# California Curriculum

FutureSchool provides online tutoring for both English and Math students and teachers with online classes. Instruction is ideal for families online homeschooling; instruction is personalized for use both on or offline. There are video tutorials to teach students how to take different skills and put them into practice. Content for lessons which is connected to work allows students to work through study plans that are personalized for them to supplement instruction of the classroom or homeschooling.

**California Curriculum Online Math Courses**

If living in California, FutureSchool online math courses follow schoolwork currently available. Math courses follow from basic kindergarten mathematics all the way to Calculus. During grade 8-12, students begin their years of Algebra, with Geometry beginning in year 8-12, as well. During year 8-12 Trigonometry and Calculus are taught. Students are allowed to strengthen their math skills with these many online classes offered from FutureSchool. There is a broad range of options for students for each year of online math courses depending on the level each individual student is at.

**California Curriculum Online English Courses**

FutureSchool is a great way for students to receive strength in English classes by taking their online classes. These online English classes are also an excellent tool to use for individual learning English as a second language. Kindergarten online English courses begin with learning the Alphabet, students are sure to be excited with topics such as – Do you like hamburgers? When they move into grade 2, it is time to begin to tell time. The first title in grade 2, learning how to tell time is a fun one – No School! It’s Sunday! What student will not enjoy that lesson? Grade 9-12 teaches a wide variety of topics, ensuring students have knowledge in every aspect of the California English curriculum.

Find out more about home schooling in America. FutureSchool English and Math online classes cover everything needed from the California curriculum!

## Mathematics

- Kindergarten Mathematics
- Grade 1 Mathematics
- Grade 2 Mathematics
- Grade 3 Mathematics
- Grade 4 Mathematics
- Grade 5 Mathematics
- Grade 6 Mathematics
- Grade 7 Mathematics
- Grade 8-12 Algebra I Mathematics
- Grade 8-12 Geometry Mathematics
- Grade 8-12 Algebra II Mathematics
- Grade 8-12 Trigonometry Mathematics
- Grade 8-12 Mathematical Analysis Mathematics
- Grade 8-12 Linear Algebra Mathematics
- Grade 8-12 Probability and Statistics Mathematics
- Grade 8-12 Probability and Statistics (Adv) Mathematics
- Grade 8-12 Calculus Mathematics
- HSEE - Stats-Data-Probability Mathematics
- HSEE - Number Sense Mathematics
- HSEE - Algebra and Functions Mathematics
- HSEE - Measurement and Geometry Mathematics
- HSEE - Mathematical Reasoning Mathematics
- HSEE - Algebra 1 Mathematics
- HSEE - complete Mathematics
- SAT Trigonometry Mathematics
- SAT Linear Algebra Mathematics
- SAT Analysis Mathematics
- SAT Advanced Probability - Statistics Mathematics
- SAT Extension Mathematics
- SAT All Lessons Mathematics

### Kindergarten Mathematics

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

1 | Self Assessment | Self Assessment – Kindergarten | |

Objective: Assessment | |||

2 | Basic mathematics part 1 | The Numbers 1 to 5 | |

Objective: To match words and numbers from 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 | Basic mathematics part 1 | Ordinal numbers 1-9 | |

Objective: To match ordinal words and numbers with groups of 1-9 objects | |||

5 | Basic mathematics part 1 | Zero and the Counting Numbers 1 to 9 | |

Objective: To identify ‘0’, to establish numerical order (1-10) and to match spelling | |||

6 | Basic mathematics part 1 | The Number 10 | |

Objective: To identify 10 things and to match groups (1-10) of things to their number | |||

7 | Basic mathematics part 1 | The Numbers 11 to 20 | |

Objective: To write the numeral and word for the numbers 11 to 20 and to count up to 20 | |||

8 | Basic mathematics part 1 | Using Place Value to Order Numbers up to 20 | |

Objective: To use place value to understand the value of numbers up to 20 | |||

9 | 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. | |||

10 | Basic mathematics part 1 | Simple addition up to the number 10 | |

Objective: To construct addition sentences (sum to 10) using + and = | |||

11 | Basic mathematics part 1 | Simple addition up to the number 20 | |

Objective: To add numbers 1 to 10 to a sum <20 using horizontal and vertical formats | |||

12 | 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. | |||

13 | Basic mathematics part 1 | Subtraction: by comparison | |

Objective: To establish concept of more and to use subtraction to work out how many more | |||

14 | Measurement – Length | Compare length by using informal units of measurement | |

Objective: To choose the most appropriate body part as a unit for measuring common objects | |||

15 | Measurement – Mass | Introducing the concept of mass | |

Objective: To distinguish between light and heavy objects | |||

16 | 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. | |||

17 | Time | Months and Seasons of the year | |

Objective: To name and order the months of the year, the number of days in each month and name the seasons in order | |||

18 | Time | Days of the Week | |

Objective: To name and recognise the days of the week in order | |||

19 | Time | Duration | |

Objective: To choose the difference between a short time and a long time | |||

20 | Time | Units of time | |

Objective: To convert units of time by reading simple timetables, timelines and calendars | |||

21 | Space | Recognise and name triangles | |

Objective: To recall properties of different triangles | |||

22 | Geometry part 1 | Special triangles | |

Objective: To use the properties of equilateral and isosceles triangles to calculate angle size | |||

23 | Geometry part 1 | Quadrilaterals | |

Objective: To use the angle sum of a quadrilateral to calculate unknown angles | |||

24 | 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. | |||

25 | Space | Recognise and name pyramids according to spatial properties | |

Objective: To name pyramids according to the shape of the base | |||

26 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

27 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

28 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

29 | Exam | Exam – Kindergarten | |

Objective: Exam |

### Grade 1 Mathematics

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

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

Objective: Assessment | |||

2 | Basic mathematics part 1 | The Numbers 1 to 5 | |

Objective: To match words and numbers from 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 | Basic mathematics part 1 | Zero and the Counting Numbers 1 to 9 | |

Objective: To identify ‘0’, to establish numerical order (1-10) and to match spelling | |||

5 | Basic mathematics part 1 | The Number 10 | |

Objective: To identify 10 things and to match groups (1-10) of things to their number | |||

6 | Basic mathematics part 1 | The Numbers 11 to 20 | |

Objective: To write the numeral and word for the numbers 11 to 20 and to count up to 20 | |||

7 | 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. | |||

8 | Basic mathematics part 1 | Simple addition up to the number 10 | |

Objective: To construct addition sentences (sum to 10) using + and = | |||

9 | Basic mathematics part 1 | Simple addition up to the number 20 | |

Objective: To add numbers 1 to 10 to a sum <20 using horizontal and vertical formats | |||

10 | 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. | |||

11 | Basic mathematics part 1 | Subtraction: by comparison | |

Objective: To establish concept of more and to use subtraction to work out how many more | |||

12 | Basic mathematics part 1 | Using Place Value to Order Numbers up to 20 | |

Objective: To use place value to understand the value of numbers up to 20 | |||

13 | Basic mathematics part 1 | Multiples of 10 up to 100 | |

Objective: To match numerals and word names for multiples of 10 and add multiples of 10 | |||

14 | Basic mathematics part 1 | Subtraction up to the number 20 | |

Objective: To accurately subtract numbers 1-20 using horizontal and vertical formats | |||

15 | Basic mathematics part 1 | Multiplication using repeated addition | |

Objective: To perform repeated addition in preparation for multiplication | |||

16 | Basic mathematics part 1 | The number 100 | |

Objective: To count by 1, 2, 5 and 10s to 100 and recognise that 10 x 10 = 100 | |||

17 | Basic mathematics part 1 | Addition up to the number 99 | |

Objective: To add two 2-digit numbers to 99 | |||

18 | Basic mathematics part 1 | Subtraction up to the number 99 | |

Objective: To subtract multiples of 10 and subtract 2-digit numbers without trading | |||

19 | Basic mathematics part 1 | Subtraction with Word Problems | |

Objective: To construct suitable subtraction sums in order to solve word problems and puzzles | |||

20 | Measurement – Length | Compare length by using informal units of measurement | |

Objective: To choose the most appropriate body part as a unit for measuring common objects | |||

21 | Measurement – Length | Using the metre as a formal unit to measure perimeter | |

Objective: To calculate the perimeter of shapes whose measurements are given in metres | |||

22 | Measurement – Mass | Introducing the concept of mass | |

Objective: To distinguish between light and heavy objects | |||

23 | 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. | |||

24 | Time | O’clock and half past using digital time | |

Objective: To use the terms ‘o’clock’ and ‘half past’ on a digital clock | |||

25 | Time | O’clock and half past on the analogue clock | |

Objective: To read and use the terms o’clock and half past on an analogue clock | |||

26 | Space | Recognise and name triangles | |

Objective: To recall properties of different triangles | |||

27 | Geometry part 1 | Special triangles | |

Objective: To use the properties of equilateral and isosceles triangles to calculate angle size | |||

28 | Geometry part 1 | Quadrilaterals | |

Objective: To use the angle sum of a quadrilateral to calculate unknown angles | |||

29 | 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. | |||

30 | Space | Recognise and name pyramids according to spatial properties | |

Objective: To name pyramids according to the shape of the base | |||

31 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

32 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

33 | Space | Position | |

Objective: To use positional terms such as behind, next to and above, accurately | |||

34 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

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 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

37 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

38 | Exam | Exam – Grade 1 | |

Objective: Exam |

### Grade 2 Mathematics

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

1 | Self Assessment | Self Assessment – 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 | Basic mathematics part 1 | The numbers 100 to 999 | |

Objective: To use pictures and numerals for numbers 100 to 999 and count by 10s and 100s | |||

4 | Basic mathematics part 1 | Using Place Value to Order Numbers up to 20 | |

Objective: To use place value to understand the value of numbers up to 20 | |||

5 | Basic mathematics part 1 | Simple addition up to the number 10 | |

Objective: To construct addition sentences (sum to 10) using + and = | |||

6 | Basic mathematics part 1 | Simple addition up to the number 20 | |

Objective: To add numbers 1 to 10 to a sum <20 using horizontal and vertical formats | |||

7 | 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. | |||

8 | Basic mathematics part 1 | Subtraction: by comparison | |

Objective: To establish concept of more and to use subtraction to work out how many more | |||

9 | Basic mathematics part 1 | Subtraction up to the number 20 | |

Objective: To accurately subtract numbers 1-20 using horizontal and vertical formats | |||

10 | Basic mathematics part 1 | Addition up to the number 99 | |

Objective: To add two 2-digit numbers to 99 | |||

11 | Basic mathematics part 1 | Subtraction up to the number 99 | |

Objective: To subtract multiples of 10 and subtract 2-digit numbers without trading | |||

12 | Basic mathematics part 1 | Subtraction with trading | |

Objective: To subtract 1 and 2-digit numbers with trading | |||

13 | Basic mathematics part 1 | Subtraction with Word Problems | |

Objective: To construct suitable subtraction sums in order to solve word problems and puzzles | |||

14 | Basic mathematics part 2 | Addition up to the number 999 | |

Objective: To add up to three 2 and 3-digit numbers with and without trading | |||

