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
- PYP Grade 1 Mathematics
- PYP Grade 2 Mathematics
- PYP Grade 3 Mathematics
- PYP Grade 4 Mathematics
- PYP Grade 5 Mathematics
- PYP Grade 6 Mathematics
- MYP Grade 7 Mathematics
- MYP Grade 8 Mathematics
- MYP Grade 9 Mathematics
- MYP Grade 10 - 1 Algebra II and Trig Mathematics
- MYP Grade 10 - 2 Algebra II and Trig Hons Mathematics
- MYP Grade 10 - 3 Pre Calculus Mathematics
- Topic 1 - The Scientific Calculator Mathematics
- Topic 2 - Number and Algebra Mathematics
- Topic 3 - Sets Mathematics
- Topic 4 - Functions and Graphs Mathematics
- Topic 5 - Geometry Mathematics
- Topic 6 - Statistics Mathematics
- Topic 7 - Differential Calculus Mathematics
- Topic 8 - Financial management Mathematics
- Topic 1 - Algebra Mathematics
- Topic 2 - Functions and Equations Mathematics
- Topic 3 - Circular functions and Trigonometry Mathematics
- Topic 4 - Matrices Mathematics
- Topic 5 - Vectors Mathematics
- Topic 6 - Statistics and Probability Mathematics
- Topic 7 - Differential Calculus Mathematics
- Topic 1 - Algebra Mathematics
- Topic 2 - Functions and Equations Mathematics
- Topic 3 - Circular functions and Trigonometry Mathematics
- Topic 4 - Matrices Mathematics
- Topic 5 - Vectors Mathematics
- Topic 6 - Statistics and Probability Mathematics
- Topic 7 - Differential Calculus Mathematics

### PYP Kindergarten Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – PYP Kindergarten | |

Objective: Assessment | |||

2 | Using and applying number | The 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 | |||

3 | Using and applying number | The 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. | |||

4 | The number system | Ordinal 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. | |||

5 | Using and applying number | Zero 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. | |||

6 | Using and applying number | The 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. | |||

7 | Using and applying number | Numbers 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. | |||

8 | Time, days of week | Days 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. | |||

9 | Time, duration | Duration | |

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. | |||

10 | Time, months | Months 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. | |||

11 | Reasoning | Simple 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. | |||

12 | Weight/mass | Introducing the concept of mass | |

Objective: On completion of the lesson the student will understand the concepts of mass. | |||

13 | Exam | Exam – PYP Kindergarten | |

Objective: Exam |

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### PYP Grade 1 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – PYP Grade 1 | |

Objective: Assessment | |||

2 | Using and applying number | The 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 | |||

3 | Using and applying number | The 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. | |||

4 | The number system | Ordinal 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. | |||

5 | Using and applying number | Zero 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. | |||

6 | Using and applying number | The 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. | |||

7 | Using and applying number | Numbers 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. | |||

8 | Calculations | The 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. | |||

9 | Calculation-multiples | Multiples 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. | |||

10 | Using and applying number | Using 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. | |||

11 | Reasoning | Simple 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. | |||

12 | Reasoning | Simple 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. | |||

13 | Calculations | Subtraction 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. | |||

14 | Calculations | Subtraction by Comparison | |

Objective: On completion of the lesson the student will be able to calculate take away or subtraction number sentences by comparison methods. | |||

15 | Calculations | Subtraction 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. | |||

16 | Length | Compare 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. | |||

17 | Length | Using 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. | |||

18 | Length | Using 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. | |||

19 | Weight/mass | Introducing the concept of mass | |

Objective: On completion of the lesson the student will understand the concepts of mass. | |||

20 | Time, days of week | Days 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. | |||

21 | Time, duration | Duration | |

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. | |||

22 | Time, months | Months 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. | |||

23 | Time, digital | O’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. | |||

24 | Time, analogue | O’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. | |||

25 | Fractions | Using 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. | |||

26 | Fractions | Using 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. | |||

27 | Exam | Exam – PYP Grade 1 | |

Objective: Exam |

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### PYP Grade 2 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – PYP Grade 2 | |

Objective: Assessment | |||

2 | Calculations | The 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. | |||

3 | Calculation-larger numbers | The 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. | |||

4 | Calculation 10-100 | Counting 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. | |||

5 | Addition | Addition 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. | |||

6 | Addition | Addition 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. | |||

7 | Calculations | Subtraction 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. | |||

8 | Subtraction | Subtraction 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. | |||

9 | Subtraction | Subtraction 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. | |||

10 | Subtraction | Subtraction 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 | |||

11 | Subtraction | Subtraction 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. | |||

12 | Time, duration | Duration | |

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. | |||

13 | Time, digital | O’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. | |||

14 | Time, analogue | O’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. | |||

15 | Time, minutes | Analogue – 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. | |||

16 | Time, quarter to, past | Quarter 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’. | |||

17 | Time, units | Units 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. | |||

18 | Calculation-grouping | Multiplication 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. | |||

19 | Calculation-grouping | Multiplication 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. | |||

20 | Calculation-multiplication | The multiplication sign | |

Objective: on completion of the lesson the student will be able to multiply single numbers to solve multiplication problems. | |||

21 | Multiplication | Multiplication – 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. | |||

22 | Length | Compare 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. | |||

23 | Length | Using 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. | |||

24 | Length | Using 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. | |||

25 | Area | Comparing 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. | |||

26 | Capacity | The 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. | |||

27 | Capacity | Estimate, 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. | |||

28 | Weight/mass | Introducing the concept of mass | |

Objective: On completion of the lesson the student will understand the concepts of mass. | |||

29 | Fractions | Using 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. | |||

30 | Fractions | Using 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. | |||

31 | Data | Pictograms | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||

32 | Exam | Exam – PYP Grade 2 | |

Objective: Exam |

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### PYP Grade 3 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – PYP Grade 3 | |

Objective: Assessment | |||

2 | Calculation-larger numbers | The 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. | |||

3 | Addition | Addition 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. | |||

4 | Place value | The 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. | |||

5 | Addition | Addition 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. | |||

6 | Subtraction | Subtraction 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. | |||

7 | Subtraction | Subtraction 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 | |||

8 | Subtraction | Subtraction 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. | |||

9 | Subtraction | Subtraction 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. | |||

10 | Data | Pictograms | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||

11 | Data | Bar Charts | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||

12 | Data | Line graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||

13 | Calculation-grouping | Multiplication 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. | |||

14 | Calculation-grouping | Multiplication 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. | |||

15 | Calculation-multiplication | The multiplication sign | |

Objective: on completion of the lesson the student will be able to multiply single numbers to solve multiplication problems. | |||

16 | Calculation-multiples | Multiples 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. | |||

17 | Multiplication | Multiplication – 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. | |||

18 | Multiplication | Multiplying 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. | |||

19 | Calculation sharing/division | Strategies 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. | |||

20 | Problems | Solve 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. | |||

21 | Angles | Measure 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. | |||

22 | 2-D shapes | Using 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. | |||

23 | 2-D shapes | Spatial properties of quadrilaterals | |

Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||

24 | Tessellating 2-D shapes | Use 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. | |||

25 | 3-D shapes | Recognise 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. | |||

26 | 3-D shapes | Viewing 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. | |||

27 | Lines and angles | Describing position. | |

Objective: On completion of the lesson the student will be able to use and understand conventional location language to describe position. | |||

28 | Lines and angles | Mapping 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. | |||

29 | Lines and angles | Informal 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. | |||

30 | Fractions | Using 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. | |||

31 | Fractions | Using 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. | |||

32 | Fractions | Fractions 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. | |||

33 | Fractions | Comparing 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. | |||

34 | Fractions | mixed 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. | |||

35 | Fractions | Improper 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. | |||

36 | Fractions | Finding 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. | |||

37 | Fractions | Subtracting 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 | |||

38 | Fractions | Adding 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. | |||

39 | Length | Compare 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. | |||

40 | Length | Using 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. | |||

41 | Length | Using 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. | |||

42 | Area | Comparing 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. | |||

43 | Area | Introduction 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. | |||

44 | Weight/mass | Introducing the concept of mass | |

Objective: On completion of the lesson the student will understand the concepts of mass. | |||

45 | Weight/mass | The 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. | |||

46 | Weight/mass | The 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. | |||

47 | Capacity | Using 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. | |||

48 | Capacity | Using 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. | |||

49 | Capacity | The 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. | |||

50 | Capacity | Estimate, 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. | |||

51 | Time, digital | O’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. | |||

52 | Time, analogue | O’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. | |||

53 | Time, minutes | Analogue – 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. | |||

54 | Time, quarter to, past | Quarter 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’. | |||

55 | Time, units | Units 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. | |||

56 | Time, minutes past the hour | Minutes 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. | |||

57 | Time, minutes to the hour | Minutes 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. | |||

58 | Time, digital, analogue | Comparing 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. | |||

59 | Decimals | Introduction to decimals | |

Objective: On completion of the lesson the student will be able to represent decimals to two decimal places. | |||

60 | Decimals | Comparing 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. | |||

61 | Decimals | Decimals 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. | |||

62 | Multiplication | Multiplying 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. | |||

63 | Multiplication | Multiplying 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. | |||

64 | Multiplication | Multiples 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. | |||

65 | Division | Division with and without a remainder. | |

Objective: On completion of the lesson the student will understand division with and without a Remainder. | |||

66 | Division | Dividing 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. | |||

67 | Exam | Exam – PYP Grade 3 | |

Objective: Exam |

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### PYP Grade 4 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – PYP Grade 4 | |

Objective: Assessment | |||

2 | Place value | The numbers 1000 to 9999 | |

3 | Counting and numeration | The 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. | |||

4 | Addition | Addition 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. | |||

5 | Counting and numeration | Addition 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. | |||

6 | Counting and numeration | Seven 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. | |||

7 | Subtraction | Subtraction 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. | |||

8 | Subtraction | Subtraction 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. | |||

9 | Angles | Measure 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. | |||

10 | 2-D shapes | Using 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. | |||

11 | 2-D shapes | Spatial properties of quadrilaterals | |

Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||

12 | 2-D shapes | Recognise and name triangles | |

Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||

13 | Tessellating 2-D shapes | Use 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. | |||

14 | 3-D shapes | Recognise 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. | |||

15 | 3-D shapes | Recognise 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. | |||

16 | 3-D shapes | Viewing 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. | |||

17 | Lines and angles | Describing position. | |

Objective: On completion of the lesson the student will be able to use and understand conventional location language to describe position. | |||

18 | Lines and angles | Mapping 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. | |||

19 | Lines and angles | Informal 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. | |||

20 | Data | Pictograms | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs. | |||

21 | Data | Bar Charts | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||

22 | Data | Line graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||

23 | Statistic-probability | Probability of Simple Events | |

Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||

24 | Calculation-grouping | Multiplication 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. | |||

25 | Calculation-grouping | Multiplication 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. | |||

26 | Calculation-multiplication | The multiplication sign | |

Objective: on completion of the lesson the student will be able to multiply single numbers to solve multiplication problems. | |||

27 | Calculation-multiples | Multiples 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. | |||

28 | Multiplication | Multiplication – 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. | |||

29 | Multiplication | Multiplying 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. | |||

30 | Multiplication | Multiplying 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. | |||

31 | Calculation sharing/division | Strategies 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. | |||

32 | Problems | Solve 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. | |||

33 | Division | Division with and without a remainder. | |

Objective: On completion of the lesson the student will understand division with and without a Remainder. | |||

34 | Division | Dividing 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. | |||

35 | Sign word problems | Solving 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. | |||

36 | Equations | Problem solving strategies | |

Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems. | |||

37 | Fractions | Fractions 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. | |||

38 | Fractions | Comparing 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. | |||

39 | Fractions | mixed 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. | |||

40 | Fractions | Improper 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. | |||

41 | Fractions | Finding 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. | |||

42 | Fractions | Multiplying 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. | |||

43 | Fractions | Reducing 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. | |||

44 | Fractions | Comparing 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. | |||

45 | Fractions | Subtracting 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 | |||

46 | Fractions | Adding 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. | |||

47 | Fractions | Adding 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. | |||

48 | Fractions | Multiplying fractions by whole numbers | |

Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. | |||

49 | Fractions | Fractions of whole numbers | |

Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||

50 | Fractions | Multiplying fractions | |

Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||

51 | Fractions | Multiplying 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. | |||

52 | Fractions | Finding 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). | |||

53 | Fractions | Dividing fractions | |

Objective: On completion of the lesson the student will be able to divide fractions. | |||

54 | Decimals | Introduction to decimals | |

Objective: On completion of the lesson the student will be able to represent decimals to two decimal places. | |||

55 | Decimals | Comparing 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. | |||

56 | Decimals | Decimals 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. | |||

57 | Decimals | Adding 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) | |||

58 | Decimals | Subtracting 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) | |||

59 | Decimals | Using 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. | |||

60 | Decimals | Using 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. | |||

61 | Decimals | Rounding 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. | |||

62 | Decimals | Decimals 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. | |||

63 | Percentages | Changing 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. | |||

64 | Length | Using the metre as a formal unit to measure perimeter | |

65 | Length | Using the formal unit of the centimetre to measure length and perimeter | |

66 | Length | Read 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. | |||

67 | Length | Compare 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. | |||

68 | Area | Comparing 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. | |||

69 | Area | Introduction 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. | |||

70 | Volume | Introduction 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 | |||

71 | 3-D shapes | Constructing 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. | |||

72 | Volume | Using 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. | |||

73 | Volume | Introducing 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. | |||

74 | Volume | Using 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 | |||

75 | Capacity | Using 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. | |||

76 | Capacity | Using 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. | |||

77 | Capacity | The 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. | |||

78 | Capacity | Converting 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. | |||

79 | Weight/mass | The 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. | |||

80 | Weight/mass | The 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. | |||

81 | Capacity | Estimate, 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. | |||

82 | Time, units | Units 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. | |||

83 | Time, minutes past the hour | Minutes 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. | |||

84 | Time, minutes to the hour | Minutes 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. | |||

85 | Time, digital, analogue | Comparing 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. | |||

86 | Multiplication | Multiplying 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. | |||

87 | Multiplication | Multiples 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. | |||

88 | Multiplication | Multiplication using extended algorithms. | |

Objective: On completion of the lesson the student will have understood multiplication using extended algorithms. | |||

89 | Multiplication | Multiplication 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. | |||

90 | Division | Divide 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. | |||

91 | Exam | Exam – PYP Grade 4 | |

Objective: Exam |

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### PYP Grade 5 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – PYP Grade 5 | |

Objective: Assessment | |||

2 | Counting and numeration | The 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. | |||

3 | Counting and numeration | Seven 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. | |||

4 | Addition | Addition up to the number 999 | |

5 | Counting and numeration | Addition 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. | |||

6 | Subtraction | Subtraction of two-digit numbers Involving comparison. | |

7 | Subtraction | Subtraction up to the number 999 using the renaming method | |

8 | Decimals | Introduction to decimals | |

Objective: On completion of the lesson the student will be able to represent decimals to two decimal places. | |||

9 | Decimals | Comparing 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. | |||

10 | Decimals | Decimals 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. | |||

11 | Decimals | Adding 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) | |||

12 | Decimals | Subtracting 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) | |||

13 | Decimals | Using 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. | |||

14 | Decimals | Using 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. | |||

15 | Decimals | Rounding 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. | |||

16 | Decimals | Decimals 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. | |||

17 | Decimals | Multiplying 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. | |||

18 | Decimals | Multiplying decimals by whole numbers | |

Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||

19 | Decimals | Multiplication 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. | |||

20 | Decimals | Dividing 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. | |||

21 | Decimals | Dividing decimal fractions by whole numbers | |

Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||

22 | Decimals | Dividing numbers by a decimal fraction | |

Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||

23 | Multiplication | Multiplying 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. | |||

24 | Multiplication | Multiplying 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. | |||

25 | Multiplication | Multiplying 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. | |||

26 | Multiplication | Multiples 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. | |||

27 | Multiplication | Multiplication using extended algorithms. | |

Objective: On completion of the lesson the student will have understood multiplication using extended algorithms. | |||

28 | Multiplication | Multiplication 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. | |||

29 | Division | Division with and without a remainder. | |

Objective: On completion of the lesson the student will understand division with and without a Remainder. | |||

30 | Division | Dividing 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. | |||

31 | Division | Divide 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. | |||

32 | Lines and angles | Mapping 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. | |||

33 | Lines and angles | Informal 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. | |||

34 | Data | Pictograms | |

35 | Data | Bar Charts | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||

36 | Data | Line graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||

37 | Length | Using the metre as a formal unit to measure perimeter | |

38 | Length | Using the formal unit of the centimetre to measure length and perimeter | |

39 | Length | Read 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. | |||

40 | Length | Compare 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. | |||

41 | Area | Comparing and ordering areas. | |

42 | Area | Introduction 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. | |||

43 | Angles | Measure 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. | |||

44 | 2-D shapes | Recognise and name triangles | |

Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||

45 | Fractions | mixed 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. | |||

46 | Fractions | Improper 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. | |||

47 | Fractions | Finding 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. | |||

48 | Fractions | Multiplying 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. | |||

49 | Fractions | Reducing 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. | |||

50 | Fractions | Comparing 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. | |||

51 | Fractions | Subtracting 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 | |||

52 | Fractions | Adding 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. | |||

53 | Fractions | Adding 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. | |||

54 | Fractions | Multiplying fractions by whole numbers | |

Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. | |||

55 | Fractions | Fractions of whole numbers | |

Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||

56 | Fractions | Multiplying fractions | |

Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||

57 | Fractions | Multiplying 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. | |||

58 | Fractions | Finding 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). | |||

59 | Fractions | Dividing fractions | |

Objective: On completion of the lesson the student will be able to divide fractions. | |||

60 | Fractions | Dividing mixed numbers (mixed numerals) | |

Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). | |||

61 | Rules properties | Using 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. | |||

62 | Percentages | Changing 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. | |||

63 | Percentages | One 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. | |||

64 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

65 | Volume | Using 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. | |||

66 | Volume | Introducing 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. | |||

67 | Volume | Using 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 | |||

68 | Volume | Solving 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. | |||

69 | Volume | Solving 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. | |||

70 | Capacity | Using 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. | |||

71 | Capacity | Using 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. | |||

72 | Capacity | The relationship between the common units of capacity, the litre and the millilitre | |

73 | Capacity | Converting 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. | |||

74 | Weight/mass | The 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. | |||

75 | Weight/mass | The 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. | |||

76 | Capacity | Estimate, measure and compare the capacity of containers | |

77 | Sign word problems | Solving 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. | |||

78 | Equations | Problem solving strategies | |

Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems. | |||

79 | Number problems | Problems with numbers. | |

Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy. | |||

80 | Money | Problems involving money | |

Objective: On completion of the lesson the student will be able to solve problems with money. | |||

81 | Length | Problems with length. | |

Objective: On completion of the lesson the student will be able to solve problems with length. | |||

82 | Area | Problems with area. | |

Objective: On completion of the lesson the student will be able to solve problems with area. | |||

83 | Exam | Exam – PYP Grade 5 | |

Objective: Exam |

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### PYP Grade 6 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – MYP Grade 6 | |

Objective: Assessment | |||

2 | Counting and numeration | The 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. | |||

3 | Counting and numeration | Seven 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. | |||

4 | Counting and numeration | Addition 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. | |||

5 | Subtraction | Subtraction up to the number 999 using the renaming method | |

6 | Decimals | Comparing and ordering decimals to two decimal places | |

7 | Decimals | Decimals with whole numbers 10th and 100th | |

8 | Decimals | Adding 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) | |||

9 | Decimals | Subtracting 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) | |||

10 | Decimals | Using 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. | |||

11 | Decimals | Using 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. | |||

12 | Decimals | Rounding 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. | |||

13 | Decimals | Decimals 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. | |||

14 | Decimals | Multiplying 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. | |||

15 | Decimals | Multiplying decimals by whole numbers | |

Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||

16 | Decimals | Multiplication 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. | |||

17 | Decimals | Dividing 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. | |||

18 | Decimals | Dividing decimal fractions by whole numbers | |

Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||

19 | Decimals | Dividing numbers by a decimal fraction | |

Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||

20 | Multiplication | Multiplying 3 and 4-digit numbers by multiples of 100 | |

21 | Multiplication | Multiplying 2-digit numbers by 2-digit numbers | |

22 | Multiplication | Multiples and factors of whole numbers | |

23 | Multiplication | Multiplication using extended algorithms. | |

Objective: On completion of the lesson the student will have understood multiplication using extended algorithms. | |||

24 | Multiplication | Multiplication 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. | |||

25 | Division | Dividing two and three digit numbers by a single digit number. | |

26 | Division | Divide 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. | |||

27 | Fractions | mixed numbers (mixed numerals) | |

28 | Fractions | Improper fractions | |

29 | Fractions | Finding equivalent fractions | |

30 | Fractions | Multiplying 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. | |||

31 | Fractions | Reducing 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. | |||

32 | Fractions | Comparing 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. | |||

33 | Fractions | Subtracting fractions from whole numbers | |

34 | Fractions | Adding and subtracting fractions with the same denominator | |

35 | Fractions | Adding 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. | |||

36 | Fractions | Multiplying fractions by whole numbers | |

Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. | |||

37 | Fractions | Fractions of whole numbers | |

Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. | |||

38 | Fractions | Multiplying fractions | |

Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. | |||

39 | Fractions | Multiplying 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. | |||

