will understand the process of completing the square.
80Quadratic equationsSolving quadratic equations by completing the square
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.
81Quadratic equationsThe quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
82Quadratic equationsProblem solving with quadratic equations
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.
83SurdsIntroducing surds
Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.
84SurdsSome rules for the operations with surds
Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds.
85SurdsSimplifying surds
Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication.
86SurdsCreating entire surds
Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds
87SurdsAdding and subtracting like surds
Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.
88SurdsExpanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
89SurdsBinomial expansions
Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.
90SurdsConjugate binomials with surds
Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds.
91SurdsRationalising the denominator
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds.
92SurdsRationalising binomial denominators
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions.
93Trigonometry-ratiosTrigonometric ratios.
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op
94Trigonometry-ratiosUsing the calculator.
Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.
95Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 1 Sine].
Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.
96Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 2 Cosine].
Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.
97Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].
Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.
98Trigonometry-ratiosUnknown in the denominator. [Case 4].
Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.
99Trigonometry-compassBearings – the compass.
Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.
100Trigonometry-elevationAngles of elevation and depression.
Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.
101Trigonometry-practicalTrigonometric ratios in practical situations.
Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.
102Circle GeometryTheorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs.
Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro
103Circle GeometryTheorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord.
Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’
104Circle GeometryTheorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal.
Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre.
105Circle GeometryTheorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc.
Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.
106Circle GeometryTheorem – Angles in the same segment of a circle are equal.
Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.
107Circle GeometryTheorem – The angle of a semi-circle is a right angle.
Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’
108Circle GeometryTheorem – The opposite angles of a cyclic quadrilateral are supplementary.
Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.
109Circle GeometryTheorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle.
Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite.
110Circle GeometryTheorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.
Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact.
111Circle GeometryTheorem – Tangents to a circle from an external point are equal.
Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.
112Circle GeometryTheorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
113VolumeFinding the volume of prisms
Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.
114VolumeVolume of a cylinder and sphere.
Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.
115VolumeVolume of pyramids and cones.
Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones.
116VolumeComposite solids.
Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately.
117Surface areaSurface area of a cube/rectangular prism.
Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.
118Surface areaSurface area of a triangular/trapezoidal prism.
Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula.
119Surface areaSurface area of a cylinder and sphere.
Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.
120Surface areaSurface area of pyramids
Objective: On completion of the lesson the student will be able to find the surface areas of pyramids.
121Surface areaSurface area of cones
Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul
122Surface areaSurface area of composite solids
Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids.
123ExamExam – MYP Grade 9
Objective: Exam
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MYP Grade 10 - 1 Algebra II and Trig Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – MYP Grade 10 – 1 Algebra II & Trig
Objective: Assessment
2Coordinate Geometry-the planeDistance formula.
Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results.
3Coordinate Geometry-midpoint, slopeMid-point formula
Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically.
4Coordinate Geometry-gradientGradient
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.
5Coordinate Geometry-gradientGradient formula.
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.
6Coordinate Geometry-straight lineThe straight line.
Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists.
7Coordinate Geometry-slope, etc.Lines through the origin.
Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.
8Coordinate Geometry-equation of lineGeneral form of a line and the x and y Intercepts.
Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.
9Coordinate Geometry-interceptSlope intercept form of a line.
Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.
10Coordinate Geometry-point slopePoint slope form of a line
Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line.
11StatisticsScatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
12Co-ordinate Geometry-Two point formulaTwo point formula: equation of a line which joins a pair of points.
Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.
13Co-ordinate Geometry-Intercept formIntercept form of a straight line: find the equation when given x and y
Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.
14Co-ordinate Geometry-Parallel lines equationsParallel lines: identify equation of a line parallel to another
Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.
15Co-ordinate Geometry-Perpendicular linesPerpendicular lines.
Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line.
16Co-ordinate Geometry-InequalitiesInequalities on the number plane.
Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.
17Uniform motionAverage speed
Objective: On completion of the lesson the student will be able to convert units for speed, distance and time.
18Uniform motionUsing subscripted variables
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, distance and time.
19Uniform motionUniform motion with equal distances
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, equal distances and time.
20Uniform motionUniform motion adding the distances
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, adding distances for total distance and time.
21Uniform motionUniform motion with unequal distances
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, unequal distances and time.
22Uniform motionUniform motion of all types
Objective: On completion of the lesson the student will use all types of subscripted variables for calculations to determine speed, distance and time.
23Absolute value equationsAbsolute value equations
Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio
24FunctionsDefinition, domain and range
Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.
25FunctionsNotation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
26FunctionsMore on domain and range
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.
27FunctionsDomain and range from graphical representations
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.
28FunctionsEvaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
29Simultaneous equnsSimultaneous equations
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method.
30Simultaneous equnsElimination method
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method.
31Simultaneous equnsElimination method part 2
Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method.
32Simultaneous equnsApplications of simultaneous equations
Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations.
33Simultaneous equationsNumber of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.
34Vectors2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.
35Linear systemsOptimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.
36Linear systemsLinear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.
37Linear systemsRow-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.
38Algebraic equationsSolving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
39Algebraic equationsEquations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
40Algebraic equationsEquations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
41Algebra- formulaeEquations resulting from substitution into formulae.
Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations.
42Algebra- formulaeChanging the subject of the formula.
Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously.
43Algebra-inequalitiesSolving Inequalities.
Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.
44Absolute value or modulusSimplifying absolute values
Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.
45Absolute value or modulusSolving for the variable
Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value.
46Absolute value or modulusSolving and graphing inequalities
Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.
47SurdsIntroducing surds
Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.
48SurdsSome rules for the operations with surds
Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds.
49SurdsSimplifying surds
Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication.
50SurdsCreating entire surds
Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds
51SurdsAdding and subtracting like surds
Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.
52SurdsExpanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
53SurdsBinomial expansions
Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.
54Functions and graphsQuadratic polynomials of the form y = ax. + bx + c.
Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.
55Functions and graphsGraphing perfect squares: y=(a-x) squared
Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.
56Graphing rootsGraphing irrational roots
Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.
57Coordinate geometrySolve by graphing
Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.
58Graphing binomialsBinomial products.
Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression.
59Graphing binomialsBinomial products with negative multiplier
Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products.
60Graphing binomialsBinomial products [non-monic].
Objective: On completion of the lesson, the student will have examined more complex examples with binomial products.
61Squaring binomialSquaring a binomial. [monic]
Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial.
62Squaring binomialSquaring a binomial [non-monic].
Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials.
63FactorisingExpansions leading to the difference of two squares
Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares.
64Algebraic expressions-productsProducts in simplification of algebraic expressions
Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing.
65Algebraic expressions-larger expansionsAlgebraic Expressions – Larger expansions.
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.
66Algebra-highest common factorHighest common factor.
Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.
67Factors by groupingFactors by grouping.
Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.
68Difference of 2 squaresDifference of two squares
Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors.
69Common fact and diffCommon factor and the difference of two squares
Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.
70Quadratic trinomialsQuadratic trinomials [monic] – Case 1.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
71Factorising quadsFactorising quadratic trinomials [monic] – Case 2.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
72Factorising quadsFactorising quadratic trinomials [monic] – Case 3.
Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.
73Factorising quadsFactorising quadratic trinomials [monic] – Case 4.
Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.
74Factorising quadsFactorisation of non-monic quadratic trinomials
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
75Factorising quadsFactorisation of non-monic quadratic trinomials – moon method
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.
76Quadratic equationsIntroduction to quadratic equations.
Objective: On completion of the lesson the student will understand simple quadratic equations.
77Quadratic equationsQuadratic equations with factorisation.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.
78Quadratic equationsSolving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
79Quadratic equationsCompleting the square
Objective: On completion of the lesson the student will understand the process of completing the square.
80Quadratic equationsSolving quadratic equations by completing the square
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.
81Quadratic equationsThe quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
82Quadratic equationsProblem solving with quadratic equations
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.
83Quadratic equationsSolving simultaneous quadratic equations graphically
Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..
84Motion under accelerationMotion under gravity – objects in vertical motion
Objective: On completion of the lesson the student will convert rates and use equations of motion that include uniform acceleration.
85Motion under accelerationIntroducing initial velocity
Objective: On completion of the lesson the student will use equations of motion that include uniform acceleration and an initial velocity.
86Algebra-polynomialsIntroduction to polynomials
Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not.
87Algebra-polynomialsThe sum, difference and product of two polynomials.
Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers.
88Algebra-polynomialsPolynomials and long division.
Objective: On completion of the lesson the student will understand the long division process with polynomials.
89Remainder theoremThe remainder theorem.
Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied.
90Remainder theoremMore on remainder theorem
Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials.
91Factor theoremThe factor theorem
Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial.
92Factor theoremMore on the factor theorem
Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials.
93Factor theoremComplete factorisations using the factor theorem
Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros.
94Polynomial equationsPolynomial equations
Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms.
95Graphs, polynomialsGraphs of polynomials
Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves.
96StatisticsFrequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.
97StatisticsFrequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
98StatisticsRelative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
99StatisticsThe range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
100Statistic-probabilityThe mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
101Statistic-probabilityThe mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
102Statistic-probabilityThe median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
103Statistic-probabilityCumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
104Statistic-probabilityCalculating the median from a frequency distribution
Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon.
105Statistics – grouped dataCalculating mean, mode and median from grouped data
Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.
106Statistics using a calculatorStatistics and the student calculator
Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems.
107Statistics – Range and dispersionRange as a measure of dispersion
Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.
108Statistics – SpreadMeasures of spread
Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.
109Statistics – Standard deviationStandard deviation applications
Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.
110Statistics – Standard deviationNormal distribution
Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.
111Statistics – Interquartile rangeMeasures of spread: the interquartile range
Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range
112StatisticsStem and Leaf Plots along with Box and Whisker Plots
Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.
113Rules for indices/exponentsAdding indices when multiplying terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.
114Rules for indices/exponentsSubtracting indices when dividing terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base.
115Rules for indices/exponentsMultiplying indices when raising a power to a power
Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.
116Rules for indices/exponentsMultiplying indices when raising to more than one term
Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.
117Rules for indices/exponentsTerms raised to the power of zero
Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.
118Rules for indices/exponentsNegative Indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices.
119Fractional indices/exponentsFractional indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.
120Fractional indices/exponentsComplex fractions as indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices.
121Graphing-polynomialsGraphing complex polynomials: quadratics with no real roots
Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it.
122Graphing-polynomialsGeneral equation of a circle: determine and graph the equation
Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning.
123Graphing-cubic curvesGraphing cubic curves
Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information.
124Rect.hyperbolaThe rectangular hyperbola.
Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features.
125Exponential functionThe exponential function.
Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1.
126Log functionsLogarithmic functions.
Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit
127Logarithms-Power of 2Powers of 2.
Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2.
128Logarithms-Equations and logsEquations of type log x to the base 3 = 4.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.
129Logarithms-Equations and logsEquations of type log 32 to the base x = 5.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.
130Logarithms-Log lawsLaws of logarithms.
Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.
131Logarithms-Log laws expansionUsing the log laws to expand logarithmic expressions.
Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.
132Logarithms-Log laws simplifyingUsing the log laws to simplify expressions involving logarithms.
Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.
133Logarithms-Log laws numbersUsing the log laws to find the logarithms of numbers.
Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples.
134Logarithms-Equations and logsEquations involving logarithms.
Objective: On completion of the lesson the student will be able to solve equations with log terms.
135Logarithms-Logs to solve equationsUsing logarithms to solve equations.
Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.
136Logarithms-Change base formulaChange of base formula
Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base.
137Logarithms-Graph-log curveThe graph of the logarithmic curve
Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves.
138Logarithms-Log curvesWorking with log curves.
Objective: On completion of the lesson the student will be able to solve problems with log curves
139Sequences and Series-Geometric meansGeometric means.
Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.
140Sequences and Series-Sum of gpThe sum to n terms of a G.P.
Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P).
141Sequences and Series-Sigma notationSigma notation
Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates.
142Sequences and Series-Sum-infinityLimiting sum or sum to infinity.
Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems.
143Sequences and Series-Recurring decimal infinityRecurring decimals and the infinite G.P.
Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number.
144Sequences and Series-Compound interestCompound interest
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.
145Sequences and Series-SuperannuationSuperannuation.
Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.
146Sequences and Series-Time paymentsTime payments.
Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.
147Sequences and SeriesApplications of arithmetic sequences
Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.
148FunctionsFunctions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
149FunctionsComposition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
150FunctionsInverse functions
Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used.
151FunctionsRational functions Part 1
Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes.
152FunctionsRational functions Part 2
Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes.
153FunctionsParametric equations (Stage 2)
Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range.
154FunctionsPolynomial addition etc in combining and simplifying functions (Stage 2)
Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra.
155FunctionsParametric functions (Stage 2)
Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion.
156Algebraic fractionsSimplifying algebraic fractions using the index laws.
Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.
157Algebra-negative indicesAlgebraic fractions resulting in negative indices.
Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.
158FactorisationFactorisation of algebraic fractions including binomials.
Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods.
159Algebraic fractions-binomialCancelling binomial factors in algebraic fractions.
Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions.
160Algebraic fractionsSimplifying algebraic fractions.
Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point.
161Statistic-probabilityProbability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
162Statistic-probabilityRolling a pair of dice
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.
163Statistic-probabilityExperimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
164Statistic-probabilityTree diagrams – not depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.
165Statistic-probabilityTree diagrams – depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.
166Statistic-probabilityThe complementary result ..
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.
167Statistic-probabilityP[A or B] When A and B are both mutually and NOT mutually exclusive
Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.
168Statistic-probabilityBinomial Theorem – Pascal’s Triangle
Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.
169Statistic-probabilityBinomial probabilities using the Binomial Theorem
Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem
170Statistic-probabilityCounting techniques and ordered selections – permutations
Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability.
171Statistic-probabilityUnordered selections – combinations
Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen.
172Trigonometry-ratiosTrigonometric ratios.
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op
173Trigonometry-ratiosUsing the calculator.
Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.
174Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 1 Sine].
Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.
175Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 2 Cosine].
Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.
176Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].
Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.
177Trigonometry-ratiosUnknown in the denominator. [Case 4].
Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.
178Trigonometry-compassBearings – the compass.
Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.
179Trigonometry-elevationAngles of elevation and depression.
Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.
180Trigonometry-practicalTrigonometric ratios in practical situations.
Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.
181Trigonometry-ratiosUsing the calculator to find an angle given a trigonometric ratio.
Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.
182Trigonometry- ratiosUsing the trigonometric ratios to find an angle in a right-angled triangle.
Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.
183Trigonometry-exact ratiosTrigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.
184Trigonometry-cosine ruleThe cosine rule to find an unknown side. [Case 1 SAS].
Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.
185Trigonometry-cosine ruleThe cosine rule to find an unknown angle. [Case 2 SSS].
Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.
186Trigonometry-sine ruleThe sine rule to find an unknown side. Case 1.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
187Trigonometry-sine ruleThe sine rule to find an unknown angle. Case 2.
Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.
188Trigonometry-areasThe area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.
189Trig-reciprocal ratiosReciprocal ratios.
Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios.
190Trig complementary anglesComplementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
191Trig identitiesTrigonometric identities
Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities.
192Trig larger anglesAngles of any magnitude
Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle.
193Trig larger anglesTrigonometric ratios of 0°, 90°, 180°, 270° and 360°
Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees.
194Graph sineGraphing the trigonometric ratios – I Sine curve.
Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period.
195Graph cosineGraphing the trigonometric ratios – II Cosine curve.
Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period.
196Graphs tan curveGraphing the trigonometric ratios – III Tangent curve.
Objective: On completion of the lesson the student will know how to recognise and draw the tan curve.
197Graph reciprocalsGraphing the trigonometric ratios – IV Reciprocal ratios.
Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.
198Trig larger anglesUsing one ratio to find another.
Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude.
199Trig equationsSolving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.
200Trig equationsSolving trigonometric equations – Type II.
Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains.
201Trig equationsSolving trigonometric equations – Type III.
Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains.
202Polar coordinatesPlotting polar coordinates and converting polar to rectangular
Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system.
203Polar coordinatesConverting rectangular coordinates to polar form
Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates.
204ExamExam – MYP Grade 10 – 1 Algebra II & Trig
Objective: Exam
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MYP Grade 10 - 2 Algebra II and Trig Hons Mathematics

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1Self AssessmentSelf Assessment – MYP Grade 10 – 2 Algebra II & Trig Hons
Objective: Assessment
2Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 1 Sine].
Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.
3Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 2 Cosine].
Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.
4Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].
Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.
5Trigonometry-ratiosUnknown in the denominator. [Case 4].
Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.
6Trigonometry-practicalTrigonometric ratios in practical situations.
Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.
7Trigonometry-ratiosUsing the calculator to find an angle given a trigonometric ratio.
Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.
8Trigonometry- ratiosUsing the trigonometric ratios to find an angle in a right-angled triangle.
Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.
9Trigonometry-cosine ruleThe cosine rule to find an unknown angle. [Case 2 SSS].
Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.
10Trigonometry-sine ruleThe sine rule to find an unknown side. Case 1.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
11Trigonometry-sine ruleThe sine rule to find an unknown angle. Case 2.
Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.
12Trigonometry-areasThe area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.
13Number theory – setsNumber sets and their members
Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system.
14Number theory – operationsProperties of real numbers using addition and multiplication
Objective: On completion of the lesson the student will know and use the closure, identity, commutative, associative, identity and distributive properties for addition and multiplication.
15Number theory – equationsTransformations that produce equivalent equations
Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations.
16FractionsSubtracting fractions from whole numbers
Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from
17FractionsAdding and subtracting fractions with the same denominator
Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator.
18FractionsAdding and subtracting fractions with different denominators
Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.
19FractionsMultiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
20FractionsFractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
21FractionsMultiplying fractions
Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form.
22FractionsMultiplying mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.
23FractionsFinding reciprocals of fractions and mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).
24FractionsDividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
25FractionsDividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
26Rules propertiesUsing Order of Operation procedures (BIDMAS) with Fractions
Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions.
27PercentagesCalculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
28PercentagesIntroduction to percentages, including relating common fractions to percentages
Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage.
29PercentagesChanging fractions and decimals to percentages using tenths and hundredths
Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.
30PercentagesChanging percentages to fractions and decimals
Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.
31PercentagesOne quantity as a percentage of another
Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.
32SurdsIntroducing surds
Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.
33SurdsSome rules for the operations with surds
Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds.
34SurdsSimplifying surds
Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication.
35SurdsCreating entire surds
Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds
36SurdsAdding and subtracting like surds
Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.
37SurdsExpanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
38Algebraic equationsSolving equations containing addition and subtraction
Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.
39Algebraic equationsSolving equations containing multiplication and division
Objective: On completion of the lesson the student will be able to solve simple equations involving all operations.
40Algebraic equationsSolving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
41Algebraic equationsSolving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
42Algebraic equationsEquations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
43Algebraic equationsEquations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
44Algebra- formulaeEquations resulting from substitution into formulae.
Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations.
45Algebra- formulaeChanging the subject of the formula.
Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously.
46Algebra-inequalitiesSolving Inequalities.
Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.
47Algebra-factorisingSimplifying easy algebraic fractions.
Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising.
48Algebraic fractionsSimplifying algebraic fractions using the index laws.
Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.
49Algebra-negative indicesAlgebraic fractions resulting in negative indices.
Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.
50FactorisationFactorisation of algebraic fractions including binomials.
Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods.
51Algebraic fractions-binomialCancelling binomial factors in algebraic fractions.
Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions.
52Absolute value or modulusSimplifying absolute values
Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.
53Absolute value or modulusSolving for the variable
Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value.