15 | Basic mathematics part 2 | Subtraction up to the number 999 | |

Objective: To subtract 3-digit numbers with and without trading and find missing digits | |||

16 | Basic mathematics part 1 | Multiplication using equal groups | |

Objective: To identify multiplication as a number of groups of objects | |||

17 | Basic mathematics part 1 | Multiplication using repeated addition | |

Objective: To perform repeated addition in preparation for multiplication | |||

18 | Basic mathematics part 1 | The Multiplication Sign | |

Objective: To use the ‘x’ sign for repeated addition and perform 1-digit multiplication | |||

19 | Basic mathematics part 1 | Multiples of 10 up to 100 | |

Objective: To match numerals and word names for multiples of 10 and add multiples of 10 | |||

20 | Basic mathematics part 1 | The number 100 | |

Objective: To count by 1, 2, 5 and 10s to 100 and recognise that 10 x 10 = 100 | |||

21 | Basic mathematics part 1 | Strategies for division | |

Objective: To perform division by arranging objects into groups | |||

22 | Basic mathematics part 2 | Solve and record division using known facts and sharing | |

Objective: To divide 100 by its factors and divide 2-digit multiples by factors 1 to 5 | |||

23 | Basic mathematics part 1 | Multiplication with important facts | |

Objective: To practice multiplication facts to 10 x 10 | |||

24 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |

Objective: To name and use the fractions 1/2, 1/4 and 1/8 in describing parts of a whole | |||

25 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |

Objective: To use the fractions 1/2, 1/4 and 1/8 to describe equal parts of a collection of objects | |||

26 | Fractions | Comparing and ordering fractions | |

Objective: To compare and order fractions with the same and different numbers of equal parts | |||

27 | Fractions | Fractions 1/5, 1/10, 1/100 | |

Objective: To compare and represent fractions with the denominator 5, 10, 100 | |||

28 | 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. | |||

29 | Fractions | Improper fractions | |

Objective: To use diagrams and number lines to recognise and represent mixed numerals and improper fractions | |||

30 | Decimals | Intro to Decimals | |

Objective: To relate the equivalent fraction to a decimal | |||

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

Objective: To compare and order decimals to two decimal places | |||

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

Objective: To use and understand place value to show whole numbers, tenths and hundredths as decimals | |||

33 | 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. | |||

34 | Basic mathematics part 2 | Multiplication using extended algorithms | |

Objective: To multiply 3-digit by 1-digit numbers and solve multiplication word problems | |||

35 | Basic mathematics part 2 | Multiplication by 2 and 3 Digits | |

Objective: To multiply 3 or 4-digit numbers by 2 or 3-digit numbers | |||

36 | Measurement – Length | Compare length by using informal units of measurement | |

Objective: To choose the most appropriate body part as a unit for measuring common objects | |||

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

Objective: To calculate the perimeter of shapes whose measurements are given in metres | |||

38 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

39 | Data | Bar Charts | |

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

40 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

41 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

42 | Measurement – Length | Compare and convert formal units of measurement | |

Objective: To change cm to mm and then convert mm, cm, m and km from one to another | |||

43 | Measurement – Length | Using the formal unit of the centimetre to measure length and perimeter | |

Objective: To use a ruler to find lengths and perimeters in centimetres | |||

44 | Time | Units of time | |

Objective: To convert units of time by reading simple timetables, timelines and calendars | |||

45 | Time | am and pm time | |

Objective: To distinguish between am and pm time and to use the correct notation for am and pm time | |||

46 | Time | Quarter past and quarter to | |

Objective: To associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes | |||

47 | Time | Relating analogue and digital time | |

Objective: To read analogue and digital clocks to the minute | |||

48 | Time | O’clock and half past using digital time | |

Objective: To use the terms ‘o’clock’ and ‘half past’ on a digital clock | |||

49 | Time | O’clock and half past on the analogue clock | |

Objective: To read and use the terms o’clock and half past on an analogue clock | |||

50 | 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. | |||

51 | Space | Recognise and name pyramids according to spatial properties | |

Objective: To name pyramids according to the shape of the base | |||

52 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

53 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

54 | Space | Recognise and name triangles | |

Objective: To recall properties of different triangles | |||

55 | Space | Use grids to enlarge/reduce 2-D shapes | |

Objective: To recognise shapes that tessellate and specify position on a grid | |||

56 | Basic mathematics part 1 | The Numbers 1 to 5 | |

Objective: To match words and numbers from 1 to 5 | |||

57 | 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. | |||

58 | Basic mathematics part 1 | The Number 10 | |

Objective: To identify 10 things and to match groups (1-10) of things to their number | |||

59 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

60 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

61 | Exam | Exam – Grade 2 | |

Objective: Exam |

### Grade 3 Mathematics

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

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

Objective: Assessment | |||

2 | Basic mathematics part 1 | The numbers 100 to 999 | |

Objective: To use pictures and numerals for numbers 100 to 999 and count by 10s and 100s | |||

3 | Basic mathematics part 2 | The numbers 1000 to 9999 | |

Objective: To write words and numbers to 9999 and count by 1, 10, 100 and 1000 to 9999 | |||

4 | Basic mathematics part 1 | Addition up to the number 99 | |

Objective: To add two 2-digit numbers to 99 | |||

5 | Basic mathematics part 1 | Subtraction up to the number 99 | |

Objective: To subtract multiples of 10 and subtract 2-digit numbers without trading | |||

6 | Basic mathematics part 1 | Subtraction with trading | |

Objective: To subtract 1 and 2-digit numbers with trading | |||

7 | Basic mathematics part 1 | Subtraction with Word Problems | |

Objective: To construct suitable subtraction sums in order to solve word problems and puzzles | |||

8 | Basic mathematics part 2 | Addition up to the number 999 | |

Objective: To add up to three 2 and 3-digit numbers with and without trading | |||

9 | Basic mathematics part 2 | Subtraction up to the number 999 | |

Objective: To subtract 3-digit numbers with and without trading and find missing digits | |||

10 | Basic mathematics part 2 | Addition to 9999 and beyond | |

Objective: To add up to five 3, 4 or 5-digit numbers from 0 to 99 999 | |||

11 | Subtraction | Subtraction involving four digit numbers and beyond using the renaming method. | |

Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers. | |||

12 | Basic mathematics part 1 | Multiplication with important facts | |

Objective: To practice multiplication facts to 10 x 10 | |||

13 | Basic mathematics part 1 | Strategies for division | |

Objective: To perform division by arranging objects into groups | |||

14 | Basic mathematics part 2 | Multiples and factors of whole numbers | |

Objective: To identify the factors, multiples and squares of numbers | |||

15 | Basic mathematics part 2 | Solve and record division using known facts and sharing | |

Objective: To divide 100 by its factors and divide 2-digit multiples by factors 1 to 5 | |||

16 | Basic mathematics part 2 | Multiplication using extended algorithms | |

Objective: To multiply 3-digit by 1-digit numbers and solve multiplication word problems | |||

17 | Basic mathematics part 2 | Dividing two and three-digit numbers by a single-digit number | |

Objective: To divide 3-digit by 1-digit numbers and solve word problems | |||

18 | 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. | |||

19 | Problem solving | Problem Solving Strategies | |

Objective: To review problem solving words and an effective problem solving approach | |||

20 | Problem solving | Word Problems with Numbers | |

Objective: To solve number word problems using + – x and / | |||

21 | Money | Problems involving money | |

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

22 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |

Objective: To name and use the fractions 1/2, 1/4 and 1/8 in describing parts of a whole | |||

23 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |

Objective: To use the fractions 1/2, 1/4 and 1/8 to describe equal parts of a collection of objects | |||

24 | Fractions | Comparing and ordering fractions | |

Objective: To compare and order fractions with the same and different numbers of equal parts | |||

25 | 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. | |||

26 | Fractions | Improper fractions | |

Objective: To use diagrams and number lines to recognise and represent mixed numerals and improper fractions | |||

27 | Fractions | Fractions 1/5, 1/10, 1/100 | |

Objective: To compare and represent fractions with the denominator 5, 10, 100 | |||

28 | Fractions | Finding equivalent fractions | |

Objective: To reduce a fraction to its lowest form | |||

29 | 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. | |||

30 | Decimals | Intro to Decimals | |

Objective: To relate the equivalent fraction to a decimal | |||

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

Objective: To compare and order decimals to two decimal places | |||

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

Objective: To use and understand place value to show whole numbers, tenths and hundredths as decimals | |||

33 | Decimals | Adding decimals to two decimal places | |

Objective: To add decimals with the same number of decimal places (to two decimal Places) | |||

34 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

35 | Decimals | Using decimals to record length | |

Objective: To interpret the everyday use of fractions and decimals | |||

36 | 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. | |||

37 | Measurement – Mass | Introducing the concept of mass | |

Objective: To distinguish between light and heavy objects | |||

38 | Measurement – Length | Compare length by using informal units of measurement | |

Objective: To choose the most appropriate body part as a unit for measuring common objects | |||

39 | Measurement – Length | Using the metre as a formal unit to measure perimeter | |

Objective: To calculate the perimeter of shapes whose measurements are given in metres | |||

40 | Problem solving | Word Problems with Length | |

Objective: To solve length word problems using + – x and / | |||

41 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

42 | 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. | |||

43 | Basic mathematics part 1 | Subtraction: by comparison | |

Objective: To establish concept of more and to use subtraction to work out how many more | |||

44 | Basic mathematics part 1 | The Multiplication Sign | |

Objective: To use the ‘x’ sign for repeated addition and perform 1-digit multiplication | |||

45 | Problem solving | Sign Words | |

Objective: To recognise words and phrases that correspond to + – x and / | |||

46 | Number sets | Addition and Multiplication Properties for Real Numbers | |

Objective: To identify and name addition and multiplication properties for real numbers | |||

47 | Basic mathematics part 1 | Multiplication using equal groups | |

Objective: To identify multiplication as a number of groups of objects | |||

48 | Basic mathematics part 1 | Multiplication using repeated addition | |

Objective: To perform repeated addition in preparation for multiplication | |||

49 | Basic mathematics part 1 | Multiples of 10 up to 100 | |

Objective: To match numerals and word names for multiples of 10 and add multiples of 10 | |||

50 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

51 | Measurement – Capacity | Using the cubic cm and displacement to measure volume and capacity | |

Objective: To find volume and capacity using displacement | |||

52 | Measurement – Capacity | Estimate, measure and compare the capacity of containers | |

Objective: To understand estimation and a way to go about it | |||

53 | Measurement – Volume | Constructing Models | |

Objective: To develop volume of prisms as layers of a number of 1 cm cubes | |||

54 | Measurement – Volume | Using the Cubic Centimetre to Measure Volume | |

Objective: To use the 1 cm cube as the unit for volume | |||

55 | Measurement – Volume | Introducing the Formula for Volume | |

Objective: To calculate the volume of rectangular prisms using V=l x b x h | |||

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

Objective: To use a ruler to find lengths and perimeters in centimetres | |||

57 | Measurement – Length | Compare and convert formal units of measurement | |

Objective: To change cm to mm and then convert mm, cm, m and km from one to another | |||

58 | Space | Using the prefix to determine polygons | |

Objective: To continue sequences of shapes and recognise prefixes and name polygons | |||