40 | Fractions | Finding 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). | |||

41 | Fractions | Dividing fractions | |

Objective: On completion of the lesson the student will be able to divide fractions. | |||

42 | Fractions | Dividing mixed numbers (mixed numerals) | |

Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). | |||

43 | Rules properties | Using 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. | |||

44 | Statistics | Frequency 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. | |||

45 | Statistics | Frequency histograms and polygons | |

Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||

46 | Statistics | Relative frequency | |

Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||

47 | Statistics | The 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. | |||

48 | Statistic-probability | The 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. | |||

49 | Statistic-probability | The 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. | |||

50 | Statistic-probability | The median | |

Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||

51 | Data | Pictograms | |

52 | Data | Bar Charts | |

53 | Data | Line graphs. | |

54 | Data | Pie 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. | |||

55 | Length | Using the metre as a formal unit to measure perimeter | |

56 | Length | Using the formal unit of the centimetre to measure length and perimeter | |

57 | Length | Read 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. | |||

58 | Length | Compare 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. | |||

59 | Area | Comparing and ordering areas. | |

60 | Area | Introduction to the square centimetre. | |

61 | Volume | Using 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. | |||

62 | Volume | Introducing 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. | |||

63 | Volume | Using 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 | |||

64 | Volume | Solving 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. | |||

65 | Volume | Solving 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. | |||

66 | Capacity | Using 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. | |||

67 | Capacity | Using the cubic cm as a standard unit of measurement for volume and capacity | |

68 | Capacity | The relationship between the common units of capacity, the litre and the millilitre | |

69 | Capacity | Converting 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. | |||

70 | Weight/mass | The kilogram | |

71 | Weight/mass | The gram and net mass | |

72 | Capacity | Estimate, measure and compare the capacity of containers | |

73 | Time, minutes past the hour | Minutes 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. | |||

74 | Time, minutes to the hour | Minutes 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. | |||

75 | Time, digital, analogue | Comparing 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. | |||

76 | Time, 24-hour | 24 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. | |||

77 | 2-D shapes | Using 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. | |||

78 | 2-D shapes | Spatial properties of quadrilaterals | |

Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||

79 | Angles | Measure and classify angles | |

80 | Geometry-angles | Measuring 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. | |||

81 | 2-D shapes | Recognise and name triangles | |

Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties. | |||

82 | Tessellating 2-D shapes | Use 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. | |||

83 | Lines and angles | Mapping and grid references | |

84 | Lines and angles | Informal coordinate system | |

85 | Percentages | Changing 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. | |||

86 | Percentages | One 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. | |||

87 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

88 | 3-D shapes | Recognise 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. | |||

89 | 3-D shapes | Recognise 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. | |||

90 | 3-D shapes | Recognise 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. | |||

91 | 3-D shapes | Viewing 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. | |||

92 | Algebraic expressions | Algebraic 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. | |||

93 | Algebraic expressions | Substitution 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. | |||

94 | Algebraic expressions | Simplifying 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. | |||

95 | Algebraic expressions | Simplifying 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. | |||

96 | Algebraic expressions | Simplifying 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. | |||

97 | Algebraic equations | Solving 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. | |||

98 | Algebraic expressions | Directed 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. | |||

99 | Algebraic expressions | Directed 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. | |||

100 | Statistic-probability | Probability of Simple Events | |

Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||

101 | Sign word problems | Solving 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. | |||

102 | Equations | Problem solving strategies | |

Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems. | |||

103 | Number problems | Problems with numbers. | |

Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy. | |||

104 | Money | Problems involving money | |

Objective: On completion of the lesson the student will be able to solve problems with money. | |||

105 | Length | Problems with length. | |

Objective: On completion of the lesson the student will be able to solve problems with length. | |||

106 | Area | Problems with area. | |

Objective: On completion of the lesson the student will be able to solve problems with area. | |||

107 | Volume/capacity | Problems with volume/capacity. | |

Objective: Problem Solving: problems involving volume/capacity | |||

108 | Exam | Exam – MYP Grade 6 | |

Objective: Exam |

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### MYP Grade 7 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – MYP Grade 7 | |

Objective: Assessment | |||

2 | Algebraic expressions | Algebraic 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. | |||

3 | Algebraic expressions | Substitution 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. | |||

4 | Algebraic expressions | Directed 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. | |||

5 | Algebraic expressions | Directed 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. | |||

6 | Algebraic expressions | Simplifying 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. | |||

7 | Algebraic expressions | Simplifying 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. | |||

8 | Algebraic expressions | Simplifying 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. | |||

9 | Algebraic expressions | Simplifying 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. | |||

10 | Algebraic expressions | Simplifying algebraic expressions: division | |

Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||

11 | Algebraic expressions | Expanding 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. | |||

12 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | |

Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. | |||

13 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||

14 | Algebraic equations | Solving 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. | |||

15 | Algebraic equations | Solving equations containing multiplication and division | |

Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||

16 | Decimals | Rounding decimals | |

17 | Decimals | Multiplying 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. | |||

18 | Decimals | Multiplying decimals by whole numbers | |

Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers. | |||

19 | Decimals | Multiplication 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. | |||

20 | Decimals | Dividing 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. | |||

21 | Decimals | Dividing decimal fractions by whole numbers | |

Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. | |||

22 | Decimals | Dividing numbers by a decimal fraction | |

Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. | |||

23 | Rules properties | Using 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. | |||

24 | Algebraic equations | Solving two step equations | |

Objective: On completion of the lesson the student will be able to solve two step equations. | |||

25 | Algebraic equations | Solving equations containing binomial expressions | |

Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||

26 | Algebraic equations | Equations involving grouping symbols. | |

Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||

27 | Algebraic equations | Equations involving fractions. | |

Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||

28 | Algebra- formulae | Equations 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. | |||

29 | Sign word problems | Solving Word Problems by recognising Sign Words | |

30 | Equations | Problem solving strategies | |

31 | Number problems | Problems with numbers. | |

Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy. | |||

32 | Money | Problems involving money | |

Objective: On completion of the lesson the student will be able to solve problems with money. | |||

33 | Length | Problems with length. | |

Objective: On completion of the lesson the student will be able to solve problems with length. | |||

34 | Area | Problems with area. | |

Objective: On completion of the lesson the student will be able to solve problems with area. | |||

35 | Volume/capacity | Problems with volume/capacity. | |

Objective: Problem Solving: problems involving volume/capacity | |||

36 | Absolute value or modulus | Simplifying 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. | |||

37 | Scientific notation | Scientific notation with larger numbers | |

Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||

38 | Scientific notation | Scientific 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. | |||

39 | Scientific notation | Changing 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. | |||

40 | Fractions | mixed numbers (mixed numerals) | |

41 | Fractions | Improper fractions | |

42 | Fractions | Finding equivalent fractions | |

43 | Fractions | Multiplying and dividing to obtain equivalent fractions | |

44 | Fractions | Reducing fractions to lowest equivalent form | |

45 | Percentages | Changing percentages to fractions and decimals | |

46 | Percentages | One 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. | |||

47 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

48 | Lines and angles | Informal coordinate system | |

49 | Algebra-inequalities | Solving 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. | |||

50 | Absolute value or modulus | Solving and graphing inequalities | |

Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value. | |||

51 | Statistic-probability | Probability of Simple Events | |

Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||

52 | Statistic-probability | Rolling 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. | |||

53 | Statistics | Frequency 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. | |||

54 | Statistics | Frequency histograms and polygons | |

Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||

55 | Statistics | Relative frequency | |

Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||

56 | Statistics | The 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. | |||

57 | Statistic-probability | The 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. | |||

58 | Statistic-probability | The 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. | |||

59 | Statistic-probability | The median | |

Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||

60 | Angles | Measure and classify angles | |

61 | 2-D shapes | Recognise and name triangles | |

62 | Geometry-angles | Measuring 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. | |||

63 | Geometry-angles | Adjacent 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. | |||

64 | Geometry-angles | Complementary 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. | |||

65 | Geometry-angles | Vertically 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. | |||

66 | Geometry-angles | Angles 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. | |||

67 | Geometry-angles | Parallel Lines. | |

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||

68 | Geometry-problems | Additional 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. | |||

69 | Geometry-triangles | Angle 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. | |||

70 | Length | Compare and convert formal units of measurement | |

71 | Area | Introducing 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. | |||

72 | Area | Finding 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. | |||

73 | Area | Area 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. | |||

74 | Area | Area 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. | |||

75 | Volume | Introducing the formula for volume. | |

76 | Volume | Using the cubic metre to measure volume. | |

77 | Volume | Solving 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. | |||

78 | Volume | Solving 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. | |||

79 | Volume | Finding 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. | |||

80 | Volume | Volume 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. | |||

81 | Exam | Exam – MYP Grade 7 | |

Objective: Exam |

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### MYP Grade 8 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – MYP Grade 8 | |

Objective: Assessment | |||

2 | Algebraic expressions | Algebraic 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. | |||

3 | Algebraic expressions | Substitution 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. | |||

4 | Algebraic expressions | Directed 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. | |||

5 | Algebraic expressions | Directed 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. | |||

6 | Algebraic expressions | Simplifying 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. | |||

7 | Algebraic expressions | Simplifying 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. | |||

8 | Algebraic expressions | Simplifying 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. | |||

9 | Algebraic expressions | Simplifying 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. | |||

10 | Algebraic expressions | Simplifying algebraic expressions: division | |

Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||

11 | Algebraic expressions | Expanding 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. | |||

12 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | |

Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. | |||

13 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||

14 | Algebraic equations | Solving 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. | |||

15 | Algebraic equations | Solving equations containing multiplication and division | |

Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||

16 | Algebraic equations | Solving two step equations | |

Objective: On completion of the lesson the student will be able to solve two step equations. | |||

17 | Algebraic equations | Solving equations containing binomial expressions | |

Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||

18 | Algebraic equations | Equations involving grouping symbols. | |

Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||

19 | Algebraic equations | Equations involving fractions. | |

Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||

20 | Algebra- formulae | Equations 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. | |||

21 | Algebra- formulae | Changing 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. | |||

22 | Algebra-factorising | Simplifying easy algebraic fractions. | |

Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. | |||

23 | Algebraic fractions | Simplifying 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. | |||

24 | Algebra-negative indices | Algebraic 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. | |||

25 | Factorisation | Factorisation 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. | |||

26 | Algebraic fractions-binomial | Cancelling binomial factors in algebraic fractions. | |

Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions. | |||

27 | Data | Line graphs. | |

28 | Coordinate Geometry-gradient | Gradient | |

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. | |||

29 | Coordinate Geometry-gradient | Gradient 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. | |||

30 | Coordinate Geometry-straight line | The 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. | |||

31 | Coordinate 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. | |||

32 | Coordinate Geometry-equation of line | General 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. | |||

33 | Coordinate Geometry-intercept | Slope 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. | |||

34 | Algebra-inequalities | Solving 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. | |||

35 | Absolute value or modulus | Solving and graphing inequalities | |

Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value. | |||

36 | Absolute value or modulus | Simplifying 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. | |||

37 | Simultaneous equns | Simultaneous equations | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. | |||

38 | Simultaneous equns | Elimination method | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||

39 | Simultaneous equns | Elimination 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. | |||

40 | Simultaneous equns | Applications 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. | |||

41 | Rules for indices/exponents | Adding 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. | |||

42 | Rules for indices/exponents | Subtracting 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. | |||

43 | Rules for indices/exponents | Multiplying 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. | |||

44 | Rules for indices/exponents | Multiplying 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. | |||

45 | Rules for indices/exponents | Terms 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. | |||

46 | Rules for indices/exponents | Negative Indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||

47 | Fractional indices/exponents | Fractional indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||

48 | Fractional indices/exponents | Complex fractions as indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. | |||

49 | Scientific notation | Scientific notation with larger numbers | |

Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||

50 | Scientific notation | Scientific 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. | |||

51 | Scientific notation | Changing 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. | |||

52 | Exponential function | The 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. | |||

53 | Statistics | Frequency 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. | |||

54 | Statistics | Frequency histograms and polygons | |

Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||

55 | Statistics | Relative frequency | |

Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||

56 | Statistics | The 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. | |||

57 | Statistic-probability | The 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. | |||

58 | Statistic-probability | The 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. | |||

59 | Statistic-probability | The median | |

Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||

60 | Statistics – grouped data | Calculating 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. | |||

61 | Statistics | Stem 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. | |||

62 | Statistics | Scatter Diagrams | |

Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||

63 | Graphing binomials | Binomial products. | |

Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression. | |||

64 | Graphing binomials | Binomial 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. | |||

65 | Graphing binomials | Binomial products [non-monic]. | |

Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. | |||

66 | Squaring binomial | Squaring a binomial. [monic] | |

Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial. | |||

67 | Squaring binomial | Squaring a binomial [non-monic]. | |

Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. | |||

68 | Factorising | Expansions leading to the difference of two squares | |

Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. | |||

69 | Algebraic expressions-products | Products in simplification of algebraic expressions | |

Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. | |||

70 | Algebraic expressions-larger expansions | Algebraic Expressions – Larger expansions. | |

Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. | |||

71 | Algebra-highest common factor | Highest 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. | |||

72 | Factors by grouping | Factors 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. | |||

73 | Difference of 2 squares | Difference of two squares | |

Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. | |||

74 | Common fact and diff | Common 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. | |||

75 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. | |

Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive. | |||

76 | Factorising quads | Factorising 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. | |||

77 | Factorising quads | Factorising 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. | |||

78 | Factorising quads | Factorising 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. | |||

79 | Factorising quads | Factorisation of non-monic quadratic trinomials | |

Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. | |||

80 | Factorising quads | Factorisation 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. | |||

81 | Quadratic equations | Introduction to quadratic equations. | |

Objective: On completion of the lesson the student will understand simple quadratic equations. | |||

82 | Quadratic equations | Quadratic equations with factorisation. | |

Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||

83 | Quadratic equations | Solving quadratic equations. | |

Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||

84 | Quadratic equations | Completing the square | |

Objective: On completion of the lesson the student will understand the process of completing the square. | |||

85 | Quadratic equations | Solving quadratic equations by completing the square | |

Objective: On completion of the lesson the student will understand the reasoning behind completing the square. | |||

86 | Quadratic equations | The quadratic formula | |

Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||

87 | Quadratic equations | Problem 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. | |||

88 | Quadratic equations | Solving 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.. | |||

89 | Percentages | Changing percentages to fractions and decimals | |

90 | Percentages | One quantity as a percentage of another | |

91 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

92 | Surds | Introducing 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. | |||

93 | Surds | Some 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. | |||

94 | Surds | Simplifying surds | |

Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. | |||

95 | Surds | Creating 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 | |||

96 | Surds | Adding 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. | |||

97 | Surds | Expanding surds | |

Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. | |||

98 | Surds | Binomial 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. | |||

99 | Surds | Conjugate binomials with surds | |

Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds. | |||

100 | Surds | Rationalising the denominator | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds. | |||

101 | Surds | Rationalising binomial denominators | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions. | |||

102 | Pythagoras | Find the hypotenuse | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||

103 | Pythagoras | Pythagorean triples | |

Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. | |||

104 | Pythagoras | Find 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. | |||

105 | Pythagoras | Calculating 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. | |||

106 | Pythagoras | Proofs of Pythagoras theorem | |

Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem | |||

107 | Exam | Exam – MYP Grade 8 | |

Objective: Exam |

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### MYP Grade 9 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – MYP Grade 9 | |

Objective: Assessment | |||

2 | Logic | Inductive and deductive reasoning | |

Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. | |||

3 | Logic | Definition and use of counter examples | |

Objective: On completion of this lesson the student will be able to create counter examples to statements. | |||

4 | Logic | Indirect 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. | |||

5 | Logic | Mathematical induction | |

Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series. | |||

6 | Logic | Conditional statements (converse, inverse and contrapositive) (Stage 2) | |

Objective: On completion of the lesson the student will be able to form related conditional statements. | |||

7 | Angles | Measure and classify angles | |

8 | Geometry-angles | Measuring 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. | |||

9 | Coordinate Geometry-the plane | Distance 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. | |||

10 | Coordinate Geometry-midpoint, slope | Mid-point formula | |

Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. | |||

11 | Pythagoras | Find the hypotenuse | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||

12 | Pythagoras | Pythagorean triples | |

Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. | |||

13 | Pythagoras | Find 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. | |||

14 | Pythagoras | Calculating 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. | |||

15 | Pythagoras | Proofs of Pythagoras theorem | |

Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem | |||

16 | Geometry-angles | Adjacent 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. | |||

17 | Geometry-angles | Complementary 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. | |||

18 | Geometry-angles | Vertically 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. | |||

19 | Geometry-angles | Angles 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. | |||

20 | Geometry-angles | Parallel Lines. | |

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||

21 | Geometry-problems | Additional 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. | |||

22 | Geometry-triangles | Angle 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. | |||

23 | Geometry-triangles | Exterior 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. | |||

24 | Special triangles | Special 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. | |||

25 | Coordinate Geometry-gradient | Gradient | |

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. | |||

26 | Coordinate Geometry-gradient | Gradient 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. | |||

27 | Coordinate Geometry-straight line | The 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. | |||

28 | Coordinate 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. | |||

29 | Coordinate Geometry-equation of line | General 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. | |||

30 | Coordinate Geometry-intercept | Slope 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. | |||

31 | Coordinate Geometry-point slope | Point 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. | |||

32 | Co-ordinate Geometry-Two point formula | Two 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. | |||

33 | Co-ordinate Geometry-Intercept form | Intercept 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. | |||

34 | Co-ordinate Geometry-Parallel lines equations | Parallel 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. | |||

35 | Geometry problems | More 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 | |||

36 | Geometry-reasoning | Further 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. | |||

37 | Geometry-polygons | Angles 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. | |||

38 | Geometry-congruence | Congruent 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. | |||

39 | Geometry-congruence | Congruent 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. | |||

40 | Geometry-congruence | Proofs 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. | |||

41 | Algebraic equations | Solving equations containing addition and subtraction | |

42 | Algebraic equations | Solving equations containing multiplication and division | |

Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. | |||

43 | Algebraic equations | Solving two step equations | |

Objective: On completion of the lesson the student will be able to solve two step equations. | |||

44 | Algebraic equations | Solving equations containing binomial expressions | |

Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||

45 | Algebraic equations | Equations involving grouping symbols. | |

Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||

46 | Algebraic equations | Equations involving fractions. | |

Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||

47 | Algebra-inequalities | Solving 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. | |||

48 | Absolute value or modulus | Solving and graphing inequalities | |

Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value. | |||

49 | Absolute value or modulus | Simplifying 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. | |||

50 | Geometry-constructions | Geometric constructions | |

Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||

51 | Geometry | To 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. | |||

52 | Geometry – angles | To 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. | |||

53 | Geometry-constructions | Angle 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. | |||

54 | Geometry-constructions | Circumcentre 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. | |||

55 | Geometry-constructions | Orthocentre 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. | |||

56 | Geometry-quadrilaterals | Midsegments 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. | |||

57 | Geometry – triangles | Triangle inequality theorem | |

Objective: On completion of the lesson the student will understand and use the triangle inequality theorem. | |||

58 | 2-D shapes | Using the prefix to determine polygons | |

59 | 2-D shapes | Spatial properties of quadrilaterals | |

60 | Geometry-quadrilaterals | Quadrilaterals | |

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. | |||

61 | Geometry-quadrilaterals | Classifying Quadrilaterals | |

Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. | |||

62 | Geometry-quadrilaterals | Using 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. | |||

63 | Geometry-quadrilaterals | Proving 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. | |||

64 | Geometry-quadrilaterals | Properties 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. | |||

65 | Geometry-quadrilaterals | Properties 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. | |||

66 | Geometry-quadrilaterals | The 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. | |||

67 | Area | Introducing 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. | |||

68 | Area | Finding 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. | |||

69 | Area | Area 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. | |||

70 | Area | Area 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. | |||

71 | Area | Area 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. | |||

72 | Area | Area 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. | |||

73 | Similar triangles | Similar triangles | |

Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||

74 | Similar triangles | Using similar triangles to calculate lengths | |

Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. | |||

75 | Overlapping triangles | Examples involving overlapping triangles | |

Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles. | |||

76 | Quadratic equations | Introduction to quadratic equations. | |

Objective: On completion of the lesson the student will understand simple quadratic equations. | |||

77 | Quadratic equations | Quadratic equations with factorisation. | |

Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||

78 | Quadratic equations | Solving quadratic equations. | |

Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||

79 | Quadratic equations | Completing the square | |

Objective: On completion of the lesson the student will understand the process of completing the square. | |||

80 | Quadratic equations | Solving quadratic equations by completing the square | |

Objective: On completion of the lesson the student will understand the reasoning behind completing the square. | |||

81 | Quadratic equations | The quadratic formula | |

Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||

82 | Quadratic equations | Problem 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. | |||

83 | Surds | Introducing 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. | |||

84 | Surds | Some 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. | |||

85 | Surds | Simplifying surds | |

Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. | |||

86 | Surds | Creating 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 | |||

87 | Surds | Adding 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. | |||

88 | Surds | Expanding surds | |

Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. | |||

89 | Surds | Binomial 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. | |||

90 | Surds | Conjugate binomials with surds | |

Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds. | |||

91 | Surds | Rationalising the denominator | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds. | |||

92 | Surds | Rationalising binomial denominators | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions. | |||

93 | Trigonometry-ratios | Trigonometric 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 | |||