54Absolute value or modulusSolving and graphing inequalities
Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.
55Algebra-highest common factorHighest common factor.
Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.
56Factors by groupingFactors by grouping.
Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.
57Difference of 2 squaresDifference of two squares
Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors.
58Common fact and diffCommon factor and the difference of two squares
Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.
59Quadratic trinomialsQuadratic trinomials [monic] – Case 1.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
60Factorising quadsFactorising quadratic trinomials [monic] – Case 2.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
61Factorising quadsFactorising quadratic trinomials [monic] – Case 3.
Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.
62Factorising quadsFactorising quadratic trinomials [monic] – Case 4.
Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.
63Factorising quadsFactorisation of non-monic quadratic trinomials
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
64Factorising quadsFactorisation of non-monic quadratic trinomials – moon method
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.
65Sum/diff 2 cubesSum and difference of two cubes.
Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them.
66Algebraic fractionsSimplifying algebraic fractions.
Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point.
67Quadratic equationsIntroduction to quadratic equations.
Objective: On completion of the lesson the student will understand simple quadratic equations.
68Quadratic equationsQuadratic equations with factorisation.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.
69Quadratic equationsSolving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
70Quadratic equationsCompleting the square
Objective: On completion of the lesson the student will understand the process of completing the square.
71Quadratic equationsSolving quadratic equations by completing the square
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.
72Quadratic equationsThe quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
73Quadratic equationsProblem solving with quadratic equations
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.
74Quadratic equationsSolving simultaneous quadratic equations graphically
Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..
75Algebra-polynomialsIntroduction to polynomials
Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not.
76Algebra-polynomialsThe sum, difference and product of two polynomials.
Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers.
77Rules for indices/exponentsAdding indices when multiplying terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.
78Rules for indices/exponentsSubtracting indices when dividing terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base.
79Rules for indices/exponentsMultiplying indices when raising a power to a power
Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.
80Rules for indices/exponentsMultiplying indices when raising to more than one term
Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.
81Rules for indices/exponentsTerms raised to the power of zero
Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.
82Rules for indices/exponentsNegative Indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices.
83Fractional indices/exponentsFractional indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.
84Fractional indices/exponentsComplex fractions as indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices.
85Graphing-polynomialsGraphing complex polynomials: quadratics with no real roots
Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it.
86Graphing-polynomialsGeneral equation of a circle: determine and graph the equation
Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning.
87Graphing-cubic curvesGraphing cubic curves
Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information.
88Absolute value equationsAbsolute value equations
Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio
89Rect.hyperbolaThe rectangular hyperbola.
Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features.
90Exponential functionThe exponential function.
Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1.
91Log functionsLogarithmic functions.
Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit
92FunctionsDefinition, domain and range
Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.
93FunctionsNotation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
94FunctionsMore on domain and range
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.
95FunctionsDomain and range from graphical representations
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.
96FunctionsEvaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
97FunctionsFunctions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
98FunctionsComposition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
99FunctionsInverse functions
Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used.
100Circle GeometryTheorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs.
Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro
101Circle GeometryTheorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord.
Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’
102Circle GeometryTheorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal.
Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre.
103Circle GeometryTheorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc.
Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.
104Circle GeometryTheorem – Angles in the same segment of a circle are equal.
Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.
105Circle GeometryTheorem – The angle of a semi-circle is a right angle.
Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’
106Circle GeometryTheorem – The opposite angles of a cyclic quadrilateral are supplementary.
Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.
107Circle GeometryTheorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle.
Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite.
108Circle GeometryTheorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.
Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact.
109Circle GeometryTheorem – Tangents to a circle from an external point are equal.
Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.
110Circle GeometryTheorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
111Trigonometry-exact ratiosTrigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.
112Trigonometry-cosine ruleThe cosine rule to find an unknown side. [Case 1 SAS].
Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.
113Trig-reciprocal ratiosReciprocal ratios.
Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios.
114Trig complementary anglesComplementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
115Trig identitiesTrigonometric identities
Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities.
116Trig larger anglesAngles of any magnitude
Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle.
117Trig larger anglesTrigonometric ratios of 0°, 90°, 180°, 270° and 360°
Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees.
118Graph sineGraphing the trigonometric ratios – I Sine curve.
Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period.
119Graph cosineGraphing the trigonometric ratios – II Cosine curve.
Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period.
120Graphs tan curveGraphing the trigonometric ratios – III Tangent curve.
Objective: On completion of the lesson the student will know how to recognise and draw the tan curve.
121Graph reciprocalsGraphing the trigonometric ratios – IV Reciprocal ratios.
Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.
122Trig larger anglesUsing one ratio to find another.
Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude.
123Trig equationsSolving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.
124StatisticsFrequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.
125StatisticsFrequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
126StatisticsRelative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
127StatisticsThe range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
128Statistic-probabilityThe mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
129Statistic-probabilityThe mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
130Statistic-probabilityThe median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
131Statistic-probabilityCumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
132Statistic-probabilityCalculating the median from a frequency distribution
Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon.
133Statistic-probabilityProbability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
134Statistic-probabilityRolling a pair of dice
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.
135Statistic-probabilityExperimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
136Statistic-probabilityTree diagrams – not depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.
137Statistic-probabilityTree diagrams – depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.
138Statistic-probabilityThe complementary result ..
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.
139Statistic-probabilityP[A or B] When A and B are both mutually and NOT mutually exclusive
Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.
140Statistic-probabilityBinomial Theorem – Pascal’s Triangle
Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.
141Sequences and SeriesGeneral sequences.
Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.
142Sequences and SeriesFinding Tn given Sn.
Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.
143Arithmetic ProgressionThe arithmetic progression
Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.
144Arithmetic ProgressionFinding the position of a term in an A.P.
Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression.
145Arithmetic ProgressionGiven two terms of A.P., find the sequence.
Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms
146Arithmetic ProgressionArithmetic means
Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.
147Arithmetic ProgressionThe sum to n terms of an A.P.
Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.
148Geometric ProgressionThe geometric progression.
Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.
149Geometric ProgressionFinding the position of a term in a G.P.
Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.
150Geometric ProgressionGiven two terms of G.P., find the sequence.
Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.
151ExamExam – MYP Grade 10 – 2 Algebra II & Trig Hons
Objective: Exam
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MYP Grade 10 - 3 Pre Calculus Mathematics

#TOPICTITLE
1Self AssessmentSelf Assessment – MYP Grade 10 – 3 Pre Calculus
Objective: Assessment
2Coordinate Geometry-the planeDistance formula.
Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results.
3Coordinate Geometry-midpoint, slopeMid-point formula
Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically.
4Coordinate Geometry-gradientGradient
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.
5Coordinate Geometry-gradientGradient formula.
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.
6Coordinate Geometry-straight lineThe straight line.
Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists.
7Coordinate Geometry-slope, etc.Lines through the origin.
Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.
8Coordinate Geometry-equation of lineGeneral form of a line and the x and y Intercepts.
Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.
9Coordinate Geometry-interceptSlope intercept form of a line.
Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.
10Coordinate Geometry-point slopePoint slope form of a line
Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line.
11Co-ordinate Geometry-Two point formulaTwo point formula: equation of a line which joins a pair of points.
Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.
12Co-ordinate Geometry-Intercept formIntercept form of a straight line: find the equation when given x and y
Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.
13Co-ordinate Geometry-Parallel lines equationsParallel lines: identify equation of a line parallel to another
Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.
14Co-ordinate Geometry-Perpendicular linesPerpendicular lines.
Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line.
15Simultaneous equnsSimultaneous equations
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method.
16Simultaneous equnsElimination method
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method.
17Simultaneous equnsElimination method part 2
Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method.
18Simultaneous equnsApplications of simultaneous equations
Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations.
19MatricesBasic concepts – Matrices
Objective: On completion of the lesson the student will have had an introduction to matrices
20MatricesAddition and subtraction of matrices
Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations.
21MatricesScalar matrix multiplication
Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix.
22MatricesMultiplication of one matrix by another matrix
Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication.
23MatricesTranslation in the number plane
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.
24MatricesTranslation by matrix multiplication
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.
25TransformationsSpecial transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
26VectorsVectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.
27Simultaneous equationsNumber of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.
28Vectors2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.
29Linear systemsOptimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.
30Linear systemsLinear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.
31Linear systemsRow-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.
32Algebra- formulaeChanging the subject of the formula.
Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously.
33Algebra-inequalitiesSolving Inequalities.
Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.
34Algebra-factorisingSimplifying easy algebraic fractions.
Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising.
35Algebraic fractionsSimplifying algebraic fractions using the index laws.
Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.
36Algebra-negative indicesAlgebraic fractions resulting in negative indices.
Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.
37FactorisationFactorisation of algebraic fractions including binomials.
Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods.
38Algebraic fractions-binomialCancelling binomial factors in algebraic fractions.
Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions.
39Absolute value or modulusSimplifying absolute values
Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.
40Absolute value or modulusSolving for the variable
Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value.
41Absolute value or modulusSolving and graphing inequalities
Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.
42Co-ordinate Geometry-InequalitiesInequalities on the number plane.
Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.
43CalculusLimits
Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.
44Calculus=1st prinDifferentiation from first principles.
Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve.
45Calculus=1st prinDifferentiation of y = x to the power of n.
Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.
46Calculus-differential, integMeaning of dy over dx – equations of tangents and normals.
Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.
47Calculus-differential, integFunction of a function rule, product rule, quotient rule.
Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule.
48Calculus-differential, integIncreasing, decreasing and stationary functions.
Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.
49CalculusFirst Derivative – turning points and curve sketching
Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve.
50Graphing-polynomialsGraphing complex polynomials: quadratics with no real roots
Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it.
51Graphing-polynomialsGeneral equation of a circle: determine and graph the equation
Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning.
52Graphing-cubic curvesGraphing cubic curves
Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information.
53Absolute value equationsAbsolute value equations
Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio
54Rect.hyperbolaThe rectangular hyperbola.
Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features.
55FunctionsDefinition, domain and range
Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.
56FunctionsNotation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
57FunctionsMore on domain and range
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.
58FunctionsDomain and range from graphical representations
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.
59FunctionsEvaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
60FunctionsFunctions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
61FunctionsComposition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
62FunctionsInverse functions
Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used.
63FunctionsRational functions Part 1
Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes.
64FunctionsRational functions Part 2
Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes.
65FunctionsPolynomial addition etc in combining and simplifying functions (Stage 2)
Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra.
66Geometry-parabolaThe parabola: to describe properties of a parabola from its equation
Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions.
67Functions and graphsQuadratic polynomials of the form y = ax. + bx + c.
Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.
68Functions and graphsGraphing perfect squares: y=(a-x) squared
Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.
69Graphing rootsGraphing irrational roots
Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.
70Coordinate geometrySolve by graphing
Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.
71Difference of 2 squaresDifference of two squares
Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors.
72Common fact and diffCommon factor and the difference of two squares
Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.
73Quadratic trinomialsQuadratic trinomials [monic] – Case 1.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
74Factorising quadsFactorising quadratic trinomials [monic] – Case 2.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
75Factorising quadsFactorising quadratic trinomials [monic] – Case 3.
Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.
76Factorising quadsFactorising quadratic trinomials [monic] – Case 4.
Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.
77Factorising quadsFactorisation of non-monic quadratic trinomials
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
78Factorising quadsFactorisation of non-monic quadratic trinomials – moon method
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.
79Quadratic equationsIntroduction to quadratic equations.
Objective: On completion of the lesson the student will understand simple quadratic equations.
80Quadratic equationsQuadratic equations with factorisation.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.
81Quadratic equationsSolving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
82Quadratic equationsCompleting the square
Objective: On completion of the lesson the student will understand the process of completing the square.
83Quadratic equationsSolving quadratic equations by completing the square
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.
84Quadratic equationsThe quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
85Quadratic equationsProblem solving with quadratic equations
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.
86Quadratic equationsSolving simultaneous quadratic equations graphically
Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..
87Algebra-polynomialsIntroduction to polynomials
Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not.
88Algebra-polynomialsThe sum, difference and product of two polynomials.
Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers.
89Algebra-polynomialsPolynomials and long division.
Objective: On completion of the lesson the student will understand the long division process with polynomials.
90Remainder theoremThe remainder theorem.
Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied.
91Remainder theoremMore on remainder theorem
Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials.
92Factor theoremThe factor theorem
Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial.
93Factor theoremMore on the factor theorem
Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials.
94Factor theoremComplete factorisations using the factor theorem
Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros.
95Logarithms-Complex numbersImaginary numbers and standard form
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction.
96Logarithms-Complex numbersComplex numbers – multiplication and division
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division.
97Logarithms-Complex numbersPlotting complex number and graphical representation
Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers.
98Logarithms-Complex numbersAbsolute value
Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers
99Logarithms-Complex numbersTrigonometric form of a complex number
Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form.
100Logarithms-Complex numbersMultiplication and division of complex numbers in trig form (Stage 2)
Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division.
101Logarithms-Complex numbersDeMoivre’s theorem (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form.
102Logarithms-Complex numbersThe nth root of real and complex numbers (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form.
103Logarithms-Complex numbersFundamental theorem of algebra (Stage 2)
Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field.
104Statistic-probabilityBinomial Theorem – Pascal’s Triangle
Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.
105Statistic-probabilityBinomial probabilities using the Binomial Theorem
Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem
106Statistic-probabilityCounting techniques and ordered selections – permutations
Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability.
107Statistic-probabilityUnordered selections – combinations
Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen.
108Statistics – grouped dataCalculating mean, mode and median from grouped data
Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.
109Statistics using a calculatorStatistics and the student calculator
Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems.
110Statistics – Range and dispersionRange as a measure of dispersion
Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.
111Statistics – SpreadMeasures of spread
Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.
112Statistics – Standard deviationStandard deviation applications
Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.
113Statistics – Standard deviationNormal distribution
Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.
114Statistics – Interquartile rangeMeasures of spread: the interquartile range
Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range
115StatisticsStem and Leaf Plots along with Box and Whisker Plots
Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.
116StatisticsScatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
117Trigonometry-elevationAngles of elevation and depression.
Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.
118Trigonometry-practicalTrigonometric ratios in practical situations.
Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.
119Trigonometry-ratiosUsing the calculator to find an angle given a trigonometric ratio.
Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.
120Trigonometry- ratiosUsing the trigonometric ratios to find an angle in a right-angled triangle.
Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.
121Trigonometry-exact ratiosTrigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.
122Trigonometry-cosine ruleThe cosine rule to find an unknown side. [Case 1 SAS].
Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.
123Trigonometry-cosine ruleThe cosine rule to find an unknown angle. [Case 2 SSS].
Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.
124Trigonometry-sine ruleThe sine rule to find an unknown side. Case 1.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
125Trigonometry-sine ruleThe sine rule to find an unknown angle. Case 2.
Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.
126Trigonometry-areasThe area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.
127Trig-reciprocal ratiosReciprocal ratios.
Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios.
128Trig complementary anglesComplementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
129Trig identitiesTrigonometric identities
Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities.
130Trig larger anglesAngles of any magnitude
Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle.
131Trig larger anglesTrigonometric ratios of 0°, 90°, 180°, 270° and 360°
Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees.
132Graph sineGraphing the trigonometric ratios – I Sine curve.
Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period.
133Graph cosineGraphing the trigonometric ratios – II Cosine curve.
Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period.
134Graphs tan curveGraphing the trigonometric ratios – III Tangent curve.
Objective: On completion of the lesson the student will know how to recognise and draw the tan curve.
135Graph reciprocalsGraphing the trigonometric ratios – IV Reciprocal ratios.
Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.
136Trig larger anglesUsing one ratio to find another.
Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude.
137Trig equationsSolving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.
138Trig equationsSolving trigonometric equations – Type II.
Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains.
139Trig equationsSolving trigonometric equations – Type III.
Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains.
140Polar coordinatesPlotting polar coordinates and converting polar to rectangular
Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system.
141Polar coordinatesConverting rectangular coordinates to polar form
Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates.
142Polar coordinatesWrite and graph points in polar form with negative vectors (Stage 2)
Objective: On completion of the lesson the student will be using negative angles and negative vector lengths.
143Conic sectionsIntroduction to conic sections and their general equation
Objective: On completion of the lesson the student will identify the conic section from the coefficients of the equation.
144Conic sectionsThe parabola x. = 4ay
Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form.
145Conic sectionsCircles
Objective: On completion of the lesson the student will identify the radius of a circle given in standard form.
146Conic sectionsEllipses
Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse.
147Conic sectionsHyperbola
Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola.
148Sequences and SeriesGeneral sequences.
Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.
149Sequences and SeriesFinding Tn given Sn.
Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.
150Arithmetic ProgressionThe arithmetic progression
Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.
151Arithmetic ProgressionFinding the position of a term in an A.P.
Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression.
152Arithmetic ProgressionGiven two terms of A.P., find the sequence.
Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms
153Arithmetic ProgressionArithmetic means
Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.
154Arithmetic ProgressionThe sum to n terms of an A.P.
Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.
155Geometric ProgressionThe geometric progression.
Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.
156Geometric ProgressionFinding the position of a term in a G.P.
Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.
157Geometric ProgressionGiven two terms of G.P., find the sequence.
Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.
158Sequences and Series-Geometric meansGeometric means.
Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.
159Sequences and Series-Sum of gpThe sum to n terms of a G.P.
Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P).
160Sequences and Series-Sigma notationSigma notation
Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates.
161Sequences and Series-Sum-infinityLimiting sum or sum to infinity.
Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems.
162Sequences and Series-Recurring decimal infinityRecurring decimals and the infinite G.P.
Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number.
163Sequences and SeriesApplications of arithmetic sequences
Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.
164ExamExam – MYP Grade 10 – 3 Pre Calculus
Objective: Exam
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Topic 1 - The Scientific Calculator Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 1 – The Scientific Calculator
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2Trigonometry-ratiosUsing the calculator.
Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.
3Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 1 Sine].
Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.
4Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 2 Cosine].
Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.
5Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].
Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.
6Trigonometry-ratiosUnknown in the denominator. [Case 4].
Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.
7Trigonometry-ratiosUsing the calculator to find an angle given a trigonometric ratio.
Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.
8Statistics using a calculatorStatistics and the student calculator
Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems.
9ExamExam – Topic 1 – The Scientific Calculator
Objective: Exam
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Topic 2 - Number and Algebra Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 2 – Number & Algebra
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2Number theory – setsNumber sets and their members
Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system.
3Number theory – operationsProperties of real numbers using addition and multiplication
Objective: On completion of the lesson the student will know and use the closure, identity, commutative, associative, identity and distributive properties for addition and multiplication.
4Number theory – equationsTransformations that produce equivalent equations
Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations.
5Significant figuresSignificant figures
Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures.
6Scientific notationScientific notation with larger numbers
Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation.
7Scientific notationScientific notation with small numbers
Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.
8Scientific notationChanging scientific notation to numerals
Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation.
9LengthProblems with length.
Objective: On completion of the lesson the student will be able to solve problems with length.
10MassProblems with mass.
Objective: On completion of the lesson the student will be able to solve problems with mass.
11Sequences and SeriesGeneral sequences.
Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.
12Sequences and SeriesFinding Tn given Sn.
Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.
13Arithmetic ProgressionThe arithmetic progression
Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.
14Arithmetic ProgressionFinding the position of a term in an A.P.
Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression.
15Arithmetic ProgressionGiven two terms of A.P., find the sequence.
Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms
16Arithmetic ProgressionArithmetic means
Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.
17Arithmetic ProgressionThe sum to n terms of an A.P.
Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.
18Geometric ProgressionThe geometric progression.
Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.
19Geometric ProgressionFinding the position of a term in a G.P.
Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.
20Geometric ProgressionGiven two terms of G.P., find the sequence.
Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.
21Sequences and Series-Sum of gpThe sum to n terms of a G.P.
Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P).
22Sequences and SeriesApplications of arithmetic sequences
Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.
23Sequences and Series-Geometric meansGeometric means.
Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.
24Algebraic expressionsAlgebraic expressions.
Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.
25Algebraic expressionsSubstitution into algebraic expressions.
Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.
26Algebraic expressionsDirected numbers: addition and subtraction.
Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.
27Algebraic expressionsDirected numbers: multiplication and division.
Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.
28Algebraic expressionsSimplifying algebraic expressions: adding like terms.
Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.
29Algebraic expressionsSimplifying algebraic Expressions: subtracting like terms.
Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.
30Algebraic expressionsSimplifying Algebraic expressions: combining addition and subtraction.
Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.
31Algebraic expressionsSimplifying algebraic expressions: multiplication
Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form.
32Algebraic expressionsSimplifying algebraic expressions: division
Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions.
33Algebraic expressionsExpanding algebraic expressions: multiplication
Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.
34Algebraic expressionsExpanding algebraic expressions: negative multiplier
Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier.
35Algebraic expressionsExpanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
36Algebraic equationsSolving equations containing addition and subtraction
Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.
37Algebraic equationsSolving equations containing multiplication and division
Objective: On completion of the lesson the student will be able to solve simple equations involving all operations.
38Algebraic equationsSolving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
39Algebraic equationsSolving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
40Algebraic equationsEquations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
41Algebraic equationsEquations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
42Algebra- formulaeEquations resulting from substitution into formulae.
Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations.
43Algebra- formulaeChanging the subject of the formula.
Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously.
44Algebra-inequalitiesSolving Inequalities.
Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.
45Algebra-factorisingSimplifying easy algebraic fractions.
Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising.
46Algebraic fractionsSimplifying algebraic fractions using the index laws.
Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.
47Algebra-negative indicesAlgebraic fractions resulting in negative indices.
Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.
48FactorisationFactorisation of algebraic fractions including binomials.
Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods.
49Algebraic fractions-binomialCancelling binomial factors in algebraic fractions.
Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions.
50Absolute value or modulusSimplifying absolute values
Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.
51Absolute value or modulusSolving for the variable
Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value.
52Absolute value or modulusSolving and graphing inequalities
Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.
53Rules for indices/exponentsAdding indices when multiplying terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.
54Rules for indices/exponentsSubtracting indices when dividing terms with the same base
Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base.
55Rules for indices/exponentsMultiplying indices when raising a power to a power
Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.
56Rules for indices/exponentsMultiplying indices when raising to more than one term
Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.
57Rules for indices/exponentsTerms raised to the power of zero
Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.
58Rules for indices/exponentsNegative Indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices.
59Fractional indices/exponentsFractional indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.
60Fractional indices/exponentsComplex fractions as indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices.
61Functions and graphsQuadratic polynomials of the form y = ax. + bx + c.
Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.
62Graphing binomialsBinomial products.
Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression.
63Graphing binomialsBinomial products with negative multiplier
Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products.
64Graphing binomialsBinomial products [non-monic].
Objective: On completion of the lesson, the student will have examined more complex examples with binomial products.
65Squaring binomialSquaring a binomial. [monic]
Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial.
66Squaring binomialSquaring a binomial [non-monic].
Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials.
67FactorisingExpansions leading to the difference of two squares
Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares.
68Algebraic expressions-productsProducts in simplification of algebraic expressions
Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing.
69Algebraic expressions-larger expansionsAlgebraic Expressions – Larger expansions.
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.
70Algebra-highest common factorHighest common factor.
Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.
71Factors by groupingFactors by grouping.
Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.
72Difference of 2 squaresDifference of two squares
Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors.
73Common fact and diffCommon factor and the difference of two squares
Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.
74Quadratic trinomialsQuadratic trinomials [monic] – Case 1.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
75Factorising quadsFactorising quadratic trinomials [monic] – Case 2.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
76Factorising quadsFactorising quadratic trinomials [monic] – Case 3.
Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.
77Factorising quadsFactorising quadratic trinomials [monic] – Case 4.
Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.
78Factorising quadsFactorisation of non-monic quadratic trinomials
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
79Factorising quadsFactorisation of non-monic quadratic trinomials – moon method
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.
80Sum/diff 2 cubesSum and difference of two cubes.
Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them.
81Algebraic fractionsSimplifying algebraic fractions.
Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point.
82Quadratic equationsIntroduction to quadratic equations.
Objective: On completion of the lesson the student will understand simple quadratic equations.
83Quadratic equationsQuadratic equations with factorisation.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.
84Quadratic equationsSolving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
85Quadratic equationsCompleting the square
Objective: On completion of the lesson the student will understand the process of completing the square.
86Quadratic equationsSolving quadratic equations by completing the square
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.
87Quadratic equationsThe quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
88Quadratic equationsProblem solving with quadratic equations
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.
89Quadratic equationsSolving simultaneous quadratic equations graphically
Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..
90ExamExam – Topic 2 – Number & Algebra
Objective: Exam
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Topic 3 - Sets Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 3 – Sets
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2Number theory – setsNumber sets and their members
Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system.
3LogicInductive and deductive reasoning
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.
4LogicDefinition and use of counter examples
Objective: On completion of this lesson the student will be able to create counter examples to statements.
5LogicMathematical induction
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.
6LogicConditional statements (converse, inverse and contrapositive) (Stage 2)
Objective: On completion of the lesson the student will be able to form related conditional statements.
7LogicIndirect proofs
Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved.
8Statistic-probabilityTree diagrams – not depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.
9Statistic-probabilityTree diagrams – depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.
10Statistic-probabilityThe complementary result ..
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.
11Statistic-probabilityProbability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
12Statistic-probabilityRolling a pair of dice
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.
13Statistic-probabilityExperimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
14Statistic-probabilityP[A or B] When A and B are both mutually and NOT mutually exclusive
Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.
15ExamExam – Topic 3 – Sets
Objective: Exam
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Topic 4 - Functions and Graphs Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 4 – Functions & Graphs
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2FunctionsDefinition, domain and range
Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.
3FunctionsNotation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
4FunctionsMore on domain and range
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.
5FunctionsDomain and range from graphical representations
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.
6FunctionsEvaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
7FunctionsFunctions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
8FunctionsComposition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
9Functions and graphsGraphing perfect squares: y=(a-x) squared
Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.
10Graphing rootsGraphing irrational roots
Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.
11Coordinate geometrySolve by graphing
Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.
12FunctionsInverse functions
Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used.
13FunctionsRational functions Part 1
Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes.
14FunctionsRational functions Part 2
Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes.
15FunctionsParametric equations (Stage 2)
Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range.
16FunctionsPolynomial addition etc in combining and simplifying functions (Stage 2)
Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra.
17FunctionsParametric functions (Stage 2)
Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion.
18Exponential functionThe exponential function.
Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1.
19Log functionsLogarithmic functions.
Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit
20Trigonometry-ratiosTrigonometric ratios.
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op
21Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 1 Sine].
Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.
22Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 2 Cosine].
Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.
23Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].
Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.
24Trigonometry-ratiosUnknown in the denominator. [Case 4].
Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.
25Trigonometry-compassBearings – the compass.
Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.
26Trigonometry-elevationAngles of elevation and depression.
Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.
27Trigonometry-practicalTrigonometric ratios in practical situations.
Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.
28Trigonometry-ratiosUsing the calculator to find an angle given a trigonometric ratio.
Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.
29Trigonometry- ratiosUsing the trigonometric ratios to find an angle in a right-angled triangle.
Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.
30Trigonometry-exact ratiosTrigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.
31Trigonometry-cosine ruleThe cosine rule to find an unknown side. [Case 1 SAS].
Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.
32Trigonometry-cosine ruleThe cosine rule to find an unknown angle. [Case 2 SSS].
Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.
33Trigonometry-sine ruleThe sine rule to find an unknown side. Case 1.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
34Trigonometry-sine ruleThe sine rule to find an unknown angle. Case 2.
Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.
35Trigonometry-areasThe area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.
36Coordinate Geometry-gradientGradient
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.
37Coordinate Geometry-gradientGradient formula.
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.
38Coordinate Geometry-straight lineThe straight line.
Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists.
39Coordinate Geometry-slope, etc.Lines through the origin.
Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.
40Coordinate Geometry-equation of lineGeneral form of a line and the x and y Intercepts.
Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.
41Coordinate Geometry-interceptSlope intercept form of a line.
Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.
42Coordinate Geometry-point slopePoint slope form of a line
Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line.
43ExamExam – Topic 4 – Functions & Graphs
Objective: Exam
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Topic 5 - Geometry Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 5 – Geometry
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2Coordinate Geometry-the planeDistance formula.
Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results.
3Coordinate Geometry-midpoint, slopeMid-point formula
Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically.
4Coordinate Geometry-gradientGradient
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.
5Coordinate Geometry-gradientGradient formula.
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.
6Coordinate Geometry-straight lineThe straight line.
Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists.
7Coordinate Geometry-slope, etc.Lines through the origin.
Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.
8Coordinate Geometry-equation of lineGeneral form of a line and the x and y Intercepts.
Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.
9Coordinate Geometry-interceptSlope intercept form of a line.
Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.
10Coordinate Geometry-point slopePoint slope form of a line
Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line.
11PythagorasFind the hypotenuse
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse.
12PythagorasPythagorean triples
Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple.
13PythagorasFind the hypotenuse Part 2
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds.
14PythagorasCalculating a leg of a right-angled triangle
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.
15PythagorasProofs of Pythagoras theorem
Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem
16Trigonometry-ratiosTrigonometric ratios.
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op
17Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 1 Sine].
Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.
18Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 2 Cosine].
Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.
19Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].
Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.
20Trigonometry-ratiosUnknown in the denominator. [Case 4].
Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.
21Trigonometry-practicalTrigonometric ratios in practical situations.
Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.
22Trigonometry-ratiosUsing the calculator to find an angle given a trigonometric ratio.
Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.
23Trigonometry-exact ratiosTrigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.
24Trigonometry-cosine ruleThe cosine rule to find an unknown side. [Case 1 SAS].
Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.
25Trigonometry-cosine ruleThe cosine rule to find an unknown angle. [Case 2 SSS].
Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.
26Trigonometry-sine ruleThe sine rule to find an unknown side. Case 1.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
27Trigonometry-sine ruleThe sine rule to find an unknown angle. Case 2.
Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.
28Trigonometry-areasThe area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.
29AreaProblems with area.
Objective: On completion of the lesson the student will be able to solve problems with area.
30Volume/capacityProblems with volume/capacity.
Objective: Problem Solving: problems involving volume/capacity
31Surface areaSurface area of a cube/rectangular prism.
Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.
32Surface areaSurface area of a triangular/trapezoidal prism.
Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula.
33Surface areaSurface area of a cylinder and sphere.
Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.
34Surface areaSurface area of pyramids
Objective: On completion of the lesson the student will be able to find the surface areas of pyramids.
35Surface areaSurface area of cones
Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul
36Surface areaSurface area of composite solids
Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids.
37Geometry-anglesMeasuring angles
Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.
38Geometry-anglesAdjacent angles
Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.
39Geometry-anglesComplementary and supplementary angles
Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.
40Geometry-anglesVertically opposite angles
Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.
41Geometry-anglesAngles at a Point.
Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.
42Geometry-anglesParallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
43Geometry-problemsAdditional questions involving parallel lines
Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.
44Geometry-trianglesAngle sum of a triangle
Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.
45Geometry-trianglesExterior angle theorem
Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.
46Special trianglesSpecial triangles
Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.
47Geometry-quadrilateralsQuadrilaterals
Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.
48Geometry-constructionsGeometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
49GeometryTo identify collinear points, coplanar lines and points in 2 and 3 dimensions
Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays.
50Geometry – anglesTo determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra
Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles.
51Geometry-constructionsAngle bisector construction and its properties (Stage 2)
Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge.
52Geometry-constructionsCircumcentre and incentre (Stage 2)
Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values.
53Geometry-constructionsOrthocentre and centroids (Stage 2)
Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values.
54Geometry-quadrilateralsMidsegments of Triangles
Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.
55Geometry-quadrilateralsClassifying Quadrilaterals
Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals.
56Geometry-quadrilateralsUsing the Properties of a Parallelogram
Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram.
57Geometry-quadrilateralsProving a Shape is a Parallelogram
Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram.
58Geometry-quadrilateralsProperties of the Rectangle, Square and Rhombus
Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values.
59Geometry-quadrilateralsProperties of the Trapezium and Kite
Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values.
60Geometry-quadrilateralsThe quadrilateral family and coordinate methods in geometry
Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties.
61Geometry-locusConstructions and loci – single condition
Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition.
62Geometry-locusConstructions and loci – multiple conditions
Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane.
63Geometry problemsMore difficult exercises involving parallel lines
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log
64Geometry-reasoningFurther difficult exercises involving formal reasoning
Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.
65Geometry-polygonsAngles of regular polygons
Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees.
66Geometry-congruenceCongruent triangles, Test 1 and 2
Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent.
67Geometry-congruenceCongruent triangles, Test 3 and 4
Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.
68Geometry-congruenceProofs and congruent triangles.
Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent.
69Similar trianglesSimilar triangles
Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar.
70Similar trianglesUsing similar triangles to calculate lengths
Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles.
71Overlapping trianglesExamples involving overlapping triangles
Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles.
72Geometry – trianglesTriangle inequality theorem
Objective: On completion of the lesson the student will understand and use the triangle inequality theorem.
73ExamExam – Topic 5 – Geometry
Objective: Exam
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Topic 6 - Statistics Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 6 – Statistics
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2StatisticsFrequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.
3StatisticsFrequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
4StatisticsRelative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
5Statistic-probabilityThe mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
6Statistic-probabilityThe mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
7Statistic-probabilityThe median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
8Statistic-probabilityCumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
9StatisticsThe range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
10Statistic-probabilityCalculating the median from a frequency distribution
Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon.
11StatisticsStem and Leaf Plots along with Box and Whisker Plots
Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.
12StatisticsScatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
13Statistics – grouped dataCalculating mean, mode and median from grouped data
Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.
14Statistics using a calculatorStatistics and the student calculator
Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems.
15Statistics – Range and dispersionRange as a measure of dispersion
Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.
16Statistics – SpreadMeasures of spread
Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.
17Statistics – Standard deviationNormal distribution
Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.
18Statistics – Standard deviationStandard deviation applications
Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.
19Statistics – Interquartile rangeMeasures of spread: the interquartile range
Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range
20ExamExam – Topic 6 – Statistics
Objective: Exam
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Topic 7 - Differential Calculus Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 7 – Differential Calculus
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2CalculusLimits
Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.
3Calculus=1st prinDifferentiation from first principles.
Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve.
4Calculus=1st prinDifferentiation of y = x to the power of n.
Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.
5Calculus-differential, integMeaning of dy over dx – equations of tangents and normals.
Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.
6Calculus-differential, integFunction of a function rule, product rule, quotient rule.
Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule.
7Calculus-differential, integIncreasing, decreasing and stationary functions.
Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.
8CalculusFirst Derivative – turning points and curve sketching
Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve.
9Calculus-2nd derivativeThe second derivative – concavity.
Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.
10Calculus – Curve sketchingCurve sketching
Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve.
11Calculus – Maxima minimaPractical applications of maxima and minima
Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems.
12Calculus – IntegrationIntegration – anti-differentiation, primitive function
Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions.
13Calculus – Computation areaComputation of an area
Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area.
14ExamExam – Topic 7 – Differential Calculus
Objective: Exam
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Topic 8 - Financial management Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 8 – Financial management
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.See the sample lesson in action here
2Sequences and Series-Compound interestCompound interest
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.See the sample lesson in action here
3Sequences and Series-SuperannuationSuperannuation.
Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.See the sample lesson in action here
4Sequences and Series-Time paymentsTime payments.
Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.See the sample lesson in action here
5ExamExam – Topic 8 – Financial management
Objective: ExamSee the sample lesson in action here
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Topic 1 - Algebra Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 1 – Algebra
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2Sequences and SeriesGeneral sequences.
Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.
3Sequences and SeriesFinding Tn given Sn.
Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.
4Arithmetic ProgressionThe arithmetic progression
Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.
5Arithmetic ProgressionFinding the position of a term in an A.P.
Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression.
6Arithmetic ProgressionGiven two terms of A.P., find the sequence.
Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms
7Arithmetic ProgressionArithmetic means
Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.
8Arithmetic ProgressionThe sum to n terms of an A.P.
Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.
9Geometric ProgressionThe geometric progression.
Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.
10Geometric ProgressionFinding the position of a term in a G.P.
Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.
11Geometric ProgressionGiven two terms of G.P., find the sequence.
Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.
12Sequences and Series-Geometric meansGeometric means.
Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.
13Sequences and Series-Sum of gpThe sum to n terms of a G.P.
Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P).
14Sequences and Series-Sigma notationSigma notation
Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates.
15Sequences and Series-Sum-infinityLimiting sum or sum to infinity.
Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems.
16Sequences and Series-Recurring decimal infinityRecurring decimals and the infinite G.P.
Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number.
17Sequences and Series-Compound interestCompound interest
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.
18Sequences and Series-SuperannuationSuperannuation.
Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.
19Sequences and Series-Time paymentsTime payments.
Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.
20Sequences and SeriesApplications of arithmetic sequences
Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.
21Logarithms-Power of 2Powers of 2.
Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2.
22Logarithms-Equations and logsEquations of type log x to the base 3 = 4.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.
23Logarithms-Equations and logsEquations of type log 32 to the base x = 5.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.
24Logarithms-Log lawsLaws of logarithms.
Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.
25Logarithms-Log laws expansionUsing the log laws to expand logarithmic expressions.
Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.
26Logarithms-Log laws simplifyingUsing the log laws to simplify expressions involving logarithms.
Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.
27Logarithms-Log laws numbersUsing the log laws to find the logarithms of numbers.
Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples.
28Logarithms-Equations and logsEquations involving logarithms.
Objective: On completion of the lesson the student will be able to solve equations with log terms.
29Logarithms-Logs to solve equationsUsing logarithms to solve equations.
Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.
30Logarithms-Change base formulaChange of base formula
Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base.
31Statistic-probabilityBinomial Theorem – Pascal’s Triangle
Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.
32Statistic-probabilityBinomial probabilities using the Binomial Theorem
Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem
33Statistic-probabilityCounting techniques and ordered selections – permutations
Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability.
34Statistic-probabilityUnordered selections – combinations
Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen.
35LogicInductive and deductive reasoning
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.
36LogicDefinition and use of counter examples
Objective: On completion of this lesson the student will be able to create counter examples to statements.
37LogicIndirect proofs
Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved.
38LogicMathematical induction
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.
39LogicConditional statements (converse, inverse and contrapositive) (Stage 2)
Objective: On completion of the lesson the student will be able to form related conditional statements.
40SurdsIntroducing surds
Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.
41SurdsSome rules for the operations with surds
Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds.
42SurdsSimplifying surds
Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication.
43SurdsCreating entire surds
Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds
44SurdsAdding and subtracting like surds
Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.
45SurdsExpanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
46SurdsBinomial expansions
Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.
47SurdsConjugate binomials with surds
Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds.
48SurdsRationalising the denominator
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds.
49SurdsRationalising binomial denominators
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions.
50Simultaneous equnsSimultaneous equations
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method.
51Simultaneous equnsElimination method
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method.
52Simultaneous equnsElimination method part 2
Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method.
53Simultaneous equnsApplications of simultaneous equations
Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations.
54Logarithms-Complex numbersImaginary numbers and standard form
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction.