59 | Space | Recognise and name triangles | |

Objective: To recall properties of different triangles | |||

60 | Space | Spatial properties of quadrilaterals | |

Objective: To recall and recognise properties of different quadrilaterals | |||

61 | Space | Measure and classify angles | |

Objective: To classify and measure angles and calculate angles in a triangle | |||

62 | 3-D shapes | Recognise and name prisms according to spatial properties | |

63 | Space | Recognise and name pyramids according to spatial properties | |

Objective: To name pyramids according to the shape of the base | |||

64 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

65 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

66 | Probability | Simple events | |

Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S) | |||

67 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

68 | Data | Bar Charts | |

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

69 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

70 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

71 | Exam | Exam – Grade 3 | |

Objective: Exam |

### Grade 4 Mathematics

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

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

Objective: Assessment | |||

2 | Basic mathematics part 2 | Seven digit numbers | |

Objective: To determine the place value of digits in, and the name of numbers to 1 000 000 | |||

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

Objective: To compare and order decimals to two decimal places | |||

4 | Decimals | Rounding Decimals | |

Objective: To round a number with one or two decimal places to the nearest whole number | |||

5 | 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. | |||

6 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |

Objective: To name and use the fractions 1/2, 1/4 and 1/8 in describing parts of a whole | |||

7 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |

Objective: To use the fractions 1/2, 1/4 and 1/8 to describe equal parts of a collection of objects | |||

8 | Fractions | Fractions 1/5, 1/10, 1/100 | |

Objective: To compare and represent fractions with the denominator 5, 10, 100 | |||

9 | Fractions | Multiplying and dividing to obtain equivalent fractions. | |

Objective: To find equivalent fractions using multiplication or division. | |||

10 | Percentages | Understanding percentages | |

Objective: To recognise the percentage symbol and relate a common percentage to a fraction | |||

11 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

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

Objective: To use and understand place value to show whole numbers, tenths and hundredths as decimals | |||

13 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

14 | Fractions | Comparing and ordering fractions greater than 1 | |

Objective: To use diagrams, number lines and equivalent fractions to compare and order fractions greater than 1 | |||

15 | Decimals | Adding decimals to two decimal places | |

Objective: To add decimals with the same number of decimal places (to two decimal Places) | |||

16 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

17 | Basic mathematics part 2 | Addition to 9999 and beyond | |

Objective: To add up to five 3, 4 or 5-digit numbers from 0 to 99 999 | |||

18 | Subtraction | Subtraction involving four digit numbers and beyond using the renaming method. | |

Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers. | |||

19 | Basic mathematics part 2 | Multiplication using extended algorithms | |

Objective: To multiply 3-digit by 1-digit numbers and solve multiplication word problems | |||

20 | Basic mathematics part 2 | Multiplication by 2 and 3 Digits | |

Objective: To multiply 3 or 4-digit numbers by 2 or 3-digit numbers | |||

21 | Basic mathematics part 2 | Dividing two and three-digit numbers by a single-digit number | |

Objective: To divide 3-digit by 1-digit numbers and solve word problems | |||

22 | Long multiplication | Multiplying 2-digit numbers by multiples of 10 | |

Objective: To multiply 2-digit numbers by multiples of 10 using long multiplication | |||

23 | Long multiplication | Multiplying 3 and 4-digit numbers by multiples of 100 | |

Objective: To multiply 4-digit numbers by multiples of 100 using long multiplication | |||

24 | Long multiplication | Multiplying 2-digit numbers by 2-digit numbers | |

Objective: To multiply 2-digit numbers by 2-digit numbers using long multiplication | |||

25 | Problem solving | Word Problems with Numbers | |

Objective: To solve number word problems using + – x and / | |||

26 | Basic mathematics part 2 | Multiples and factors of whole numbers | |

Objective: To identify the factors, multiples and squares of numbers | |||

27 | Basic mathematics part 1 | Subtraction: by comparison | |

Objective: To establish concept of more and to use subtraction to work out how many more | |||

28 | Basic mathematics part 1 | The Multiplication Sign | |

Objective: To use the ‘x’ sign for repeated addition and perform 1-digit multiplication | |||

29 | Basic mathematics part 1 | Strategies for division | |

Objective: To perform division by arranging objects into groups | |||

30 | Basic mathematics part 1 | Multiplication with important facts | |

Objective: To practice multiplication facts to 10 x 10 | |||

31 | 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. | |||

32 | Measurement – Area | Introduction to the square centimetre | |

Objective: To determine the area of a shape by counting the number of square centimetres | |||

33 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height | |||

34 | Algebra – Basic | Algebraic Expressions | |

Objective: To simplify numerical expressions and simplify and expand algebraic expressions | |||

35 | Number sets | Addition and Multiplication Properties for Real Numbers | |

Objective: To identify and name addition and multiplication properties for real numbers | |||

36 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

37 | Measurement – Area | Larger Areas: Square Metre, Hectare, Square Kilometre | |

Objective: To calculate areas in square centimetres, square metres, square kilometres and hectares and convert one to another | |||

38 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

39 | 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. | |||

40 | Co-ordinate geometry part 1 | The Gradient | |

Objective: To find the gradient of a line given its angle of inclination or given rise and run | |||

41 | Geometry-angles | Parallel Lines. | |

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

42 | Co-ordinate geometry part 1 | The Gradient Formula | |

Objective: To use the gradient formula to find the gradient of straight lines | |||

43 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

44 | Space | Spatial properties of quadrilaterals | |

Objective: To recall and recognise properties of different quadrilaterals | |||

45 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

46 | Geometry transformations | Geometry Transformations without Matrices: Dilation or Enlargement | |

Objective: To describe dilations and to calculate lengths and scale factors of dilated figures | |||

47 | Space | Measure and classify angles | |

Objective: To classify and measure angles and calculate angles in a triangle | |||

48 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

49 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

50 | Space | Recognise and name triangles | |

Objective: To recall properties of different triangles | |||

51 | Space | Informal coordinate system | |

Objective: To specify location using a map coordinate system – origin top left | |||

52 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

53 | Data | Bar Charts | |

54 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

55 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

56 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

57 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

58 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

59 | Statistics part 2 | Measures of Spread | |

Objective: To determine a range and use it in decision making | |||

60 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

61 | Probability | Simple events | |

Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S) | |||

62 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

63 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

64 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

65 | Exam | Exam – Grade 4 | |

Objective: Exam |

### Grade 5 Mathematics

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

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

Objective: Assessment | |||

2 | Subtraction | Subtraction involving four digit numbers and beyond using the renaming method. | |

Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers. | |||

3 | Measurement – Volume | Solving Problems about Volume Part 1 | |

Objective: To solve volume problems using same and mixed units of length | |||

4 | Measurement – Volume | Solving Problems about Volume Part 2 | |

Objective: To solve volume problems involving larger objects | |||

5 | Measurement – Capacity | Converting between volume and capacity using milliliters and liters | |

Objective: To solve capacity problems involving mixed dimensional units | |||

6 | Measurement – Mass | The Tonne | |

Objective: To convert kg to tonnes and solve problems involving heavy masses | |||

7 | Percentages | Calculating Percentages and Fractions of Quantities | |

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

8 | Percentages | Understanding percentages | |

Objective: To recognise the percentage symbol and relate a common percentage to a fraction | |||

9 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

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

Objective: To change percentages to fractions and decimals | |||

11 | 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. | |||

12 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

13 | Decimals | Dividing decimals by whole numbers | |

Objective: To divide decimals by whole numbers | |||

14 | Decimals | Dividing numbers by decimals | |

Objective: To divide a whole number by a decimal fraction | |||

15 | Basic mathematics part 2 | Divide whole numbers by a 2-digit divisor | |

Objective: To divide up to 4-digit by 1 or 2-digit numbers with remainders as reduced fractions | |||

16 | Fractions | Multiplying fractions | |

Objective: To multiply fractions and reduce the answer to its lowest form | |||

17 | Fractions | Multiplying mixed numbers | |

Objective: To multiply mixed numbers and reduce the answer to its lowest form | |||

18 | Fractions | Finding reciprocals of fractions and mixed numbers | |

Objective: To find the reciprocals of fractions and mixed numbers | |||

19 | Fractions | Dividing fractions | |

Objective: To divide fractions by other fractions | |||

20 | Fractions | Dividing mixed numbers | |

Objective: To divide mixed numbers | |||

21 | 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. | |||

22 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

23 | Data | Bar Charts | |

24 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

25 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

26 | Algebra – Basic | Algebraic Expressions | |

Objective: To simplify numerical expressions and simplify and expand algebraic expressions | |||

27 | Algebra – Basic | Substitution into Algebraic Expressions | |

Objective: To evaluate simple algebraic expressions using whole numbers, fractions and decimals | |||

28 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

29 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

30 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

31 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

32 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

33 | Space | Mapping | |

Objective: To locate places and describe navigation on a map and use a row/column grid | |||

34 | Space | Main and intermediate compass points | |

Objective: To specify direction using the eight points of a compass | |||

35 | Space | Informal coordinate system | |

Objective: To specify location using a map coordinate system – origin top left | |||

36 | Co-ordinate geometry part 1 | The Mid-Point Formula | |

Objective: To determine the mid-point of an interval using the mid-point formula | |||

37 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height | |||

38 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

39 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

40 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

41 | Measurement – Volume | Introduction to Volume: using the cubic centimetre as a standard unit | |

Objective: To count volume using 1 cm cubes | |||

42 | Measurement – Volume | Constructing Models | |

Objective: To develop volume of prisms as layers of a number of 1 cm cubes | |||

43 | Measurement – Volume | Using the Cubic Centimetre to Measure Volume | |

Objective: To use the 1 cm cube as the unit for volume | |||

44 | Measurement – Volume | Introducing the Formula for Volume | |

Objective: To calculate the volume of rectangular prisms using V=l x b x h | |||

45 | 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 | |||

46 | Measurement – Length | Using the metre as a formal unit to measure perimeter | |

Objective: To calculate the perimeter of shapes whose measurements are given in metres | |||

47 | Measurement – Length | Using the formal unit of the centimetre to measure length and perimeter | |

Objective: To use a ruler to find lengths and perimeters in centimetres | |||

48 | Measurement – Area | Introduction to the square centimetre | |

Objective: To determine the area of a shape by counting the number of square centimetres | |||

49 | Geometry part 1 | Measuring Angles | |

Objective: To use a protractor to measure angles and identify angles as acute, obtuse or reflex | |||

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 part 3 | Points, Lines and Planes | |

Objective: To identify collinear points and coplanar lines and points in 2 and 3 dimensions | |||

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 part 1 | Angle Sum of a Triangle | |

Objective: To use the angle sum for a triangle to calculate unknown angles | |||

54 | Geometry part 1 | Quadrilaterals | |

Objective: To use the angle sum of a quadrilateral to calculate unknown angles | |||

55 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

56 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

57 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

58 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

59 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |

Objective: To use the fractions 1/2, 1/4 and 1/8 to describe equal parts of a collection of objects | |||

60 | Fractions | Comparing and ordering fractions | |

Objective: To compare and order fractions with the same and different numbers of equal parts | |||