94 | Trigonometry-ratios | Using 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. | |||

95 | Trigonometry-ratios | Using 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. | |||

96 | Trigonometry-ratios | Using 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. | |||

97 | Trigonometry-ratios | Using 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. | |||

98 | Trigonometry-ratios | Unknown 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. | |||

99 | Trigonometry-compass | Bearings – 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. | |||

100 | Trigonometry-elevation | Angles 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. | |||

101 | Trigonometry-practical | Trigonometric 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. | |||

102 | Circle Geometry | Theorem – 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 | |||

103 | Circle Geometry | Theorem – 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’ | |||

104 | Circle Geometry | Theorem – 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. | |||

105 | Circle Geometry | Theorem – 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. | |||

106 | Circle Geometry | Theorem – 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. | |||

107 | Circle Geometry | Theorem – 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.’ | |||

108 | Circle Geometry | Theorem – 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. | |||

109 | Circle Geometry | Theorem – 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. | |||

110 | Circle Geometry | Theorem – 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. | |||

111 | Circle Geometry | Theorem – 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. | |||

112 | Circle Geometry | Theorem – 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. | |||

113 | Volume | Finding 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. | |||

114 | Volume | Volume 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. | |||

115 | Volume | Volume 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. | |||

116 | Volume | Composite 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. | |||

117 | Surface area | Surface 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. | |||

118 | Surface area | Surface 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. | |||

119 | Surface area | Surface 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. | |||

120 | Surface area | Surface area of pyramids | |

Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. | |||

121 | Surface area | Surface 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 | |||

122 | Surface area | Surface area of composite solids | |

Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. | |||

123 | Exam | Exam – MYP Grade 9 | |

Objective: Exam |

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### MYP Grade 10 - 1 Algebra II and Trig Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – MYP Grade 10 – 1 Algebra II & Trig | |

Objective: Assessment | |||

2 | Coordinate Geometry-the plane | Distance 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. | |||

3 | Coordinate Geometry-midpoint, slope | Mid-point formula | |

Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. | |||

4 | Coordinate Geometry-gradient | Gradient | |

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. | |||

5 | Coordinate Geometry-gradient | Gradient 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. | |||

6 | Coordinate Geometry-straight line | The 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. | |||

7 | Coordinate 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. | |||

8 | Coordinate Geometry-equation of line | General 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. | |||

9 | Coordinate Geometry-intercept | Slope 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. | |||

10 | Coordinate Geometry-point slope | Point 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. | |||

11 | Statistics | Scatter Diagrams | |

Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||

12 | Co-ordinate Geometry-Two point formula | Two 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. | |||

13 | Co-ordinate Geometry-Intercept form | Intercept 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. | |||

14 | Co-ordinate Geometry-Parallel lines equations | Parallel 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. | |||

15 | Co-ordinate Geometry-Perpendicular lines | Perpendicular 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. | |||

16 | Co-ordinate Geometry-Inequalities | Inequalities 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. | |||

17 | Uniform motion | Average speed | |

Objective: On completion of the lesson the student will be able to convert units for speed, distance and time. | |||

18 | Uniform motion | Using subscripted variables | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, distance and time. | |||

19 | Uniform motion | Uniform motion with equal distances | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, equal distances and time. | |||

20 | Uniform motion | Uniform 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. | |||

21 | Uniform motion | Uniform motion with unequal distances | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, unequal distances and time. | |||

22 | Uniform motion | Uniform 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. | |||

23 | Absolute value equations | Absolute 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 | |||

24 | Functions | Definition, 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. | |||

25 | Functions | Notation and evaluations | |

Objective: On completion of the lesson the student will be understand different notations for functions. | |||

26 | Functions | More 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. | |||

27 | Functions | Domain 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. | |||

28 | Functions | Evaluating and graphing piecewise functions | |

Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. | |||

29 | Simultaneous equns | Simultaneous equations | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. | |||

30 | Simultaneous equns | Elimination method | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||

31 | Simultaneous equns | Elimination 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. | |||

32 | Simultaneous equns | Applications 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. | |||

33 | Simultaneous equations | Number 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. | |||

34 | Vectors | 2 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. | |||

35 | Linear systems | Optimal solutions (Stage 2) – Vectors | |

Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions. | |||

36 | Linear systems | Linear systems with matrices (Stage 2) | |

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations. | |||

37 | Linear systems | Row-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. | |||

38 | Algebraic equations | Solving equations containing binomial expressions | |

Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||

39 | Algebraic equations | Equations involving grouping symbols. | |

40 | Algebraic equations | Equations involving fractions. | |

Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||

41 | Algebra- formulae | Equations 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. | |||

42 | Algebra- formulae | Changing 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. | |||

43 | Algebra-inequalities | Solving Inequalities. | |

44 | Absolute value or modulus | Simplifying absolute values | |

45 | Absolute value or modulus | Solving for the variable | |

Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value. | |||

46 | Absolute value or modulus | Solving and graphing inequalities | |

47 | Surds | Introducing 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. | |||

48 | Surds | Some 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. | |||

49 | Surds | Simplifying surds | |

Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. | |||

50 | Surds | Creating 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 | |||

51 | Surds | Adding 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. | |||

52 | Surds | Expanding surds | |

Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. | |||

53 | Surds | Binomial 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. | |||

54 | Functions and graphs | Quadratic 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. | |||

55 | Functions and graphs | Graphing 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. | |||

56 | Graphing roots | Graphing 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. | |||

57 | Coordinate geometry | Solve 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. | |||

58 | Graphing binomials | Binomial products. | |

Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression. | |||

59 | Graphing binomials | Binomial 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. | |||

60 | Graphing binomials | Binomial products [non-monic]. | |

Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. | |||

61 | Squaring binomial | Squaring a binomial. [monic] | |

Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial. | |||

62 | Squaring binomial | Squaring a binomial [non-monic]. | |

Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. | |||

63 | Factorising | Expansions leading to the difference of two squares | |

Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. | |||

64 | Algebraic expressions-products | Products in simplification of algebraic expressions | |

Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. | |||

65 | Algebraic expressions-larger expansions | Algebraic Expressions – Larger expansions. | |

Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. | |||

66 | Algebra-highest common factor | Highest 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. | |||

67 | Factors by grouping | Factors 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. | |||

68 | Difference of 2 squares | Difference of two squares | |

Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. | |||

69 | Common fact and diff | Common 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. | |||

70 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. | |

Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive. | |||

71 | Factorising quads | Factorising 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. | |||

72 | Factorising quads | Factorising 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. | |||

73 | Factorising quads | Factorising 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. | |||

74 | Factorising quads | Factorisation of non-monic quadratic trinomials | |

Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. | |||

75 | Factorising quads | Factorisation 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. | |||

76 | Quadratic equations | Introduction to quadratic equations. | |

Objective: On completion of the lesson the student will understand simple quadratic equations. | |||

77 | Quadratic equations | Quadratic equations with factorisation. | |

Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||

78 | Quadratic equations | Solving quadratic equations. | |

Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||

79 | Quadratic equations | Completing the square | |

Objective: On completion of the lesson the student will understand the process of completing the square. | |||

80 | Quadratic equations | Solving quadratic equations by completing the square | |

Objective: On completion of the lesson the student will understand the reasoning behind completing the square. | |||

81 | Quadratic equations | The quadratic formula | |

Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||

82 | Quadratic equations | Problem 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. | |||

83 | Quadratic equations | Solving 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.. | |||

84 | Motion under acceleration | Motion 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. | |||

85 | Motion under acceleration | Introducing initial velocity | |

Objective: On completion of the lesson the student will use equations of motion that include uniform acceleration and an initial velocity. | |||

86 | Algebra-polynomials | Introduction 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. | |||

87 | Algebra-polynomials | The 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. | |||

88 | Algebra-polynomials | Polynomials and long division. | |

Objective: On completion of the lesson the student will understand the long division process with polynomials. | |||

89 | Remainder theorem | The remainder theorem. | |

Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied. | |||

90 | Remainder theorem | More 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. | |||

91 | Factor theorem | The 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. | |||

92 | Factor theorem | More 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. | |||

93 | Factor theorem | Complete 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. | |||

94 | Polynomial equations | Polynomial equations | |

Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms. | |||

95 | Graphs, polynomials | Graphs 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. | |||

96 | Statistics | Frequency distribution table | |

97 | Statistics | Frequency histograms and polygons | |

98 | Statistics | Relative frequency | |

99 | Statistics | The range. | |

100 | Statistic-probability | The mode | |

101 | Statistic-probability | The mean | |

102 | Statistic-probability | The median | |

103 | Statistic-probability | Cumulative frequency | |

Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||

104 | Statistic-probability | Calculating 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. | |||

105 | Statistics – grouped data | Calculating 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. | |||

106 | Statistics using a calculator | Statistics 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. | |||

107 | Statistics – Range and dispersion | Range 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. | |||

108 | Statistics – Spread | Measures 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. | |||

109 | Statistics – Standard deviation | Standard 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. | |||

110 | Statistics – Standard deviation | Normal 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. | |||

111 | Statistics – Interquartile range | Measures 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 | |||

112 | Statistics | Stem 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. | |||

113 | Rules for indices/exponents | Adding 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. | |||

114 | Rules for indices/exponents | Subtracting 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. | |||

115 | Rules for indices/exponents | Multiplying 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. | |||

116 | Rules for indices/exponents | Multiplying 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. | |||

117 | Rules for indices/exponents | Terms 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. | |||

118 | Rules for indices/exponents | Negative Indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||

119 | Fractional indices/exponents | Fractional indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||

120 | Fractional indices/exponents | Complex fractions as indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. | |||

121 | Graphing-polynomials | Graphing 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. | |||

122 | Graphing-polynomials | General 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. | |||

123 | Graphing-cubic curves | Graphing 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. | |||

124 | Rect.hyperbola | The 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. | |||

125 | Exponential function | The 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. | |||

126 | Log functions | Logarithmic 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 | |||

127 | Logarithms-Power of 2 | Powers 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. | |||

128 | Logarithms-Equations and logs | Equations 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. | |||

129 | Logarithms-Equations and logs | Equations 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. | |||

130 | Logarithms-Log laws | Laws of logarithms. | |

Objective: On completion of the lesson the student will be familiar with 5 logarithm laws. | |||

131 | Logarithms-Log laws expansion | Using 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. | |||

132 | Logarithms-Log laws simplifying | Using 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. | |||

133 | Logarithms-Log laws numbers | Using 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. | |||

134 | Logarithms-Equations and logs | Equations involving logarithms. | |

Objective: On completion of the lesson the student will be able to solve equations with log terms. | |||

135 | Logarithms-Logs to solve equations | Using 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. | |||

136 | Logarithms-Change base formula | Change 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. | |||

137 | Logarithms-Graph-log curve | The 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. | |||

138 | Logarithms-Log curves | Working with log curves. | |

Objective: On completion of the lesson the student will be able to solve problems with log curves | |||

139 | Sequences and Series-Geometric means | Geometric 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. | |||

140 | Sequences and Series-Sum of gp | The 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). | |||

141 | Sequences and Series-Sigma notation | Sigma notation | |

Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates. | |||

142 | Sequences and Series-Sum-infinity | Limiting 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. | |||

143 | Sequences and Series-Recurring decimal infinity | Recurring 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. | |||

144 | Sequences and Series-Compound interest | Compound 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. | |||

145 | Sequences and Series-Superannuation | Superannuation. | |

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. | |||

146 | Sequences and Series-Time payments | Time 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. | |||

147 | Sequences and Series | Applications of arithmetic sequences | |

Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series. | |||

148 | Functions | Functions combinations | |

Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. | |||

149 | Functions | Composition of functions | |

Objective: On completion of the lesson the student will understand composition of functions or a function of a function. | |||

150 | Functions | Inverse 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. | |||

151 | Functions | Rational 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. | |||

152 | Functions | Rational 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. | |||

153 | Functions | Parametric 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. | |||

154 | Functions | Polynomial 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. | |||

155 | Functions | Parametric 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. | |||

156 | Algebraic fractions | Simplifying 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. | |||

157 | Algebra-negative indices | Algebraic 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. | |||

158 | Factorisation | Factorisation 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. | |||

159 | Algebraic fractions-binomial | Cancelling binomial factors in algebraic fractions. | |

Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions. | |||

160 | Algebraic fractions | Simplifying algebraic fractions. | |

Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point. | |||

161 | Statistic-probability | Probability of Simple Events | |

162 | Statistic-probability | Rolling 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. | |||

163 | Statistic-probability | Experimental probability | |

Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||

164 | Statistic-probability | Tree 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. | |||

165 | Statistic-probability | Tree 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. | |||

166 | Statistic-probability | The 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. | |||

167 | Statistic-probability | P[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. | |||

168 | Statistic-probability | Binomial 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. | |||

169 | Statistic-probability | Binomial 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 | |||

170 | Statistic-probability | Counting 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. | |||

171 | Statistic-probability | Unordered 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. | |||

172 | Trigonometry-ratios | Trigonometric 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 | |||

173 | Trigonometry-ratios | Using 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. | |||

174 | Trigonometry-ratios | Using 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. | |||

175 | Trigonometry-ratios | Using 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. | |||

176 | Trigonometry-ratios | Using 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. | |||

177 | Trigonometry-ratios | Unknown 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. | |||

178 | Trigonometry-compass | Bearings – 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. | |||

179 | Trigonometry-elevation | Angles 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. | |||

180 | Trigonometry-practical | Trigonometric 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. | |||

181 | Trigonometry-ratios | Using 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. | |||

182 | Trigonometry- ratios | Using 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. | |||

183 | Trigonometry-exact ratios | Trigonometric 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. | |||

184 | Trigonometry-cosine rule | The 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. | |||

185 | Trigonometry-cosine rule | The 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. | |||

186 | Trigonometry-sine rule | The 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. | |||

187 | Trigonometry-sine rule | The 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. | |||

188 | Trigonometry-areas | The 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. | |||

189 | Trig-reciprocal ratios | Reciprocal 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. | |||

190 | Trig complementary angles | Complementary 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. | |||

191 | Trig identities | Trigonometric 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. | |||

192 | Trig larger angles | Angles 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. | |||

193 | Trig larger angles | Trigonometric 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. | |||

194 | Graph sine | Graphing 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. | |||

195 | Graph cosine | Graphing 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. | |||

196 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |

Objective: On completion of the lesson the student will know how to recognise and draw the tan curve. | |||

197 | Graph reciprocals | Graphing 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. | |||

198 | Trig larger angles | Using 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. | |||

199 | Trig equations | Solving trigonometric equations – Type I. | |

Objective: On completion of the lesson the student will solve simple trig equations with restricted domains. | |||

200 | Trig equations | Solving trigonometric equations – Type II. | |

Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains. | |||

201 | Trig equations | Solving trigonometric equations – Type III. | |

Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains. | |||

202 | Polar coordinates | Plotting 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. | |||

203 | Polar coordinates | Converting 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. | |||

204 | Exam | Exam – MYP Grade 10 – 1 Algebra II & Trig | |

Objective: Exam |

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### MYP Grade 10 - 2 Algebra II and Trig Hons Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – MYP Grade 10 – 2 Algebra II & Trig Hons | |

Objective: Assessment | |||

2 | Trigonometry-ratios | Using 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. | |||

3 | Trigonometry-ratios | Using 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. | |||

4 | Trigonometry-ratios | Using 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. | |||

5 | Trigonometry-ratios | Unknown 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. | |||

6 | Trigonometry-practical | Trigonometric 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. | |||

7 | Trigonometry-ratios | Using 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. | |||

8 | Trigonometry- ratios | Using 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. | |||

9 | Trigonometry-cosine rule | The 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. | |||

10 | Trigonometry-sine rule | The 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. | |||

11 | Trigonometry-sine rule | The 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. | |||

12 | Trigonometry-areas | The 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. | |||

13 | Number theory – sets | Number 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. | |||

14 | Number theory – operations | Properties 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. | |||

15 | Number theory – equations | Transformations 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. | |||

16 | Fractions | Subtracting fractions from whole numbers | |

17 | Fractions | Adding and subtracting fractions with the same denominator | |

18 | Fractions | Adding and subtracting fractions with different denominators | |

19 | Fractions | Multiplying fractions by whole numbers | |

20 | Fractions | Fractions of whole numbers | |

21 | Fractions | Multiplying fractions | |

22 | Fractions | Multiplying mixed numbers (mixed numerals) | |

23 | Fractions | Finding reciprocals of fractions and mixed numbers (mixed numerals) | |

24 | Fractions | Dividing fractions | |

Objective: On completion of the lesson the student will be able to divide fractions. | |||

25 | Fractions | Dividing mixed numbers (mixed numerals) | |

Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). | |||

26 | Rules properties | Using Order of Operation procedures (BIDMAS) with Fractions | |

27 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

28 | Percentages | Introduction 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. | |||

29 | Percentages | Changing 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. | |||

30 | Percentages | Changing percentages to fractions and decimals | |

31 | Percentages | One quantity as a percentage of another | |

32 | Surds | Introducing surds | |

33 | Surds | Some rules for the operations with surds | |

34 | Surds | Simplifying surds | |

35 | Surds | Creating entire surds | |

36 | Surds | Adding and subtracting like surds | |

37 | Surds | Expanding surds | |

38 | Algebraic equations | Solving equations containing addition and subtraction | |

39 | Algebraic equations | Solving equations containing multiplication and division | |

40 | Algebraic equations | Solving two step equations | |

Objective: On completion of the lesson the student will be able to solve two step equations. | |||

41 | Algebraic equations | Solving equations containing binomial expressions | |

Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||

42 | Algebraic equations | Equations involving grouping symbols. | |

43 | Algebraic equations | Equations involving fractions. | |

Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||

44 | Algebra- formulae | Equations resulting from substitution into formulae. | |

45 | Algebra- formulae | Changing 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. | |||

46 | Algebra-inequalities | Solving Inequalities. | |

47 | Algebra-factorising | Simplifying easy algebraic fractions. | |

Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. | |||

48 | Algebraic fractions | Simplifying 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. | |||

49 | Algebra-negative indices | Algebraic 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. | |||

50 | Factorisation | Factorisation 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. | |||

51 | Algebraic fractions-binomial | Cancelling binomial factors in algebraic fractions. | |

Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions. | |||

52 | Absolute value or modulus | Simplifying absolute values | |

53 | Absolute value or modulus | Solving for the variable | |

Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value. | |||

54 | Absolute value or modulus | Solving and graphing inequalities | |

55 | Algebra-highest common factor | Highest 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. | |||

56 | Factors by grouping | Factors 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. | |||

57 | Difference of 2 squares | Difference of two squares | |

Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. | |||

58 | Common fact and diff | Common 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. | |||

59 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. | |

Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive. | |||

60 | Factorising quads | Factorising 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. | |||

61 | Factorising quads | Factorising 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. | |||

62 | Factorising quads | Factorising 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. | |||

63 | Factorising quads | Factorisation of non-monic quadratic trinomials | |

Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. | |||

64 | Factorising quads | Factorisation 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. | |||

65 | Sum/diff 2 cubes | Sum 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. | |||

66 | Algebraic fractions | Simplifying algebraic fractions. | |

Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point. | |||

67 | Quadratic equations | Introduction to quadratic equations. | |

Objective: On completion of the lesson the student will understand simple quadratic equations. | |||

68 | Quadratic equations | Quadratic equations with factorisation. | |

69 | Quadratic equations | Solving quadratic equations. | |

70 | Quadratic equations | Completing the square | |

71 | Quadratic equations | Solving quadratic equations by completing the square | |

72 | Quadratic equations | The quadratic formula | |

Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||

73 | Quadratic equations | Problem solving with quadratic equations | |

74 | Quadratic equations | Solving 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.. | |||

75 | Algebra-polynomials | Introduction 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. | |||

76 | Algebra-polynomials | The 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. | |||

77 | Rules for indices/exponents | Adding 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. | |||

78 | Rules for indices/exponents | Subtracting 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. | |||

79 | Rules for indices/exponents | Multiplying 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. | |||

80 | Rules for indices/exponents | Multiplying 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. | |||

81 | Rules for indices/exponents | Terms 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. | |||

82 | Rules for indices/exponents | Negative Indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||

83 | Fractional indices/exponents | Fractional indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||

84 | Fractional indices/exponents | Complex fractions as indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. | |||

85 | Graphing-polynomials | Graphing 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. | |||

86 | Graphing-polynomials | General 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. | |||

87 | Graphing-cubic curves | Graphing 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. | |||

88 | Absolute value equations | Absolute 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 | |||

89 | Rect.hyperbola | The 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. | |||

90 | Exponential function | The 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. | |||

91 | Log functions | Logarithmic 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 | |||

92 | Functions | Definition, 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. | |||

93 | Functions | Notation and evaluations | |

Objective: On completion of the lesson the student will be understand different notations for functions. | |||

94 | Functions | More 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. | |||

95 | Functions | Domain 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. | |||

96 | Functions | Evaluating and graphing piecewise functions | |

Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. | |||

97 | Functions | Functions combinations | |

Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. | |||

98 | Functions | Composition of functions | |

Objective: On completion of the lesson the student will understand composition of functions or a function of a function. | |||

99 | Functions | Inverse 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. | |||

100 | Circle Geometry | Theorem – 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 | |||

101 | Circle Geometry | Theorem – 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’ | |||

102 | Circle Geometry | Theorem – 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. | |||