55Logarithms-Complex numbersComplex numbers – multiplication and division
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division.
56Logarithms-Complex numbersPlotting complex number and graphical representation
Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers.
57Logarithms-Complex numbersAbsolute value
Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers
58Logarithms-Complex numbersTrigonometric form of a complex number
Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form.
59Logarithms-Complex numbersMultiplication and division of complex numbers in trig form (Stage 2)
Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division.
60Logarithms-Complex numbersDeMoivre’s theorem (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form.
61Logarithms-Complex numbersThe nth root of real and complex numbers (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form.
62Logarithms-Complex numbersFundamental theorem of algebra (Stage 2)
Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field.
63Algebra-polynomialsIntroduction to polynomials
Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not.
64Algebra-polynomialsThe sum, difference and product of two polynomials.
Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers.
65Algebra-polynomialsPolynomials and long division.
Objective: On completion of the lesson the student will understand the long division process with polynomials.
66Remainder theoremThe remainder theorem.
Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied.
67Remainder theoremMore on remainder theorem
Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials.
68Factor theoremThe factor theorem
Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial.
69Factor theoremMore on the factor theorem
Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials.
70Factor theoremComplete factorisations using the factor theorem
Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros.
71Polynomial equationsPolynomial equations
Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms.
72Graphs, polynomialsGraphs of polynomials
Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves.
73Roots quad equationsSum and product of roots of quadratic equations
Objective: On completion of the lesson the student will understand the formulas for the sum and product of roots of quadratic polynomials and how to use them. The student will understand how to form a quadratic equation given its roots.
74Roots quad equationsSum and product of roots of cubic and quartic equations
Objective: On completion of the lesson the student will be able to do problems on the sum and products of roots of cubic and quartic equations.
75Approx rootsMethods of approximating roots
Objective: On completion of the lesson the student will be capable of finding approximate roots of polynomial equations using half the interval method. The student will be able to make a number of applications of this rule within the one question.
76Newton’s approxNewton’s method of approximation
Objective: On completion of the lesson the student will be able to use Newton’s method in finding approximate roots of polynomial equations and be capable of more than one application of this method.
77ExamExam – Topic 1 – Algebra
Objective: Exam
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Topic 2 - Functions and Equations Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 2 – Functions & Equations
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2Logarithms-Power of 2Powers of 2.
Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2.
3Logarithms-Equations and logsEquations of type log x to the base 3 = 4.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.
4Logarithms-Equations and logsEquations of type log 32 to the base x = 5.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.
5Logarithms-Log lawsLaws of logarithms.
Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.
6Logarithms-Log laws expansionUsing the log laws to expand logarithmic expressions.
Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.
7Logarithms-Log laws simplifyingUsing the log laws to simplify expressions involving logarithms.
Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.
8Logarithms-Log laws numbersUsing the log laws to find the logarithms of numbers.
Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples.
9Logarithms-Equations and logsEquations involving logarithms.
Objective: On completion of the lesson the student will be able to solve equations with log terms.
10Logarithms-Logs to solve equationsUsing logarithms to solve equations.
Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.
11Logarithms-Change base formulaChange of base formula
Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base.
12MatricesTranslation in the number plane
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.
13MatricesTranslation by matrix multiplication
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.
14TransformationsSpecial transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
15VectorsVectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.
16Simultaneous equationsNumber of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.
17Vectors2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.
18Linear systemsOptimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.
19Linear systemsLinear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.
20Linear systemsRow-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.
21Linear systemsGauss Jordan elimination method (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.
22FunctionsDefinition, domain and range
Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.
23FunctionsNotation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
24FunctionsMore on domain and range
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.
25FunctionsDomain and range from graphical representations
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.
26FunctionsEvaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
27FunctionsFunctions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
28FunctionsComposition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
29FunctionsInverse functions
Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used.
30FunctionsRational functions Part 1
Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes.
31FunctionsRational functions Part 2
Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes.
32FunctionsParametric equations (Stage 2)
Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range.
33FunctionsPolynomial addition etc in combining and simplifying functions (Stage 2)
Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra.
34FunctionsParametric functions (Stage 2)
Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion.
35Co-ordinate Geometry-Two point formulaTwo point formula: equation of a line which joins a pair of points.
Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.
36Co-ordinate Geometry-Intercept formIntercept form of a straight line: find the equation when given x and y
Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.
37Co-ordinate Geometry-Parallel lines equationsParallel lines: identify equation of a line parallel to another
Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.
38Co-ordinate Geometry-Perpendicular linesPerpendicular lines.
Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line.
39Co-ordinate Geometry-InequalitiesInequalities on the number plane.
Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.
40Co-ordinate Geometry-TheoremsPerpendicular distance
Objective: On completion of the lesson the student will be able to derive the formula to calculate the distance between a given point and a given line. The student will also be able to calculate the distance between parallel lines.
41Co-ordinate Geometry-TheoremsLine through intersection of two given lines
Objective: On completion of the lesson the student will be able to calculate the equation of a line which goes through the intersection of two given lines and also through another named point or satisfies some other specified condition.
42Co-ordinate Geometry-TheoremsAngles between two lines
Objective: On completion of the lesson the student will be able to calculate the angle between given lines and derive the equation of a line given its angle to another line.
43Co-ordinate Geometry-TheoremsInternal and external division of an interval
Objective: On completion of the lesson the student will be able to divide an interval according to a given ratio and to calculate what point divides an interval in a given ratio for both internal and external divisions.
44TranslationsTransformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.
45Geometric transformationsGeometry transformations without matrices: reflection (Stage 2)
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.
46Geometric transformationsGeometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.
47Geometric transformationsGeometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.
48Geometric transformationsGeometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.
49Geometric transformationsThe definition and concept of combined transformations resulting in an equivalent single transformation.
Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations.
50Graphs, polynomialsGraphs of polynomials
Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves.
51Quadratic equationsIntroduction to quadratic equations.
Objective: On completion of the lesson the student will understand simple quadratic equations.
52Quadratic equationsQuadratic equations with factorisation.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.
53Quadratic equationsSolving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
54Quadratic equationsCompleting the square
Objective: On completion of the lesson the student will understand the process of completing the square.
55Quadratic equationsSolving quadratic equations by completing the square
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.
56Quadratic equationsThe quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
57Quadratic equationsProblem solving with quadratic equations
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.
58Quadratic equationsSolving simultaneous quadratic equations graphically
Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..
59Functions and graphsQuadratic polynomials of the form y = ax. + bx + c.
Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.
60Functions and graphsGraphing perfect squares: y=(a-x) squared
Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.
61Graphing rootsGraphing irrational roots
Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.
62Coordinate geometrySolve by graphing
Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.
63Logarithms-Graph-log curveThe graph of the logarithmic curve
Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves.
64Logarithms-Log curvesWorking with log curves.
Objective: On completion of the lesson the student will be able to solve problems with log curves
65Logarithms-Complex numbersImaginary numbers and standard form
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction.
66Logarithms-Complex numbersComplex numbers – multiplication and division
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division.
67Logarithms-Complex numbersPlotting complex number and graphical representation
Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers.
68Logarithms-Complex numbersAbsolute value
Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers
69Logarithms-Complex numbersTrigonometric form of a complex number
Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form.
70Logarithms-Complex numbersMultiplication and division of complex numbers in trig form (Stage 2)
Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division.
71Logarithms-Complex numbersDeMoivre’s theorem (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form.
72Logarithms-Complex numbersThe nth root of real and complex numbers (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form.
73Logarithms-Complex numbersFundamental theorem of algebra (Stage 2)
Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field.
74Sequences and Series-Compound interestCompound interest
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.
75Sequences and Series-SuperannuationSuperannuation.
Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.
76Sequences and Series-Time paymentsTime payments.
Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.
77Sequences and SeriesApplications of arithmetic sequences
Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.
78ExamExam – Topic 2 – Functions & Equations
Objective: Exam
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Topic 3 - Circular functions and Trigonometry Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 3 – Circular functions & Trigonometry
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2Geometry-circlesThe equation of a circle: to find radii of circles
Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius.
3Geometry-circlesThe semicircle: to select the equation given the semi circle and vice versa
Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle.
4Geometry-parabolaThe parabola: to describe properties of a parabola from its equation
Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions.
5Circle GeometryTheorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs.
Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro
6Circle GeometryTheorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord.
Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’
7Circle GeometryTheorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal.
Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre.
8Circle GeometryTheorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc.
Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.
9Circle GeometryTheorem – Angles in the same segment of a circle are equal.
Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.
10Circle GeometryTheorem – The angle of a semi-circle is a right angle.
Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’
11Circle GeometryTheorem – The opposite angles of a cyclic quadrilateral are supplementary.
Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.
12Circle GeometryTheorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle.
Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite.
13Circle GeometryTheorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.
Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact.
14Circle GeometryTheorem – Tangents to a circle from an external point are equal.
Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.
15Circle GeometryTheorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
16Circle Geometry-chordsTheorem – The products of the intercepts of two intersecting chords are equal.
Objective: On completion of the lesson the student will be able to prove that ‘The product of the intercepts of two intersecting chords are equal.’, and use this result to complete questions that require this knowledge.
17Circle Geometry-tangentsTheorem – The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point. [Including Alternate Proof]
Objective: On completion of the lesson the student will be able to prove and apply ‘The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point ‘, and use this result to complete q
18Circle Geometry-cyclic quadsTheorem – If the opposite angles in a quadrilateral are supplementary then the quadrilateral is cyclic.
Objective: On completion of the lesson the student will be able to prove that a quadrilateral is cyclic using the supplementary angles theorem.
19Circle Geometry-subtendingTheorem – If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic.
Objective: On completion of the lesson the student will be able to prove that ‘ If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic’, and use this result to complete the ques
20Circle GeometryTheorem – When circles touch, the line of the centres passes through the point of contact.
Objective: On completion of the lesson the student will be able to prove that ‘ When two circles touch, the line of the centres passes through the point of contact’, and use this result to complete questions that require it.
21Circle Geometry-non-collinearTheorem – Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points.
Objective: On completion of the lesson the student will be able to prove that ‘ Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points’, and use this knowled
22Trig-reciprocal ratiosReciprocal ratios.
Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios.
23Trig complementary anglesComplementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
24Trig identitiesTrigonometric identities
Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities.
25Trig larger anglesAngles of any magnitude
Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle.
26Trig larger anglesTrigonometric ratios of 0°, 90°, 180°, 270° and 360°
Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees.
27Graph sineGraphing the trigonometric ratios – I Sine curve.
Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period.
28Graph cosineGraphing the trigonometric ratios – II Cosine curve.
Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period.
29Graphs tan curveGraphing the trigonometric ratios – III Tangent curve.
Objective: On completion of the lesson the student will know how to recognise and draw the tan curve.
30Graph reciprocalsGraphing the trigonometric ratios – IV Reciprocal ratios.
Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.
31Trig larger anglesUsing one ratio to find another.
Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude.
32Trig equationsSolving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.
33Trig equationsSolving trigonometric equations – Type II.
Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains.
34Trig equationsSolving trigonometric equations – Type III.
Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains.
35Polar coordinatesPlotting polar coordinates and converting polar to rectangular
Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system.
36Polar coordinatesConverting rectangular coordinates to polar form
Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates.
37Polar coordinatesWrite and graph points in polar form with negative vectors (Stage 2)
Objective: On completion of the lesson the student will be using negative angles and negative vector lengths.
38TrigonometrySin(A+B) etc sum and difference identities (Stage 2)
Objective: On completion of the lesson the student will be using the reference triangles for 30, 45 and 60 degrees with the sum and difference of angles to find additional exact values of trigonometric ratios.
39TrigonometryDouble angle formulas (Stage 2)
Objective: On completion of the lesson the student will derive and use the double angle trig identities.
40TrigonometryHalf angle identities (Stage 2)
Objective: On completion of the lesson the student will derive and use the power reducing formulas and the half angle trig identities.
41Trigonometryt Formulas (Stage 2)
Objective: On completion of the lesson the student will solve trig equations using the t substitution.
42Trigonometry-ratiosTrigonometric ratios.
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op
43Trigonometry-ratiosUsing the calculator.
Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.
44Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 1 Sine].
Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.
45Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 2 Cosine].
Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.
46Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].
Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.
47Trigonometry-ratiosUnknown in the denominator. [Case 4].
Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.
48Trigonometry-compassBearings – the compass.
Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.
49Trigonometry-elevationAngles of elevation and depression.
Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.
50Trigonometry-practicalTrigonometric ratios in practical situations.
Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.
51Trigonometry-ratiosUsing the calculator to find an angle given a trigonometric ratio.
Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.
52Trigonometry- ratiosUsing the trigonometric ratios to find an angle in a right-angled triangle.
Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.
53Trigonometry-exact ratiosTrigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.
54Trigonometry-cosine ruleThe cosine rule to find an unknown side. [Case 1 SAS].
Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.
55Trigonometry-cosine ruleThe cosine rule to find an unknown angle. [Case 2 SSS].
Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.
56Trigonometry-sine ruleThe sine rule to find an unknown side. Case 1.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
57Trigonometry-sine ruleThe sine rule to find an unknown angle. Case 2.
Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.
58Trigonometry-areasThe area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.
59ExamExam – Topic 3 – Circular functions & Trigonometry
Objective: Exam
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Topic 4 - Matrices Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 4 – Matrices
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2MatricesBasic concepts – Matrices
Objective: On completion of the lesson the student will have had an introduction to matrices
3MatricesAddition and subtraction of matrices
Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations.
4MatricesScalar matrix multiplication
Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix.
5MatricesMultiplication of one matrix by another matrix
Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication.
6MatricesTranslation in the number plane
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.
7MatricesTranslation by matrix multiplication
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.
8TransformationsSpecial transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
9VectorsVectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.
10Simultaneous equationsNumber of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.
11Vectors2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.
12Linear systemsOptimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.
13Linear systemsLinear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.
14Linear systemsRow-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.
15Linear systemsGauss Jordan elimination method (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.
16ExamExam – Topic 4 – Matrices
Objective: Exam
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Topic 5 - Vectors Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 5 – Vectors
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2VectorsVectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.
3Simultaneous equationsNumber of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.
4Vectors2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.
5Linear systemsOptimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.
6Linear systemsLinear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.
7Linear systemsRow-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.
8Linear systemsGauss Jordan elimination method (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.
9ExamExam – Topic 5 – Vectors
Objective: Exam
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Topic 6 - Statistics and Probability Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 6 – Statistics & Probability
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2StatisticsFrequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.
3StatisticsFrequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
4StatisticsRelative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
5StatisticsThe range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
6Statistic-probabilityThe mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
7Statistic-probabilityThe mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
8Statistic-probabilityThe median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
9Statistic-probabilityCumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
10Statistic-probabilityCalculating the median from a frequency distribution
Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon.
11Statistic-probabilityBinomial Theorem – Pascal’s Triangle
Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.
12Statistic-probabilityBinomial probabilities using the Binomial Theorem
Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem
13Statistic-probabilityCounting techniques and ordered selections – permutations
Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability.
14Statistic-probabilityUnordered selections – combinations
Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen.
15Statistics – grouped dataCalculating mean, mode and median from grouped data
Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.
16Statistics using a calculatorStatistics and the student calculator
Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems.
17Statistics – Range and dispersionRange as a measure of dispersion
Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.
18Statistics – SpreadMeasures of spread
Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.
19Statistics – Standard deviationStandard deviation applications
Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.
20Statistics – Standard deviationNormal distribution
Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.
21Statistics – Interquartile rangeMeasures of spread: the interquartile range
Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range
22StatisticsStem and Leaf Plots along with Box and Whisker Plots
Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.
23StatisticsScatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
24Statistic-probabilityProbability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
25Statistic-probabilityRolling a pair of dice
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.
26Statistic-probabilityExperimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
27Statistic-probabilityTree diagrams – not depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.
28Statistic-probabilityTree diagrams – depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.
29Statistic-probabilityThe complementary result ..
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.
30Statistic-probabilityP[A or B] When A and B are both mutually and NOT mutually exclusive
Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.
31ExamExam – Topic 6 – Statistics & Probability
Objective: Exam
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Topic 7 - Differential Calculus Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 7 – Differential Calculus
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2CalculusLimits
Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.
3Calculus=1st prinDifferentiation from first principles.
Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve.
4Calculus=1st prinDifferentiation of y = x to the power of n.
Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.
5Calculus-differential, integMeaning of dy over dx – equations of tangents and normals.
Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.
6Calculus-differential, integFunction of a function rule, product rule, quotient rule.
Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule.
7Calculus-differential, integIncreasing, decreasing and stationary functions.
Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.
8CalculusFirst Derivative – turning points and curve sketching
Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve.
9Calculus-2nd derivativeThe second derivative – concavity.
Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.
10Calculus – Curve sketchingCurve sketching
Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve.
11Calculus – Maxima minimaPractical applications of maxima and minima
Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems.
12Calculus – IntegrationIntegration – anti-differentiation, primitive function
Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions.
13Calculus – Computation areaComputation of an area
Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area.
14Calculus – Computation volumesComputation of volumes of revolution
Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy.
15Calculus – Trapezoidal and Simpson’s rulesThe Trapezium rule and Simpson’s rule
Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve.
16ExamExam – Topic 7 – Differential Calculus
Objective: Exam
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Topic 1 - Algebra Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 1 – Algebra
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.See the sample lesson in action here
2Sequences and SeriesGeneral sequences.
Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.See the sample lesson in action here
3Sequences and SeriesFinding Tn given Sn.
Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.See the sample lesson in action here
4Arithmetic ProgressionThe arithmetic progression
Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.See the sample lesson in action here
5Arithmetic ProgressionFinding the position of a term in an A.P.
Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression.See the sample lesson in action here
6Arithmetic ProgressionGiven two terms of A.P., find the sequence.
Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two termsSee the sample lesson in action here
7Arithmetic ProgressionArithmetic means
Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.See the sample lesson in action here
8Arithmetic ProgressionThe sum to n terms of an A.P.
Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.See the sample lesson in action here
9Geometric ProgressionThe geometric progression.
Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.See the sample lesson in action here
10Geometric ProgressionFinding the position of a term in a G.P.
Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.See the sample lesson in action here
11Geometric ProgressionGiven two terms of G.P., find the sequence.
Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.See the sample lesson in action here
12Sequences and Series-Geometric meansGeometric means.
Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.See the sample lesson in action here
13Sequences and Series-Sum of gpThe sum to n terms of a G.P.
Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P).See the sample lesson in action here
14Sequences and Series-Sigma notationSigma notation
Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates.See the sample lesson in action here
15Sequences and Series-Sum-infinityLimiting sum or sum to infinity.
Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems.See the sample lesson in action here
16Sequences and Series-Recurring decimal infinityRecurring decimals and the infinite G.P.
Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number.See the sample lesson in action here
17Sequences and Series-Compound interestCompound interest
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.See the sample lesson in action here
18Sequences and Series-SuperannuationSuperannuation.
Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.See the sample lesson in action here
19Sequences and Series-Time paymentsTime payments.
Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.See the sample lesson in action here
20Sequences and SeriesApplications of arithmetic sequences
Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.See the sample lesson in action here
21Logarithms-Power of 2Powers of 2.
Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2.See the sample lesson in action here
22Logarithms-Equations and logsEquations of type log x to the base 3 = 4.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.See the sample lesson in action here
23Logarithms-Equations and logsEquations of type log 32 to the base x = 5.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.See the sample lesson in action here
24Logarithms-Log lawsLaws of logarithms.
Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.See the sample lesson in action here
25Logarithms-Log laws expansionUsing the log laws to expand logarithmic expressions.
Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.See the sample lesson in action here
26Logarithms-Log laws simplifyingUsing the log laws to simplify expressions involving logarithms.
Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.See the sample lesson in action here
27Logarithms-Log laws numbersUsing the log laws to find the logarithms of numbers.
Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples.See the sample lesson in action here
28Logarithms-Equations and logsEquations involving logarithms.
Objective: On completion of the lesson the student will be able to solve equations with log terms.See the sample lesson in action here
29Logarithms-Logs to solve equationsUsing logarithms to solve equations.
Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.See the sample lesson in action here
30Logarithms-Change base formulaChange of base formula
Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base.See the sample lesson in action here
31Statistic-probabilityBinomial Theorem – Pascal’s Triangle
Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.See the sample lesson in action here
32Statistic-probabilityBinomial probabilities using the Binomial Theorem
Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theoremSee the sample lesson in action here
33Statistic-probabilityCounting techniques and ordered selections – permutations
Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability.See the sample lesson in action here
34Statistic-probabilityUnordered selections – combinations
Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen.See the sample lesson in action here
35LogicInductive and deductive reasoning
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.See the sample lesson in action here
36LogicDefinition and use of counter examples
Objective: On completion of this lesson the student will be able to create counter examples to statements.See the sample lesson in action here
37LogicIndirect proofs
Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved.See the sample lesson in action here
38LogicMathematical induction
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.See the sample lesson in action here
39LogicConditional statements (converse, inverse and contrapositive) (Stage 2)
Objective: On completion of the lesson the student will be able to form related conditional statements.See the sample lesson in action here
40SurdsIntroducing surds
Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.See the sample lesson in action here
41SurdsSome rules for the operations with surds
Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds.See the sample lesson in action here
42SurdsSimplifying surds
Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication.See the sample lesson in action here
43SurdsCreating entire surds
Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surdsSee the sample lesson in action here
44SurdsAdding and subtracting like surds
Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.See the sample lesson in action here
45SurdsExpanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.See the sample lesson in action here
46SurdsBinomial expansions
Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.See the sample lesson in action here
47SurdsConjugate binomials with surds
Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds.See the sample lesson in action here
48SurdsRationalising the denominator
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds.See the sample lesson in action here
49SurdsRationalising binomial denominators
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions.See the sample lesson in action here
50Simultaneous equnsSimultaneous equations
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method.See the sample lesson in action here
51Simultaneous equnsElimination method
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method.See the sample lesson in action here
52Simultaneous equnsElimination method part 2
Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method.See the sample lesson in action here
53Simultaneous equnsApplications of simultaneous equations
Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations.See the sample lesson in action here
54Logarithms-Complex numbersImaginary numbers and standard form
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction.See the sample lesson in action here
55Logarithms-Complex numbersComplex numbers – multiplication and division
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division.See the sample lesson in action here
56Logarithms-Complex numbersPlotting complex number and graphical representation
Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers.See the sample lesson in action here
57Logarithms-Complex numbersAbsolute value
Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbersSee the sample lesson in action here
58Logarithms-Complex numbersTrigonometric form of a complex number
Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form.See the sample lesson in action here
59Logarithms-Complex numbersMultiplication and division of complex numbers in trig form (Stage 2)
Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division.See the sample lesson in action here
60Logarithms-Complex numbersDeMoivre’s theorem (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form.See the sample lesson in action here
61Logarithms-Complex numbersThe nth root of real and complex numbers (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form.See the sample lesson in action here
62Logarithms-Complex numbersFundamental theorem of algebra (Stage 2)
Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field.See the sample lesson in action here
63Algebra-polynomialsIntroduction to polynomials
Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not.See the sample lesson in action here
64Algebra-polynomialsThe sum, difference and product of two polynomials.
Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers.See the sample lesson in action here
65Algebra-polynomialsPolynomials and long division.
Objective: On completion of the lesson the student will understand the long division process with polynomials.See the sample lesson in action here
66Remainder theoremThe remainder theorem.
Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied.See the sample lesson in action here
67Remainder theoremMore on remainder theorem
Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials.See the sample lesson in action here
68Factor theoremThe factor theorem
Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial.See the sample lesson in action here
69Factor theoremMore on the factor theorem
Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials.See the sample lesson in action here
70Factor theoremComplete factorisations using the factor theorem
Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros.See the sample lesson in action here
71Polynomial equationsPolynomial equations
Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms.See the sample lesson in action here
72Graphs, polynomialsGraphs of polynomials
Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves.See the sample lesson in action here
73Roots quad equationsSum and product of roots of quadratic equations
Objective: On completion of the lesson the student will understand the formulas for the sum and product of roots of quadratic polynomials and how to use them. The student will understand how to form a quadratic equation given its roots.See the sample lesson in action here
74Roots quad equationsSum and product of roots of cubic and quartic equations
Objective: On completion of the lesson the student will be able to do problems on the sum and products of roots of cubic and quartic equations.See the sample lesson in action here
75Approx rootsMethods of approximating roots
Objective: On completion of the lesson the student will be capable of finding approximate roots of polynomial equations using half the interval method. The student will be able to make a number of applications of this rule within the one question.See the sample lesson in action here
76Newton’s approxNewton’s method of approximation
Objective: On completion of the lesson the student will be able to use Newton’s method in finding approximate roots of polynomial equations and be capable of more than one application of this method.See the sample lesson in action here
77ExamExam – Topic 1 – Algebra
Objective: ExamSee the sample lesson in action here
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Topic 2 - Functions and Equations Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 2 – Functions & Equations
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.See the sample lesson in action here
2Logarithms-Power of 2Powers of 2.
Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2.See the sample lesson in action here
3Logarithms-Equations and logsEquations of type log x to the base 3 = 4.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.See the sample lesson in action here
4Logarithms-Equations and logsEquations of type log 32 to the base x = 5.
Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.See the sample lesson in action here
5Logarithms-Log lawsLaws of logarithms.
Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.See the sample lesson in action here
6Logarithms-Log laws expansionUsing the log laws to expand logarithmic expressions.
Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.See the sample lesson in action here
7Logarithms-Log laws simplifyingUsing the log laws to simplify expressions involving logarithms.
Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.See the sample lesson in action here
8Logarithms-Log laws numbersUsing the log laws to find the logarithms of numbers.
Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples.See the sample lesson in action here
9Logarithms-Equations and logsEquations involving logarithms.
Objective: On completion of the lesson the student will be able to solve equations with log terms.See the sample lesson in action here
10Logarithms-Logs to solve equationsUsing logarithms to solve equations.
Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.See the sample lesson in action here
11Logarithms-Change base formulaChange of base formula
Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base.See the sample lesson in action here
12MatricesTranslation in the number plane
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.See the sample lesson in action here
13MatricesTranslation by matrix multiplication
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.See the sample lesson in action here
14TransformationsSpecial transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.See the sample lesson in action here
15VectorsVectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.See the sample lesson in action here
16Simultaneous equationsNumber of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.See the sample lesson in action here
17Vectors2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.See the sample lesson in action here
18Linear systemsOptimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.See the sample lesson in action here
19Linear systemsLinear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.See the sample lesson in action here
20Linear systemsRow-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.See the sample lesson in action here
21Linear systemsGauss Jordan elimination method (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.See the sample lesson in action here
22FunctionsDefinition, domain and range
Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.See the sample lesson in action here
23FunctionsNotation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.See the sample lesson in action here
24FunctionsMore on domain and range
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.See the sample lesson in action here
25FunctionsDomain and range from graphical representations
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.See the sample lesson in action here
26FunctionsEvaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.See the sample lesson in action here
27FunctionsFunctions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.See the sample lesson in action here
28FunctionsComposition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.See the sample lesson in action here
29FunctionsInverse functions
Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used.See the sample lesson in action here
30FunctionsRational functions Part 1
Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes.See the sample lesson in action here
31FunctionsRational functions Part 2
Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes.See the sample lesson in action here
32FunctionsParametric equations (Stage 2)
Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range.See the sample lesson in action here
33FunctionsPolynomial addition etc in combining and simplifying functions (Stage 2)
Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra.See the sample lesson in action here
34FunctionsParametric functions (Stage 2)
Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion.See the sample lesson in action here
35Co-ordinate Geometry-Two point formulaTwo point formula: equation of a line which joins a pair of points.
Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.See the sample lesson in action here
36Co-ordinate Geometry-Intercept formIntercept form of a straight line: find the equation when given x and y
Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.See the sample lesson in action here
37Co-ordinate Geometry-Parallel lines equationsParallel lines: identify equation of a line parallel to another
Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.See the sample lesson in action here
38Co-ordinate Geometry-Perpendicular linesPerpendicular lines.
Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line.See the sample lesson in action here
39Co-ordinate Geometry-InequalitiesInequalities on the number plane.
Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.See the sample lesson in action here
40Co-ordinate Geometry-TheoremsPerpendicular distance
Objective: On completion of the lesson the student will be able to derive the formula to calculate the distance between a given point and a given line. The student will also be able to calculate the distance between parallel lines.See the sample lesson in action here
41Co-ordinate Geometry-TheoremsLine through intersection of two given lines
Objective: On completion of the lesson the student will be able to calculate the equation of a line which goes through the intersection of two given lines and also through another named point or satisfies some other specified condition.See the sample lesson in action here
42Co-ordinate Geometry-TheoremsAngles between two lines
Objective: On completion of the lesson the student will be able to calculate the angle between given lines and derive the equation of a line given its angle to another line.See the sample lesson in action here
43Co-ordinate Geometry-TheoremsInternal and external division of an interval
Objective: On completion of the lesson the student will be able to divide an interval according to a given ratio and to calculate what point divides an interval in a given ratio for both internal and external divisions.See the sample lesson in action here
44TranslationsTransformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.See the sample lesson in action here
45Geometric transformationsGeometry transformations without matrices: reflection (Stage 2)
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.See the sample lesson in action here
46Geometric transformationsGeometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.See the sample lesson in action here
47Geometric transformationsGeometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.See the sample lesson in action here
48Geometric transformationsGeometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.See the sample lesson in action here
49Geometric transformationsThe definition and concept of combined transformations resulting in an equivalent single transformation.
Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations.See the sample lesson in action here
50Graphs, polynomialsGraphs of polynomials
Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves.See the sample lesson in action here
51Quadratic equationsIntroduction to quadratic equations.
Objective: On completion of the lesson the student will understand simple quadratic equations.See the sample lesson in action here
52Quadratic equationsQuadratic equations with factorisation.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.See the sample lesson in action here
53Quadratic equationsSolving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.See the sample lesson in action here
54Quadratic equationsCompleting the square
Objective: On completion of the lesson the student will understand the process of completing the square.See the sample lesson in action here
55Quadratic equationsSolving quadratic equations by completing the square
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.See the sample lesson in action here
56Quadratic equationsThe quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.See the sample lesson in action here
57Quadratic equationsProblem solving with quadratic equations
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.See the sample lesson in action here
58Quadratic equationsSolving simultaneous quadratic equations graphically
Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..See the sample lesson in action here
59Functions and graphsQuadratic polynomials of the form y = ax. + bx + c.
Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.See the sample lesson in action here
60Functions and graphsGraphing perfect squares: y=(a-x) squared
Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.See the sample lesson in action here
61Graphing rootsGraphing irrational roots
Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.See the sample lesson in action here
62Coordinate geometrySolve by graphing
Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.See the sample lesson in action here
63Logarithms-Graph-log curveThe graph of the logarithmic curve
Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves.See the sample lesson in action here
64Logarithms-Log curvesWorking with log curves.
Objective: On completion of the lesson the student will be able to solve problems with log curvesSee the sample lesson in action here
65Logarithms-Complex numbersImaginary numbers and standard form
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction.See the sample lesson in action here
66Logarithms-Complex numbersComplex numbers – multiplication and division
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division.See the sample lesson in action here
67Logarithms-Complex numbersPlotting complex number and graphical representation
Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers.See the sample lesson in action here
68Logarithms-Complex numbersAbsolute value
Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbersSee the sample lesson in action here
69Logarithms-Complex numbersTrigonometric form of a complex number
Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form.See the sample lesson in action here
70Logarithms-Complex numbersMultiplication and division of complex numbers in trig form (Stage 2)
Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division.See the sample lesson in action here
71Logarithms-Complex numbersDeMoivre’s theorem (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form.See the sample lesson in action here
72Logarithms-Complex numbersThe nth root of real and complex numbers (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form.See the sample lesson in action here
73Logarithms-Complex numbersFundamental theorem of algebra (Stage 2)
Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field.See the sample lesson in action here
74Sequences and Series-Compound interestCompound interest
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.See the sample lesson in action here
75Sequences and Series-SuperannuationSuperannuation.
Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.See the sample lesson in action here
76Sequences and Series-Time paymentsTime payments.
Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.See the sample lesson in action here
77Sequences and SeriesApplications of arithmetic sequences
Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.See the sample lesson in action here
78ExamExam – Topic 2 – Functions & Equations
Objective: ExamSee the sample lesson in action here
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Topic 3 - Circular functions and Trigonometry Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 3 – Circular functions & Trigonometry
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.See the sample lesson in action here
2Geometry-circlesThe equation of a circle: to find radii of circles
Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius.See the sample lesson in action here
3Geometry-circlesThe semicircle: to select the equation given the semi circle and vice versa
Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle.See the sample lesson in action here
4Geometry-parabolaThe parabola: to describe properties of a parabola from its equation
Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions.See the sample lesson in action here
5Circle GeometryTheorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs.
Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these proSee the sample lesson in action here
6Circle GeometryTheorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord.
Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’See the sample lesson in action here
7Circle GeometryTheorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal.
Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre.See the sample lesson in action here
8Circle GeometryTheorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc.
Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.See the sample lesson in action here
9Circle GeometryTheorem – Angles in the same segment of a circle are equal.
Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.See the sample lesson in action here
10Circle GeometryTheorem – The angle of a semi-circle is a right angle.
Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’See the sample lesson in action here
11Circle GeometryTheorem – The opposite angles of a cyclic quadrilateral are supplementary.
Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.See the sample lesson in action here
12Circle GeometryTheorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle.
Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite.See the sample lesson in action here
13Circle GeometryTheorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.
Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact.See the sample lesson in action here
14Circle GeometryTheorem – Tangents to a circle from an external point are equal.
Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.See the sample lesson in action here
15Circle GeometryTheorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.See the sample lesson in action here
16Circle Geometry-chordsTheorem – The products of the intercepts of two intersecting chords are equal.
Objective: On completion of the lesson the student will be able to prove that ‘The product of the intercepts of two intersecting chords are equal.’, and use this result to complete questions that require this knowledge.See the sample lesson in action here
17Circle Geometry-tangentsTheorem – The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point. [Including Alternate Proof]
Objective: On completion of the lesson the student will be able to prove and apply ‘The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point ‘, and use this result to complete qSee the sample lesson in action here
18Circle Geometry-cyclic quadsTheorem – If the opposite angles in a quadrilateral are supplementary then the quadrilateral is cyclic.
Objective: On completion of the lesson the student will be able to prove that a quadrilateral is cyclic using the supplementary angles theorem.See the sample lesson in action here
19Circle Geometry-subtendingTheorem – If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic.
Objective: On completion of the lesson the student will be able to prove that ‘ If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic’, and use this result to complete the quesSee the sample lesson in action here
20Circle GeometryTheorem – When circles touch, the line of the centres passes through the point of contact.
Objective: On completion of the lesson the student will be able to prove that ‘ When two circles touch, the line of the centres passes through the point of contact’, and use this result to complete questions that require it.See the sample lesson in action here
21Circle Geometry-non-collinearTheorem – Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points.
Objective: On completion of the lesson the student will be able to prove that ‘ Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points’, and use this knowledSee the sample lesson in action here
22Trig-reciprocal ratiosReciprocal ratios.
Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios.See the sample lesson in action here
23Trig complementary anglesComplementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.See the sample lesson in action here
24Trig identitiesTrigonometric identities
Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities.See the sample lesson in action here
25Trig larger anglesAngles of any magnitude
Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle.See the sample lesson in action here
26Trig larger anglesTrigonometric ratios of 0°, 90°, 180°, 270° and 360°
Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees.See the sample lesson in action here
27Graph sineGraphing the trigonometric ratios – I Sine curve.
Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period.See the sample lesson in action here
28Graph cosineGraphing the trigonometric ratios – II Cosine curve.
Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period.See the sample lesson in action here
29Graphs tan curveGraphing the trigonometric ratios – III Tangent curve.
Objective: On completion of the lesson the student will know how to recognise and draw the tan curve.See the sample lesson in action here
30Graph reciprocalsGraphing the trigonometric ratios – IV Reciprocal ratios.
Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.See the sample lesson in action here
31Trig larger anglesUsing one ratio to find another.
Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude.See the sample lesson in action here
32Trig equationsSolving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.See the sample lesson in action here
33Trig equationsSolving trigonometric equations – Type II.
Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains.See the sample lesson in action here
34Trig equationsSolving trigonometric equations – Type III.
Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains.See the sample lesson in action here
35Polar coordinatesPlotting polar coordinates and converting polar to rectangular
Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system.See the sample lesson in action here
36Polar coordinatesConverting rectangular coordinates to polar form
Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates.See the sample lesson in action here
37Polar coordinatesWrite and graph points in polar form with negative vectors (Stage 2)
Objective: On completion of the lesson the student will be using negative angles and negative vector lengths.See the sample lesson in action here
38TrigonometrySin(A+B) etc sum and difference identities (Stage 2)
Objective: On completion of the lesson the student will be using the reference triangles for 30, 45 and 60 degrees with the sum and difference of angles to find additional exact values of trigonometric ratios.See the sample lesson in action here
39TrigonometryDouble angle formulas (Stage 2)
Objective: On completion of the lesson the student will derive and use the double angle trig identities.See the sample lesson in action here
40TrigonometryHalf angle identities (Stage 2)
Objective: On completion of the lesson the student will derive and use the power reducing formulas and the half angle trig identities.See the sample lesson in action here
41Trigonometryt Formulas (Stage 2)
Objective: On completion of the lesson the student will solve trig equations using the t substitution.See the sample lesson in action here
42Trigonometry-ratiosTrigonometric ratios.
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is opSee the sample lesson in action here
43Trigonometry-ratiosUsing the calculator.
Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.See the sample lesson in action here
44Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 1 Sine].
Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.See the sample lesson in action here
45Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 2 Cosine].
Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.See the sample lesson in action here
46Trigonometry-ratiosUsing the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].
Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.See the sample lesson in action here
47Trigonometry-ratiosUnknown in the denominator. [Case 4].
Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.See the sample lesson in action here
48Trigonometry-compassBearings – the compass.
Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.See the sample lesson in action here
49Trigonometry-elevationAngles of elevation and depression.
Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.See the sample lesson in action here
50Trigonometry-practicalTrigonometric ratios in practical situations.
Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.See the sample lesson in action here
51Trigonometry-ratiosUsing the calculator to find an angle given a trigonometric ratio.
Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.See the sample lesson in action here
52Trigonometry- ratiosUsing the trigonometric ratios to find an angle in a right-angled triangle.
Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.See the sample lesson in action here
53Trigonometry-exact ratiosTrigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.See the sample lesson in action here
54Trigonometry-cosine ruleThe cosine rule to find an unknown side. [Case 1 SAS].
Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.See the sample lesson in action here
55Trigonometry-cosine ruleThe cosine rule to find an unknown angle. [Case 2 SSS].
Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.See the sample lesson in action here
56Trigonometry-sine ruleThe sine rule to find an unknown side. Case 1.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.See the sample lesson in action here
57Trigonometry-sine ruleThe sine rule to find an unknown angle. Case 2.
Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.See the sample lesson in action here
58Trigonometry-areasThe area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.See the sample lesson in action here
59ExamExam – Topic 3 – Circular functions & Trigonometry
Objective: ExamSee the sample lesson in action here
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Topic 4 - Matrices Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 4 – Matrices
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.See the sample lesson in action here
2MatricesBasic concepts – Matrices
Objective: On completion of the lesson the student will have had an introduction to matricesSee the sample lesson in action here
3MatricesAddition and subtraction of matrices
Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations.See the sample lesson in action here
4MatricesScalar matrix multiplication
Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix.See the sample lesson in action here
5MatricesMultiplication of one matrix by another matrix
Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication.See the sample lesson in action here
6MatricesTranslation in the number plane
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.See the sample lesson in action here
7MatricesTranslation by matrix multiplication
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.See the sample lesson in action here
8TransformationsSpecial transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.See the sample lesson in action here
9VectorsVectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.See the sample lesson in action here
10Simultaneous equationsNumber of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.See the sample lesson in action here
11Vectors2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.See the sample lesson in action here
12Linear systemsOptimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.See the sample lesson in action here
13Linear systemsLinear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.See the sample lesson in action here
14Linear systemsRow-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.See the sample lesson in action here
15Linear systemsGauss Jordan elimination method (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.See the sample lesson in action here
16ExamExam – Topic 4 – Matrices
Objective: ExamSee the sample lesson in action here
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Topic 5 - Vectors Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 5 – Vectors
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.See the sample lesson in action here
2VectorsVectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.See the sample lesson in action here
3Simultaneous equationsNumber of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.See the sample lesson in action here
4Vectors2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.See the sample lesson in action here
5Linear systemsOptimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.See the sample lesson in action here
6Linear systemsLinear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.See the sample lesson in action here
7Linear systemsRow-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.See the sample lesson in action here
8Linear systemsGauss Jordan elimination method (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.See the sample lesson in action here
9ExamExam – Topic 5 – Vectors
Objective: ExamSee the sample lesson in action here
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Topic 6 - Statistics and Probability Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 6 – Statistics & Probability
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.See the sample lesson in action here
2StatisticsFrequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.See the sample lesson in action here
3StatisticsFrequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.See the sample lesson in action here
4StatisticsRelative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.See the sample lesson in action here
5StatisticsThe range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.See the sample lesson in action here
6Statistic-probabilityThe mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.See the sample lesson in action here
7Statistic-probabilityThe mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.See the sample lesson in action here
8Statistic-probabilityThe median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scoresSee the sample lesson in action here
9Statistic-probabilityCumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.See the sample lesson in action here
10Statistic-probabilityCalculating the median from a frequency distribution
Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon.See the sample lesson in action here
11Statistic-probabilityBinomial Theorem – Pascal’s Triangle
Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.See the sample lesson in action here
12Statistic-probabilityBinomial probabilities using the Binomial Theorem
Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theoremSee the sample lesson in action here
13Statistic-probabilityCounting techniques and ordered selections – permutations
Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability.See the sample lesson in action here
14Statistic-probabilityUnordered selections – combinations
Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen.See the sample lesson in action here
15Statistics – grouped dataCalculating mean, mode and median from grouped data
Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.See the sample lesson in action here
16Statistics using a calculatorStatistics and the student calculator
Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems.See the sample lesson in action here
17Statistics – Range and dispersionRange as a measure of dispersion
Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.See the sample lesson in action here
18Statistics – SpreadMeasures of spread
Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.See the sample lesson in action here
19Statistics – Standard deviationStandard deviation applications
Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.See the sample lesson in action here
20Statistics – Standard deviationNormal distribution
Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.See the sample lesson in action here
21Statistics – Interquartile rangeMeasures of spread: the interquartile range
Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile rangeSee the sample lesson in action here
22StatisticsStem and Leaf Plots along with Box and Whisker Plots
Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.See the sample lesson in action here
23StatisticsScatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.See the sample lesson in action here
24Statistic-probabilityProbability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.See the sample lesson in action here
25Statistic-probabilityRolling a pair of dice
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.See the sample lesson in action here
26Statistic-probabilityExperimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.See the sample lesson in action here
27Statistic-probabilityTree diagrams – not depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.See the sample lesson in action here
28Statistic-probabilityTree diagrams – depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.See the sample lesson in action here
29Statistic-probabilityThe complementary result ..
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.See the sample lesson in action here
30Statistic-probabilityP[A or B] When A and B are both mutually and NOT mutually exclusive
Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.See the sample lesson in action here
31ExamExam – Topic 6 – Statistics & Probability
Objective: ExamSee the sample lesson in action here
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Topic 7 - Differential Calculus Mathematics

#TOPICTITLE
1Study PlanStudy plan – Topic 7 – Differential Calculus
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.See the sample lesson in action here
2CalculusLimits
Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.See the sample lesson in action here
3Calculus=1st prinDifferentiation from first principles.
Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve.See the sample lesson in action here
4Calculus=1st prinDifferentiation of y = x to the power of n.
Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.See the sample lesson in action here
5Calculus-differential, integMeaning of dy over dx – equations of tangents and normals.
Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.See the sample lesson in action here
6Calculus-differential, integFunction of a function rule, product rule, quotient rule.
Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule.See the sample lesson in action here
7Calculus-differential, integIncreasing, decreasing and stationary functions.
Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.See the sample lesson in action here
8CalculusFirst Derivative – turning points and curve sketching
Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve.See the sample lesson in action here
9Calculus-2nd derivativeThe second derivative – concavity.
Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.See the sample lesson in action here
10Calculus – Curve sketchingCurve sketching
Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve.See the sample lesson in action here
11Calculus – Maxima minimaPractical applications of maxima and minima
Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems.See the sample lesson in action here
12Calculus – IntegrationIntegration – anti-differentiation, primitive function
Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions.See the sample lesson in action here
13Calculus – Computation areaComputation of an area
Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area.See the sample lesson in action here
14Calculus – Computation volumesComputation of volumes of revolution
Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy.See the sample lesson in action here
15Calculus – Trapezoidal and Simpson’s rulesThe Trapezium rule and Simpson’s rule
Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve.See the sample lesson in action here
16ExamExam – Topic 7 – Differential Calculus
Objective: ExamSee the sample lesson in action here
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Literacy

Kindergarten/Year 1 Literacy

#TOPICTITLE
1Do you like hamburgers?It’s the alphabet!
Objective: Students will develop their listening skills and practise saying the alphabet.
2It’s time to learn your A B C!The Alphabet! Full lesson available
Objective: Students will practise reading the letters of the alphabet and practise recognition of: a, b, c, d, e, f.
3Hello! How are you?Hello! I’m Lulu.
Objective: Students will develop their comprehension skills by reading, and listening to, a picture story in which they will meet some new friends.
4Hello! How are you?My name is Jack!
Objective: Students will develop their comprehension skills by reading, and listening to, a picture story in which new friends and new vocabulary are introduced.
5Eight Purple Stars!Ten Little Pandas Full lesson available
Objective: Students will read a picture story and practise the numbers 1-10.
6Eight Purple Stars!What colour is it?
Objective: Students will read and practise the words for basic colours. They will learn to answer the question: ‘What colour is …?’ and reply with ‘It’s …’.
7Fun at SchoolThis is my father and mother.
Objective: Students will develop their reading skills. They will read a picture story and become familiar with ‘This is …’ and ‘That is …’.
8What’s this?It’s my green eraser!
Objective: Students will develop their language skills by reading, and listening to, a picture story in which some possessive pronouns are used. They will also become familiar with the questions: ‘What’s this?’ and ‘What’s that?’.
9What’s this?What’s in the box?
Objective: Students will develop their language skills by reading, and listening to, a picture story. They will learn to ask and answer the question ‘Is it a …?’.
10A New Boy at SchoolA Letter from Peter
Objective: Students will develop their language skills by reading, and listening to, a picture story. They will also revise colours and numbers, and learn to talk about their families.
11A New Boy at SchoolWhere’s my dog?
Objective: Students will develop their language skills by reading, and listening to, a picture story. They will also become familiar with some prepositions.
12My FamilyWhere’s the red kite?
Objective: Students will develop their comprehension skills by reading and listening to a picture story. They will also practise the use of ‘in’, ‘on’ and ‘under’.
13My FamilyMy Family Tree
Objective: Students will develop their comprehension skills by reading a text about the family. They will increase their vocabulary for family relationships and occupations, and they will learn to use ‘this’ and ‘that’.
14About PeopleThat’s his cow!
Objective: Students will develop their comprehension skills by reading a text about occupations. They will also learn about the possessive adjectives ‘his’, ‘her’ and ‘their’.
15About PeopleThese are my feet.
Objective: Students will develop their comprehension skills and vocabulary by reading a text about the parts of the body. They will practise using ‘this’ and ‘these’, and learn to form plurals.
16Animal Mania!What animal is that? Full lesson available
Objective: Students will develop their comprehension skills by reading a text about animals. Students will practise asking and answering questions, and they will revise colours and numbers.
17Animal Mania!A Very Tall Giraffe
Objective: Students will develop their comprehension skills by reading a text about animals in which more adjectives are used.
18We like to play games.Holidays!
Objective: Students will develop their comprehension skills by reading a picture story about fun activities to do in the holidays. Students will practise using ‘let’s’ and learn the days of the week.
19We like to play games.What’s your favourite? Full lesson available
Objective: Students will develop their comprehension skills by reading a picture story about activities they like to do. They will learn to talk about their preferences.
20Do you like hamburgers?At a Café
Objective: Students will develop their comprehension skills by reading a picture story about food preferences.
21Do you like hamburgers?This is Bobby.
Objective: Students will develop their comprehension skills by reading a picture story. They will also learn to ask questions about likes and dislikes.
22It’s time to learn your A B C!It’s time!
Objective: Students will develop their comprehension skills by reading a short text about asking and telling the time on the hour and half hour.
23It’s time to learn how to tell the time!No school! It’s Sunday!
Objective: Students will increase their vocabulary and develop their reading skills by reading a short text about daily routines.
24It’s time to learn how to tell the time!Where are my clothes?
Objective: Students will increase their vocabulary and develop their reading skills by reading a short text about items of clothing. They will learn about the prepositions – ‘on’, ‘under’, ‘in’.
25SentencesThe Sentence
Objective: To identify and use complete sentences.
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Year 2 Literacy

#TOPICTITLE
1It’s time to learn your A B C!It’s time!
Objective: Students will develop their comprehension skills by reading a short text about asking and telling the time on the hour and half hour.
2It’s time to learn how to tell the time!No school! It’s Sunday!
Objective: Students will increase their vocabulary and develop their reading skills by reading a short text about daily routines.
3It’s time to learn how to tell the time!Where are my clothes?
Objective: Students will increase their vocabulary and develop their reading skills by reading a short text about items of clothing. They will learn about the prepositions – ‘on’, ‘under’, ‘in’.
4School and PlayI have lots of subjects! Full lesson available
Objective: Students will practise reading, and saying words and simple sentences to describe school subjects and the days of the week.
5School and PlayOn the Weekend
Objective: Students will practise reading and recognising simple sentences about weekend activities.
6It’s Christmas time!It’s time for Maths!
Objective: Students will develop their comprehension skills by reading a short text in which quarter past, quarter to, 5 past, 5 to, 10 past and 10 to the hour are used.
7It’s Christmas time!Festivals are fun!
Objective: Students will develop their comprehension skills by reading a short text about Christmas and Chinese New Year.
8I walk in the summer.The Seasons
Objective: Students will develop their reading skills and practise new words to describe the seasons.
9I walk in the summer.How do you go to school?
Objective: Students will develop their reading skills and practise new words that describe modes of transport. They will also ask and answer questions about transport to different places.
10What’s the weather like today?It’s a sunny day!
Objective: Students will develop their comprehension skills by reading a story about the weather.
11What are you doing now?Shhhh! Dad is sleeping!
Objective: Students will develop their comprehension skills by reading a story in which the present continuous tense is used.
12What are you doing now?We are having a picnic!
Objective: Students will develop their comprehension skills by reading a story in which the present continuous tense is used to ask and answer questions.
13They’re usually in the lounge room.Hide and Seek
Objective: Students will develop their comprehension skills by reading a story about finding people.
14They’re usually in the lounge room.An Unusual Day
Objective: Students will develop their comprehension skills by reading a story in which the simple present and the continuous present tenses are used. They will also learn the little words that help to sequence a story.
15Left! Right! Let’s go!Where’s the shop?
Objective: Students will develop their comprehension skills by reading a story in which simple directions are given using the imperative.
16Left! Right! Let’s go!Ladies and Gentlemen!
Objective: Students will develop their comprehension skills by reading a story in which the present continuous tense is used to talk about a concert.
17Up, down and around we go!Roller-coaster Ride
Objective: Students will develop their comprehension skills by reading a story in which routes are described using the present continuous tense.
18Up, down and around we go!Catch that car!
Objective: Students will develop their comprehension skills by reading a story which focuses on street directions and places.
19SentencesThe Sentence
Objective: To identify and use complete sentences.
20SpellingSpelling
Objective: To use the ‘Look, Say, Write’ method for learning spelling. Plus 300 spelling words.
21CapitalisationCapital Letters 1
Objective: To use capital letters correctly: to begin sentences, for proper nouns.
22Vowels and ConsonantsVowels and Consonants
Objective: To identify and use vowels and consonants.
23Common NounsCommon Nouns
Objective: To show a common noun names an object or thing.
24PunctuationSentence Endings
Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
25VerbsSimple Verbs
Objective: To identify and use verbs. To understand a verb can be: an action or doing word, a state of being or ownership.
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Year 3 Literacy

#TOPICTITLE
1We’re very busy.Fast Food
Objective: Students will increase their vocabulary and develop their reading skills by reading what Peter and Chen say about fast food. They will also practise using the present tense, and asking and answering questions using ‘do’.
2We’re very busy.On the farm Full lesson available
Objective: Students will increase their vocabulary and develop their reading skills by reading, in which the present continuous tense is used.
3I can’t do that!This is a great park!
Objective: Students will increase their vocabulary and develop their reading skills by reading a story about a park. They will also become familiar with the use of ‘this’ and ‘these’ for things that are near and ‘that’ and ‘those’ for things that are far away.
4I can’t do that!I can speak English!
Objective: Students will increase their vocabulary and develop their reading skills by reading a short speech about what a person ‘can’ and ‘can’t’ do.
5Can I look at your new kite?Can I help you?
Objective: Students will increase their vocabulary and develop their reading skills by reading a text using ‘can’ and ‘can’t’ to make offers and requests.
6Oh, no! Not the Doctor!Doctor, what have I got?
Objective: Students will increase their vocabulary and develop their reading skills by reading a text about illnesses.
7Oh, no! Not the Doctor!There is a zoo in Sydney!
Objective: Students will increase their vocabulary and develop their reading skills by reading a text in which ‘There is’ and ‘There are’ in relation to zoo animals is used.
8It’s all in the future!One World, One Dream
Objective: Students will increase their vocabulary and develop their reading skills by reading a text in which ‘going to’ is used to talk about the future.
9It’s all in the future!You are going to have a great time!
Objective: Students will increase their vocabulary and develop their reading skills by reading a text in which ‘going to’ is used to make future plans.
10Maybe she’ll be funny!My animal friends are wonderful!
Objective: Students will develop their language skills by reading, and listening to, a picture story. They will revise adjectives that describe personality.
11Maybe she’ll be funny!What will Fido do next?
Objective: Students will develop their language skills by reading, and listening to, a picture story. They will also become familiar with the use of ‘will’ to express a future action.
12First we’ll see a big city.Sydney: It’s special!
Objective: Students will develop their language skills by reading, and listening to, a picture story. They will focus on the use of adjectives to describe cities.
13First we’ll see a big city.Then we’ll eat it!
Objective: Students will develop their comprehension skills by reading, and listening to, a picture story. They will also become familiar with the use of ‘will’ when describing a process.
14We need to take a metal pan.What’s it made of? Full lesson available
Objective: Students will develop their comprehension skills by reading, and listening to, a picture story about what things are made of. They will also revise prepositions of location.
15We need to take a metal pan.They want to go camping.
Objective: Students will develop their comprehension skills by reading, and listening to, a picture story about a camping trip. They will also become familiar with the terms ‘need to’ and ‘want to’.
16First we’ll go to the eighth floor.Let’s make pancakes!
Objective: Students will develop their language skills by reading, and listening to, an illustrated recipe. They will also revise words that help them tell a story – ‘First’, ‘Then’, ‘Next’, ‘After that’ and ‘Finally’.
17First we’ll go to the eighth floor.Who’s shopping at Sunsets?
Objective: Students will develop their language skills by reading, and listening to, a picture story about shopping in a department store. They will also revise some prepositions and learn some more in simple phrases.
18On Monday I’ll buy new jeans.Whose Shoes?
Objective: Students will develop their comprehension skills by reading, and listening to, a picture poem about shopping. They will also revise colours and pronouns.
19On Monday I’ll buy new jeans.Chen’s Holiday Plans
Objective: Students will develop their comprehension skills by reading a short story about Chen’s plans for his holidays. They will also practise verbs.
20SentencesThe Sentence
Objective: To identify and use complete sentences.
21SpellingSpelling
Objective: To use the ‘Look, Say, Write’ method for learning spelling. Plus 300 spelling words.
22CapitalisationCapital Letters 1
Objective: To use capital letters correctly: to begin sentences, for proper nouns.
23Vowels and ConsonantsVowels and Consonants
Objective: To identify and use vowels and consonants.
24Common NounsCommon Nouns
Objective: To show a common noun names an object or thing.
25PunctuationSentence Endings
Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
26VerbsSimple Verbs
Objective: To identify and use verbs. To understand a verb can be: an action or doing word, a state of being or ownership.
27VowelsVowels – Long and Short
Objective: To identify long and short vowel sounds, and their use.
28PluralsPlurals 1 – simple
Objective: To form plurals (more than one) by adding ‘s’ and ‘es’ correctly.
29Basic Dictionary UseBasic Dictionary Use
Objective: To find words arranged alphabetically and identify word meanings in dictionaries.
30NounsProper Nouns
Objective: To show a proper noun is used to name a person, place or a title.
31AdjectivesAdjectives
Objective: To show an adjective is a word that describes a noun.
32AdverbsAdverbs
Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
33PronounsPronouns
Objective: To show a pronoun is used in place of a noun.
34Parts of Speech Part bConjunctions
Objective: To identify and use conjunctions correctly.
35Common ErrorsCommon Errors in spelling and punctuation
Objective: To identify and eliminate common errors.
36PunctuationCommas 1
Objective: To use commas: to list, to make meaning clear, and when writing the date.
37ContractionsContractions
Objective: To identify and use contractions.
38Other Places and Other TimesA New Penfriend
Objective: Students will develop their reading comprehensions skills by reading a letter of introduction to a penfriend. They will also practise the present continuous tense and become familiar with vocabulary about different nationalities.
39Other Places and Other TimesWill we have robots?
Objective: Students will develop their comprehension skills by reading a text in which the future tense is used.
40It was different yesterday.We all change.
Objective: Students will increase their vocabulary, particularly adjectives, and develop their reading skills. They will practise using the verb’ to be’ in the present and past tenses.