61 | Exam | Exam – Grade 5 | |

Objective: Exam |

### Grade 6 Mathematics

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

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

Objective: Assessment | |||

2 | 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. | |||

3 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |

Objective: To name and use the fractions 1/2, 1/4 and 1/8 in describing parts of a whole | |||

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

Objective: To compare and order decimals to two decimal places | |||

5 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

6 | Fractions | Finding equivalent fractions | |

Objective: To reduce a fraction to its lowest form | |||

7 | Fractions | Multiplying and dividing to obtain equivalent fractions. | |

Objective: To find equivalent fractions using multiplication or division. | |||

8 | Uniform motion | The Speed Formula | |

Objective: To calculate speed, distance or time using speed = distance/time | |||

9 | Geometry transformations | Geometry Transformations without Matrices: Mixed and Combined Transformations | |

Objective: To identify images produced by a given sequence of transformations | |||

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 | Percentages | Understanding percentages | |

Objective: To recognise the percentage symbol and relate a common percentage to a fraction | |||

12 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

13 | Money | Problems involving money | |

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

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

Objective: To reduce a fraction to its lowest form | |||

15 | Fractions | Comparing and ordering fractions greater than 1 | |

Objective: To use diagrams, number lines and equivalent fractions to compare and order fractions greater than 1 | |||

16 | Fractions | Subtracting fractions from whole numbers | |

Objective: To use a diagram and mental strategies to subtract fractions from whole numbers | |||

17 | 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. | |||

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

Objective: To add fractions with different denominators and the answer is less than 1 | |||

19 | Fractions | Multiplying fractions by whole numbers | |

Objective: To multiply common fractions by whole numbers | |||

20 | Fractions | Fractions of whole numbers | |

Objective: To find fractions of whole numbers | |||

21 | Fractions | Multiplying fractions | |

Objective: To multiply fractions and reduce the answer to its lowest form | |||

22 | Fractions | Multiplying mixed numbers | |

Objective: To multiply mixed numbers and reduce the answer to its lowest form | |||

23 | Fractions | Finding reciprocals of fractions and mixed numbers | |

Objective: To find the reciprocals of fractions and mixed numbers | |||

24 | Fractions | Dividing fractions | |

Objective: To divide fractions by other fractions | |||

25 | Fractions | Dividing mixed numbers | |

Objective: To divide mixed numbers | |||

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

27 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

28 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

29 | Algebra – Basic | Substitution into Algebraic Expressions | |

Objective: To evaluate simple algebraic expressions using whole numbers, fractions and decimals | |||

30 | Number sets | Addition and Multiplication Properties for Real Numbers | |

Objective: To identify and name addition and multiplication properties for real numbers | |||

31 | Number sets | Transformations That Produce Equivalent Equations | |

Objective: To name properties of equality used to create equivalent equations and solve equations | |||

32 | Measurement – Length | Compare and convert formal units of measurement | |

Objective: To change cm to mm and then convert mm, cm, m and km from one to another | |||

33 | Time | Average speed | |

Objective: To understand what is meant by the speed and average speed of an object and read the instantaneous speed of a vehicle on a speedometer | |||

34 | Uniform motion | Using Subscripted Variables | |

Objective: To use subscripted variables to solve motion problems | |||

35 | Uniform motion | Uniform Motion With Equal Distances | |

Objective: To solve motion problems where distances are equal | |||

36 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height | |||

37 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

38 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

39 | Geometry part 1 | Complementary and Supplementary Angles | |

Objective: To recognise and calculate the size of complementary and supplementary angles | |||

40 | Geometry part 1 | Angle Sum of a Triangle | |

Objective: To use the angle sum for a triangle to calculate unknown angles | |||

41 | Geometry part 1 | Exterior angle theorem | |

Objective: To use the external angle of a triangle theorem to calculate unknown angles | |||

42 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

43 | Geometry part 1 | Measuring Angles | |

Objective: To use a protractor to measure angles and identify angles as acute, obtuse or reflex | |||

44 | Geometry part 1 | Adjacent Angles | |

Objective: To recognise and calculate the size of adjacent angles | |||

45 | Geometry part 1 | Vertically Opposite Angles | |

Objective: To determine values of pronumerals in vertically opposite angles | |||

46 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

47 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

48 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

49 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

50 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

51 | Decimals | Multiplying decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are multiplied by 10, 100 and 1000 | |||

52 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

53 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

54 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

55 | Probability | Simple events | |

Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S) | |||

56 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

57 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

58 | Exam | Exam – Grade 6 | |

Objective: Exam |

### Grade 7 Mathematics

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

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

Objective: Assessment | |||

2 | Standard/Scientific notation | Scientific notation with larger numbers | |

Objective: To write large numbers in standard or scientific notation | |||

3 | Standard/Scientific notation | Scientific notation with small numbers | |

Objective: To write small numbers in standard or scientific notation | |||

4 | 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. | |||

5 | Basic mathematics part 2 | Solve and record division using known facts and sharing | |

Objective: To divide 100 by its factors and divide 2-digit multiples by factors 1 to 5 | |||

6 | Basic mathematics part 1 | Subtraction with trading | |

Objective: To subtract 1 and 2-digit numbers with trading | |||

7 | Basic mathematics part 1 | Addition up to the number 99 | |

Objective: To add two 2-digit numbers to 99 | |||

8 | Basic mathematics part 1 | Subtraction with Word Problems | |

Objective: To construct suitable subtraction sums in order to solve word problems and puzzles | |||

9 | Basic mathematics part 2 | Multiplication using extended algorithms | |

Objective: To multiply 3-digit by 1-digit numbers and solve multiplication word problems | |||

10 | Subtraction | Subtraction involving four digit numbers and beyond using the renaming method. | |

11 | Basic mathematics part 2 | Divide whole numbers by a 2-digit divisor | |

Objective: To divide up to 4-digit by 1 or 2-digit numbers with remainders as reduced fractions | |||

12 | Fractions | Subtracting fractions from whole numbers | |

Objective: To use a diagram and mental strategies to subtract fractions from whole numbers | |||

13 | 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. | |||

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

Objective: To add fractions with different denominators and the answer is less than 1 | |||

15 | Fractions | Multiplying fractions by whole numbers | |

Objective: To multiply common fractions by whole numbers | |||

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

Objective: To reduce a fraction to its lowest form | |||

17 | Decimals | Adding decimals with a different number of decimal places | |

Objective: To add decimal numbers with a different number of decimal places | |||

18 | Decimals | Multiplication of decimals by decimals to two decimal places | |

Objective: To multiply decimals to two digits | |||

19 | Decimals | Dividing numbers by decimals | |

Objective: To divide a whole number by a decimal fraction | |||

20 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

21 | Algebra – Basic | Directed Numbers: Multiplication and Division | |

Objective: To multiply and divide directed numbers and evaluate powers of directed numbers | |||

22 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

23 | Percentages | Understanding percentages | |

Objective: To recognise the percentage symbol and relate a common percentage to a fraction | |||

24 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

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

Objective: To change percentages to fractions and decimals | |||

26 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

27 | Number sets | Number Sets and Their Members | |

Objective: To distinguish between number sets and identify elements and subsets of number sets | |||

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

29 | Decimals | Using decimals – shopping problems | |

30 | Series and sequences part 2 | Compound Interest | |

Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n | |||

31 | Indices/Exponents | Negative Indices | |

Objective: To evaluate or simplify expressions containing negative indices | |||

32 | 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. | |||

33 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

34 | Graphs part 2 | Absolute Value Equations | |

Objective: To graph equations involving absolute values | |||

35 | Algebra – Basic | Algebraic Expressions | |

Objective: To simplify numerical expressions and simplify and expand algebraic expressions | |||

36 | Algebra – Basic | Simplifying Algebraic Expressions: Adding Like Terms | |

Objective: To simplify numeric and algebraic addition expressions by collecting like terms | |||

37 | Algebra – Basic | Simplifying Algebraic Expressions: Subtracting Like Terms | |

Objective: To simplify algebraic subtractions by collecting like terms | |||

38 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

39 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

40 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

41 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

42 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

43 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

44 | Number sets | Addition and Multiplication Properties for Real Numbers | |

Objective: To identify and name addition and multiplication properties for real numbers | |||

45 | Number sets | Transformations That Produce Equivalent Equations | |

Objective: To name properties of equality used to create equivalent equations and solve equations | |||

46 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

47 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

48 | Data | Bar Charts | |

49 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

50 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

51 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

52 | Algebra – Basic | Algebraic fractions resulting in negative Indices | |

Objective: To simplify algebraic fractions using negative indices (as required) in the answer | |||

53 | 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. | |||

54 | Graphs part 2 | Graphing cubic curves | |

Objective: To graph cubic curves whose equation is of the form y = (x – a)^3 + b or y = (a – x)^3 + b | |||

55 | Co-ordinate geometry part 1 | The Gradient | |

Objective: To find the gradient of a line given its angle of inclination or given rise and run | |||

56 | 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. | |||

57 | Problem solving | Problem Solving Strategies | |

Objective: To review problem solving words and an effective problem solving approach | |||

58 | Problem solving | Word Problems with Length | |

Objective: To solve length word problems using + – x and / | |||

59 | Problem solving | Word Problems with Volume/Capacity | |

Objective: To solve volume and capacity word problems using + – x and / | |||

60 | Algebraic equations | Solving two step equations | |

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

61 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

62 | Algebra – Basic | Inequalities | |

Objective: To solve algebraic inequalities requiring (at times) change of direction of inequality sign | |||

63 | Uniform motion | The Speed Formula | |

Objective: To calculate speed, distance or time using speed = distance/time | |||

64 | Uniform motion | Using Subscripted Variables | |

Objective: To use subscripted variables to solve motion problems | |||

65 | Uniform motion | Uniform Motion With Equal Distances | |

Objective: To solve motion problems where distances are equal | |||

66 | Uniform motion | Uniform Motion Adding the Distances | |

Objective: To solve motion problems where total distance travelled is given | |||

67 | 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. | |||

68 | Uniform motion | Uniform Motion Problems Where the Rate is Constant | |

Objective: To solve miscellaneous motion problems where the rate is constant | |||

69 | Measurement – Length | Compare and convert formal units of measurement | |

Objective: To change cm to mm and then convert mm, cm, m and km from one to another | |||

70 | 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. | |||

71 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

72 | Measurement – Advanced area | Area of a Trapezium | |

Objective: To calculate the area of trapezia using A=(h/2)(a+b) | |||

73 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

74 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

75 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

76 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

77 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

78 | Measurement – Advanced volume | Volume of Pyramids and Cones | |

Objective: To calculate the volumes of pyramids and cones | |||

79 | 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. | |||

80 | Measurement – Volume | Using the Cubic Centimetre to Measure Volume | |

Objective: To use the 1 cm cube as the unit for volume | |||

81 | Geometry-constructions | Geometric constructions | |

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

82 | Geometry part 3 | Points, Lines and Planes | |

Objective: To identify collinear points and coplanar lines and points in 2 and 3 dimensions | |||