103 | Circle Geometry | Theorem – 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. | |||

104 | Circle Geometry | Theorem – 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. | |||

105 | Circle Geometry | Theorem – 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.’ | |||

106 | Circle Geometry | Theorem – 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. | |||

107 | Circle Geometry | Theorem – 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. | |||

108 | Circle Geometry | Theorem – 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. | |||

109 | Circle Geometry | Theorem – 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. | |||

110 | Circle Geometry | Theorem – 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. | |||

111 | Trigonometry-exact ratios | Trigonometric 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. | |||

112 | Trigonometry-cosine rule | The 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. | |||

113 | Trig-reciprocal ratios | Reciprocal 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. | |||

114 | Trig complementary angles | Complementary 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. | |||

115 | Trig identities | Trigonometric 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. | |||

116 | Trig larger angles | Angles 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. | |||

117 | Trig larger angles | Trigonometric 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. | |||

118 | Graph sine | Graphing 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. | |||

119 | Graph cosine | Graphing 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. | |||

120 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |

Objective: On completion of the lesson the student will know how to recognise and draw the tan curve. | |||

121 | Graph reciprocals | Graphing 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. | |||

122 | Trig larger angles | Using 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. | |||

123 | Trig equations | Solving trigonometric equations – Type I. | |

Objective: On completion of the lesson the student will solve simple trig equations with restricted domains. | |||

124 | Statistics | Frequency distribution table | |

125 | Statistics | Frequency histograms and polygons | |

126 | Statistics | Relative frequency | |

127 | Statistics | The range. | |

128 | Statistic-probability | The mode | |

129 | Statistic-probability | The mean | |

130 | Statistic-probability | The median | |

131 | Statistic-probability | Cumulative frequency | |

Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||

132 | Statistic-probability | Calculating 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. | |||

133 | Statistic-probability | Probability of Simple Events | |

134 | Statistic-probability | Rolling 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. | |||

135 | Statistic-probability | Experimental probability | |

Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||

136 | Statistic-probability | Tree 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. | |||

137 | Statistic-probability | Tree 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. | |||

138 | Statistic-probability | The 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. | |||

139 | Statistic-probability | P[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. | |||

140 | Statistic-probability | Binomial 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. | |||

141 | Sequences and Series | General 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. | |||

142 | Sequences and Series | Finding 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. | |||

143 | Arithmetic Progression | The 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. | |||

144 | Arithmetic Progression | Finding 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. | |||

145 | Arithmetic Progression | Given 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 | |||

146 | Arithmetic Progression | Arithmetic 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. | |||

147 | Arithmetic Progression | The 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. | |||

148 | Geometric Progression | The 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. | |||

149 | Geometric Progression | Finding 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. | |||

150 | Geometric Progression | Given 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. | |||

151 | Exam | Exam – MYP Grade 10 – 2 Algebra II & Trig Hons | |

Objective: Exam |

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### MYP Grade 10 - 3 Pre Calculus Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – MYP Grade 10 – 3 Pre Calculus | |

Objective: Assessment | |||

2 | Coordinate Geometry-the plane | Distance 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. | |||

3 | Coordinate Geometry-midpoint, slope | Mid-point formula | |

Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. | |||

4 | Coordinate Geometry-gradient | Gradient | |

5 | Coordinate Geometry-gradient | Gradient formula. | |

6 | Coordinate Geometry-straight line | The straight line. | |

7 | Coordinate Geometry-slope, etc. | Lines through the origin. | |

8 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |

9 | Coordinate Geometry-intercept | Slope intercept form of a line. | |

10 | Coordinate Geometry-point slope | Point 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. | |||

11 | Co-ordinate Geometry-Two point formula | Two 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. | |||

12 | Co-ordinate Geometry-Intercept form | Intercept 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. | |||

13 | Co-ordinate Geometry-Parallel lines equations | Parallel 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. | |||

14 | Co-ordinate Geometry-Perpendicular lines | Perpendicular 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. | |||

15 | Simultaneous equns | Simultaneous equations | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. | |||

16 | Simultaneous equns | Elimination method | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||

17 | Simultaneous equns | Elimination 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. | |||

18 | Simultaneous equns | Applications 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. | |||

19 | Matrices | Basic concepts – Matrices | |

Objective: On completion of the lesson the student will have had an introduction to matrices | |||

20 | Matrices | Addition 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. | |||

21 | Matrices | Scalar matrix multiplication | |

Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix. | |||

22 | Matrices | Multiplication 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. | |||

23 | Matrices | Translation 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. | |||

24 | Matrices | Translation 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. | |||

25 | Transformations | Special 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. | |||

26 | Vectors | Vectors | |

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. | |||

27 | Simultaneous equations | Number 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. | |||

28 | Vectors | 2 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. | |||

29 | Linear systems | Optimal solutions (Stage 2) – Vectors | |

Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions. | |||

30 | Linear systems | Linear systems with matrices (Stage 2) | |

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations. | |||

31 | Linear systems | Row-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. | |||

32 | Algebra- formulae | Changing the subject of the formula. | |

33 | Algebra-inequalities | Solving Inequalities. | |

34 | Algebra-factorising | Simplifying easy algebraic fractions. | |

Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. | |||

35 | Algebraic fractions | Simplifying algebraic fractions using the index laws. | |

36 | Algebra-negative indices | Algebraic fractions resulting in negative indices. | |

37 | Factorisation | Factorisation of algebraic fractions including binomials. | |

38 | Algebraic fractions-binomial | Cancelling binomial factors in algebraic fractions. | |

39 | Absolute value or modulus | Simplifying absolute values | |

40 | Absolute value or modulus | Solving for the variable | |

Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value. | |||

41 | Absolute value or modulus | Solving and graphing inequalities | |

42 | Co-ordinate Geometry-Inequalities | Inequalities 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. | |||

43 | Calculus | Limits | |

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. | |||

44 | Calculus=1st prin | Differentiation 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. | |||

45 | Calculus=1st prin | Differentiation 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. | |||

46 | Calculus-differential, integ | Meaning 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. | |||

47 | Calculus-differential, integ | Function 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. | |||

48 | Calculus-differential, integ | Increasing, 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. | |||

49 | Calculus | First 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. | |||

50 | Graphing-polynomials | Graphing 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. | |||

51 | Graphing-polynomials | General 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. | |||

52 | Graphing-cubic curves | Graphing 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. | |||

53 | Absolute value equations | Absolute 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 | |||

54 | Rect.hyperbola | The 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. | |||

55 | Functions | Definition, 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. | |||

56 | Functions | Notation and evaluations | |

Objective: On completion of the lesson the student will be understand different notations for functions. | |||

57 | Functions | More 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. | |||

58 | Functions | Domain 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. | |||

59 | Functions | Evaluating and graphing piecewise functions | |

Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. | |||

60 | Functions | Functions combinations | |

Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. | |||

61 | Functions | Composition of functions | |

Objective: On completion of the lesson the student will understand composition of functions or a function of a function. | |||

62 | Functions | Inverse 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. | |||

63 | Functions | Rational 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. | |||

64 | Functions | Rational 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. | |||

65 | Functions | Polynomial 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. | |||

66 | Geometry-parabola | The 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. | |||

67 | Functions and graphs | Quadratic 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. | |||

68 | Functions and graphs | Graphing 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. | |||

69 | Graphing roots | Graphing 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. | |||

70 | Coordinate geometry | Solve 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. | |||

71 | Difference of 2 squares | Difference of two squares | |

72 | Common fact and diff | Common factor and the difference of two squares | |

73 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. | |

74 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |

75 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |

76 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |

77 | Factorising quads | Factorisation of non-monic quadratic trinomials | |

78 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method | |

79 | Quadratic equations | Introduction to quadratic equations. | |

Objective: On completion of the lesson the student will understand simple quadratic equations. | |||

80 | Quadratic equations | Quadratic equations with factorisation. | |

81 | Quadratic equations | Solving quadratic equations. | |

82 | Quadratic equations | Completing the square | |

83 | Quadratic equations | Solving quadratic equations by completing the square | |

84 | Quadratic equations | The quadratic formula | |

Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||

85 | Quadratic equations | Problem solving with quadratic equations | |

86 | Quadratic equations | Solving simultaneous quadratic equations graphically | |

87 | Algebra-polynomials | Introduction 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. | |||

88 | Algebra-polynomials | The 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. | |||

89 | Algebra-polynomials | Polynomials and long division. | |

Objective: On completion of the lesson the student will understand the long division process with polynomials. | |||

90 | Remainder theorem | The remainder theorem. | |

Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied. | |||

91 | Remainder theorem | More 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. | |||

92 | Factor theorem | The 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. | |||

93 | Factor theorem | More 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. | |||

94 | Factor theorem | Complete 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. | |||

95 | Logarithms-Complex numbers | Imaginary 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. | |||

96 | Logarithms-Complex numbers | Complex 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. | |||

97 | Logarithms-Complex numbers | Plotting 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. | |||

98 | Logarithms-Complex numbers | Absolute value | |

Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers | |||

99 | Logarithms-Complex numbers | Trigonometric 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. | |||

100 | Logarithms-Complex numbers | Multiplication 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. | |||

101 | Logarithms-Complex numbers | DeMoivre’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. | |||

102 | Logarithms-Complex numbers | The 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. | |||

103 | Logarithms-Complex numbers | Fundamental 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. | |||

104 | Statistic-probability | Binomial 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. | |||

105 | Statistic-probability | Binomial 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 | |||

106 | Statistic-probability | Counting 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. | |||

107 | Statistic-probability | Unordered 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. | |||

108 | Statistics – grouped data | Calculating 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. | |||

109 | Statistics using a calculator | Statistics 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. | |||

110 | Statistics – Range and dispersion | Range 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. | |||

111 | Statistics – Spread | Measures 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. | |||

112 | Statistics – Standard deviation | Standard 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. | |||

113 | Statistics – Standard deviation | Normal 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. | |||

114 | Statistics – Interquartile range | Measures 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 | |||

115 | Statistics | Stem 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. | |||

116 | Statistics | Scatter Diagrams | |

Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||

117 | Trigonometry-elevation | Angles 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. | |||

118 | Trigonometry-practical | Trigonometric ratios in practical situations. | |

119 | Trigonometry-ratios | Using 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. | |||

120 | Trigonometry- ratios | Using 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. | |||

121 | Trigonometry-exact ratios | Trigonometric 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. | |||

122 | Trigonometry-cosine rule | The 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. | |||

123 | Trigonometry-cosine rule | The 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. | |||

124 | Trigonometry-sine rule | The 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. | |||

125 | Trigonometry-sine rule | The 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. | |||

126 | Trigonometry-areas | The 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. | |||

127 | Trig-reciprocal ratios | Reciprocal 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. | |||

128 | Trig complementary angles | Complementary 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. | |||

129 | Trig identities | Trigonometric 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. | |||

130 | Trig larger angles | Angles 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. | |||

131 | Trig larger angles | Trigonometric 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. | |||

132 | Graph sine | Graphing 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. | |||

133 | Graph cosine | Graphing 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. | |||

134 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |

Objective: On completion of the lesson the student will know how to recognise and draw the tan curve. | |||

135 | Graph reciprocals | Graphing 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. | |||

136 | Trig larger angles | Using 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. | |||

137 | Trig equations | Solving trigonometric equations – Type I. | |

Objective: On completion of the lesson the student will solve simple trig equations with restricted domains. | |||

138 | Trig equations | Solving trigonometric equations – Type II. | |

Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains. | |||

139 | Trig equations | Solving trigonometric equations – Type III. | |

Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains. | |||

140 | Polar coordinates | Plotting 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. | |||

141 | Polar coordinates | Converting 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. | |||

142 | Polar coordinates | Write 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. | |||

143 | Conic sections | Introduction 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. | |||

144 | Conic sections | The parabola x. = 4ay | |

Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form. | |||

145 | Conic sections | Circles | |

Objective: On completion of the lesson the student will identify the radius of a circle given in standard form. | |||

146 | Conic sections | Ellipses | |

Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse. | |||

147 | Conic sections | Hyperbola | |

Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola. | |||

148 | Sequences and Series | General 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. | |||

149 | Sequences and Series | Finding 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. | |||

150 | Arithmetic Progression | The 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. | |||

151 | Arithmetic Progression | Finding 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. | |||

152 | Arithmetic Progression | Given 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 | |||

153 | Arithmetic Progression | Arithmetic 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. | |||

154 | Arithmetic Progression | The 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. | |||

155 | Geometric Progression | The 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. | |||

156 | Geometric Progression | Finding 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. | |||

157 | Geometric Progression | Given 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. | |||

158 | Sequences and Series-Geometric means | Geometric 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. | |||

159 | Sequences and Series-Sum of gp | The 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). | |||

160 | Sequences and Series-Sigma notation | Sigma notation | |

Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates. | |||

161 | Sequences and Series-Sum-infinity | Limiting 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. | |||

162 | Sequences and Series-Recurring decimal infinity | Recurring 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. | |||

163 | Sequences and Series | Applications of arithmetic sequences | |

Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series. | |||

164 | Exam | Exam – MYP Grade 10 – 3 Pre Calculus | |

Objective: Exam |

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### Topic 1 - The Scientific Calculator Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study 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. | |||

2 | Trigonometry-ratios | Using 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. | |||

3 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |

4 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |

5 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |

6 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |

7 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |

8 | Statistics using a calculator | Statistics 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. | |||

9 | Exam | Exam – Topic 1 – The Scientific Calculator | |

Objective: Exam |

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### Topic 2 - Number and Algebra Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 2 – Number & Algebra | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Number theory – sets | Number 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. | |||

3 | Number theory – operations | Properties 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. | |||

4 | Number theory – equations | Transformations 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. | |||

5 | Significant figures | Significant 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. | |||

6 | Scientific notation | Scientific notation with larger numbers | |

Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||

7 | Scientific notation | Scientific 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. | |||

8 | Scientific notation | Changing 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. | |||

9 | Length | Problems with length. | |

Objective: On completion of the lesson the student will be able to solve problems with length. | |||

10 | Mass | Problems with mass. | |

Objective: On completion of the lesson the student will be able to solve problems with mass. | |||

11 | Sequences and Series | General 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. | |||

12 | Sequences and Series | Finding 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. | |||

13 | Arithmetic Progression | The 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. | |||

14 | Arithmetic Progression | Finding 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. | |||

15 | Arithmetic Progression | Given 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 | |||

16 | Arithmetic Progression | Arithmetic 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. | |||

17 | Arithmetic Progression | The 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. | |||

18 | Geometric Progression | The 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. | |||

19 | Geometric Progression | Finding 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. | |||

20 | Geometric Progression | Given 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. | |||

21 | Sequences and Series-Sum of gp | The 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). | |||

22 | Sequences and Series | Applications of arithmetic sequences | |

Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series. | |||

23 | Sequences and Series-Geometric means | Geometric 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. | |||

24 | Algebraic expressions | Algebraic expressions. | |

25 | Algebraic expressions | Substitution into algebraic expressions. | |

26 | Algebraic expressions | Directed numbers: addition and subtraction. | |

27 | Algebraic expressions | Directed numbers: multiplication and division. | |

28 | Algebraic expressions | Simplifying algebraic expressions: adding like terms. | |

29 | Algebraic expressions | Simplifying algebraic Expressions: subtracting like terms. | |

30 | Algebraic expressions | Simplifying Algebraic expressions: combining addition and subtraction. | |

31 | Algebraic expressions | Simplifying 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. | |||

32 | Algebraic expressions | Simplifying algebraic expressions: division | |

Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. | |||

33 | Algebraic expressions | Expanding 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. | |||

34 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | |

Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. | |||

35 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||

36 | Algebraic equations | Solving equations containing addition and subtraction | |

37 | Algebraic equations | Solving equations containing multiplication and division | |

38 | Algebraic equations | Solving two step equations | |

Objective: On completion of the lesson the student will be able to solve two step equations. | |||

39 | Algebraic equations | Solving equations containing binomial expressions | |

Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||

40 | Algebraic equations | Equations involving grouping symbols. | |

41 | Algebraic equations | Equations involving fractions. | |

Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||

42 | Algebra- formulae | Equations resulting from substitution into formulae. | |

43 | Algebra- formulae | Changing the subject of the formula. | |

44 | Algebra-inequalities | Solving Inequalities. | |

45 | Algebra-factorising | Simplifying easy algebraic fractions. | |

46 | Algebraic fractions | Simplifying algebraic fractions using the index laws. | |

47 | Algebra-negative indices | Algebraic fractions resulting in negative indices. | |

48 | Factorisation | Factorisation of algebraic fractions including binomials. | |

49 | Algebraic fractions-binomial | Cancelling binomial factors in algebraic fractions. | |

50 | Absolute value or modulus | Simplifying absolute values | |

51 | Absolute value or modulus | Solving for the variable | |

52 | Absolute value or modulus | Solving and graphing inequalities | |

53 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |

54 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |

55 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |

56 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |

57 | Rules for indices/exponents | Terms raised to the power of zero | |

58 | Rules for indices/exponents | Negative Indices | |

59 | Fractional indices/exponents | Fractional indices | |

60 | Fractional indices/exponents | Complex fractions as indices | |

61 | Functions and graphs | Quadratic 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. | |||

62 | Graphing binomials | Binomial products. | |

Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression. | |||

63 | Graphing binomials | Binomial 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. | |||

64 | Graphing binomials | Binomial products [non-monic]. | |

Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. | |||

65 | Squaring binomial | Squaring a binomial. [monic] | |

Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial. | |||

66 | Squaring binomial | Squaring a binomial [non-monic]. | |

Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. | |||

67 | Factorising | Expansions leading to the difference of two squares | |

Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. | |||

68 | Algebraic expressions-products | Products in simplification of algebraic expressions | |

Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. | |||

69 | Algebraic expressions-larger expansions | Algebraic Expressions – Larger expansions. | |

Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. | |||

70 | Algebra-highest common factor | Highest common factor. | |

71 | Factors by grouping | Factors by grouping. | |

72 | Difference of 2 squares | Difference of two squares | |

73 | Common fact and diff | Common factor and the difference of two squares | |

74 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. | |

75 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |

76 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |

77 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |

78 | Factorising quads | Factorisation of non-monic quadratic trinomials | |

79 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method | |

80 | Sum/diff 2 cubes | Sum 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. | |||

81 | Algebraic fractions | Simplifying algebraic fractions. | |

Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point. | |||

82 | Quadratic equations | Introduction to quadratic equations. | |

Objective: On completion of the lesson the student will understand simple quadratic equations. | |||

83 | Quadratic equations | Quadratic equations with factorisation. | |

84 | Quadratic equations | Solving quadratic equations. | |

85 | Quadratic equations | Completing the square | |

86 | Quadratic equations | Solving quadratic equations by completing the square | |

87 | Quadratic equations | The quadratic formula | |

Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||

88 | Quadratic equations | Problem solving with quadratic equations | |

89 | Quadratic equations | Solving simultaneous quadratic equations graphically | |

90 | Exam | Exam – Topic 2 – Number & Algebra | |

Objective: Exam |

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### Topic 3 - Sets Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 3 – Sets | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Number theory – sets | Number 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. | |||

3 | Logic | Inductive and deductive reasoning | |

Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. | |||

4 | Logic | Definition and use of counter examples | |

Objective: On completion of this lesson the student will be able to create counter examples to statements. | |||

5 | Logic | Mathematical induction | |

Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series. | |||

6 | Logic | Conditional statements (converse, inverse and contrapositive) (Stage 2) | |

Objective: On completion of the lesson the student will be able to form related conditional statements. | |||

7 | Logic | Indirect 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. | |||

8 | Statistic-probability | Tree 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. | |||

9 | Statistic-probability | Tree 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. | |||

10 | Statistic-probability | The 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. | |||

11 | Statistic-probability | Probability of Simple Events | |

12 | Statistic-probability | Rolling a pair of dice | |

13 | Statistic-probability | Experimental probability | |

Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||

14 | Statistic-probability | P[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. | |||

15 | Exam | Exam – Topic 3 – Sets | |

Objective: Exam |

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### Topic 4 - Functions and Graphs Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 4 – Functions & Graphs | |

2 | Functions | Definition, domain and range | |

3 | Functions | Notation and evaluations | |

4 | Functions | More on domain and range | |

5 | Functions | Domain and range from graphical representations | |

6 | Functions | Evaluating and graphing piecewise functions | |

7 | Functions | Functions combinations | |

8 | Functions | Composition of functions | |

9 | Functions and graphs | Graphing 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. | |||

10 | Graphing roots | Graphing 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. | |||

11 | Coordinate geometry | Solve 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. | |||

12 | Functions | Inverse functions | |

13 | Functions | Rational 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. | |||

14 | Functions | Rational 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. | |||

15 | Functions | Parametric 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. | |||

16 | Functions | Polynomial 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. | |||

17 | Functions | Parametric 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. | |||

18 | Exponential function | The exponential function. | |

19 | Log functions | Logarithmic 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 | |||

20 | Trigonometry-ratios | Trigonometric 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 | |||

21 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |

22 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |

23 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |

24 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |

25 | Trigonometry-compass | Bearings – 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. | |||

26 | Trigonometry-elevation | Angles of elevation and depression. | |

27 | Trigonometry-practical | Trigonometric ratios in practical situations. | |

28 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |

29 | Trigonometry- ratios | Using the trigonometric ratios to find an angle in a right-angled triangle. | |

30 | Trigonometry-exact ratios | Trigonometric ratios of 30., 45. and 60. – exact ratios. | |