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Year 4 Literacy

#TOPICTITLE
1It was different yesterday.Kate worked hard!
Objective: Students will increase their vocabulary, particularly adjectives, and develop their reading skills. They will also practise using the simple past tense.
2We learned about another culture.Guess who we met today!
Objective: Students will increase their vocabulary and develop their reading skills. They will also practise using the simple past tense of irregular verbs.
3We learned about another culture.How the world was made!
Objective: Students will increase their vocabulary and develop their reading skills. They will also learn to identify some storytelling words and narrative structures.
4They won!Australian Boy Wins!
Objective: Students will increase their vocabulary and develop their comprehension skills by reading a newspaper report. They will also practise using the ‘why/because’ structure.
5They won!Always be honest!
Objective: Students will increase their vocabulary and develop their comprehension skills by reading a fable in which the simple past tense of regular and irregular verbs is used.
6There was an accident!A Police Report
Objective: Students will increase their vocabulary and develop their reading skills by reading a simple report about an accident in which the simple past tense is used.
7There was an accident!I feel sick!
Objective: Students will increase their vocabulary and develop their reading skills by reading a narrative about a visit to the doctor.
8Let’s compare!A Maths Lesson
Objective: Students will develop their comprehension skills by reading, and listening to, a picture story. They will focus on the use of comparative adjectives.
9Let’s compare!Be careful! They’re dangerous!
Objective: Students will develop their comprehension skills by reading, and listening to, a picture story in which instructions are given using the imperative. They will also learn more comparative adjectives.
10A New CD PlayerThe Perfect CD Player
Objective: Students will develop their comprehension skills by reading a text in which comparative adjectives are used.
11A New CD PlayerWhich do you prefer?
Objective: Students will develop their comprehension skills by reading a story about preferences.
12That’s a great idea!A Visit to the Art Gallery
Objective: Students will develop their comprehension skills by reading a text in which irregular comparative adjectives are used.
13That’s a great idea!That’s a great idea!
Objective: Students will develop their comprehension skills by reading a story in which plans for an activity are made.
14Let’s find out!About the Stars
Objective: Students will develop their comprehension skills by reading a text in which superlative adjectives are used and facts are given.
15Let’s find out!Two Great Countries
Objective: Students will develop their comprehension skills by reading a text in which China and Australia are described and compared.
16The Most Beautiful PlanetThis is my country. Full lesson available
Objective: Students will develop their comprehension skills by reading a text about two countries. They will also practise using superlative adjectives.
17The Most Beautiful PlanetWhen the rain stops!
Objective: Students will develop their comprehension skills by reading a text in which ‘going to’ and ‘will’ are used to talk about future plans.
18CapitalisationCapital Letters 1
Objective: To use capital letters correctly: to begin sentences, for proper nouns.
19Common NounsCommon Nouns
Objective: To show a common noun names an object or thing.
20PunctuationSentence Endings
Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
21VerbsSimple Verbs
Objective: To identify and use verbs. To understand a verb can be: an action or doing word, a state of being or ownership.
22VowelsVowels – Long and Short
Objective: To identify long and short vowel sounds, and their use.
23PluralsPlurals 1 – simple
Objective: To form plurals (more than one) by adding ‘s’ and ‘es’ correctly.
24Basic Dictionary UseBasic Dictionary Use
Objective: To find words arranged alphabetically and identify word meanings in dictionaries.
25NounsProper Nouns
Objective: To show a proper noun is used to name a person, place or a title.
26AdjectivesAdjectives
Objective: To show an adjective is a word that describes a noun.
27AdverbsAdverbs
Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
28PronounsPronouns
Objective: To show a pronoun is used in place of a noun.
29Parts of Speech Part bConjunctions
Objective: To identify and use conjunctions correctly.
30PunctuationCommas 1
Objective: To use commas: to list, to make meaning clear, and when writing the date.
31ContractionsContractions
Objective: To identify and use contractions.
32There weren’t many …There weren’t any flowers!
Objective: Students will increase their vocabulary, develop their reading skills and practise using the simple past tense of the verb ‘to be’.
33There weren’t many …A Shopping List
Objective: Students will increase their vocabulary, develop their reading skills and practise asking questions using ‘How much …’ and ‘How many …’.
34It couldn’t be mine!Uncle Bill said we could!
Objective: Students will increase their vocabulary, develop their reading skills and practise using ‘could’ and ‘couldn’t’ to refer to past events.
35It couldn’t be mine!The Riding Lesson
Objective: Students will build vocabulary, answer comprehension questions and practise using possessive pronouns and adjectives.
36Clean up Australia!Too much rubbish!
Objective: Students will increase their vocabulary and reading comprehension skills. They will also practise using ‘too much’, ‘too many’ and ‘enough’.
37Clean up Australia!Sports Report
Objective: Students will increase their vocabulary and reading comprehension skills. They will also practise using the adverbs ‘well’ and ‘badly’.
38Friends all over the WorldNow I can do it by myself.
Objective: Students will increase their vocabulary and develop their reading skills. They will practise using ‘too much’, ‘too many’ and ‘enough’.
39Friends all over the WorldA Letter to a Pen Pal
Objective: Students will increase their vocabulary, develop their comprehension skills and practise using the simple present tense.
40What’s the problem?What’s the matter?
Objective: Students will read and comprehend a passage in which words are used to describe feelings.
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Year 5 Literacy

#TOPICTITLE
1What’s the problem?A School Outing
Objective: Students will read and comprehend a notice. They will learn about the use of ‘should’ and ‘shouldn’t’.
2When I was YoungLife used to be different.
Objective: Students will develop their comprehension skills by reading, and listening to, an interview. They will learn how to describe finished activities using ‘used to’.
3When I was YoungHave you tidied your room?
Objective: Students will develop their comprehension skills by reading, and listening to, a rhyme. They will also learn the imperfect tense and its use.
4Space and TimeWe’ve done our research. Full lesson available
Objective: Students will develop their comprehension skills by reading, and listening to, a picture story. They will learn some irregular verbs in the present perfect tense.
5Space and TimeWe’ve written a poem!
Objective: Students will develop their comprehension skills by reading, and listening to, a rhyme. They will learn more irregular verbs in the present perfect tense.
6Choices and PlacesA New Jacket
Objective: Students will develop their comprehension skills by reading a text in which preferences are discussed and comparisons are made.
7Choices and PlacesHe has travelled a lot.
Objective: Students will develop their comprehension skills by reading a text in which the present perfect and the simple past tenses are used.
8What’s the best way to do it?A Text Message
Objective: Students will develop their comprehension skills by reading a text which focuses on the use of ‘have to’ and adverbs of time.
9What’s the best way to do it?What will we make?
Objective: Students will develop their comprehension skills by reading a text in which the children discuss a project.
10Class CampDear Parents, …
Objective: Students will develop their comprehension skills by reading a letter which uses a variety of verb tenses.
11Class CampA Postcard from Kate
Objective: Students will develop their comprehension skills by reading an informal letter in which the simple past tense of the verb is used.
12SentencesThe Sentence
Objective: To identify and use complete sentences.
13CapitalisationCapital Letters 1
Objective: To use capital letters correctly: to begin sentences, for proper nouns.
14Common NounsCommon Nouns
Objective: To show a common noun names an object or thing.
15PunctuationSentence Endings
Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
16VerbsSimple Verbs
Objective: To identify and use verbs. To understand a verb can be: an action or doing word, a state of being or ownership.
17Basic Dictionary UseBasic Dictionary Use
Objective: To find words arranged alphabetically and identify word meanings in dictionaries.
18NounsProper Nouns
Objective: To show a proper noun is used to name a person, place or a title.
19AdjectivesAdjectives
Objective: To show an adjective is a word that describes a noun.
20AdverbsAdverbs
Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
21PronounsPronouns
Objective: To show a pronoun is used in place of a noun.
22Parts of Speech Part bConjunctions
Objective: To identify and use conjunctions correctly.
23PunctuationCommas 1
Objective: To use commas: to list, to make meaning clear, and when writing the date.
24ContractionsContractions
Objective: To identify and use contractions.
25Parts of Speech Part hArticles and Demonstratives
Objective: To identify and use articles and demonstratives correctly.
26Antonyms and SynonymsAntonyms and Synonyms
Objective: To identify and use antonyms and synonyms.
27Spelling SkillsSpelling
Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’.
28Spelling SkillsSyllabification
Objective: To improve spelling by dividing words correctly into syllables.
29PluralsPlurals 2 – special rules
Objective: To form plurals with special rules: words ending in ‘y’ and ‘f’.
30NounsCollective and Abstract Nouns
Objective: To identify and use collective and abstract nouns.
31VerbsVerbs – Tense
Objective: To identify and use the correct tense of verbs: past, present and future.
32AdjectivesAdjectives – Comparatives and Superlatives
Objective: To identify and use comparative and superlative adjectives.
33Parts of Speech Part aPrepositions
Objective: To identify and use prepositions correctly.
34Punctuation Skills Part bQuotation Marks
Objective: To use quotation marks for direct speech.
35Common ErrorsCommon Errors in writing
Objective: To identify and eliminate common errors.
36Apostrophe – PossessionApostrophe – Possession
Objective: To use the apostrophe of possession correctly.
37MnemonicsSpelling – Mnemonics
Objective: To identify and use mnemonics to assist in correct spelling.
38PrefixesPrefixes
Objective: The identify and use prefixes.
39SuffixesSuffixes
Objective: The identify and use suffixes.
40Similes and MetaphorsSimiles and Metaphors
Objective: To identify and use similes and metaphors.
41Figurative LanguageOnomatopoeia, Assonance and Alliteration
Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
42Homonyms – Homophones and HomographsHomonyms – Homophones and Homographs
Objective: To identify and use correctly homonyms, both homophones and homographs.
43Advanced Dictionary UseAdvanced Dictionary Use
Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
44CapitalisationCapital Letters 2
Objective: To use capital letters correctly: in titles and letters.
45AdjectivesAdjectives – from Nouns and Verbs
Objective: To create adjectives from nouns and verbs. E.g. China – Chinese
46There’s a …It’s famous! Full lesson available
Objective: Students will increase their vocabulary, develop their reading skills and practise using the verb ‘to be’.
47There’s a …There are lots of things in my town.
Objective: Students will increase their reading comprehension skills and their vocabulary. They will also become familiar with the use of ‘There is …’ and ‘There are …’.
48Hobbies and FestivalsCollecting things
Objective: Students will develop their reading skills and increase their vocabulary. They will learn the verb ‘to have’. They will also learn to use ‘this’ and ‘these’ correctly.
49Hobbies and FestivalsMy favourite festival
Objective: Students will build vocabulary; begin to use conjunctions ‘and’, ‘but’ or ‘because’.
50What can you do?Letter to a penfriend
Objective: Students will be able to read and understand an informal letter and use the present tense of ‘can’ and ‘can’t’.
51What’s Homestay?Simple Present
Objective: Learn the correct structure for the simple present.
52What’s Homestay?Simple Past
Objective: Learn the correct structure for the past simple.
53Setting offPresent perfect
Objective: Learn the correct structure for the present perfect.
54Here we are!Adjectives
Objective: Learn the use of adjectives.
55Here we are!Comparatives and superlatives
Objective: Learn how to use comparatives and superlatives in English.
56A new homePrepositions of location
Objective: Learn about prepositions of location.
57Let’s hit the beach!Modals of obligation
Objective: Learn about modals of obligation.
58Amazing Aussie animalsPresent continuous
Objective: Learn about the present continuous tense.
59Amazing Aussie animalsPast continuous
Objective: Learn about the past continuous tense.
60Amazing Aussie animalsGiving facts and opinions
Objective: Present phrases that ask for and give opinions.
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Year 6 Literacy

#TOPICTITLE
1A visit to the ZooAbout Koalas
Objective: Students will be able to answer questions about the text, identify the target language point ‘like’ + the infinitive) and distinguish between simple facts and opinions.
2A visit to the ZooI’m a zookeeper.
Objective: Students will be able to answer comprehension questions on reading, increase their vocabulary and use the frequency adverbs, ‘always’, ‘sometimes’, ‘often’ and ‘never’.
3What do you want to do?Big Dreams
Objective: Students will be able to answer comprehension questions, increase their vocabulary and be able to use ‘want’ + the infinitive in positive and negative sentences, and in a question.
4What do you want to do?Fruit Bowl
Objective: Students will be able to read and understand the text, to answer questions and to notice the use of the imperative form.
5It’s going to be fun!It’s going to be fantastic!
Objective: Students will develop their comprehension skills by reading, and listening to, a story. They will learn how to talk about the future using the verb ‘to go + the infinitive’.
6It’s going to be fun!What’s on the menu?
Objective: Students will develop their comprehension skills by reading various menus. They will also learn to ask questions politely.
7We are all doing things!I’m having a great time!
Objective: Students will develop their comprehension skills by reading a letter which focuses on the use of the present continuous tense.
8We are all doing things!Who can help me?
Objective: Students will develop their comprehension skills by reading a story in which requests for help are made.
9To Australia and Back!Getting There! Full lesson available
Objective: Students will develop their comprehension skills by reading a text about travel plans. They will also learn about coordinate conjunctions.
10To Australia and Back!I came back!
Objective: Students will develop their comprehension skills by reading a text in which Chen talks about going home to China. They will also revise the simple past tense.
11Famous PeopleBruce Lee
Objective: Students will develop their comprehension skills by reading a text about Bruce Lee. They will also practise the use of the simple past tense and learn more irregular verbs.
12Famous PeopleAlexander Bell
Objective: Students will develop their comprehension skills by reading a text about Alexander Bell. They will also learn how to use ‘could’ and ‘couldn’t’, and review questions using ‘Wh’ words.
13Finding Buster!Finding Buster! – A Movie Review
Objective: Students will develop their reading comprehension skills and increase their vocabulary by reading a movie review. They will also learn how to use the conjunction ‘because’ to answer ‘why’ questions.
14Finding Buster!I’m going to be busy!
Objective: Students will develop their reading comprehension skills by reading a story about plans for the weekend. They will revise the use of the verb ‘to go’ in the present tense + the infinitive to talk about the future.
15SentencesThe Sentence
Objective: To identify and use complete sentences.
16Common NounsCommon Nouns
Objective: To show a common noun names an object or thing.
17NounsProper Nouns
Objective: To show a proper noun is used to name a person, place or a title.
18AdjectivesAdjectives
Objective: To show an adjective is a word that describes a noun.
19AdverbsAdverbs
Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
20PronounsPronouns
Objective: To show a pronoun is used in place of a noun.
21Parts of Speech Part bConjunctions
Objective: To identify and use conjunctions correctly.
22Parts of Speech Part hArticles and Demonstratives
Objective: To identify and use articles and demonstratives correctly.
23Antonyms and SynonymsAntonyms and Synonyms
Objective: To identify and use antonyms and synonyms.
24Spelling SkillsSyllabification
Objective: To improve spelling by dividing words correctly into syllables.
25PluralsPlurals 1 – simple
Objective: To form plurals (more than one) by adding ‘s’ and ‘es’ correctly.
26PluralsPlurals 2 – special rules
Objective: To form plurals with special rules: words ending in ‘y’ and ‘f’.
27NounsCollective and Abstract Nouns
Objective: To identify and use collective and abstract nouns.
28VerbsVerbs – Tense
Objective: To identify and use the correct tense of verbs: past, present and future.
29AdjectivesAdjectives – Comparatives and Superlatives
Objective: To identify and use comparative and superlative adjectives.
30Parts of Speech Part aPrepositions
Objective: To identify and use prepositions correctly.
31Punctuation Skills Part bQuotation Marks
Objective: To use quotation marks for direct speech.
32Apostrophe – PossessionApostrophe – Possession
Objective: To use the apostrophe of possession correctly.
33MnemonicsSpelling – Mnemonics
Objective: To identify and use mnemonics to assist in correct spelling.
34PrefixesPrefixes
Objective: The identify and use prefixes.
35SuffixesSuffixes
Objective: The identify and use suffixes.
36Similes and MetaphorsSimiles and Metaphors
Objective: To identify and use similes and metaphors.
37Figurative LanguageOnomatopoeia, Assonance and Alliteration
Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
38Homonyms – Homophones and HomographsHomonyms – Homophones and Homographs
Objective: To identify and use correctly homonyms, both homophones and homographs.
39Advanced Dictionary UseAdvanced Dictionary Use
Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
40CapitalisationCapital Letters 2
Objective: To use capital letters correctly: in titles and letters.
41AdjectivesAdjectives – from Nouns and Verbs
Objective: To create adjectives from nouns and verbs. E.g. China – Chinese
42PronounsPronouns 2
Objective: To recognise and use personal, possessive and relative pronouns.
43Commas 2Commas 2
Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech.
44Conjunctions – SentencesConjunctions – Sentences
Objective: To use conjunctions to increase the variety of sentence structure in written expression.
45PhrasesPhrases
Objective: To identify and use phrases including adjectival and adverbial phrases.
46ClausesClauses
Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
47Simple and Compound VerbsSimple and Compound Verbs
Objective: To identify and use simple and compound verbs.
48Auxiliary VerbsAuxiliary Verbs
Objective: To identify and use auxiliary verbs within compound verbs.
49Subject-Verb AgreementSubject-Verb Agreement
Objective: To identify and use correct tense, number and person in forming verbs.
50Verb tense – CompoundVerb tense – Compound
Objective: To identify and use ‘to be’ and ‘to have’ with the appropriate participle of the main verb.
51PluralsPlurals 3 – Unusual
Objective: To create unusual plurals: for words ending in ‘o'; by changing the vowels or by adding letters.
52Common ErrorsCommon Errors in verb usage, spelling and punctuation
Objective: To identify and eliminate common errors.
53PunctuationPunctuation – Various
Objective: To use hyphens, dashes, apostrophes, quotation marks, parentheses and brackets correctly.
54Vocabulary DevelopmentVocabulary
Objective: To identify and use better words than ‘got’ and ‘said’.
55What do you like to do?Adverbs of frequency
Objective: Learn about the past continuous tense.
56BBQ Party!Expressions of quantity
Objective: Learn the words used to express quantity.
57BBQ Party!Sequence markers
Objective: Learn the words used in sequences or ordering.
58Big day out!First and second conditionals
Objective: Learn the use of first conditionals. Learn the use of second conditionals.
59Big day out!The future with ‘will’ and ‘going to’
Objective: Learn the uses of ‘will’ and ‘going to’ to talk about the future.
60Thanks and goodbyeTime clauses
Objective: Learn how to use time clauses.
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Year 7 Literacy

#TOPICTITLE
1Have you met?Hello!
Objective: Use the present tense verb to be (am, is and are) correctly in written and spoken work. Answer comprehension questions and apply am, is and are correctly.
2Have you met?The world in a classroom! Full lesson available
Objective: At the end of this lesson, students will have learnt how to ask a question in English, and how to use the definite and indefinite articles.
3Let’s get organised!First week fun!
Objective: Students will be able to read a schedule of activities, including a number of time expressions, and answer comprehension questions about the information given.
4Let’s get organised!Organising your subject timetable.
Objective: Students will read scheduling information, correctly name school subjects in English, use information to complete a weekly timetable and answer simple present questions in affirmative and negative.
5I like your hat!We are all different!
Objective: At the end of the reading students will be able to answer comprehension questions and use the correct pronouns to replace nouns. They will use correct forms to indicate a person, number, gender or ownership.