83 | 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. | |||

84 | Geometry part 3 | Angle Bisector Construction and its Properties | |

Objective: To geometrically bisect angles and calculate angle size given bisection | |||

85 | Geometry part 3 | Circumcenter and Incenter | |

Objective: To use properties of triangles, circles, circumcentres and incentres | |||

86 | Geometry part 3 | Orthocentre and Centroids | |

Objective: To use properties of triangles, circles orthocentres and centroids | |||

87 | Geometry part 3 | Midsegments | |

Objective: To determine midsegments, their length, slope and other properties | |||

88 | Co-ordinate geometry part 2 | Transformations: Reflections | |

Objective: To identify reflections and to use isometric properties of reflections | |||

89 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

90 | Geometry transformations | Geometry Transformations without Matrices: Rotation | |

Objective: To determine rotation angle and to perform prescribed rotations | |||

91 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

92 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

93 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

94 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

95 | 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. | |||

96 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | |

Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS | |||

97 | Geometry part 2 | Proofs and Congruent Triangles | |

Objective: To use congruency in formal proofs in order to determine unknown angles and sides | |||

98 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

99 | Surface area | Surface Area of Composite Solids | |

Objective: To calculate the surface area of composite solids | |||

100 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

101 | Decimals | Multiplying decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are multiplied by 10, 100 and 1000 | |||

102 | Decimals | Intro to Decimals | |

Objective: To relate the equivalent fraction to a decimal | |||

103 | Exam | Exam – Grade 7 | |

Objective: Exam |

### Grade 8-12 Algebra I Mathematics

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

1 | Self Assessment | Self Assessment – Grade 8-12 Algebra I | |

Objective: Assessment | |||

2 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

3 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

4 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

5 | 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. | |||

6 | Indices/Exponents | Multiplying indices when raising a power to a power | |

Objective: To multiply indices when raising a power to a power | |||

7 | Indices/Exponents | Multiplying indices when raising to more than one term | |

Objective: To raise power products to a power | |||

8 | Indices/Exponents | Terms raised to the power of zero | |

Objective: To evaluate expressions where quantities are raised to the power 0 | |||

9 | Indices/Exponents | Negative Indices | |

Objective: To evaluate or simplify expressions containing negative indices | |||

10 | Fractional indices/exponents | Fractional indices | |

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

11 | Indices/Exponents | Complex fractions as indices | |

Objective: To evaluate or simplify expressions containing complex fractional indices and radicals | |||

12 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

13 | Absolute value | Solving Absolute Value Equations | |

Objective: To solve equations involving absolute values | |||

14 | Absolute value | Solving and Graphing Inequalities | |

Objective: To graph the solution set of absolute value inequalities | |||

15 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

16 | Algebra – Basic | Equations involving Grouping Symbols | |

Objective: To solve equations containing grouping symbols on each side | |||

17 | Algebra – Basic | Equations involving fractions | |

Objective: To solve fraction equations with the unknown in either the numerator or denominator | |||

18 | Algebra – Basic | Equations Resulting from Substitution into Formulae | |

Objective: To solve equations created by substituting values into formulae | |||

19 | 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. | |||

20 | Number sets | Transformations That Produce Equivalent Equations | |

Objective: To name properties of equality used to create equivalent equations and solve equations | |||

21 | Co-ordinate geometry part 1 | General Form of a Line and the x and y Intercepts | |

Objective: To write linear equations in general form, to find the x and y intercepts and to calculate area | |||

22 | Co-ordinate geometry part 2 | Inequalities on the Number Plane | |

Objective: To identify the graph which matches a given inequality | |||

23 | Co-ordinate geometry part 2 | Intercept form of a straight line: find the equation when given x and y | |

Objective: To find the equation of a line given the x-axis and y-axis intercepts | |||

24 | Co-ordinate geometry part 1 | Point Slope Form of a Line | |

Objective: To find the equation of a line given its slope and a point on the line (y-y1) = m(x-x1) | |||

25 | Co-ordinate geometry part 2 | Parallel Lines: identify equation of a line parallel to another | |

Objective: To change the standard form of a straight line equation to the y = mx + b form | |||

26 | Co-ordinate geometry part 2 | Perpendicular Lines | |

Objective: To identify the equation of a line that is perpendicular to a given linear equation | |||

27 | Simultaneous equations | Simultaneous Equations | |

Objective: To solve simultaneous equations by substitution | |||

28 | Simultaneous equations | Elimination method | |

Objective: To solve simultaneous equations by elimination | |||

29 | Simultaneous equations | Elimination method part 2 | |

Objective: To solve more difficult simultaneous equations by elimination | |||

30 | 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. | |||

31 | Matrices – Linear systems | Number of Solutions | |

Objective: To determine solutions to systems of equations | |||

32 | Algebra – Basic | Simplifying Algebraic Expressions: Adding Like Terms | |

Objective: To simplify numeric and algebraic addition expressions by collecting like terms | |||

33 | Algebra – Basic | Simplifying Algebraic Expressions: Subtracting Like Terms | |

Objective: To simplify algebraic subtractions by collecting like terms | |||

34 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

35 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

36 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

37 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

38 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

39 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

40 | Algebra – Basic | Factorisation of algebraic fractions including binomials | |

Objective: To simplify algebraic fractions requiring the factorisation of binomial expressions | |||

41 | Algebra – Products and factors | Binomial Products | |

Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b) | |||

42 | Algebra – Products and factors | Binomial products with negative multiplier | |

Objective: To expand and simplify monic binomial products of the form (x – a)(x +/- b) | |||

43 | Algebra – Products and factors | Binomial Products (nonmonic) | |

Objective: To expand and simplify nonmonic binomial products | |||

44 | Algebra – Products and factors | Squaring a Binomial (monic) | |

Objective: To expand the square of a binomial by multiplication and by inspection | |||

45 | 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. | |||

46 | Algebra – Products and factors | Expansions Leading to the Difference of Two Squares | |

Objective: To expand the product of conjugate binomials leading to differences of squares | |||

47 | Algebra – Products and factors | Products in Simplification of Algebraic Expressions | |

Objective: To simplify algebraic expressions containing binomial products | |||

48 | Algebra – Products and factors | Larger Expansions | |

Objective: To expand and simplify the product of a binomial and a trinomial | |||

49 | Algebra – Products and factors | Highest Common Factor | |

Objective: To factorise an expression by identifying and extracting the highest common factor | |||

50 | Algebra – Products and factors | Factors by Grouping | |

Objective: To factorise a four-term expression by grouping | |||

51 | Algebra – Products and factors | Difference of Two Squares | |

Objective: To factorise differences of two squares | |||

52 | Algebra – Products and factors | Common factor and the difference of two squares | |

Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares. | |||

53 | Algebra – Basic | Simplifying easy algebraic fractions | |

Objective: To simplify simple algebraic fractions using cancellation of common factors | |||

54 | Algebra – Basic | Simplifying algebraic fractions using the Index Laws | |

Objective: To use the index laws for division to simplify algebraic fractions | |||

55 | Algebra – Basic | Algebraic fractions resulting in negative Indices | |

Objective: To simplify algebraic fractions using negative indices (as required) in the answer | |||

56 | Algebra – Basic | Cancelling binomial factors in algebraic fractions | |

Objective: To simplify algebraic fractions with binomials in both the numerator and denominator | |||

57 | 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. | |||

58 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

59 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

60 | Algebraic equations | Solving two step equations | |

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

61 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

62 | Function | Evaluating and Graphing Piecewise Functions | |

Objective: To evaluate and graph piecewise functions | |||

63 | Function | Combining Functions | |

Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide | |||

64 | Algebra – Products and factors | 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. | |||

65 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 3 | |

Objective: On completion of the lesson the student will have an increased knowledge on factorizing quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||

66 | 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. | |||

67 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials | |

Objective: To factorise nonmonic quadratic trinomials using the ‘X’ method | |||

68 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials: Moon method | |

Objective: To factorise nonmonic quadratic trinomials using the ‘Moon’ method | |||

69 | Algebra – Quadratic equations | Introduction to Quadratic Equations | |

Objective: To find the solutions of quadratic equations presented as a product of factors | |||

70 | Algebra – Quadratic equations | Solving Quadratic Equations with Factorisation | |

Objective: To solve quadratic equations requiring factorisation | |||

71 | Algebra – Quadratic equations | Solving Quadratic Equations | |

Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 | |||

72 | Algebra – Quadratic equations | Completing the square | |

Objective: To complete an incomplete square | |||

73 | Algebra – Quadratic equations | Solving Quadratic Equations by Completing the Square | |

Objective: To solve quadratic equations by completing the square | |||

74 | Uniform motion | The Speed Formula | |

Objective: To calculate speed, distance or time using speed = distance/time | |||

75 | Uniform motion | Using Subscripted Variables | |

Objective: To use subscripted variables to solve motion problems | |||

76 | Uniform motion | Uniform Motion With Equal Distances | |

Objective: To solve motion problems where distances are equal | |||

77 | Uniform motion | Uniform Motion Adding the Distances | |

Objective: To solve motion problems where total distance travelled is given | |||

78 | 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. | |||

79 | Uniform motion | Uniform Motion Problems Where the Rate is Constant | |

Objective: To solve miscellaneous motion problems where the rate is constant | |||

80 | Uniform motion | Vertical Motion under gravity: Object Dropped from Rest | |

Objective: To calculate velocity, time and distance for vertically falling objects dropped from rest | |||

81 | Uniform motion | Vertical Motion under gravity: Initial Velocity not Zero | |

Objective: To calculate velocity, time and distance for vertical motion with initial velocity not zero | |||

82 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

83 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

84 | 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. | |||

85 | Algebra – Quadratic equations | The Quadratic Formula | |

Objective: To find the roots of a quadratic equation by using the quadratic formula | |||

86 | 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. | |||

87 | Algebra – Quadratic equations | Solving Simultaneous Quadratic Equations Graphically | |

Objective: To determine points of intersection of quadratic and linear equations | |||

88 | 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. | |||

89 | Graphs part 1 | Quadratic Polynomials of the form y = ax^2 + bx + c | |

Objective: To describe and sketch parabolas of the form y = x^2 + bx + c | |||

90 | Graphs part 1 | Graphing perfect squares: y=(a-x) squared | |

Objective: To describe and sketch parabolas of the form y = (x – a)^2 | |||

91 | Graphs part 1 | Graphing irrational roots | |

Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola | |||

92 | Graphs part 1 | Solving Simultaneous Equations graphically | |

Objective: To solve simultaneous equations graphically | |||

93 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

94 | Logic | Proof by Disproof of a Contradictory Statement | |

Objective: To prove that a statement is true by proving that the contradictory statement is false | |||

95 | 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. | |||

96 | Exam | Exam – Grade 8-12 Algebra I | |

Objective: Exam |

### Grade 8-12 Geometry Mathematics

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

1 | Self Assessment | Self Assessment – Grade 8-12 Geometry | |

Objective: Assessment | |||

2 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

3 | Logic | Mathematical induction | |

Objective: To use proof by mathematical induction | |||

4 | Logic | Proof by Disproof of a Contradictory Statement | |

Objective: To prove that a statement is true by proving that the contradictory statement is false | |||