31 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |

32 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |

33 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |

34 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |

35 | Trigonometry-areas | The area formula | |

36 | Coordinate Geometry-gradient | Gradient | |

37 | Coordinate Geometry-gradient | Gradient formula. | |

38 | Coordinate Geometry-straight line | The straight line. | |

39 | Coordinate Geometry-slope, etc. | Lines through the origin. | |

40 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |

41 | Coordinate Geometry-intercept | Slope intercept form of a line. | |

42 | Coordinate Geometry-point slope | Point slope form of a line | |

43 | Exam | Exam – Topic 4 – Functions & Graphs | |

Objective: Exam |

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### Topic 5 - Geometry Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 5 – Geometry | |

2 | Coordinate Geometry-the plane | Distance formula. | |

3 | Coordinate Geometry-midpoint, slope | Mid-point formula | |

4 | Coordinate Geometry-gradient | Gradient | |

5 | Coordinate Geometry-gradient | Gradient formula. | |

6 | Coordinate Geometry-straight line | The straight line. | |

7 | Coordinate Geometry-slope, etc. | Lines through the origin. | |

8 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |

9 | Coordinate Geometry-intercept | Slope intercept form of a line. | |

10 | Coordinate Geometry-point slope | Point slope form of a line | |

11 | Pythagoras | Find the hypotenuse | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||

12 | Pythagoras | Pythagorean triples | |

Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. | |||

13 | Pythagoras | Find 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. | |||

14 | Pythagoras | Calculating 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. | |||

15 | Pythagoras | Proofs of Pythagoras theorem | |

Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem | |||

16 | Trigonometry-ratios | Trigonometric ratios. | |

17 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |

18 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |

19 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |

20 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |

21 | Trigonometry-practical | Trigonometric ratios in practical situations. | |

22 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |

23 | Trigonometry-exact ratios | Trigonometric ratios of 30., 45. and 60. – exact ratios. | |

24 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |

25 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |

26 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |

27 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |

28 | Trigonometry-areas | The area formula | |

29 | Area | Problems with area. | |

Objective: On completion of the lesson the student will be able to solve problems with area. | |||

30 | Volume/capacity | Problems with volume/capacity. | |

Objective: Problem Solving: problems involving volume/capacity | |||

31 | Surface area | Surface 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. | |||

32 | Surface area | Surface 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. | |||

33 | Surface area | Surface 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. | |||

34 | Surface area | Surface area of pyramids | |

Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. | |||

35 | Surface area | Surface 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 | |||

36 | Surface area | Surface area of composite solids | |

Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. | |||

37 | Geometry-angles | Measuring angles | |

38 | Geometry-angles | Adjacent 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. | |||

39 | Geometry-angles | Complementary 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. | |||

40 | Geometry-angles | Vertically 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. | |||

41 | Geometry-angles | Angles 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. | |||

42 | Geometry-angles | Parallel Lines. | |

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||

43 | Geometry-problems | Additional 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. | |||

44 | Geometry-triangles | Angle 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. | |||

45 | Geometry-triangles | Exterior 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. | |||

46 | Special triangles | Special 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. | |||

47 | Geometry-quadrilaterals | Quadrilaterals | |

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. | |||

48 | Geometry-constructions | Geometric constructions | |

Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||

49 | Geometry | To 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. | |||

50 | Geometry – angles | To 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. | |||

51 | Geometry-constructions | Angle 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. | |||

52 | Geometry-constructions | Circumcentre 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. | |||

53 | Geometry-constructions | Orthocentre 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. | |||

54 | Geometry-quadrilaterals | Midsegments 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. | |||

55 | Geometry-quadrilaterals | Classifying Quadrilaterals | |

Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. | |||

56 | Geometry-quadrilaterals | Using 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. | |||

57 | Geometry-quadrilaterals | Proving 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. | |||

58 | Geometry-quadrilaterals | Properties 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. | |||

59 | Geometry-quadrilaterals | Properties 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. | |||

60 | Geometry-quadrilaterals | The 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. | |||

61 | Geometry-locus | Constructions and loci – single condition | |

Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||

62 | Geometry-locus | Constructions and loci – multiple conditions | |

Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||

63 | Geometry problems | More 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 | |||

64 | Geometry-reasoning | Further 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. | |||

65 | Geometry-polygons | Angles 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. | |||

66 | Geometry-congruence | Congruent 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. | |||

67 | Geometry-congruence | Congruent 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. | |||

68 | Geometry-congruence | Proofs 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. | |||

69 | Similar triangles | Similar triangles | |

Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||

70 | Similar triangles | Using similar triangles to calculate lengths | |

Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. | |||

71 | Overlapping triangles | Examples involving overlapping triangles | |

Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles. | |||

72 | Geometry – triangles | Triangle inequality theorem | |

Objective: On completion of the lesson the student will understand and use the triangle inequality theorem. | |||

73 | Exam | Exam – Topic 5 – Geometry | |

Objective: Exam |

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### Topic 6 - Statistics Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 6 – Statistics | |

2 | Statistics | Frequency distribution table | |

3 | Statistics | Frequency histograms and polygons | |

4 | Statistics | Relative frequency | |

5 | Statistic-probability | The mode | |

6 | Statistic-probability | The mean | |

7 | Statistic-probability | The median | |

8 | Statistic-probability | Cumulative frequency | |

Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||

9 | Statistics | The range. | |

10 | Statistic-probability | Calculating 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. | |||

11 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |

12 | Statistics | Scatter Diagrams | |

13 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |

14 | Statistics using a calculator | Statistics and the student calculator | |

15 | Statistics – Range and dispersion | Range 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. | |||

16 | Statistics – Spread | Measures 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. | |||

17 | Statistics – Standard deviation | Normal 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. | |||

18 | Statistics – Standard deviation | Standard 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. | |||

19 | Statistics – Interquartile range | Measures 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 | |||

20 | Exam | Exam – Topic 6 – Statistics | |

Objective: Exam |

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### Topic 7 - Differential Calculus Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 7 – Differential Calculus | |

2 | Calculus | Limits | |

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. | |||

3 | Calculus=1st prin | Differentiation 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. | |||

4 | Calculus=1st prin | Differentiation 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. | |||

5 | Calculus-differential, integ | Meaning 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. | |||

6 | Calculus-differential, integ | Function 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. | |||

7 | Calculus-differential, integ | Increasing, 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. | |||

8 | Calculus | First 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. | |||

9 | Calculus-2nd derivative | The 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. | |||

10 | Calculus – Curve sketching | Curve 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. | |||

11 | Calculus – Maxima minima | Practical 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. | |||

12 | Calculus – Integration | Integration – 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. | |||

13 | Calculus – Computation area | Computation 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. | |||

14 | Exam | Exam – Topic 7 – Differential Calculus | |

Objective: Exam |

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### Topic 8 - Financial management Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study 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 | |||

2 | Sequences and Series-Compound interest | Compound 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 | |||

3 | Sequences and Series-Superannuation | Superannuation. | |

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 | |||

4 | Sequences and Series-Time payments | Time 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 | |||

5 | Exam | Exam – Topic 8 – Financial management | |

Objective: ExamSee the sample lesson in action here |

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### Topic 1 - Algebra Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 1 – Algebra | |

2 | Sequences and Series | General sequences. | |

3 | Sequences and Series | Finding Tn given Sn. | |

4 | Arithmetic Progression | The arithmetic progression | |

5 | Arithmetic Progression | Finding the position of a term in an A.P. | |

6 | Arithmetic Progression | Given two terms of A.P., find the sequence. | |

7 | Arithmetic Progression | Arithmetic means | |

8 | Arithmetic Progression | The sum to n terms of an A.P. | |

9 | Geometric Progression | The geometric progression. | |

10 | Geometric Progression | Finding the position of a term in a G.P. | |

11 | Geometric Progression | Given two terms of G.P., find the sequence. | |

12 | Sequences and Series-Geometric means | Geometric means. | |

13 | Sequences and Series-Sum of gp | The sum to n terms of a G.P. | |

14 | Sequences and Series-Sigma notation | Sigma notation | |

Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates. | |||

15 | Sequences and Series-Sum-infinity | Limiting 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. | |||

16 | Sequences and Series-Recurring decimal infinity | Recurring 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. | |||

17 | Sequences and Series-Compound interest | Compound 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. | |||

18 | Sequences and Series-Superannuation | Superannuation. | |

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. | |||

19 | Sequences and Series-Time payments | Time 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. | |||

20 | Sequences and Series | Applications of arithmetic sequences | |

21 | Logarithms-Power of 2 | Powers 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. | |||

22 | Logarithms-Equations and logs | Equations 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. | |||

23 | Logarithms-Equations and logs | Equations 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. | |||

24 | Logarithms-Log laws | Laws of logarithms. | |

Objective: On completion of the lesson the student will be familiar with 5 logarithm laws. | |||

25 | Logarithms-Log laws expansion | Using 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. | |||

26 | Logarithms-Log laws simplifying | Using 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. | |||

27 | Logarithms-Log laws numbers | Using 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. | |||

28 | Logarithms-Equations and logs | Equations involving logarithms. | |

Objective: On completion of the lesson the student will be able to solve equations with log terms. | |||

29 | Logarithms-Logs to solve equations | Using 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. | |||

30 | Logarithms-Change base formula | Change 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. | |||

31 | Statistic-probability | Binomial Theorem – Pascal’s Triangle | |

32 | Statistic-probability | Binomial 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 | |||

33 | Statistic-probability | Counting 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. | |||

34 | Statistic-probability | Unordered 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. | |||

35 | Logic | Inductive and deductive reasoning | |

Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. | |||

36 | Logic | Definition and use of counter examples | |

Objective: On completion of this lesson the student will be able to create counter examples to statements. | |||

37 | Logic | Indirect 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. | |||

38 | Logic | Mathematical induction | |

Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series. | |||

39 | Logic | Conditional statements (converse, inverse and contrapositive) (Stage 2) | |

Objective: On completion of the lesson the student will be able to form related conditional statements. | |||

40 | Surds | Introducing surds | |

41 | Surds | Some rules for the operations with surds | |

42 | Surds | Simplifying surds | |

43 | Surds | Creating entire surds | |

44 | Surds | Adding and subtracting like surds | |

45 | Surds | Expanding surds | |

46 | Surds | Binomial expansions | |

47 | Surds | Conjugate binomials with surds | |

Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds. | |||

48 | Surds | Rationalising the denominator | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds. | |||

49 | Surds | Rationalising binomial denominators | |

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions. | |||

50 | Simultaneous equns | Simultaneous equations | |

51 | Simultaneous equns | Elimination method | |

52 | Simultaneous equns | Elimination method part 2 | |

53 | Simultaneous equns | Applications of simultaneous equations | |

54 | Logarithms-Complex numbers | Imaginary 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. | |||

55 | Logarithms-Complex numbers | Complex 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. | |||

56 | Logarithms-Complex numbers | Plotting 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. | |||

57 | Logarithms-Complex numbers | Absolute value | |

Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers | |||

58 | Logarithms-Complex numbers | Trigonometric 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. | |||

59 | Logarithms-Complex numbers | Multiplication 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. | |||

60 | Logarithms-Complex numbers | DeMoivre’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. | |||

61 | Logarithms-Complex numbers | The 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. | |||

62 | Logarithms-Complex numbers | Fundamental 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. | |||

63 | Algebra-polynomials | Introduction to polynomials | |

64 | Algebra-polynomials | The sum, difference and product of two polynomials. | |

65 | Algebra-polynomials | Polynomials and long division. | |

Objective: On completion of the lesson the student will understand the long division process with polynomials. | |||

66 | Remainder theorem | The remainder theorem. | |

Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied. | |||

67 | Remainder theorem | More 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. | |||

68 | Factor theorem | The 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. | |||

69 | Factor theorem | More 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. | |||

70 | Factor theorem | Complete 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. | |||

71 | Polynomial equations | Polynomial equations | |

Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms. | |||

72 | Graphs, polynomials | Graphs 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. | |||

73 | Roots quad equations | Sum 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. | |||

74 | Roots quad equations | Sum 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. | |||

75 | Approx roots | Methods 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. | |||

76 | Newton’s approx | Newton’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. | |||

77 | Exam | Exam – Topic 1 – Algebra | |

Objective: Exam |

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### Topic 2 - Functions and Equations Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 2 – Functions & Equations | |

2 | Logarithms-Power of 2 | Powers 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. | |||

3 | Logarithms-Equations and logs | Equations 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. | |||

4 | Logarithms-Equations and logs | Equations 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. | |||

5 | Logarithms-Log laws | Laws of logarithms. | |

Objective: On completion of the lesson the student will be familiar with 5 logarithm laws. | |||

6 | Logarithms-Log laws expansion | Using 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. | |||

7 | Logarithms-Log laws simplifying | Using 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. | |||

8 | Logarithms-Log laws numbers | Using 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. | |||

9 | Logarithms-Equations and logs | Equations involving logarithms. | |

Objective: On completion of the lesson the student will be able to solve equations with log terms. | |||

10 | Logarithms-Logs to solve equations | Using 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. | |||

11 | Logarithms-Change base formula | Change 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. | |||

12 | Matrices | Translation 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. | |||

13 | Matrices | Translation 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. | |||

14 | Transformations | Special 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. | |||

15 | Vectors | Vectors | |

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. | |||

16 | Simultaneous equations | Number 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. | |||

17 | Vectors | 2 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. | |||

18 | Linear systems | Optimal solutions (Stage 2) – Vectors | |

Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions. | |||

19 | Linear systems | Linear systems with matrices (Stage 2) | |

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations. | |||

20 | Linear systems | Row-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. | |||

21 | Linear systems | Gauss 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. | |||

22 | Functions | Definition, domain and range | |

23 | Functions | Notation and evaluations | |

24 | Functions | More on domain and range | |

25 | Functions | Domain and range from graphical representations | |

26 | Functions | Evaluating and graphing piecewise functions | |

27 | Functions | Functions combinations | |

28 | Functions | Composition of functions | |

29 | Functions | Inverse functions | |

30 | Functions | Rational functions Part 1 | |

31 | Functions | Rational functions Part 2 | |

32 | Functions | Parametric 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. | |||

33 | Functions | Polynomial addition etc in combining and simplifying functions (Stage 2) | |

34 | Functions | Parametric 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. | |||

35 | Co-ordinate Geometry-Two point formula | Two point formula: equation of a line which joins a pair of points. | |

36 | Co-ordinate Geometry-Intercept form | Intercept form of a straight line: find the equation when given x and y | |

37 | Co-ordinate Geometry-Parallel lines equations | Parallel lines: identify equation of a line parallel to another | |

38 | Co-ordinate Geometry-Perpendicular lines | Perpendicular 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. | |||

39 | Co-ordinate Geometry-Inequalities | Inequalities 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. | |||

40 | Co-ordinate Geometry-Theorems | Perpendicular 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. | |||

41 | Co-ordinate Geometry-Theorems | Line 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. | |||

42 | Co-ordinate Geometry-Theorems | Angles 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. | |||

43 | Co-ordinate Geometry-Theorems | Internal 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. | |||

44 | Translations | Transformations – 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. | |||

45 | Geometric transformations | Geometry 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. | |||

46 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |

Objective: On completion of this lesson the student will perform translations in a number plane. | |||

47 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) | |

Objective: On completion of this lesson the student will perform and construct rotations. | |||

48 | Geometric transformations | Geometry 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. | |||

49 | Geometric transformations | The 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. | |||

50 | Graphs, polynomials | Graphs 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. | |||

51 | Quadratic equations | Introduction to quadratic equations. | |

Objective: On completion of the lesson the student will understand simple quadratic equations. | |||

52 | Quadratic equations | Quadratic equations with factorisation. | |

53 | Quadratic equations | Solving quadratic equations. | |

54 | Quadratic equations | Completing the square | |

55 | Quadratic equations | Solving quadratic equations by completing the square | |

56 | Quadratic equations | The quadratic formula | |

Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||

57 | Quadratic equations | Problem solving with quadratic equations | |

58 | Quadratic equations | Solving simultaneous quadratic equations graphically | |

59 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |

60 | Functions and graphs | Graphing perfect squares: y=(a-x) squared | |

61 | Graphing roots | Graphing irrational roots | |

62 | Coordinate geometry | Solve by graphing | |

63 | Logarithms-Graph-log curve | The 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. | |||

64 | Logarithms-Log curves | Working with log curves. | |

Objective: On completion of the lesson the student will be able to solve problems with log curves | |||

65 | Logarithms-Complex numbers | Imaginary 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. | |||

66 | Logarithms-Complex numbers | Complex 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. | |||

67 | Logarithms-Complex numbers | Plotting 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. | |||

68 | Logarithms-Complex numbers | Absolute value | |

Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers | |||

69 | Logarithms-Complex numbers | Trigonometric 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. | |||

70 | Logarithms-Complex numbers | Multiplication 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. | |||

71 | Logarithms-Complex numbers | DeMoivre’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. | |||

72 | Logarithms-Complex numbers | The 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. | |||

73 | Logarithms-Complex numbers | Fundamental 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. | |||

74 | Sequences and Series-Compound interest | Compound 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. | |||

75 | Sequences and Series-Superannuation | Superannuation. | |

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. | |||

76 | Sequences and Series-Time payments | Time 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. | |||

77 | Sequences and Series | Applications of arithmetic sequences | |

78 | Exam | Exam – Topic 2 – Functions & Equations | |

Objective: Exam |

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### Topic 3 - Circular functions and Trigonometry Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 3 – Circular functions & Trigonometry | |

2 | Geometry-circles | The 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. | |||

3 | Geometry-circles | The 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. | |||

4 | Geometry-parabola | The 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. | |||

5 | Circle Geometry | Theorem – 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 | |||

6 | Circle Geometry | Theorem – 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’ | |||

7 | Circle Geometry | Theorem – 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. | |||

8 | Circle Geometry | Theorem – 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. | |||

9 | Circle Geometry | Theorem – 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. | |||

10 | Circle Geometry | Theorem – 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.’ | |||

11 | Circle Geometry | Theorem – 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. | |||

12 | Circle Geometry | Theorem – 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. | |||

13 | Circle Geometry | Theorem – 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. | |||

14 | Circle Geometry | Theorem – 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. | |||

15 | Circle Geometry | Theorem – 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. | |||

16 | Circle Geometry-chords | Theorem – 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. | |||

17 | Circle Geometry-tangents | Theorem – 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 | |||

18 | Circle Geometry-cyclic quads | Theorem – 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. | |||

19 | Circle Geometry-subtending | Theorem – 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 | |||

20 | Circle Geometry | Theorem – 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. | |||

21 | Circle Geometry-non-collinear | Theorem – 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 | |||

22 | Trig-reciprocal ratios | Reciprocal ratios. | |

23 | Trig complementary angles | Complementary angle results. | |

24 | Trig identities | Trigonometric identities | |

25 | Trig larger angles | Angles of any magnitude | |

26 | Trig larger angles | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |

27 | Graph sine | Graphing the trigonometric ratios – I Sine curve. | |

28 | Graph cosine | Graphing the trigonometric ratios – II Cosine curve. | |

29 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |

30 | Graph reciprocals | Graphing the trigonometric ratios – IV Reciprocal ratios. | |

31 | Trig larger angles | Using one ratio to find another. | |

32 | Trig equations | Solving trigonometric equations – Type I. | |

33 | Trig equations | Solving trigonometric equations – Type II. | |

Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains. | |||

34 | Trig equations | Solving trigonometric equations – Type III. | |

Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains. | |||

35 | Polar coordinates | Plotting 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. | |||

36 | Polar coordinates | Converting 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. | |||

37 | Polar coordinates | Write 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. | |||

38 | Trigonometry | Sin(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. | |||

39 | Trigonometry | Double angle formulas (Stage 2) | |

Objective: On completion of the lesson the student will derive and use the double angle trig identities. | |||

40 | Trigonometry | Half 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. | |||

41 | Trigonometry | t Formulas (Stage 2) | |

Objective: On completion of the lesson the student will solve trig equations using the t substitution. | |||

42 | Trigonometry-ratios | Trigonometric ratios. | |

43 | Trigonometry-ratios | Using the calculator. | |

44 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |

45 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |

46 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |

47 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |

48 | Trigonometry-compass | Bearings – the compass. | |

49 | Trigonometry-elevation | Angles of elevation and depression. | |

50 | Trigonometry-practical | Trigonometric ratios in practical situations. | |

51 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |

52 | Trigonometry- ratios | Using the trigonometric ratios to find an angle in a right-angled triangle. | |

53 | Trigonometry-exact ratios | Trigonometric ratios of 30., 45. and 60. – exact ratios. | |

54 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |

55 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |

56 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |

57 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |

58 | Trigonometry-areas | The area formula | |

59 | Exam | Exam – Topic 3 – Circular functions & Trigonometry | |

Objective: Exam |

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### Topic 4 - Matrices Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 4 – Matrices | |

2 | Matrices | Basic concepts – Matrices | |

Objective: On completion of the lesson the student will have had an introduction to matrices | |||

3 | Matrices | Addition 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. | |||

4 | Matrices | Scalar matrix multiplication | |

Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix. | |||

5 | Matrices | Multiplication 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. | |||

6 | Matrices | Translation 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. | |||

7 | Matrices | Translation 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. | |||

8 | Transformations | Special 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. | |||