6I like your hat!Fashion tips from Junko!
Objective: At the end of the reading students will be able to answer comprehension questions and identify different articles of clothing. They will be able to use descriptive adjectives and possessive adjectives.
7Where is it?Getting around the ILC campus.
Objective: At the end of the reading students will be able to locate specific places based on descriptions using prepositions of location.
8Where is it?Come to my party!
Objective: At the end of this lesson students will be able to give and understand simple directions using the imperative mode.
9How much is it?Shopping list.
Objective: Students will read and answer comprehension questions, recognise count and uncount nouns and be able to use some/any and much/many correctly.
10How much is it?Where can I buy it?
Objective: Students will read a brochure describing different types of shops. They will be able to answer comprehension questions and recognise and use comparative adjectives.
11Tell me what happened!Eyewitness.
Objective: Students will read and understand a text talking about a past experience using the simple past tense with regular and irregular verbs, both positive and negative.
12Tell me what happened!She screamed loudly!
Objective: Students will read and understand a short newspaper article using the past tense. They will answer comprehension questions and practise identifying and using adverbs and expressions of past time.
13What’s your favourite?Would you like to play?
Objective: At the end of the reading students will be able to elicit information from a written text. They will be able to recognise the use of the infinitive form ‘to + verb’ to express purpose.
14What’s your favourite?Do you enjoy going out?
Objective: Students will read ads for different leisure activities. They will be able to answer comprehension questions and recognise the use of gerunds. (verb + ing)
15May I take your order?Are you eating well?
Objective: At the end of the lesson students will be able to answer comprehension questions based on the text and recognise and use the present continuous.
16May I take your order?Would you like some tea?
Objective: Students will be able to answer comprehension questions and distinguish between ‘like’ and ‘would like.
17What will we do?What will we do there?
Objective: At the end of the reading students will be able to elicit information from a reading and identify the use of ‘will’ and ‘going to’ to show future plans and hopes.
18What will we do?What kind of job?
Objective: At the end of this lesson students will be able to answer questions about different jobs and occupations. They will also be able to talk about ongoing future activities using the ‘present continuous’ form and ‘before’, ‘when’, ‘after’ and ‘as soon as’ in future tense.
19Let’s celebrateMerry Christmas!
Objective: At the end of this lesson students will be able to answer comprehension questions and distinguish between the present perfect and simple past.
20Let’s celebrateThe Diwali Festival.
Objective: At the end of this reading students will be able to describe an event in some detail using the present perfect/past simple and identify the differences between conjunctions ‘and’, ‘but’ and ‘because’.
21SentencesThe Sentence
Objective: To identify and use complete sentences.
22CapitalisationCapital Letters 1
Objective: To use capital letters correctly: to begin sentences, for proper nouns.
23PunctuationSentence Endings
Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
24Common NounsCommon Nouns
Objective: To show a common noun names an object or thing.
25NounsProper Nouns
Objective: To show a proper noun is used to name a person, place or a title.
26VerbsSimple Verbs
Objective: To identify and use verbs. To understand a verb can be: an action or doing word, a state of being or ownership.
27AdjectivesAdjectives
Objective: To show an adjective is a word that describes a noun.
28AdverbsAdverbs
Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
29PronounsPronouns
Objective: To show a pronoun is used in place of a noun.
30Parts of Speech Part bConjunctions
Objective: To identify and use conjunctions correctly.
31Conjunctions – SentencesConjunctions – Sentences
Objective: To use conjunctions to increase the variety of sentence structure in written expression.
32CapitalisationCapital Letters 2
Objective: To use capital letters correctly: in titles and letters.
33Parts of Speech Part hArticles and Demonstratives
Objective: To identify and use articles and demonstratives correctly.
34Antonyms and SynonymsAntonyms and Synonyms
Objective: To identify and use antonyms and synonyms.
35PunctuationCommas 1
Objective: To use commas: to list, to make meaning clear, and when writing the date.
36Commas 2Commas 2
Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech.
37Spelling SkillsSpelling
Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’.
38Spelling SkillsSyllabification
Objective: To improve spelling by dividing words correctly into syllables.
39PluralsPlurals 2 – special rules
Objective: To form plurals with special rules: words ending in ‘y’ and ‘f’.
40NounsCollective and Abstract Nouns
Objective: To identify and use collective and abstract nouns.
41VerbsVerbs – Tense
Objective: To identify and use the correct tense of verbs: past, present and future.
42AdjectivesAdjectives – Comparatives and Superlatives
Objective: To identify and use comparative and superlative adjectives.
43Parts of Speech Part aPrepositions
Objective: To identify and use prepositions correctly.
44Punctuation Skills Part bQuotation Marks
Objective: To use quotation marks for direct speech.
45Apostrophe – PossessionApostrophe – Possession
Objective: To use the apostrophe of possession correctly.
46MnemonicsSpelling – Mnemonics
Objective: To identify and use mnemonics to assist in correct spelling.
47PrefixesPrefixes
Objective: The identify and use prefixes.
48SuffixesSuffixes
Objective: The identify and use suffixes.
49Similes and MetaphorsSimiles and Metaphors
Objective: To identify and use similes and metaphors.
50Figurative LanguageOnomatopoeia, Assonance and Alliteration
Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
51Homonyms – Homophones and HomographsHomonyms – Homophones and Homographs
Objective: To identify and use correctly homonyms, both homophones and homographs.
52Advanced Dictionary UseAdvanced Dictionary Use
Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
53Vocabulary DevelopmentVocabulary
Objective: To identify and use better words than ‘got’ and ‘said’.
54PhrasesPhrases
Objective: To identify and use phrases including adjectival and adverbial phrases.
55ClausesClauses
Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
56Simple and Compound VerbsSimple and Compound Verbs
Objective: To identify and use simple and compound verbs.
57Auxiliary VerbsAuxiliary Verbs
Objective: To identify and use auxiliary verbs within compound verbs.
58Subject-Verb AgreementSubject-Verb Agreement
Objective: To identify and use correct tense, number and person in forming verbs.
59Verb tense – CompoundVerb tense – Compound
Objective: To identify and use ‘to be’ and ‘to have’ with the appropriate participle of the main verb.
60PluralsPlurals 3 – Unusual
Objective: To create unusual plurals: for words ending in ‘o'; by changing the vowels or by adding letters.
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Year 8 Literacy

#TOPICTITLE
1What’s Homestay?Want to improve your English?
Objective: Learn how to elicit information from an advertisement and text.
2What’s Homestay?Homestay application
Objective: Learn how to fill in an application form.
3Setting offDestination ‘Downunder’
Objective: Expand vocabulary, read and understand a travel brochure.
4Setting offA letter to the Carters Full lesson available
Objective: Read and understand an informal letter of introduction.
5Here we are!Who are the Carters?
Objective: Elicit information from a letter about people’s physical appearance.
6Here we are!My new family
Objective: Learn how to elicit information about personality traits from the text.
7A new homeThis is our house.
Objective: Read a description of a house using prepositions of location.
8A new homeOur room!
Objective: Read a text using prepositions of location.
9Let’s hit the beach!Meet Tim. He’s a lifesaver.
Objective: Elicit information to answer questions from the text. Identify strong versus mild obligation.
10Let’s hit the beach!Be safe at the beach this summer!
Objective: Read and understand a safety pamphlet for Australian beaches. Identify imperatives in the reading.
11Amazing Aussie animalsMarsupials
Objective: Identify factual information within a text, answer questions and recognise a topic sentence.
12Amazing Aussie animalsWhen we were watching …
Objective: Read postcards about Australian animals. Identify past and present continuous.
13What do you like to do?Would you like to join?
Objective: Select factual information from a text to answer questions. Identify the different ways to use like, like to and would like to.
14What do you like to do?How often do you …?
Objective: Use adverbs of frequency and calculate how often activities occur.
15BBQ Party!A famous Aussie dessert
Objective: Answer comprehension questions and identify expressions of quantity.
16BBQ Party!A new ‘barbie’!
Objective: Read a set of instructions and complete activities based on comprehension and sequencing details.
17Big day out!The big three Full lesson available
Objective: Answer comprehension questions and identify first and second conditionals.
18Big day out!The big plan
Objective: Identify the different uses of ‘going to’. Use different ways of expressing time.
19Thanks and goodbyeMy Australian experience
Objective: Read a text and answer comprehension questions. Identify expressions about ‘feelings’.
20Thanks and goodbyeThank you letter
Objective: Recognise time clauses and identify ‘feeling’ adjectives.
21SentencesThe Sentence
Objective: To identify and use complete sentences.
22PunctuationSentence Endings
Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
23CapitalisationCapital Letters 2
Objective: To use capital letters correctly: in titles and letters.
24PronounsPronouns 2
Objective: To recognise and use personal, possessive and relative pronouns.
25Parts of Speech Part aPrepositions
Objective: To identify and use prepositions correctly.
26Punctuation Skills Part bQuotation Marks
Objective: To use quotation marks for direct speech.
27ContractionsContractions
Objective: To identify and use contractions.
28Common ErrorsCommon Errors in writing
Objective: To identify and eliminate common errors.
29Commas 2Commas 2
Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech.
30Conjunctions – SentencesConjunctions – Sentences
Objective: To use conjunctions to increase the variety of sentence structure in written expression.
31PhrasesPhrases
Objective: To identify and use phrases including adjectival and adverbial phrases.
32ClausesClauses
Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
33Subject-Verb AgreementSubject-Verb Agreement
Objective: To identify and use correct tense, number and person in forming verbs.
34Verb tense – CompoundVerb tense – Compound
Objective: To identify and use ‘to be’ and ‘to have’ with the appropriate participle of the main verb.
35Verbs – Active and Passive voiceVerbs – Active and Passive voice
Objective: To identify and use active and passive voice.
36Apostrophe – PossessionApostrophe – Possession
Objective: To use the apostrophe of possession correctly.
37Similes and MetaphorsSimiles and Metaphors
Objective: To identify and use similes and metaphors.
38Figurative LanguageOnomatopoeia, Assonance and Alliteration
Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
39Common ErrorsCommon Errors in verb usage, spelling and punctuation
Objective: To identify and eliminate common errors.
40Colons and Semi-ColonsColons and Semi-Colons
Objective: To use colons and semi-colons correctly.
41Sentence Structure Part aSubject and Predicate
Objective: To identify the subject and predicate within a sentence and to understand they are the two main parts of a sentence.
42Regular and Irregular VerbsRegular and Irregular Verbs
Objective: To identify and use regular and irregular verbs in the present and past tense.
43Verbs – InfinitivesVerbs – Infinitives
Objective: To identify and use the infinitive form of the verb.
44Modal VerbsModal Verbs
Objective: To identify and use modal verbs with the appropriate form of the main verb.
45Participles – as Verbs and AdjectivesParticiples – as Verbs and Adjectives
Objective: To identify and use participles as verbs or adjectives as indicators of continuing action.
46GerundsGerunds
Objective: To identify and use gerunds.
47InterjectionsInterjections
Objective: To identify and use interjections correctly.
48PluralsPlurals 4 – Unusual
Objective: To use nouns whose singular and plural forms are the same. To use compound noun plurals.
49Sentence ImprovementSentence Improvement
Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
50PunctuationPunctuation – Various
Objective: To use hyphens, dashes, apostrophes, quotation marks, parentheses and brackets correctly.
51Mass and Count NounsDeterminers
Objective: To identify and use determiners correctly with mass and count nouns.
52Transitive and Intransitive VerbsTransitive and Intransitive Verbs
Objective: To identify and use transitive and intransitive verbs.
53Case – Nouns and PronounsCase – Nouns, Pronouns and Possessive Adjectives
Objective: To identify the case of nouns and pronouns.
54Plurals of Foreign NounsPlurals 5 – Foreign
Objective: To form plurals of foreign nouns.
55Variety of ExpressionSentence Construction
Objective: To construct expressive and precise sentences to improve meaning.
56Figurative LanguageSymbolism and Personification
Objective: To identify, and make use of, symbolism and personification.
57Review of Figures of SpeechReview of Figures of Speech
Objective: To identify multiple uses of figures of speech within writing.
58Spelling SkillsWord Usage
Objective: To correctly choose words with similar spelling, sound and meaning.
59Essay Writing 1Essay Writing 1
Objective: To develop and write essays (expositions).
60Essay Writing 2Essay Writing 2
Objective: To develop and write essays.
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Year 9-12 Literacy

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1SentencesThe Sentence
Objective: To identify and use complete sentences.
2VowelsVowels – Long and Short
Objective: To identify long and short vowel sounds, and their use.
3Basic Dictionary UseBasic Dictionary Use
Objective: To find words arranged alphabetically and identify word meanings in dictionaries.
4CapitalisationCapital Letters 1
Objective: To use capital letters correctly: to begin sentences, for proper nouns.
5PunctuationSentence Endings
Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
6Common NounsCommon Nouns
Objective: To show a common noun names an object or thing.
7NounsProper Nouns
Objective: To show a proper noun is used to name a person, place or a title.
8VerbsSimple Verbs
Objective: To identify and use verbs. To understand a verb can be: an action or doing word, a state of being or ownership.
9AdjectivesAdjectives
Objective: To show an adjective is a word that describes a noun.
10AdverbsAdverbs
Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
11PronounsPronouns
Objective: To show a pronoun is used in place of a noun.
12Parts of Speech Part bConjunctions
Objective: To identify and use conjunctions correctly.
13Common ErrorsCommon Errors in spelling and punctuation
Objective: To identify and eliminate common errors.
14Conjunctions – SentencesConjunctions – Sentences
Objective: To use conjunctions to increase the variety of sentence structure in written expression.
15CapitalisationCapital Letters 2
Objective: To use capital letters correctly: in titles and letters.
16Parts of Speech Part hArticles and Demonstratives
Objective: To identify and use articles and demonstratives correctly.
17Antonyms and SynonymsAntonyms and Synonyms
Objective: To identify and use antonyms and synonyms.
18PunctuationCommas 1
Objective: To use commas: to list, to make meaning clear, and when writing the date.
19Commas 2Commas 2
Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech.
20Spelling SkillsSpelling
Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’.
21Spelling SkillsSyllabification
Objective: To improve spelling by dividing words correctly into syllables.
22PluralsPlurals 1 – simple
Objective: To form plurals (more than one) by adding ‘s’ and ‘es’ correctly.
23PluralsPlurals 2 – special rules
Objective: To form plurals with special rules: words ending in ‘y’ and ‘f’.
24NounsCollective and Abstract Nouns
Objective: To identify and use collective and abstract nouns.
25VerbsVerbs – Tense
Objective: To identify and use the correct tense of verbs: past, present and future.
26AdjectivesAdjectives – from Nouns and Verbs
Objective: To create adjectives from nouns and verbs. E.g. China – Chinese
27AdjectivesAdjectives – Comparatives and Superlatives
Objective: To identify and use comparative and superlative adjectives.
28Parts of Speech Part aPrepositions
Objective: To identify and use prepositions correctly.
29Punctuation Skills Part bQuotation Marks
Objective: To use quotation marks for direct speech.
30Apostrophe – PossessionApostrophe – Possession
Objective: To use the apostrophe of possession correctly.
31MnemonicsSpelling – Mnemonics
Objective: To identify and use mnemonics to assist in correct spelling.
32PrefixesPrefixes
Objective: The identify and use prefixes.
33SuffixesSuffixes
Objective: The identify and use suffixes.
34Similes and MetaphorsSimiles and Metaphors
Objective: To identify and use similes and metaphors.
35Figurative LanguageOnomatopoeia, Assonance and Alliteration
Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
36Homonyms – Homophones and HomographsHomonyms – Homophones and Homographs
Objective: To identify and use correctly homonyms, both homophones and homographs.
37Advanced Dictionary UseAdvanced Dictionary Use
Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
38Vocabulary DevelopmentVocabulary
Objective: To identify and use better words than ‘got’ and ‘said’.
39PhrasesPhrases
Objective: To identify and use phrases including adjectival and adverbial phrases.
40ClausesClauses
Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
41Simple and Compound VerbsSimple and Compound Verbs
Objective: To identify and use simple and compound verbs.
42Auxiliary VerbsAuxiliary Verbs
Objective: To identify and use auxiliary verbs within compound verbs.
43Subject-Verb AgreementSubject-Verb Agreement
Objective: To identify and use correct tense, number and person in forming verbs.
44Verb tense – CompoundVerb tense – Compound
Objective: To identify and use ‘to be’ and ‘to have’ with the appropriate participle of the main verb.
45PluralsPlurals 3 – Unusual
Objective: To create unusual plurals: for words ending in ‘o'; by changing the vowels or by adding letters.
46PronounsPronouns 2
Objective: To recognise and use personal, possessive and relative pronouns.
47ContractionsContractions
Objective: To identify and use contractions.
48Common ErrorsCommon Errors in writing
Objective: To identify and eliminate common errors.
49Verbs – Active and Passive voiceVerbs – Active and Passive voice
Objective: To identify and use active and passive voice.
50Common ErrorsCommon Errors in verb usage, spelling and punctuation
Objective: To identify and eliminate common errors.
51Colons and Semi-ColonsColons and Semi-Colons
Objective: To use colons and semi-colons correctly.
52Sentence Structure Part aSubject and Predicate
Objective: To identify the subject and predicate within a sentence and to understand they are the two main parts of a sentence.
53Regular and Irregular VerbsRegular and Irregular Verbs
Objective: To identify and use regular and irregular verbs in the present and past tense.
54Verbs – InfinitivesVerbs – Infinitives
Objective: To identify and use the infinitive form of the verb.
55Modal VerbsModal Verbs
Objective: To identify and use modal verbs with the appropriate form of the main verb.
56Participles – as Verbs and AdjectivesParticiples – as Verbs and Adjectives
Objective: To identify and use participles as verbs or adjectives as indicators of continuing action.
57GerundsGerunds
Objective: To identify and use gerunds.
58InterjectionsInterjections
Objective: To identify and use interjections correctly.
59PluralsPlurals 4 – Unusual
Objective: To use nouns whose singular and plural forms are the same. To use compound noun plurals.
60Sentence ImprovementSentence Improvement
Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
61PunctuationPunctuation – Various
Objective: To use hyphens, dashes, apostrophes, quotation marks, parentheses and brackets correctly.
62Mass and Count NounsDeterminers
Objective: To identify and use determiners correctly with mass and count nouns.
63Transitive and Intransitive VerbsTransitive and Intransitive Verbs
Objective: To identify and use transitive and intransitive verbs.
64Case – Nouns and PronounsCase – Nouns, Pronouns and Possessive Adjectives
Objective: To identify the case of nouns and pronouns.
65Plurals of Foreign NounsPlurals 5 – Foreign
Objective: To form plurals of foreign nouns.
66Variety of ExpressionSentence Construction
Objective: To construct expressive and precise sentences to improve meaning.
67Figurative LanguageSymbolism and Personification
Objective: To identify, and make use of, symbolism and personification.
68Review of Figures of SpeechReview of Figures of Speech
Objective: To identify multiple uses of figures of speech within writing.
69Spelling SkillsWord Usage
Objective: To correctly choose words with similar spelling, sound and meaning.
70Essay Writing 1Essay Writing 1
Objective: To develop and write essays (expositions).
71Essay Writing 2Essay Writing 2
Objective: To develop and write essays.
72Letter WritingPersonal and Business Letters
Objective: To use correct setting out and format for personal and business letters.
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