5 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

6 | 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. | |||

7 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | |

Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS | |||

8 | Geometry part 2 | Proofs and Congruent Triangles | |

Objective: To use congruency in formal proofs in order to determine unknown angles and sides | |||

9 | Geometry part 2 | Similar Triangles | |

Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles | |||

10 | 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. | |||

11 | Geometry part 2 | Examples involving overlapping triangles | |

Objective: To determine the lengths of unknown sides in overlapping or adjacent similar triangles | |||

12 | Geometry part 3 | The Triangle Inequality Theorem | |

Objective: To use the triangle inequality theorem to determine constructability of triangles | |||

13 | Geometry-angles | Parallel Lines. | |

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

14 | Geometry part 1 | Additional questions involving parallel lines | |

Objective: To determine angle magnitude for angles formed by parallel lines and transversals | |||

15 | Geometry part 2 | More difficult exercises involving parallel lines | |

Objective: To determine the angles of geometric figures using known properties and theorems | |||

16 | Geometry part 2 | Further difficult exercises involving formal reasoning | |

Objective: To determine formally angles of geometric figures using known properties and theorems | |||

17 | Circle geometry part 1 | Theorem – Equal arcs subtend equal angles at the centre | |

Objective: To know that equal arcs on circles of equal radii subtend equal angles at the centre | |||

18 | Circle geometry part 1 | Theorem – The perpendicular from the centre to a chord bisects the chord | |

Objective: To know that the perpendicular from the centre of a circle to a chord bisects the chord and to know that the line from the centre of a circle to the mid-point of a chord is perpendicular to the chord | |||

19 | Circle geometry part 1 | Theorem – Equal chords in a circle are equidistant from the centre | |

Objective: To know that equal chords in equal circles are equidistant from the centres | |||

20 | Circle geometry part 1 | Theorem – The angle at the centre is double the angle at the circumference | |

Objective: To know that the angle at the centre of a circle is double the angle at the circumference standing on the same arc | |||

21 | Circle geometry part 1 | Theorem: Angles in the same segment of a circle are equal | |

Objective: To know that angles in the same segment of a circle are equal | |||

22 | 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.’ | |||

23 | Circle geometry part 1 | Theorem: The opposite angles of a cyclic quadrilateral are supplementary | |

Objective: To know that the opposite angles of a cyclic quadrilateral are supplementary | |||

24 | Circle geometry part 1 | Theorem – Exterior angle of cyclic quadrilateral equals interior opposite angles | |

Objective: To know that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle | |||

25 | Circle geometry part 1 | Theorem – At the point of contact a tangent is perpendicular to the radius | |

Objective: To know that the tangent to a circle is perpendicular to the radius drawn to it | |||

26 | Circle geometry part 1 | Theorem: Tangents to a circle from an external point are equal | |

Objective: To know that the tangents to a circle from an external point are equal | |||

27 | Measurement – Advanced area | Area of a Trapezium | |

Objective: To calculate the area of trapezia using A=(h/2)(a+b) | |||

28 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

29 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

30 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

31 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

32 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

33 | Measurement – Advanced volume | Volume of Pyramids and Cones | |

Objective: To calculate the volumes of pyramids and cones | |||

34 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

35 | 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. | |||

36 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

37 | Surface area | Surface Area of Pyramids | |

Objective: To calculate the surface area of pyramids | |||

38 | Surface area | Surface Area of Composite Solids | |

Objective: To calculate the surface area of composite solids | |||

39 | 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. | |||

40 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

41 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

42 | Geometry part 1 | Angle Sum of a Triangle | |

Objective: To use the angle sum for a triangle to calculate unknown angles | |||

43 | Geometry part 1 | Exterior angle theorem | |

Objective: To use the external angle of a triangle theorem to calculate unknown angles | |||

44 | Geometry part 1 | Special triangles | |

Objective: To use the properties of equilateral and isosceles triangles to calculate angle size | |||

45 | Geometry part 1 | Quadrilaterals | |

Objective: To use the angle sum of a quadrilateral to calculate unknown angles | |||

46 | Quadrilaterals | Quadrilaterals 1 | |

Objective: To recognise, name and describe the properties of quadrilaterals | |||

47 | Quadrilaterals | Properties of Parallelograms – Opposite Angles Equal | |

Objective: To prove and use ‘Opposite angles of a parallelogram are congruent’ | |||

48 | Quadrilaterals | Properties of Parallelograms – Diagonals, Sides and Angles | |

Objective: To prove parallelogram properties and calculate unknown angles and lengths | |||

49 | Quadrilaterals | The Parallelogram Umbrella | |

Objective: To prove properties of specific parallelograms and find angles and lengths | |||

50 | Quadrilaterals | Properties of Trapezoids | |

Objective: To prove properties of trapezoids and find unknown lengths and angles | |||

51 | 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. | |||

52 | Pythagoras | Proofs of Pythagoras’ Theorem | |

Objective: To examine and complete proofs of Pythagoras’ Theorem | |||

53 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

54 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

55 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

56 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

57 | Geometry-constructions | Geometric constructions | |

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

58 | Geometry part 3 | Points, Lines and Planes | |

Objective: To identify collinear points and coplanar lines and points in 2 and 3 dimensions | |||

59 | 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. | |||

60 | Geometry part 3 | Angle Bisector Construction and its Properties | |

Objective: To geometrically bisect angles and calculate angle size given bisection | |||

61 | Geometry part 3 | Circumcenter and Incenter | |

Objective: To use properties of triangles, circles, circumcentres and incentres | |||

62 | Geometry part 3 | Orthocentre and Centroids | |

Objective: To use properties of triangles, circles orthocentres and centroids | |||

63 | Trigonometry part 1 | Trigonometric Ratios | |

Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle | |||

64 | Trigonometry part 2 | Trigonometric Identities | |

Objective: To simplify expressions using trigonometric equalities | |||

65 | Trigonometry part 1 | Using the Calculator | |

Objective: To determine trigonometric ratios using a calculator | |||

66 | 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. | |||

67 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | |

Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle | |||

68 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | |

Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle | |||

69 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | |

Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator | |||

70 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | |

Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees | |||

71 | Circle geometry part 1 | Theorem – Angle between a tangent and chord equals angle in alternate segment | |

Objective: To know that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment | |||

72 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

73 | Geometry transformations | Geometry Transformations without Matrices: Rotation | |

Objective: To determine rotation angle and to perform prescribed rotations | |||

74 | Geometry transformations | Geometry Transformations without Matrices: Dilation or Enlargement | |

Objective: To describe dilations and to calculate lengths and scale factors of dilated figures | |||

75 | Exam | Exam – Grade 8-12 Geometry | |

Objective: Exam |

### Grade 8-12 Algebra II Mathematics

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

1 | Self Assessment | Self Assessment – Grade 8-12 Algebra II | |

Objective: Assessment | |||

2 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

3 | Absolute value | Solving Absolute Value Equations | |

Objective: To solve equations involving absolute values | |||

4 | Absolute value | Solving and Graphing Inequalities | |

Objective: To graph the solution set of absolute value inequalities | |||

5 | Simultaneous equations | Simultaneous Equations | |

Objective: To solve simultaneous equations by substitution | |||

6 | Simultaneous equations | Elimination method | |

Objective: To solve simultaneous equations by elimination | |||

7 | Simultaneous equations | Elimination method part 2 | |

Objective: To solve more difficult simultaneous equations by elimination | |||

8 | 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. | |||

9 | Matrices – Linear systems | Number of Solutions | |

Objective: To determine solutions to systems of equations | |||

10 | Matrices – Linear systems | Vector Addition in 2 and 3D | |

Objective: To represent, add, subtract and determine the direction of vectors | |||

11 | Matrices – Linear systems | Optimal Solutions | |

Objective: To use linear programming to maximise or minimise an objective function | |||

12 | Matrices – Linear systems | Linear Systems with Matrices | |

Objective: To identify and describe matrices and perform row operations in matrices | |||

13 | Matrices – Linear systems | Row Echelon Form | |

Objective: To identify and create matrices in row echelon form and to solve systems of equations | |||

14 | 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. | |||

15 | Algebra – Basic | Factorisation of algebraic fractions including binomials | |

Objective: To simplify algebraic fractions requiring the factorisation of binomial expressions | |||

16 | Algebra – Basic | Cancelling binomial factors in algebraic fractions | |

Objective: To simplify algebraic fractions with binomials in both the numerator and denominator | |||

17 | Function | Polynomial Addition: in Combining and Simplifying Functions | |

Objective: To evaluate, simplify and graph rational functions | |||

18 | Algebra – Products and factors | Binomial Products | |

Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b) | |||

19 | Algebra – Products and factors | Binomial products with negative multiplier | |

Objective: To expand and simplify monic binomial products of the form (x – a)(x +/- b) | |||

20 | Algebra – Products and factors | Binomial Products (nonmonic) | |

Objective: To expand and simplify nonmonic binomial products | |||

21 | Algebra – Products and factors | Squaring a Binomial (monic) | |

Objective: To expand the square of a binomial by multiplication and by inspection | |||

22 | 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. | |||

23 | Algebra – Products and factors | Expansions Leading to the Difference of Two Squares | |

Objective: To expand the product of conjugate binomials leading to differences of squares | |||

24 | Algebra – Products and factors | Products in Simplification of Algebraic Expressions | |

Objective: To simplify algebraic expressions containing binomial products | |||

25 | Algebra – Products and factors | Larger Expansions | |

Objective: To expand and simplify the product of a binomial and a trinomial | |||

26 | Algebra – Products and factors | Highest Common Factor | |

Objective: To factorise an expression by identifying and extracting the highest common factor | |||

27 | Algebra – Products and factors | Factors by Grouping | |

Objective: To factorise a four-term expression by grouping | |||

28 | Algebra – Products and factors | Difference of Two Squares | |

Objective: To factorise differences of two squares | |||

29 | Algebra – Products and factors | Common factor and the difference of two squares | |

Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares. | |||

30 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 1 | |

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

31 | Algebra – Products and factors | 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. | |||

32 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 3 | |

Objective: On completion of the lesson the student will have an increased knowledge on factorizing quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||

33 | 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. | |||

34 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials | |

Objective: To factorise nonmonic quadratic trinomials using the ‘X’ method | |||

35 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials: Moon method | |

Objective: To factorise nonmonic quadratic trinomials using the ‘Moon’ method | |||

36 | Algebra – Products and factors | Sum and Difference of Two Cubes | |

Objective: To factorise the sum and difference of two cubes | |||

37 | 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. | |||

38 | Trigonometry part 2 | Solving Trigonometric Equations – Type III | |

Objective: To solve trigonometric equations using tan? = sin?/cos?. | |||

39 | Polar coordinates | Polar Coordinates – Plotting and Converting | |

Objective: To plot polar points and convert polar coordinates to rectangular coordinates | |||

40 | Algebra – Basic | Simplifying easy algebraic fractions | |

Objective: To simplify simple algebraic fractions using cancellation of common factors | |||

41 | Algebra – Basic | Simplifying algebraic fractions using the Index Laws | |

Objective: To use the index laws for division to simplify algebraic fractions | |||