9 | Vectors | Vectors | |

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. | |||

10 | Simultaneous equations | Number of solutions (Stage 2) | |

11 | Vectors | 2 vector addition in 2 and 3D (stage 2) | |

12 | Linear systems | Optimal solutions (Stage 2) – Vectors | |

13 | Linear systems | Linear systems with matrices (Stage 2) | |

14 | Linear systems | Row-echelon form (Stage 2) | |

15 | Linear systems | Gauss 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. | |||

16 | Exam | Exam – Topic 4 – Matrices | |

Objective: Exam |

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### Topic 5 - Vectors Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 5 – Vectors | |

2 | Vectors | Vectors | |

3 | Simultaneous equations | Number of solutions (Stage 2) | |

4 | Vectors | 2 vector addition in 2 and 3D (stage 2) | |

5 | Linear systems | Optimal solutions (Stage 2) – Vectors | |

6 | Linear systems | Linear systems with matrices (Stage 2) | |

7 | Linear systems | Row-echelon form (Stage 2) | |

8 | Linear systems | Gauss 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. | |||

9 | Exam | Exam – Topic 5 – Vectors | |

Objective: Exam |

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### Topic 6 - Statistics and Probability Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 6 – Statistics & Probability | |

2 | Statistics | Frequency distribution table | |

3 | Statistics | Frequency histograms and polygons | |

4 | Statistics | Relative frequency | |

5 | Statistics | The range. | |

6 | Statistic-probability | The mode | |

7 | Statistic-probability | The mean | |

8 | Statistic-probability | The median | |

9 | Statistic-probability | Cumulative frequency | |

10 | Statistic-probability | Calculating the median from a frequency distribution | |

11 | Statistic-probability | Binomial Theorem – Pascal’s Triangle | |

12 | Statistic-probability | Binomial probabilities using the Binomial Theorem | |

13 | Statistic-probability | Counting techniques and ordered selections – permutations | |

14 | Statistic-probability | Unordered selections – combinations | |

15 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |

16 | Statistics using a calculator | Statistics and the student calculator | |

17 | Statistics – Range and dispersion | Range as a measure of dispersion | |

18 | Statistics – Spread | Measures of spread | |

19 | Statistics – Standard deviation | Standard deviation applications | |

20 | Statistics – Standard deviation | Normal distribution | |

21 | Statistics – Interquartile range | Measures of spread: the interquartile range | |

22 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |

23 | Statistics | Scatter Diagrams | |

24 | Statistic-probability | Probability of Simple Events | |

25 | Statistic-probability | Rolling a pair of dice | |

26 | Statistic-probability | Experimental probability | |

27 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |

28 | Statistic-probability | Tree diagrams – depending on previous outcomes | |

29 | Statistic-probability | The complementary result .. | |

30 | Statistic-probability | P[A or B] When A and B are both mutually and NOT mutually exclusive | |

31 | Exam | Exam – Topic 6 – Statistics & Probability | |

Objective: Exam |

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### Topic 7 - Differential Calculus Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Topic 7 – Differential Calculus | |

2 | Calculus | Limits | |

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. | |||

3 | Calculus=1st prin | Differentiation 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. | |||

4 | Calculus=1st prin | Differentiation 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. | |||

5 | Calculus-differential, integ | Meaning 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. | |||

6 | Calculus-differential, integ | Function 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. | |||

7 | Calculus-differential, integ | Increasing, 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. | |||

8 | Calculus | First 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. | |||

9 | Calculus-2nd derivative | The 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. | |||

10 | Calculus – Curve sketching | Curve 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. | |||

11 | Calculus – Maxima minima | Practical 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. | |||

12 | Calculus – Integration | Integration – 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. | |||

13 | Calculus – Computation area | Computation 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. | |||

14 | Calculus – Computation volumes | Computation 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. | |||

15 | Calculus – Trapezoidal and Simpson’s rules | The 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. | |||

16 | Exam | Exam – Topic 7 – Differential Calculus | |

Objective: Exam |

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### Topic 1 - Algebra Mathematics

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | Study Plan | Study 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 | ||||

2 | Sequences and Series | General 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 | ||||

3 | Sequences and Series | Finding 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 | ||||

4 | Arithmetic Progression | The 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 | ||||

5 | Arithmetic Progression | Finding 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 | ||||

6 | Arithmetic Progression | Given 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 | ||||

7 | Arithmetic Progression | Arithmetic 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 | ||||

8 | Arithmetic Progression | The 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 | ||||

9 | Geometric Progression | The 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 | ||||

10 | Geometric Progression | Finding 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 | ||||

11 | Geometric Progression | Given 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 | ||||

12 | Sequences and Series-Geometric means | Geometric 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 | ||||

13 | Sequences and Series-Sum of gp | The 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 | ||||

14 | Sequences and Series-Sigma notation | Sigma 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 | ||||

15 | Sequences and Series-Sum-infinity | Limiting 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 | ||||

16 | Sequences and Series-Recurring decimal infinity | Recurring 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 | ||||

17 | Sequences and Series-Compound interest | Compound 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 | ||||

18 | Sequences and Series-Superannuation | Superannuation. | ||

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 | ||||

19 | Sequences and Series-Time payments | Time 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 | ||||

20 | Sequences and Series | Applications 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 | ||||

21 | Logarithms-Power of 2 | Powers 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 | ||||

22 | Logarithms-Equations and logs | Equations 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 | ||||

23 | Logarithms-Equations and logs | Equations 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 | ||||

24 | Logarithms-Log laws | Laws of logarithms. | ||

Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.See the sample lesson in action here | ||||

25 | Logarithms-Log laws expansion | Using 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 | ||||

26 | Logarithms-Log laws simplifying | Using 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 | ||||

27 | Logarithms-Log laws numbers | Using 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 | ||||

28 | Logarithms-Equations and logs | Equations 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 | ||||

29 | Logarithms-Logs to solve equations | Using 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 | ||||

30 | Logarithms-Change base formula | Change 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 | ||||

31 | Statistic-probability | Binomial 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 | ||||

32 | Statistic-probability | Binomial 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 | ||||

33 | Statistic-probability | Counting 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 | ||||

34 | Statistic-probability | Unordered 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 | ||||

35 | Logic | Inductive 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 | ||||

36 | Logic | Definition 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 | ||||

37 | Logic | Indirect 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 | ||||

38 | Logic | Mathematical 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 | ||||

39 | Logic | Conditional 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 | ||||

40 | Surds | Introducing 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 | ||||

41 | Surds | Some 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 | ||||

42 | Surds | Simplifying 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 | ||||

43 | Surds | Creating 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 | ||||

44 | Surds | Adding 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 | ||||

45 | Surds | Expanding 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 | ||||

46 | Surds | Binomial 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 | ||||

47 | Surds | Conjugate 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 | ||||

48 | Surds | Rationalising 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 | ||||

49 | Surds | Rationalising 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 | ||||

50 | Simultaneous equns | Simultaneous 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 | ||||

51 | Simultaneous equns | Elimination 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 | ||||

52 | Simultaneous equns | Elimination 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 | ||||

53 | Simultaneous equns | Applications 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 | ||||

54 | Logarithms-Complex numbers | Imaginary 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 | ||||

55 | Logarithms-Complex numbers | Complex 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 | ||||

56 | Logarithms-Complex numbers | Plotting 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 | ||||

57 | Logarithms-Complex numbers | Absolute 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 | ||||

58 | Logarithms-Complex numbers | Trigonometric 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 | ||||

59 | Logarithms-Complex numbers | Multiplication 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 | ||||

60 | Logarithms-Complex numbers | DeMoivre’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 | ||||

61 | Logarithms-Complex numbers | The 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 | ||||

62 | Logarithms-Complex numbers | Fundamental 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 | ||||

63 | Algebra-polynomials | Introduction 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 | ||||

64 | Algebra-polynomials | The 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 | ||||

65 | Algebra-polynomials | Polynomials 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 | ||||

66 | Remainder theorem | The 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 | ||||

67 | Remainder theorem | More 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 | ||||

68 | Factor theorem | The 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 | ||||

69 | Factor theorem | More 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 | ||||

70 | Factor theorem | Complete 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 | ||||

71 | Polynomial equations | Polynomial 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 | ||||

72 | Graphs, polynomials | Graphs 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 | ||||

73 | Roots quad equations | Sum 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 | ||||

74 | Roots quad equations | Sum 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 | ||||

75 | Approx roots | Methods 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 | ||||

76 | Newton’s approx | Newton’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 | ||||

77 | Exam | Exam – Topic 1 – Algebra | ||

Objective: ExamSee the sample lesson in action here |

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### Topic 2 - Functions and Equations Mathematics

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | Study Plan | Study 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 | ||||

2 | Logarithms-Power of 2 | Powers 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 | ||||

3 | Logarithms-Equations and logs | Equations 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 | ||||

4 | Logarithms-Equations and logs | Equations 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 | ||||

5 | Logarithms-Log laws | Laws of logarithms. | ||

Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.See the sample lesson in action here | ||||

6 | Logarithms-Log laws expansion | Using 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 | ||||

7 | Logarithms-Log laws simplifying | Using 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 | ||||

8 | Logarithms-Log laws numbers | Using 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 | ||||

9 | Logarithms-Equations and logs | Equations 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 | ||||

10 | Logarithms-Logs to solve equations | Using 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 | ||||

11 | Logarithms-Change base formula | Change 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 | ||||

12 | Matrices | Translation 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 | ||||

13 | Matrices | Translation 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 | ||||

14 | Transformations | Special 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 | ||||

15 | Vectors | Vectors | ||

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 | ||||

16 | Simultaneous equations | Number 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 | ||||

17 | Vectors | 2 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 | ||||

18 | Linear systems | Optimal 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 | ||||

19 | Linear systems | Linear 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 | ||||

20 | Linear systems | Row-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 | ||||

21 | Linear systems | Gauss 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 | ||||

22 | Functions | Definition, 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 | ||||

23 | Functions | Notation and evaluations | ||

Objective: On completion of the lesson the student will be understand different notations for functions.See the sample lesson in action here | ||||

24 | Functions | More 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 | ||||

25 | Functions | Domain 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 | ||||

26 | Functions | Evaluating 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 | ||||

27 | Functions | Functions 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 | ||||

28 | Functions | Composition 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 | ||||

29 | Functions | Inverse 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 | ||||

30 | Functions | Rational 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 | ||||

31 | Functions | Rational 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 | ||||

32 | Functions | Parametric 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 | ||||

33 | Functions | Polynomial 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 | ||||

34 | Functions | Parametric 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 | ||||

35 | Co-ordinate Geometry-Two point formula | Two 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 | ||||

36 | Co-ordinate Geometry-Intercept form | Intercept 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 | ||||

37 | Co-ordinate Geometry-Parallel lines equations | Parallel 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 | ||||

38 | Co-ordinate Geometry-Perpendicular lines | Perpendicular 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 | ||||

39 | Co-ordinate Geometry-Inequalities | Inequalities 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 | ||||

40 | Co-ordinate Geometry-Theorems | Perpendicular 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 | ||||

41 | Co-ordinate Geometry-Theorems | Line 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 | ||||

42 | Co-ordinate Geometry-Theorems | Angles 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 | ||||

43 | Co-ordinate Geometry-Theorems | Internal 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 | ||||

44 | Translations | Transformations – 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 | ||||

45 | Geometric transformations | Geometry 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 | ||||

46 | Geometric transformations | Geometry 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 | ||||

47 | Geometric transformations | Geometry 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 | ||||

48 | Geometric transformations | Geometry 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 | ||||

49 | Geometric transformations | The 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 | ||||

50 | Graphs, polynomials | Graphs 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 | ||||

51 | Quadratic equations | Introduction to quadratic equations. | ||

Objective: On completion of the lesson the student will understand simple quadratic equations.See the sample lesson in action here | ||||

52 | Quadratic equations | Quadratic 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 | ||||

53 | Quadratic equations | Solving 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 | ||||

54 | Quadratic equations | Completing 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 | ||||

55 | Quadratic equations | Solving 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 | ||||

56 | Quadratic equations | The quadratic formula | ||

Objective: On completion of the lesson the student will be familiar with the quadratic formula.See the sample lesson in action here | ||||

57 | Quadratic equations | Problem 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 | ||||

58 | Quadratic equations | Solving 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 | ||||

59 | Functions and graphs | Quadratic 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 | ||||

60 | Functions and graphs | Graphing 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 | ||||

61 | Graphing roots | Graphing 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 | ||||

62 | Coordinate geometry | Solve 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 | ||||

63 | Logarithms-Graph-log curve | The 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 | ||||

64 | Logarithms-Log curves | Working 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 | ||||

65 | Logarithms-Complex numbers | Imaginary 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 | ||||

66 | Logarithms-Complex numbers | Complex 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 | ||||

67 | Logarithms-Complex numbers | Plotting 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 | ||||

68 | Logarithms-Complex numbers | Absolute 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 | ||||

69 | Logarithms-Complex numbers | Trigonometric 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 | ||||

70 | Logarithms-Complex numbers | Multiplication 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 | ||||

71 | Logarithms-Complex numbers | DeMoivre’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 | ||||

72 | Logarithms-Complex numbers | The 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 | ||||

73 | Logarithms-Complex numbers | Fundamental 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 | ||||

74 | Sequences and Series-Compound interest | Compound 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 | ||||

75 | Sequences and Series-Superannuation | Superannuation. | ||

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 | ||||

76 | Sequences and Series-Time payments | Time 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 | ||||

77 | Sequences and Series | Applications 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 | ||||

78 | Exam | Exam – Topic 2 – Functions & Equations | ||

Objective: ExamSee the sample lesson in action here |

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### Topic 3 - Circular functions and Trigonometry Mathematics

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | Study Plan | Study plan – Topic 3 – Circular functions & Trigonometry | ||

2 | Geometry-circles | The 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 | ||||

3 | Geometry-circles | The 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 | ||||

4 | Geometry-parabola | The 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 | ||||

5 | Circle Geometry | |||

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 | ||||

6 | Circle Geometry | |||

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 | ||||

7 | Circle Geometry | |||

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 | ||||

8 | Circle Geometry | |||

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 | ||||

9 | Circle Geometry | Theorem – 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 | ||||

10 | Circle Geometry | Theorem – 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 | ||||

11 | Circle Geometry | Theorem – 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 | ||||

12 | Circle Geometry | |||

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 | ||||

13 | Circle Geometry | |||

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 | ||||

14 | Circle Geometry | Theorem – 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 | ||||

15 | Circle Geometry | |||

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 | ||||

16 | Circle Geometry-chords | Theorem – 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 | ||||

17 | Circle Geometry-tangents | Theorem – 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 | ||||

18 | Circle Geometry-cyclic quads | Theorem – 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 | ||||

19 | Circle Geometry-subtending | Theorem – 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 | ||||

20 | Circle Geometry | Theorem – 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 | ||||

21 | Circle Geometry-non-collinear | Theorem – 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 | ||||

22 | Trig-reciprocal ratios | Reciprocal 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 | ||||

23 | Trig complementary angles | Complementary 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 | ||||

24 | Trig identities | Trigonometric 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 | ||||

25 | Trig larger angles | Angles 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 | ||||

26 | Trig larger angles | Trigonometric 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 | ||||

27 | Graph sine | Graphing 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 | ||||

28 | Graph cosine | Graphing 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 | ||||

29 | Graphs tan curve | Graphing 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 | ||||

30 | Graph reciprocals | Graphing 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 | ||||

31 | Trig larger angles | Using 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 | ||||

32 | Trig equations | Solving 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 | ||||

33 | Trig equations | Solving 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 | ||||

34 | Trig equations | Solving 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 | ||||

35 | Polar coordinates | Plotting 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 | ||||

36 | Polar coordinates | Converting 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 | ||||

37 | Polar coordinates | Write 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 | ||||

38 | Trigonometry | Sin(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 | ||||

39 | Trigonometry | Double 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 | ||||

40 | Trigonometry | Half 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 | ||||

41 | Trigonometry | t 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 | ||||

42 | Trigonometry-ratios | Trigonometric 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 | ||||

43 | Trigonometry-ratios | Using 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 | ||||

44 | Trigonometry-ratios | Using 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 | ||||

45 | Trigonometry-ratios | Using 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 | ||||

46 | Trigonometry-ratios | Using 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 | ||||

47 | Trigonometry-ratios | Unknown 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 | ||||

48 | Trigonometry-compass | Bearings – 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 | ||||

49 | Trigonometry-elevation | Angles 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 | ||||

50 | Trigonometry-practical | Trigonometric 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 | ||||

51 | Trigonometry-ratios | Using 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 | ||||

52 | Trigonometry- ratios | Using 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 | ||||

53 | Trigonometry-exact ratios | Trigonometric 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 | ||||

54 | Trigonometry-cosine rule | The 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 | ||||

55 | Trigonometry-cosine rule | The 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 | ||||

56 | Trigonometry-sine rule | The 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 | ||||

57 | Trigonometry-sine rule | The 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 | ||||

58 | Trigonometry-areas | The 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 | ||||

59 | Exam | Exam – Topic 3 – Circular functions & Trigonometry | ||

Objective: ExamSee the sample lesson in action here |

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### Topic 4 - Matrices Mathematics

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | Study Plan | Study plan – Topic 4 – Matrices | ||

2 | Matrices | Basic concepts – Matrices | ||

Objective: On completion of the lesson the student will have had an introduction to matricesSee the sample lesson in action here | ||||

3 | Matrices | Addition 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 | ||||

4 | Matrices | Scalar 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 | ||||

5 | Matrices | Multiplication 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 | ||||

6 | Matrices | Translation 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 | ||||

7 | Matrices | Translation 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 | ||||

8 | Transformations | Special 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 | ||||

9 | Vectors | Vectors | ||

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 | ||||

10 | Simultaneous equations | Number 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 | ||||

11 | Vectors | 2 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 | ||||

12 | Linear systems | Optimal 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 | ||||

13 | Linear systems | Linear 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 | ||||

14 | Linear systems | Row-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 | ||||

15 | Linear systems | Gauss 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 | ||||

16 | Exam | Exam – Topic 4 – Matrices | ||

Objective: ExamSee the sample lesson in action here |

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### Topic 5 - Vectors Mathematics

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | Study Plan | Study plan – Topic 5 – Vectors | ||

2 | Vectors | Vectors | ||

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 | ||||

3 | Simultaneous equations | Number 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 | ||||

4 | Vectors | 2 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 | ||||

5 | Linear systems | Optimal 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 | ||||

6 | Linear systems | Linear 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 | ||||

7 | Linear systems | Row-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 | ||||

8 | Linear systems | Gauss 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 | ||||

9 | Exam | Exam – Topic 5 – Vectors | ||

Objective: ExamSee the sample lesson in action here |

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### Topic 6 - Statistics and Probability Mathematics

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | Study Plan | Study plan – Topic 6 – Statistics & Probability | ||

2 | Statistics | Frequency 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 | ||||

3 | Statistics | Frequency 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 | ||||

4 | Statistics | Relative 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 | ||||

5 | Statistics | The 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 | ||||

6 | Statistic-probability | The 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 | ||||

7 | Statistic-probability | The 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 | ||||

8 | Statistic-probability | The 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 | ||||

9 | Statistic-probability | Cumulative 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 | ||||

10 | Statistic-probability | Calculating 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 | ||||

11 | Statistic-probability | Binomial 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 | ||||

12 | Statistic-probability | Binomial 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 | ||||

13 | Statistic-probability | Counting 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 | ||||

14 | Statistic-probability | Unordered 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 | ||||

15 | Statistics – grouped data | Calculating 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 | ||||

16 | Statistics using a calculator | Statistics 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 | ||||

17 | Statistics – Range and dispersion | Range 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 | ||||

18 | Statistics – Spread | Measures 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 | ||||

19 | Statistics – Standard deviation | Standard 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 | ||||

20 | Statistics – Standard deviation | Normal 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 | ||||

21 | Statistics – Interquartile range | Measures 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 | ||||

22 | Statistics | Stem 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 | ||||

23 | Statistics | Scatter 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 | ||||

24 | Statistic-probability | Probability 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 | ||||

25 | Statistic-probability | Rolling 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 | ||||

26 | Statistic-probability | Experimental 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 | ||||

27 | Statistic-probability | Tree 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 | ||||

28 | Statistic-probability | Tree 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 | ||||

29 | Statistic-probability | The 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 | ||||

30 | Statistic-probability | P[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 | ||||

31 | Exam | Exam – Topic 6 – Statistics & Probability | ||

Objective: ExamSee the sample lesson in action here |

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### Topic 7 - Differential Calculus Mathematics

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | Study Plan | Study plan – Topic 7 – Differential Calculus | ||

2 | Calculus | Limits | ||

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 | ||||

3 | Calculus=1st prin | Differentiation 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 | ||||

4 | Calculus=1st prin | Differentiation 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 | ||||

5 | Calculus-differential, integ | Meaning 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 | ||||

6 | Calculus-differential, integ | Function 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 | ||||

7 | Calculus-differential, integ | Increasing, 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 | ||||

8 | Calculus | First 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 | ||||

9 | Calculus-2nd derivative | The 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 | ||||

10 | Calculus – Curve sketching | Curve 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 | ||||

11 | Calculus – Maxima minima | Practical 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 | ||||

12 | Calculus – Integration | Integration – 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 | ||||

13 | Calculus – Computation area | Computation 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 | ||||