42 | Algebra – Basic | Algebraic fractions resulting in negative Indices | |

Objective: To simplify algebraic fractions using negative indices (as required) in the answer | |||

43 | Function | Graphing Rational Functions Part 1 | |

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes | |||

44 | Algebra – Quadratic equations | Introduction to Quadratic Equations | |

Objective: To find the solutions of quadratic equations presented as a product of factors | |||

45 | Algebra – Quadratic equations | Solving Quadratic Equations with Factorisation | |

Objective: To solve quadratic equations requiring factorisation | |||

46 | Algebra – Quadratic equations | Solving Quadratic Equations | |

Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 | |||

47 | Algebra – Quadratic equations | Completing the square | |

Objective: To complete an incomplete square | |||

48 | Algebra – Quadratic equations | Solving Quadratic Equations by Completing the Square | |

Objective: To solve quadratic equations by completing the square | |||

49 | Algebra – Quadratic equations | The Quadratic Formula | |

Objective: To find the roots of a quadratic equation by using the quadratic formula | |||

50 | 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. | |||

51 | Algebra – Quadratic equations | Solving Simultaneous Quadratic Equations Graphically | |

Objective: To determine points of intersection of quadratic and linear equations | |||

52 | Complex numbers | Complex Numbers: Adding and Subtracting | |

Objective: To recognise and manipulate simple complex numbers and expressions | |||

53 | 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. | |||

54 | Graphs part 1 | Quadratic Polynomials of the form y = ax^2 + bx + c | |

Objective: To describe and sketch parabolas of the form y = x^2 + bx + c | |||

55 | Graphs part 1 | Graphing perfect squares: y=(a-x) squared | |

Objective: To describe and sketch parabolas of the form y = (x – a)^2 | |||

56 | Graphs part 1 | Graphing irrational roots | |

Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola | |||

57 | 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. | |||

58 | Logarithms | Equations of type log x to the base 3 = 4 | |

Objective: To find the value of x in a statement of type log x to the base 3 = 4 | |||

59 | Logarithms | Equations of type log 32 to the base x = 5 | |

Objective: To solve Logrithmic Equation where the variable is the base x = 5 | |||

60 | Logarithms | Laws of Logarithms | |

Objective: To review the logarithm laws | |||

61 | Logarithms | Using the Log Laws to Expand Logarithmic Expressions | |

Objective: To expand expressions using the logarithm laws | |||

62 | Logarithms | Using the Log Laws to Simplify Expressions Involving Logarithms | |

Objective: To simplify expressions using the logarithm laws | |||

63 | Logarithms | Using the Log Laws to Find the Logarithms of Numbers | |

Objective: To find the logarithm of a number, with an unknown base, using the logarithm laws | |||

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

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

65 | Logarithms | Using Logarithms to Solve Equations | |

Objective: To use logarithms to solve exponential equations | |||

66 | Logarithms | Change of Base Formula | |

Objective: To evaluate log expressions using logarithms | |||

67 | Fractional indices/exponents | Fractional indices | |

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

68 | Indices/Exponents | Complex fractions as indices | |

Objective: To evaluate or simplify expressions containing complex fractional indices and radicals | |||

69 | Graphs part 2 | The Exponential Function | |

Objective: To graph exponential curves whose exponents are either positive or negative | |||

70 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

71 | 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. | |||

72 | Conic sections | The Parabola | |

Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px | |||

73 | Conic sections | Circles | |

Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles | |||

74 | Conic sections | The Ellipsis | |

Objective: To identify ellipses of the form x^2/a^2 + y^2/b^2 = 1 and to find the equation of ellipses | |||

75 | Conic sections | The Hyperbola | |

Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation | |||

76 | Probability | Counting techniques and ordered selections | |

Objective: To use counting techniques in probability | |||

77 | 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. | |||

78 | Probability | The Binomial Theorem and Binomial Coefficients | |

Objective: To calculate binomial coefficients and expand binomial powers. | |||

79 | Probability | Binomial probabilities using the Binomial Theorem | |

Objective: To calculate the binomial probability of a given number of successful trials | |||

80 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

81 | Series and sequences part 1 | General Sequences | |

Objective: To use the general form of the n’th term of a sequence to find the first 3 terms | |||

82 | 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. | |||

83 | Series and sequences part 1 | The Arithmetic Progression | |

Objective: To find the common difference of a given arithmetic progression | |||

84 | 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. | |||

85 | Series and sequences part 1 | Given two terms of A.P. find the sequence | |

Objective: To find the first term and the common difference in an A.P. given the values and positions of two terms | |||

86 | Series and sequences part 1 | Arithmetic Means | |

Objective: To find the arithmetic mean of two values | |||

87 | Series and sequences part 1 | The sum to n terms of an A.P. | |

Objective: To find the sum of n terms of an arithmetic progression given the first three terms | |||

88 | Series and sequences part 1 | The Geometric Progression | |

Objective: To find the common ratio of a given geometric progression | |||

89 | Series and sequences part 1 | Finding the position of a term in a G.P. | |

Objective: To find the place of a term in a given geometric progression | |||

90 | Series and sequences part 1 | Given two terms of G.P. find the sequence | |

Objective: To find the first term given two terms of a geometric progression | |||

91 | Series and sequences part 2 | Geometric Means | |

Objective: To find geometric means of a and b and insert geometric means between 2 endpoints | |||

92 | Series and sequences part 2 | The sum to n terms of a G.P. | |

Objective: To find the sum of n terms of a sequence | |||

93 | Series and sequences part 2 | Sigma notation | |

Objective: To evaluate progressions using sigma notation | |||

94 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | |

Objective: To find the limiting sum of a sequence | |||

95 | Function | Combining Functions | |

Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide | |||

96 | Function | Simplifying Composite Functions | |

Objective: To simplify, evaluate and determine the domain of composite functions | |||

97 | Function | Inverse Functions | |

Objective: To find the inverse of a function and determine whether this inverse is itself a function | |||

98 | 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. | |||

99 | Exam | Exam – Grade 8-12 Algebra II | |

Objective: Exam |

### Grade 8-12 Trigonometry Mathematics

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

1 | Self Assessment | Self Assessment – Grade 8-12 Trigonometry | |

Objective: Assessment | |||

2 | Space | Measure and classify angles | |

Objective: To classify and measure angles and calculate angles in a triangle | |||

3 | Trigonometry part 1 | Trigonometric Ratios | |

Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle | |||

4 | Trigonometry part 2 | Angles of Any Magnitude | |

Objective: To assign angles to quadrants and to find trigonometric values for angles | |||

5 | Trigonometry part 2 | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |

Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees | |||

6 | 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. | |||

7 | 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. | |||

8 | Trigonometry part 2 | Trigonometric Identities | |

Objective: To simplify expressions using trigonometric equalities | |||

9 | Function | Combining Functions | |

Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide | |||

10 | Function | Simplifying Composite Functions | |

Objective: To simplify, evaluate and determine the domain of composite functions | |||

11 | Function | Parametric Equations | |

Objective: To interchange parametric and Cartesian equations and to identify graphs | |||

12 | Trigonometry part 2 | Solving Trigonometric Equations – Type I | |

Objective: To Solve trigonometric equations for angles from 0 to 360 degrees. | |||

13 | Trigonometry part 2 | Solving Trigonometric Equations – Type II | |

Objective: To solve trigonometric equations for angles from 0 to 360 degrees. | |||

14 | Trigonometry part 2 | Solving Trigonometric Equations – Type III | |

Objective: To solve trigonometric equations using tan? = sin?/cos?. | |||

15 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | |

Objective: To recognise the tangent curve and explore shifts of phase and amplitude | |||

16 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | |

Objective: To graph the primary trigonometric functions and their inverses | |||

17 | Trigonometry part 2 | Reciprocal Ratios | |

Objective: To find the trigonometric ratios for a given right-angled triangle | |||

18 | Co-ordinate geometry part 1 | The Gradient | |

Objective: To find the gradient of a line given its angle of inclination or given rise and run | |||

19 | Function | Inverse Functions | |

Objective: To find the inverse of a function and determine whether this inverse is itself a function | |||

20 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | |

Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees | |||

21 | Trigonometry part 2 | Trigonometric Sum and Difference Identities | |

Objective: To evaluate trig functions of angles using sum and difference identities | |||

22 | Trigonometry part 2 | Double Angle Identities | |

Objective: To use double angle identities to evaluate trig. functions and solve trig equations | |||

23 | Trigonometry part 2 | Half-angle Identities | |

Objective: To evaluate trig. functions of angles using half-angle identities | |||

24 | Trigonometry part 2 | t Formulas | |

Objective: To write t-formulae for trig. functions. To solve equations using t-formulae | |||

25 | Trigonometry part 1 | Using the Calculator | |

Objective: To determine trigonometric ratios using a calculator | |||

26 | 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. | |||

27 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | |

Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle | |||

28 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | |

Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle | |||

29 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | |

Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator | |||

30 | 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. | |||

31 | Trigonometry part 1 | Angles of Elevation and Depression | |

Objective: To identify and distinguish between angles of depression and elevation | |||

32 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | |

Objective: To solve problems involving bearings and angles of elevation and depression | |||

33 | Trigonometry part 1 | Using the Calculator to Find an Angle Given a Trigonometric Ratio | |

Objective: To find angles in right-angled triangles given trigonometric ratios | |||

34 | Trigonometry part 1 | Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle | |

Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems | |||

35 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | |

Objective: To complete the cosine rule to find a subject side for given triangles | |||

36 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | |

Objective: To complete the cosine rule to find a subject angle for given triangles | |||

37 | 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. | |||

38 | Trigonometry part 1 | The Sine Rule: Finding an Angle | |

Objective: To find an unknown angle of a triangle using the sine rule | |||

39 | Trigonometry part 1 | The Sine Area Formula for a Triangle | |

Objective: To use the sine formula for the area of a triangle to calculate area | |||

40 | Polar coordinates | Polar Coordinates – Plotting and Converting | |

Objective: To plot polar points and convert polar coordinates to rectangular coordinates | |||

41 | 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. | |||

42 | Polar coordinates | Graphing Polar Functions | |

Objective: To write the polar coordinates of a point for selected argument ranges | |||

43 | Complex numbers | Complex Numbers: Adding and Subtracting | |

Objective: To recognise and manipulate simple complex numbers and expressions | |||

44 | 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. | |||

45 | Complex numbers | Adding and Subtracting Complex Numbers using Vectors | |

Objective: To perform complex number operations graphically using vectors | |||

46 | Complex numbers | The Absolute Value of a Complex Number | |

Objective: To find the absolute value of a complex number | |||

47 | Complex numbers | Trigonometric Form of a Complex Number | |

Objective: To find the trigonometric form of a complex number | |||

48 | Complex numbers | Multiplication and Division of Complex Numbers in Trigonometric Form | |

Objective: To multiply and divide complex numbers using DeMoivre’s Theorem | |||

49 | Complex numbers | DeMoivre’s theorem | |

Objective: To find powers of complex numbers using DeMoivre’s theorem | |||

50 | Exam | Exam – Grade 8-12 Trigonometry | |

Objective: Exam |

### Grade 8-12 Mathematical Analysis Mathematics

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

1 | Self Assessment | Self Assessment – Grade 8-12 Mathematical Analysis | |

Objective: Assessment | |||

2 | Polar coordinates | Polar Coordinates – Plotting and Converting | |

Objective: To plot polar points and convert polar coordinates to rectangular coordinates | |||