14 | Calculus – Computation volumes | Computation 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 | ||||

15 | Calculus – Trapezoidal and Simpson’s rules | The 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 | ||||

16 | Exam | Exam – Topic 7 – Differential Calculus | ||

Objective: ExamSee the sample lesson in action here |

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### Kindergarten/Year 1 Literacy

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | Do you like hamburgers? | It’s the alphabet! | ||

Objective: Students will develop their listening skills and practise saying the alphabet. | ||||

2 | It’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. | ||||

3 | Hello! 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. | ||||

4 | Hello! 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. | ||||

5 | Eight Purple Stars! | Ten Little Pandas Full lesson available |
||

Objective: Students will read a picture story and practise the numbers 1-10. | ||||

6 | Eight 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 …’. | ||||

7 | Fun at School | This 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 …’. | ||||

8 | What’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?’. | ||||

9 | What’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 …?’. | ||||

10 | A New Boy at School | A 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. | ||||

11 | A New Boy at School | Where’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. | ||||

12 | My Family | Where’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’. | ||||

13 | My Family | My 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’. | ||||

14 | About People | That’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’. | ||||

15 | About People | These 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. | ||||

16 | Animal 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. | ||||

17 | Animal Mania! | A Very Tall Giraffe | ||

Objective: Students will develop their comprehension skills by reading a text about animals in which more adjectives are used. | ||||

18 | We 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. | ||||

19 | We 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. | ||||

20 | Do you like hamburgers? | At a Café | ||

Objective: Students will develop their comprehension skills by reading a picture story about food preferences. | ||||

21 | Do 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. | ||||

22 | It’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. | ||||

23 | It’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. | ||||

24 | It’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’. | ||||

25 | Sentences | The Sentence | ||

Objective: To identify and use complete sentences. |

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### Year 2 Literacy

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | It’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. | ||||

2 | It’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. | ||||

3 | It’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’. | ||||

4 | School and Play | I 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. | ||||

5 | School and Play | On the Weekend | ||

Objective: Students will practise reading and recognising simple sentences about weekend activities. | ||||

6 | It’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. | ||||

7 | It’s Christmas time! | Festivals are fun! | ||

Objective: Students will develop their comprehension skills by reading a short text about Christmas and Chinese New Year. | ||||

8 | I walk in the summer. | The Seasons | ||

Objective: Students will develop their reading skills and practise new words to describe the seasons. | ||||

9 | I 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. | ||||

10 | What’s the weather like today? | It’s a sunny day! | ||

Objective: Students will develop their comprehension skills by reading a story about the weather. | ||||

11 | What 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. | ||||

12 | What 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. | ||||

13 | They’re usually in the lounge room. | Hide and Seek | ||

Objective: Students will develop their comprehension skills by reading a story about finding people. | ||||

14 | They’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. | ||||

15 | Left! 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. | ||||

16 | Left! 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. | ||||

17 | Up, 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. | ||||

18 | Up, 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. | ||||

19 | Sentences | The Sentence | ||

Objective: To identify and use complete sentences. | ||||

20 | Spelling | Spelling | ||

Objective: To use the ‘Look, Say, Write’ method for learning spelling. Plus 300 spelling words. | ||||

21 | Capitalisation | Capital Letters 1 | ||

Objective: To use capital letters correctly: to begin sentences, for proper nouns. | ||||

22 | Vowels and Consonants | Vowels and Consonants | ||

Objective: To identify and use vowels and consonants. | ||||

23 | Common Nouns | Common Nouns | ||

Objective: To show a common noun names an object or thing. | ||||

24 | Punctuation | Sentence Endings | ||

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly. | ||||

25 | Verbs | Simple 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

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | We’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’. | ||||

2 | We’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. | ||||

3 | I 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. | ||||

4 | I 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. | ||||

5 | Can 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. | ||||

6 | Oh, 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. | ||||

7 | Oh, 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. | ||||

8 | It’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. | ||||

9 | It’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. | ||||

10 | Maybe 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. | ||||

11 | Maybe 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. | ||||

12 | First 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. | ||||

13 | First 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. | ||||

14 | We 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. | ||||

15 | We 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’. | ||||

16 | First 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’. | ||||

17 | First 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. | ||||

18 | On 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. | ||||

19 | On 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. | ||||

20 | Sentences | The Sentence | ||

Objective: To identify and use complete sentences. | ||||

21 | Spelling | Spelling | ||

Objective: To use the ‘Look, Say, Write’ method for learning spelling. Plus 300 spelling words. | ||||

22 | Capitalisation | Capital Letters 1 | ||

Objective: To use capital letters correctly: to begin sentences, for proper nouns. | ||||

23 | Vowels and Consonants | Vowels and Consonants | ||

Objective: To identify and use vowels and consonants. | ||||

24 | Common Nouns | Common Nouns | ||

Objective: To show a common noun names an object or thing. | ||||

25 | Punctuation | Sentence Endings | ||

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly. | ||||

26 | Verbs | Simple Verbs | ||

Objective: To identify and use verbs. To understand a verb can be: an action or doing word, a state of being or ownership. | ||||

27 | Vowels | Vowels – Long and Short | ||

Objective: To identify long and short vowel sounds, and their use. | ||||

28 | Plurals | Plurals 1 – simple | ||

Objective: To form plurals (more than one) by adding ‘s’ and ‘es’ correctly. | ||||

29 | Basic Dictionary Use | Basic Dictionary Use | ||

Objective: To find words arranged alphabetically and identify word meanings in dictionaries. | ||||

30 | Nouns | Proper Nouns | ||

Objective: To show a proper noun is used to name a person, place or a title. | ||||

31 | Adjectives | Adjectives | ||

Objective: To show an adjective is a word that describes a noun. | ||||

32 | Adverbs | Adverbs | ||

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb. | ||||

33 | Pronouns | Pronouns | ||

Objective: To show a pronoun is used in place of a noun. | ||||

34 | Parts of Speech Part b | Conjunctions | ||

Objective: To identify and use conjunctions correctly. | ||||

35 | Common Errors | Common Errors in spelling and punctuation | ||

Objective: To identify and eliminate common errors. | ||||

36 | Punctuation | Commas 1 | ||

Objective: To use commas: to list, to make meaning clear, and when writing the date. | ||||

37 | Contractions | Contractions | ||

Objective: To identify and use contractions. | ||||

38 | Other Places and Other Times | A 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. | ||||

39 | Other Places and Other Times | Will we have robots? | ||

Objective: Students will develop their comprehension skills by reading a text in which the future tense is used. | ||||

40 | It 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

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | It 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. | ||||

2 | We 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. | ||||

3 | We 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. | ||||

4 | They 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. | ||||

5 | They 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. | ||||

6 | There 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. | ||||

7 | There 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. | ||||

8 | Let’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. | ||||

9 | Let’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. | ||||

10 | A New CD Player | The Perfect CD Player | ||

Objective: Students will develop their comprehension skills by reading a text in which comparative adjectives are used. | ||||

11 | A New CD Player | Which do you prefer? | ||

Objective: Students will develop their comprehension skills by reading a story about preferences. | ||||

12 | That’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. | ||||

13 | That’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. | ||||

14 | Let’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. | ||||

15 | Let’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. | ||||

16 | The Most Beautiful Planet | This 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. | ||||

17 | The Most Beautiful Planet | When 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. | ||||

18 | Capitalisation | Capital Letters 1 | ||

Objective: To use capital letters correctly: to begin sentences, for proper nouns. | ||||

19 | Common Nouns | Common Nouns | ||

Objective: To show a common noun names an object or thing. | ||||

20 | Punctuation | Sentence Endings | ||

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly. | ||||

21 | Verbs | Simple Verbs | ||

Objective: To identify and use verbs. To understand a verb can be: an action or doing word, a state of being or ownership. | ||||

22 | Vowels | Vowels – Long and Short | ||

Objective: To identify long and short vowel sounds, and their use. | ||||

23 | Plurals | Plurals 1 – simple | ||

Objective: To form plurals (more than one) by adding ‘s’ and ‘es’ correctly. | ||||

24 | Basic Dictionary Use | Basic Dictionary Use | ||

Objective: To find words arranged alphabetically and identify word meanings in dictionaries. | ||||

25 | Nouns | Proper Nouns | ||

Objective: To show a proper noun is used to name a person, place or a title. | ||||

26 | Adjectives | Adjectives | ||

Objective: To show an adjective is a word that describes a noun. | ||||

27 | Adverbs | Adverbs | ||

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb. | ||||

28 | Pronouns | Pronouns | ||

Objective: To show a pronoun is used in place of a noun. | ||||

29 | Parts of Speech Part b | Conjunctions | ||

Objective: To identify and use conjunctions correctly. | ||||

30 | Punctuation | Commas 1 | ||

Objective: To use commas: to list, to make meaning clear, and when writing the date. | ||||

31 | Contractions | Contractions | ||

Objective: To identify and use contractions. | ||||

32 | There 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’. | ||||

33 | There 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 …’. | ||||

34 | It 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. | ||||

35 | It couldn’t be mine! | The Riding Lesson | ||

Objective: Students will build vocabulary, answer comprehension questions and practise using possessive pronouns and adjectives. | ||||

36 | Clean 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’. | ||||

37 | Clean up Australia! | Sports Report | ||

Objective: Students will increase their vocabulary and reading comprehension skills. They will also practise using the adverbs ‘well’ and ‘badly’. | ||||

38 | Friends all over the World | Now 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’. | ||||

39 | Friends all over the World | A Letter to a Pen Pal | ||

Objective: Students will increase their vocabulary, develop their comprehension skills and practise using the simple present tense. | ||||

40 | What’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

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | What’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’. | ||||

2 | When I was Young | Life 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’. | ||||

3 | When I was Young | Have 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. | ||||

4 | Space and Time | We’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. | ||||

5 | Space and Time | We’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. | ||||

6 | Choices and Places | A New Jacket | ||

Objective: Students will develop their comprehension skills by reading a text in which preferences are discussed and comparisons are made. | ||||

7 | Choices and Places | He 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. | ||||

8 | What’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. | ||||

9 | What’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. | ||||

10 | Class Camp | Dear Parents, … | ||

Objective: Students will develop their comprehension skills by reading a letter which uses a variety of verb tenses. | ||||

11 | Class Camp | A 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. | ||||

12 | Sentences | The Sentence | ||

Objective: To identify and use complete sentences. | ||||

13 | Capitalisation | Capital Letters 1 | ||

Objective: To use capital letters correctly: to begin sentences, for proper nouns. | ||||

14 | Common Nouns | Common Nouns | ||

Objective: To show a common noun names an object or thing. | ||||

15 | Punctuation | Sentence Endings | ||

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly. | ||||

16 | Verbs | Simple Verbs | ||

17 | Basic Dictionary Use | Basic Dictionary Use | ||

Objective: To find words arranged alphabetically and identify word meanings in dictionaries. | ||||

18 | Nouns | Proper Nouns | ||

Objective: To show a proper noun is used to name a person, place or a title. | ||||

19 | Adjectives | Adjectives | ||

Objective: To show an adjective is a word that describes a noun. | ||||

20 | Adverbs | Adverbs | ||

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb. | ||||

21 | Pronouns | Pronouns | ||

Objective: To show a pronoun is used in place of a noun. | ||||

22 | Parts of Speech Part b | Conjunctions | ||

Objective: To identify and use conjunctions correctly. | ||||

23 | Punctuation | Commas 1 | ||

Objective: To use commas: to list, to make meaning clear, and when writing the date. | ||||

24 | Contractions | Contractions | ||

Objective: To identify and use contractions. | ||||

25 | Parts of Speech Part h | Articles and Demonstratives | ||

Objective: To identify and use articles and demonstratives correctly. | ||||

26 | Antonyms and Synonyms | Antonyms and Synonyms | ||

Objective: To identify and use antonyms and synonyms. | ||||

27 | Spelling Skills | Spelling | ||

Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’. | ||||

28 | Spelling Skills | Syllabification | ||

Objective: To improve spelling by dividing words correctly into syllables. | ||||

29 | Plurals | Plurals 2 – special rules | ||

Objective: To form plurals with special rules: words ending in ‘y’ and ‘f’. | ||||

30 | Nouns | Collective and Abstract Nouns | ||

Objective: To identify and use collective and abstract nouns. | ||||

31 | Verbs | Verbs – Tense | ||

Objective: To identify and use the correct tense of verbs: past, present and future. | ||||

32 | Adjectives | Adjectives – Comparatives and Superlatives | ||

Objective: To identify and use comparative and superlative adjectives. | ||||

33 | Parts of Speech Part a | Prepositions | ||

Objective: To identify and use prepositions correctly. | ||||

34 | Punctuation Skills Part b | Quotation Marks | ||

Objective: To use quotation marks for direct speech. | ||||

35 | Common Errors | Common Errors in writing | ||

Objective: To identify and eliminate common errors. | ||||

36 | Apostrophe – Possession | Apostrophe – Possession | ||

Objective: To use the apostrophe of possession correctly. | ||||

37 | Mnemonics | Spelling – Mnemonics | ||

Objective: To identify and use mnemonics to assist in correct spelling. | ||||

38 | Prefixes | Prefixes | ||

Objective: The identify and use prefixes. | ||||

39 | Suffixes | Suffixes | ||

Objective: The identify and use suffixes. | ||||

40 | Similes and Metaphors | Similes and Metaphors | ||

Objective: To identify and use similes and metaphors. | ||||

41 | Figurative Language | Onomatopoeia, Assonance and Alliteration | ||

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration. | ||||

42 | Homonyms – Homophones and Homographs | Homonyms – Homophones and Homographs | ||

Objective: To identify and use correctly homonyms, both homophones and homographs. | ||||

43 | Advanced Dictionary Use | Advanced Dictionary Use | ||

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus. | ||||

44 | Capitalisation | Capital Letters 2 | ||

Objective: To use capital letters correctly: in titles and letters. | ||||

45 | Adjectives | Adjectives – from Nouns and Verbs | ||

Objective: To create adjectives from nouns and verbs. E.g. China – Chinese | ||||

46 | There’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’. | ||||

47 | There’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 …’. | ||||

48 | Hobbies and Festivals | Collecting 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. | ||||

49 | Hobbies and Festivals | My favourite festival | ||

Objective: Students will build vocabulary; begin to use conjunctions ‘and’, ‘but’ or ‘because’. | ||||

50 | What 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’. | ||||

51 | What’s Homestay? | Simple Present | ||

Objective: Learn the correct structure for the simple present. | ||||

52 | What’s Homestay? | Simple Past | ||

Objective: Learn the correct structure for the past simple. | ||||

53 | Setting off | Present perfect | ||

Objective: Learn the correct structure for the present perfect. | ||||

54 | Here we are! | Adjectives | ||

Objective: Learn the use of adjectives. | ||||

55 | Here we are! | Comparatives and superlatives | ||

Objective: Learn how to use comparatives and superlatives in English. | ||||

56 | A new home | Prepositions of location | ||

Objective: Learn about prepositions of location. | ||||

57 | Let’s hit the beach! | Modals of obligation | ||

Objective: Learn about modals of obligation. | ||||

58 | Amazing Aussie animals | Present continuous | ||

Objective: Learn about the present continuous tense. | ||||

59 | Amazing Aussie animals | Past continuous | ||

Objective: Learn about the past continuous tense. | ||||

60 | Amazing Aussie animals | Giving facts and opinions | ||

Objective: Present phrases that ask for and give opinions. |

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### Year 6 Literacy

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | A visit to the Zoo | About 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. | ||||

2 | A visit to the Zoo | I’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’. | ||||

3 | What 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. | ||||

4 | What 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. | ||||

5 | It’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’. | ||||

6 | It’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. | ||||

7 | We 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. | ||||

8 | We 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. | ||||

9 | To 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. | ||||

10 | To 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. | ||||

11 | Famous People | Bruce 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. | ||||

12 | Famous People | Alexander 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. | ||||

13 | Finding 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. | ||||

14 | Finding 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. | ||||

15 | Sentences | The Sentence | ||

Objective: To identify and use complete sentences. | ||||

16 | Common Nouns | Common Nouns | ||

Objective: To show a common noun names an object or thing. | ||||

17 | Nouns | Proper Nouns | ||

Objective: To show a proper noun is used to name a person, place or a title. | ||||

18 | Adjectives | Adjectives | ||

Objective: To show an adjective is a word that describes a noun. | ||||

19 | Adverbs | Adverbs | ||

20 | Pronouns | Pronouns | ||

Objective: To show a pronoun is used in place of a noun. | ||||

21 | Parts of Speech Part b | Conjunctions | ||

Objective: To identify and use conjunctions correctly. | ||||

22 | Parts of Speech Part h | Articles and Demonstratives | ||

Objective: To identify and use articles and demonstratives correctly. | ||||

23 | Antonyms and Synonyms | Antonyms and Synonyms | ||

Objective: To identify and use antonyms and synonyms. | ||||

24 | Spelling Skills | Syllabification | ||

Objective: To improve spelling by dividing words correctly into syllables. | ||||

25 | Plurals | Plurals 1 – simple | ||

Objective: To form plurals (more than one) by adding ‘s’ and ‘es’ correctly. | ||||

26 | Plurals | Plurals 2 – special rules | ||

Objective: To form plurals with special rules: words ending in ‘y’ and ‘f’. | ||||

27 | Nouns | Collective and Abstract Nouns | ||

Objective: To identify and use collective and abstract nouns. | ||||

28 | Verbs | Verbs – Tense | ||

Objective: To identify and use the correct tense of verbs: past, present and future. | ||||

29 | Adjectives | Adjectives – Comparatives and Superlatives | ||

Objective: To identify and use comparative and superlative adjectives. | ||||

30 | Parts of Speech Part a | Prepositions | ||

Objective: To identify and use prepositions correctly. | ||||

31 | Punctuation Skills Part b | Quotation Marks | ||

Objective: To use quotation marks for direct speech. | ||||

32 | Apostrophe – Possession | Apostrophe – Possession | ||

Objective: To use the apostrophe of possession correctly. | ||||

33 | Mnemonics | Spelling – Mnemonics | ||

Objective: To identify and use mnemonics to assist in correct spelling. | ||||

34 | Prefixes | Prefixes | ||

Objective: The identify and use prefixes. | ||||

35 | Suffixes | Suffixes | ||

Objective: The identify and use suffixes. | ||||

36 | Similes and Metaphors | Similes and Metaphors | ||

Objective: To identify and use similes and metaphors. | ||||

37 | Figurative Language | Onomatopoeia, Assonance and Alliteration | ||

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration. | ||||

38 | Homonyms – Homophones and Homographs | Homonyms – Homophones and Homographs | ||

Objective: To identify and use correctly homonyms, both homophones and homographs. | ||||

39 | Advanced Dictionary Use | Advanced Dictionary Use | ||

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus. | ||||

40 | Capitalisation | Capital Letters 2 | ||

Objective: To use capital letters correctly: in titles and letters. | ||||

41 | Adjectives | Adjectives – from Nouns and Verbs | ||

Objective: To create adjectives from nouns and verbs. E.g. China – Chinese | ||||

42 | Pronouns | Pronouns 2 | ||

Objective: To recognise and use personal, possessive and relative pronouns. | ||||

43 | Commas 2 | Commas 2 | ||

Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech. | ||||

44 | Conjunctions – Sentences | Conjunctions – Sentences | ||

Objective: To use conjunctions to increase the variety of sentence structure in written expression. | ||||

45 | Phrases | Phrases | ||

Objective: To identify and use phrases including adjectival and adverbial phrases. | ||||

46 | Clauses | Clauses | ||

Objective: To identify and use clauses including adjectival, adverbial and noun clauses. | ||||

47 | Simple and Compound Verbs | Simple and Compound Verbs | ||

Objective: To identify and use simple and compound verbs. | ||||

48 | Auxiliary Verbs | Auxiliary Verbs | ||

Objective: To identify and use auxiliary verbs within compound verbs. | ||||

49 | Subject-Verb Agreement | Subject-Verb Agreement | ||

Objective: To identify and use correct tense, number and person in forming verbs. | ||||

50 | Verb tense – Compound | Verb tense – Compound | ||

Objective: To identify and use ‘to be’ and ‘to have’ with the appropriate participle of the main verb. | ||||

51 | Plurals | Plurals 3 – Unusual | ||

Objective: To create unusual plurals: for words ending in ‘o'; by changing the vowels or by adding letters. | ||||

52 | Common Errors | Common Errors in verb usage, spelling and punctuation | ||

Objective: To identify and eliminate common errors. | ||||

53 | Punctuation | Punctuation – Various | ||

Objective: To use hyphens, dashes, apostrophes, quotation marks, parentheses and brackets correctly. | ||||

54 | Vocabulary Development | Vocabulary | ||

Objective: To identify and use better words than ‘got’ and ‘said’. | ||||

55 | What do you like to do? | Adverbs of frequency | ||

Objective: Learn about the past continuous tense. | ||||

56 | BBQ Party! | Expressions of quantity | ||

Objective: Learn the words used to express quantity. | ||||

57 | BBQ Party! | Sequence markers | ||

Objective: Learn the words used in sequences or ordering. | ||||

58 | Big day out! | First and second conditionals | ||

Objective: Learn the use of first conditionals. Learn the use of second conditionals. | ||||

59 | Big day out! | The future with ‘will’ and ‘going to’ | ||

Objective: Learn the uses of ‘will’ and ‘going to’ to talk about the future. | ||||

60 | Thanks and goodbye | Time clauses | ||

Objective: Learn how to use time clauses. |

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### Year 7 Literacy

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | Have 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. | ||||

2 | Have 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. | ||||

3 | Let’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. | ||||

4 | Let’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. | ||||

5 | I 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. | ||||

6 | I 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. | ||||

7 | Where 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. | ||||

8 | Where 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. | ||||

9 | How 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. | ||||

10 | How 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. | ||||

11 | Tell 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. | ||||

12 | Tell 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. | ||||

13 | What’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. | ||||

14 | What’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) | ||||

15 | May 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. | ||||

16 | May 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. | ||||

17 | What 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. | ||||

18 | What 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. | ||||

19 | Let’s celebrate | Merry 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. | ||||

20 | Let’s celebrate | The 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’. | ||||

21 | Sentences | The Sentence | ||

Objective: To identify and use complete sentences. | ||||

22 | Capitalisation | Capital Letters 1 | ||

Objective: To use capital letters correctly: to begin sentences, for proper nouns. | ||||

23 | Punctuation | Sentence Endings | ||

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly. | ||||

24 | Common Nouns | Common Nouns | ||

Objective: To show a common noun names an object or thing. | ||||

25 | Nouns | Proper Nouns | ||

Objective: To show a proper noun is used to name a person, place or a title. | ||||

26 | Verbs | Simple Verbs | ||

27 | Adjectives | Adjectives | ||

Objective: To show an adjective is a word that describes a noun. | ||||

28 | Adverbs | Adverbs | ||

29 | Pronouns | Pronouns | ||

Objective: To show a pronoun is used in place of a noun. | ||||

30 | Parts of Speech Part b | Conjunctions | ||

Objective: To identify and use conjunctions correctly. | ||||

31 | Conjunctions – Sentences | Conjunctions – Sentences | ||

Objective: To use conjunctions to increase the variety of sentence structure in written expression. | ||||

32 | Capitalisation | Capital Letters 2 | ||

Objective: To use capital letters correctly: in titles and letters. | ||||

33 | Parts of Speech Part h | Articles and Demonstratives | ||

Objective: To identify and use articles and demonstratives correctly. | ||||

34 | Antonyms and Synonyms | Antonyms and Synonyms | ||

Objective: To identify and use antonyms and synonyms. | ||||

35 | Punctuation | Commas 1 | ||

Objective: To use commas: to list, to make meaning clear, and when writing the date. | ||||

36 | Commas 2 | Commas 2 | ||

Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech. | ||||

37 | Spelling Skills | Spelling | ||

Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’. | ||||

38 | Spelling Skills | Syllabification | ||

Objective: To improve spelling by dividing words correctly into syllables. | ||||

39 | Plurals | Plurals 2 – special rules | ||

Objective: To form plurals with special rules: words ending in ‘y’ and ‘f’. | ||||

40 | Nouns | Collective and Abstract Nouns | ||

Objective: To identify and use collective and abstract nouns. | ||||

41 | Verbs | Verbs – Tense | ||

Objective: To identify and use the correct tense of verbs: past, present and future. | ||||

42 | Adjectives | Adjectives – Comparatives and Superlatives | ||

Objective: To identify and use comparative and superlative adjectives. | ||||

43 | Parts of Speech Part a | Prepositions | ||

Objective: To identify and use prepositions correctly. | ||||

44 | Punctuation Skills Part b | Quotation Marks | ||

Objective: To use quotation marks for direct speech. | ||||

45 | Apostrophe – Possession | Apostrophe – Possession | ||

Objective: To use the apostrophe of possession correctly. | ||||

46 | Mnemonics | Spelling – Mnemonics | ||

Objective: To identify and use mnemonics to assist in correct spelling. | ||||

47 | Prefixes | Prefixes | ||

Objective: The identify and use prefixes. | ||||

48 | Suffixes | Suffixes | ||

Objective: The identify and use suffixes. | ||||

49 | Similes and Metaphors | Similes and Metaphors | ||

Objective: To identify and use similes and metaphors. | ||||

50 | Figurative Language | Onomatopoeia, Assonance and Alliteration | ||

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration. | ||||

51 | Homonyms – Homophones and Homographs | Homonyms – Homophones and Homographs | ||

Objective: To identify and use correctly homonyms, both homophones and homographs. | ||||

52 | Advanced Dictionary Use | Advanced Dictionary Use | ||

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus. | ||||

53 | Vocabulary Development | Vocabulary | ||

Objective: To identify and use better words than ‘got’ and ‘said’. | ||||

54 | Phrases | Phrases | ||

Objective: To identify and use phrases including adjectival and adverbial phrases. | ||||

55 | Clauses | Clauses | ||

Objective: To identify and use clauses including adjectival, adverbial and noun clauses. | ||||

56 | Simple and Compound Verbs | Simple and Compound Verbs | ||

Objective: To identify and use simple and compound verbs. | ||||

57 | Auxiliary Verbs | Auxiliary Verbs | ||

Objective: To identify and use auxiliary verbs within compound verbs. | ||||

58 | Subject-Verb Agreement | Subject-Verb Agreement | ||

Objective: To identify and use correct tense, number and person in forming verbs. | ||||

59 | Verb tense – Compound | Verb tense – Compound | ||

Objective: To identify and use ‘to be’ and ‘to have’ with the appropriate participle of the main verb. | ||||

60 | Plurals | Plurals 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

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | What’s Homestay? | Want to improve your English? | ||

Objective: Learn how to elicit information from an advertisement and text. | ||||

2 | What’s Homestay? | Homestay application | ||

Objective: Learn how to fill in an application form. | ||||

3 | Setting off | Destination ‘Downunder’ | ||

Objective: Expand vocabulary, read and understand a travel brochure. | ||||

4 | Setting off | A letter to the Carters Full lesson available |
||

Objective: Read and understand an informal letter of introduction. | ||||

5 | Here we are! | Who are the Carters? | ||

Objective: Elicit information from a letter about people’s physical appearance. | ||||

6 | Here we are! | My new family | ||

Objective: Learn how to elicit information about personality traits from the text. | ||||

7 | A new home | This is our house. | ||

Objective: Read a description of a house using prepositions of location. | ||||

8 | A new home | Our room! | ||

Objective: Read a text using prepositions of location. | ||||

9 | Let’s hit the beach! | Meet Tim. He’s a lifesaver. | ||

Objective: Elicit information to answer questions from the text. Identify strong versus mild obligation. | ||||

10 | Let’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. | ||||

11 | Amazing Aussie animals | Marsupials | ||

Objective: Identify factual information within a text, answer questions and recognise a topic sentence. | ||||

12 | Amazing Aussie animals | When we were watching … | ||

Objective: Read postcards about Australian animals. Identify past and present continuous. | ||||

13 | What 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. | ||||

14 | What do you like to do? | How often do you …? | ||

Objective: Use adverbs of frequency and calculate how often activities occur. | ||||

15 | BBQ Party! | A famous Aussie dessert | ||

Objective: Answer comprehension questions and identify expressions of quantity. | ||||

16 | BBQ Party! | A new ‘barbie’! | ||

Objective: Read a set of instructions and complete activities based on comprehension and sequencing details. | ||||

17 | Big day out! | The big three Full lesson available |
||

Objective: Answer comprehension questions and identify first and second conditionals. | ||||

18 | Big day out! | The big plan | ||

Objective: Identify the different uses of ‘going to’. Use different ways of expressing time. | ||||

19 | Thanks and goodbye | My Australian experience | ||

Objective: Read a text and answer comprehension questions. Identify expressions about ‘feelings’. | ||||

20 | Thanks and goodbye | Thank you letter | ||

Objective: Recognise time clauses and identify ‘feeling’ adjectives. | ||||

21 | Sentences | The Sentence | ||

Objective: To identify and use complete sentences. | ||||

22 | Punctuation | Sentence Endings | ||

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly. | ||||

23 | Capitalisation | Capital Letters 2 | ||

Objective: To use capital letters correctly: in titles and letters. | ||||

24 | Pronouns | Pronouns 2 | ||

Objective: To recognise and use personal, possessive and relative pronouns. | ||||

25 | Parts of Speech Part a | Prepositions | ||

Objective: To identify and use prepositions correctly. | ||||

26 | Punctuation Skills Part b | Quotation Marks | ||

Objective: To use quotation marks for direct speech. | ||||

27 | Contractions | Contractions | ||

Objective: To identify and use contractions. | ||||

28 | Common Errors | Common Errors in writing | ||

Objective: To identify and eliminate common errors. | ||||

29 | Commas 2 | Commas 2 | ||

Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech. | ||||

30 | Conjunctions – Sentences | Conjunctions – Sentences | ||

Objective: To use conjunctions to increase the variety of sentence structure in written expression. | ||||

31 | Phrases | Phrases | ||

Objective: To identify and use phrases including adjectival and adverbial phrases. | ||||

32 | Clauses | Clauses | ||

Objective: To identify and use clauses including adjectival, adverbial and noun clauses. | ||||

33 | Subject-Verb Agreement | Subject-Verb Agreement | ||

Objective: To identify and use correct tense, number and person in forming verbs. | ||||

34 | Verb tense – Compound | Verb tense – Compound | ||

Objective: To identify and use ‘to be’ and ‘to have’ with the appropriate participle of the main verb. | ||||

35 | Verbs – Active and Passive voice | Verbs – Active and Passive voice | ||

Objective: To identify and use active and passive voice. | ||||

36 | Apostrophe – Possession | Apostrophe – Possession | ||

Objective: To use the apostrophe of possession correctly. | ||||

37 | Similes and Metaphors | Similes and Metaphors | ||

Objective: To identify and use similes and metaphors. | ||||

38 | Figurative Language | Onomatopoeia, Assonance and Alliteration | ||

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration. | ||||

39 | Common Errors | Common Errors in verb usage, spelling and punctuation | ||

Objective: To identify and eliminate common errors. | ||||

40 | Colons and Semi-Colons | Colons and Semi-Colons | ||

Objective: To use colons and semi-colons correctly. | ||||

41 | Sentence Structure Part a | Subject and Predicate | ||

Objective: To identify the subject and predicate within a sentence and to understand they are the two main parts of a sentence. | ||||

42 | Regular and Irregular Verbs | Regular and Irregular Verbs | ||

Objective: To identify and use regular and irregular verbs in the present and past tense. | ||||

43 | Verbs – Infinitives | Verbs – Infinitives | ||

Objective: To identify and use the infinitive form of the verb. | ||||

44 | Modal Verbs | Modal Verbs | ||

Objective: To identify and use modal verbs with the appropriate form of the main verb. | ||||

45 | Participles – as Verbs and Adjectives | Participles – as Verbs and Adjectives | ||

Objective: To identify and use participles as verbs or adjectives as indicators of continuing action. | ||||

46 | Gerunds | Gerunds | ||

Objective: To identify and use gerunds. | ||||

47 | Interjections | Interjections | ||

Objective: To identify and use interjections correctly. | ||||

48 | Plurals | Plurals 4 – Unusual | ||

Objective: To use nouns whose singular and plural forms are the same. To use compound noun plurals. | ||||

49 | Sentence Improvement | Sentence Improvement | ||

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses. | ||||

50 | Punctuation | Punctuation – Various | ||

Objective: To use hyphens, dashes, apostrophes, quotation marks, parentheses and brackets correctly. | ||||

51 | Mass and Count Nouns | Determiners | ||

Objective: To identify and use determiners correctly with mass and count nouns. | ||||

52 | Transitive and Intransitive Verbs | Transitive and Intransitive Verbs | ||

Objective: To identify and use transitive and intransitive verbs. | ||||

53 | Case – Nouns and Pronouns | Case – Nouns, Pronouns and Possessive Adjectives | ||

Objective: To identify the case of nouns and pronouns. | ||||

54 | Plurals of Foreign Nouns | Plurals 5 – Foreign | ||

Objective: To form plurals of foreign nouns. | ||||

55 | Variety of Expression | Sentence Construction | ||

Objective: To construct expressive and precise sentences to improve meaning. | ||||

56 | Figurative Language | Symbolism and Personification | ||

Objective: To identify, and make use of, symbolism and personification. | ||||

57 | Review of Figures of Speech | Review of Figures of Speech | ||

Objective: To identify multiple uses of figures of speech within writing. | ||||

58 | Spelling Skills | Word Usage | ||

Objective: To correctly choose words with similar spelling, sound and meaning. | ||||

59 | Essay Writing 1 | Essay Writing 1 | ||

Objective: To develop and write essays (expositions). | ||||

60 | Essay Writing 2 | Essay Writing 2 | ||

Objective: To develop and write essays. |

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### Year 9-12 Literacy

# | TOPIC | TITLE | ||
---|---|---|---|---|

1 | Sentences | The Sentence | ||

Objective: To identify and use complete sentences. | ||||

2 | Vowels | Vowels – Long and Short | ||

Objective: To identify long and short vowel sounds, and their use. | ||||

3 | Basic Dictionary Use | Basic Dictionary Use | ||

Objective: To find words arranged alphabetically and identify word meanings in dictionaries. | ||||

4 | Capitalisation | Capital Letters 1 | ||

Objective: To use capital letters correctly: to begin sentences, for proper nouns. | ||||

5 | Punctuation | Sentence Endings | ||

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly. | ||||

6 | Common Nouns | Common Nouns | ||

Objective: To show a common noun names an object or thing. | ||||

7 | Nouns | Proper Nouns | ||

Objective: To show a proper noun is used to name a person, place or a title. | ||||

8 | Verbs | Simple Verbs | ||

9 | Adjectives | Adjectives | ||

Objective: To show an adjective is a word that describes a noun. | ||||

10 | Adverbs | Adverbs | ||

11 | Pronouns | Pronouns | ||

Objective: To show a pronoun is used in place of a noun. | ||||

12 | Parts of Speech Part b | Conjunctions | ||

Objective: To identify and use conjunctions correctly. | ||||

13 | Common Errors | Common Errors in spelling and punctuation | ||

Objective: To identify and eliminate common errors. | ||||

14 | Conjunctions – Sentences | Conjunctions – Sentences | ||

Objective: To use conjunctions to increase the variety of sentence structure in written expression. | ||||

15 | Capitalisation | Capital Letters 2 | ||

Objective: To use capital letters correctly: in titles and letters. | ||||

16 | Parts of Speech Part h | Articles and Demonstratives | ||

Objective: To identify and use articles and demonstratives correctly. | ||||

17 | Antonyms and Synonyms | Antonyms and Synonyms | ||

Objective: To identify and use antonyms and synonyms. | ||||

18 | Punctuation | Commas 1 | ||

Objective: To use commas: to list, to make meaning clear, and when writing the date. | ||||

19 | Commas 2 | Commas 2 | ||

20 | Spelling Skills | Spelling | ||

Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’. | ||||

21 | Spelling Skills | Syllabification | ||

Objective: To improve spelling by dividing words correctly into syllables. | ||||

22 | Plurals | Plurals 1 – simple | ||

Objective: To form plurals (more than one) by adding ‘s’ and ‘es’ correctly. | ||||

23 | Plurals | Plurals 2 – special rules | ||

Objective: To form plurals with special rules: words ending in ‘y’ and ‘f’. | ||||

24 | Nouns | Collective and Abstract Nouns | ||

Objective: To identify and use collective and abstract nouns. | ||||

25 | Verbs | Verbs – Tense | ||

Objective: To identify and use the correct tense of verbs: past, present and future. | ||||

26 | Adjectives | Adjectives – from Nouns and Verbs | ||

Objective: To create adjectives from nouns and verbs. E.g. China – Chinese | ||||

27 | Adjectives | Adjectives – Comparatives and Superlatives | ||

Objective: To identify and use comparative and superlative adjectives. | ||||

28 | Parts of Speech Part a | Prepositions | ||

Objective: To identify and use prepositions correctly. | ||||

29 | Punctuation Skills Part b | Quotation Marks | ||

Objective: To use quotation marks for direct speech. | ||||

30 | Apostrophe – Possession | Apostrophe – Possession | ||

Objective: To use the apostrophe of possession correctly. | ||||

31 | Mnemonics | Spelling – Mnemonics | ||

Objective: To identify and use mnemonics to assist in correct spelling. | ||||

32 | Prefixes | Prefixes | ||

Objective: The identify and use prefixes. | ||||

33 | Suffixes | Suffixes | ||

Objective: The identify and use suffixes. | ||||

34 | Similes and Metaphors | Similes and Metaphors | ||

Objective: To identify and use similes and metaphors. | ||||

35 | Figurative Language | Onomatopoeia, Assonance and Alliteration | ||

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration. | ||||

36 | Homonyms – Homophones and Homographs | Homonyms – Homophones and Homographs | ||

Objective: To identify and use correctly homonyms, both homophones and homographs. | ||||

37 | Advanced Dictionary Use | Advanced Dictionary Use | ||

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus. | ||||

38 | Vocabulary Development | Vocabulary | ||

Objective: To identify and use better words than ‘got’ and ‘said’. | ||||

39 | Phrases | Phrases | ||

Objective: To identify and use phrases including adjectival and adverbial phrases. | ||||

40 | Clauses | Clauses | ||

Objective: To identify and use clauses including adjectival, adverbial and noun clauses. | ||||

41 | Simple and Compound Verbs | Simple and Compound Verbs | ||

Objective: To identify and use simple and compound verbs. | ||||

42 | Auxiliary Verbs | Auxiliary Verbs | ||

Objective: To identify and use auxiliary verbs within compound verbs. | ||||

43 | Subject-Verb Agreement | Subject-Verb Agreement | ||

Objective: To identify and use correct tense, number and person in forming verbs. | ||||

44 | Verb tense – Compound | Verb tense – Compound | ||

45 | Plurals | Plurals 3 – Unusual | ||

Objective: To create unusual plurals: for words ending in ‘o'; by changing the vowels or by adding letters. | ||||

46 | Pronouns | Pronouns 2 | ||

Objective: To recognise and use personal, possessive and relative pronouns. | ||||

47 | Contractions | Contractions | ||

Objective: To identify and use contractions. | ||||

48 | Common Errors | Common Errors in writing | ||

Objective: To identify and eliminate common errors. | ||||

49 | Verbs – Active and Passive voice | Verbs – Active and Passive voice | ||

Objective: To identify and use active and passive voice. | ||||

50 | Common Errors | Common Errors in verb usage, spelling and punctuation | ||

Objective: To identify and eliminate common errors. | ||||

51 | Colons and Semi-Colons | Colons and Semi-Colons | ||

Objective: To use colons and semi-colons correctly. | ||||

52 | Sentence Structure Part a | Subject and Predicate | ||

Objective: To identify the subject and predicate within a sentence and to understand they are the two main parts of a sentence. | ||||

53 | Regular and Irregular Verbs | Regular and Irregular Verbs | ||

Objective: To identify and use regular and irregular verbs in the present and past tense. | ||||

54 | Verbs – Infinitives | Verbs – Infinitives | ||

Objective: To identify and use the infinitive form of the verb. | ||||

55 | Modal Verbs | Modal Verbs | ||

Objective: To identify and use modal verbs with the appropriate form of the main verb. | ||||

56 | Participles – as Verbs and Adjectives | Participles – as Verbs and Adjectives | ||

Objective: To identify and use participles as verbs or adjectives as indicators of continuing action. | ||||

57 | Gerunds | Gerunds | ||

Objective: To identify and use gerunds. | ||||

58 | Interjections | Interjections | ||

Objective: To identify and use interjections correctly. | ||||

59 | Plurals | Plurals 4 – Unusual | ||

Objective: To use nouns whose singular and plural forms are the same. To use compound noun plurals. | ||||

60 | Sentence Improvement | Sentence Improvement | ||

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses. | ||||

61 | Punctuation | Punctuation – Various | ||

Objective: To use hyphens, dashes, apostrophes, quotation marks, parentheses and brackets correctly. | ||||

62 | Mass and Count Nouns | Determiners | ||

Objective: To identify and use determiners correctly with mass and count nouns. | ||||

63 | Transitive and Intransitive Verbs | Transitive and Intransitive Verbs | ||

Objective: To identify and use transitive and intransitive verbs. | ||||

64 | Case – Nouns and Pronouns | Case – Nouns, Pronouns and Possessive Adjectives | ||

Objective: To identify the case of nouns and pronouns. | ||||

65 | Plurals of Foreign Nouns | Plurals 5 – Foreign | ||

Objective: To form plurals of foreign nouns. | ||||

66 | Variety of Expression | Sentence Construction | ||

Objective: To construct expressive and precise sentences to improve meaning. | ||||

67 | Figurative Language | Symbolism and Personification | ||

Objective: To identify, and make use of, symbolism and personification. | ||||

68 | Review of Figures of Speech | Review of Figures of Speech | ||

Objective: To identify multiple uses of figures of speech within writing. | ||||

69 | Spelling Skills | Word Usage | ||

Objective: To correctly choose words with similar spelling, sound and meaning. | ||||

70 | Essay Writing 1 | Essay Writing 1 | ||

Objective: To develop and write essays (expositions). | ||||

71 | Essay Writing 2 | Essay Writing 2 | ||

Objective: To develop and write essays. | ||||

72 | Letter Writing | Personal and Business Letters | ||

Objective: To use correct setting out and format for personal and business letters. |

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