3 | 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. | |||

4 | Polar coordinates | Graphing Polar Functions | |

Objective: To write the polar coordinates of a point for selected argument ranges | |||

5 | Trigonometry part 2 | Solving Trigonometric Equations – Type III | |

Objective: To solve trigonometric equations using tan? = sin?/cos?. | |||

6 | Trigonometry part 2 | Trigonometric Sum and Difference Identities | |

Objective: To evaluate trig functions of angles using sum and difference identities | |||

7 | Trigonometry part 2 | Double Angle Identities | |

Objective: To use double angle identities to evaluate trig. functions and solve trig equations | |||

8 | Trigonometry part 2 | Half-angle Identities | |

Objective: To evaluate trig. functions of angles using half-angle identities | |||

9 | Trigonometry part 2 | t Formulas | |

Objective: To write t-formulae for trig. functions. To solve equations using t-formulae | |||

10 | Logic | Mathematical induction | |

Objective: To use proof by mathematical induction | |||

11 | 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. | |||

12 | 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. | |||

13 | Conic sections | The Parabola | |

Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px | |||

14 | Conic sections | Circles | |

Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles | |||

15 | Conic sections | The Ellipsis | |

Objective: To identify ellipses of the form x^2/a^2 + y^2/b^2 = 1 and to find the equation of ellipses | |||

16 | Conic sections | The Hyperbola | |

Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation | |||

17 | Function | Graphing Rational Functions Part 1 | |

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes | |||

18 | 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. | |||

19 | Function | Parametric Equations | |

Objective: To interchange parametric and Cartesian equations and to identify graphs | |||

20 | Function | Polynomial Addition: in Combining and Simplifying Functions | |

Objective: To evaluate, simplify and graph rational functions | |||

21 | Function | Parametric Functions | |

Objective: To change Cartesian and parametric equations and to graph parametric functions | |||

22 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | |

Objective: To find the limiting sum of a sequence | |||

23 | Series and sequences part 2 | Recurring Decimals and the Infinite G.P. | |

Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction | |||

24 | Calculus part 1 | Limits | |

Objective: To find the limit value of a function as x approaches n | |||

25 | Exam | Exam – Grade 8-12 Mathematical Analysis | |

Objective: Exam |

### Grade 8-12 Linear Algebra Mathematics

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

1 | Self Assessment | Self Assessment – Grade 8-12 Linear Algebra | |

Objective: Assessment | |||

2 | Matrices – Linear systems | Linear Systems with Matrices | |

Objective: To identify and describe matrices and perform row operations in matrices | |||

3 | Matrices – Linear systems | Row Echelon Form | |

Objective: To identify and create matrices in row echelon form and to solve systems of equations | |||

4 | 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. | |||

5 | Matrices | Basic concepts – Matrices | |

Objective: On completion of the lesson the student will have had an introduction to matrices | |||

6 | Matrices | Addition and Subtraction of Matrices | |

Objective: To add and subtract matrices | |||

7 | Matrices | Scalar matrix: multiplication | |

Objective: To multiply a matrix by a scalar | |||

8 | Matrices | Multiplication of one matrix by another matrix | |

Objective: To perform matrix multiplication and to recognise that AB is not equal to BA | |||

9 | Matrices | Translation in the number plane | |

Objective: To use matrix addition to translate points | |||

10 | Matrices | Translation by matrix multiplication | |

Objective: To transform points and objects by matrix multiplication | |||

11 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | |

Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication | |||

12 | Matrices | Vectors | |

Objective: To use vectors to find resultant speeds and displacements | |||

13 | Matrices – Linear systems | Number of Solutions | |

Objective: To determine solutions to systems of equations | |||

14 | Matrices – Linear systems | Vector Addition in 2 and 3D | |

Objective: To represent, add, subtract and determine the direction of vectors | |||

15 | Graphs part 1 | Solving Simultaneous Equations graphically | |

Objective: To solve simultaneous equations graphically | |||

16 | Exam | Exam – Grade 8-12 Linear Algebra | |

Objective: Exam |

### Grade 8-12 Probability and Statistics Mathematics

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

1 | Self Assessment | Self Assessment – Grade 8-12 Probability and Statistics | |

Objective: Assessment | |||

2 | Probability | Simple events | |

3 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

4 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

5 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

6 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

7 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

8 | Probability | P[A or B] When A and B are NOT mutually exclusive | |

Objective: To calculate the probability of non exclusive events using P(A or B) = P(A)+P(B) | |||

9 | Probability | The Binomial Theorem and Binomial Coefficients | |

Objective: To calculate binomial coefficients and expand binomial powers. | |||

10 | Probability | Binomial probabilities using the Binomial Theorem | |

Objective: To calculate the binomial probability of a given number of successful trials | |||

11 | Probability | Counting techniques and ordered selections | |

Objective: To use counting techniques in probability | |||

12 | 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. | |||

13 | Statistics part 2 | Measures of Spread | |

Objective: To determine a range and use it in decision making | |||

14 | Statistics part 2 | Standard deviation applications | |

Objective: To find a standard deviation, using a data set or a frequency distribution table and calculator | |||

15 | Statistics part 2 | Applications of Standard Deviation | |

Objective: To use standard deviation as a measure of deviation from a mean | |||

16 | Statistics part 2 | The Normal Distribution | |

Objective: To use the standard deviation of a normal distribution to find a percentage of scores within ranges | |||

17 | Statistics part 2 | Measures of Spread: the interquartile range | |

Objective: To find the upper and lower quartiles and the interquartile range | |||

18 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

19 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

20 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

21 | Statistics part 2 | Calculating mean, mode and median from grouped data | |

Objective: To identify class centres, get frequency counts and determine mean, mode and median values | |||

22 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

23 | Data | Bar Charts | |

24 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

25 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

26 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

27 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

28 | Statistics | Relative frequency | |

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

29 | Statistics part 1 | Cumulative Frequency | |

Objective: To construct cumulative frequency columns, histograms and polygons | |||

30 | 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. | |||

31 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots | |||

32 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

33 | Exam | Exam – Grade 8-12 Probability and Statistics | |

Objective: Exam |

### Grade 8-12 Probability and Statistics (Adv) Mathematics

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

1 | Self Assessment | Self Assessment – Grade 8-12 Probability and Statistics (Adv) | |

Objective: Assessment | |||

2 | Probability | Simple events | |

3 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

4 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

5 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

6 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

7 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

8 | Probability | P[A or B] When A and B are NOT mutually exclusive | |

Objective: To calculate the probability of non exclusive events using P(A or B) = P(A)+P(B) | |||

9 | Probability | The Binomial Theorem and Binomial Coefficients | |

Objective: To calculate binomial coefficients and expand binomial powers. | |||

10 | Probability | Binomial probabilities using the Binomial Theorem | |

Objective: To calculate the binomial probability of a given number of successful trials | |||

11 | Probability | Counting techniques and ordered selections | |

Objective: To use counting techniques in probability | |||

12 | 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. | |||

13 | Statistics part 2 | Measures of Spread | |

Objective: To determine a range and use it in decision making | |||

14 | Statistics part 2 | Standard deviation applications | |

Objective: To find a standard deviation, using a data set or a frequency distribution table and calculator | |||

15 | Statistics part 2 | Applications of Standard Deviation | |

Objective: To use standard deviation as a measure of deviation from a mean | |||

16 | Statistics part 2 | The Normal Distribution | |

Objective: To use the standard deviation of a normal distribution to find a percentage of scores within ranges | |||

17 | Statistics part 2 | Measures of Spread: the interquartile range | |

Objective: To find the upper and lower quartiles and the interquartile range | |||

18 | Statistics part 2 | Calculating mean, mode and median from grouped data | |

Objective: To identify class centres, get frequency counts and determine mean, mode and median values | |||

19 | Statistics part 2 | Using the Calculator for Statistics | |

Objective: To find a mean, using a data set or a frequency distribution table and calculator. | |||

20 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

21 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

22 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

23 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

24 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

25 | Data | Bar Charts | |

26 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

27 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

28 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

29 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

30 | Statistics | Relative frequency | |

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

31 | Statistics part 1 | Cumulative Frequency | |

Objective: To construct cumulative frequency columns, histograms and polygons | |||

32 | 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. | |||

33 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots | |||

34 | Exam | Exam – Grade 8-12 Probability and Statistics (Adv) | |

Objective: Exam |

### Grade 8-12 Calculus Mathematics

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

1 | Self Assessment | Self Assessment – Grade 8-12 Calculus | |

Objective: Assessment | |||

2 | Polynomials | Introduction to polynomials | |

Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic | |||

3 | Polynomials | The Sum, Difference and Product of Two Polynomials | |

Objective: To add, subtract and multiply polynomials | |||

4 | Polynomials | Polynomials and Long Division | |

Objective: To perform long division of polynomials, finding quotient and remainder | |||

5 | Calculus part 1 | Limits | |

Objective: To find the limit value of a function as x approaches n | |||

6 | Polynomials | Graphs of polynomials | |

Objective: To derive graphs of polynomials by factorising | |||

7 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

8 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

9 | 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. | |||

10 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

11 | Function | Evaluating and Graphing Piecewise Functions | |

Objective: To evaluate and graph piecewise functions | |||

12 | Function | Combining Functions | |

13 | Function | Simplifying Composite Functions | |

Objective: To simplify, evaluate and determine the domain of composite functions | |||

14 | Function | Inverse Functions | |

Objective: To find the inverse of a function and determine whether this inverse is itself a function | |||

15 | Function | Graphing Rational Functions Part 1 | |

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes | |||

16 | 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. | |||

17 | 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. | |||

18 | Calculus part 1 | Differentiation of y = x to the power of n | |

Objective: To differentiate algebraic functions using the laws of differentiation | |||

19 | Calculus part 1 | Meaning of dy over dx – Equations of Tangents and Normals | |

Objective: To find and use the slope of tangents and normals | |||

20 | Calculus part 1 | Function of a Function Rule, Product Rule, Quotient Rule. | |

Objective: To differentiate functions using the product, quotient and chain rules. | |||

21 | Calculus part 1 | Increasing, Decreasing and Stationary Functions. | |

Objective: To determine values of x for which f(x) is increasing, decreasing or stationary. | |||

22 | 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. | |||

23 | Function | Parametric Equations | |

Objective: To interchange parametric and Cartesian equations and to identify graphs | |||

24 | Function | Polynomial Addition: in Combining and Simplifying Functions | |

Objective: To evaluate, simplify and graph rational functions | |||

25 | Function | Parametric Functions | |

Objective: To change Cartesian and parametric equations and to graph parametric functions | |||

26 | Calculus part 1 | Classification of Stationary Points. | |

Objective: To Locate and describe stationary points and points of inflection using differention. | |||

27 | Calculus part 2 | Curve Sketching. | |

Objective: To practice curve sketching of polynomials using calculus techniques. | |||

28 | Calculus part 2 | Practical Applications of Maxima and Minima. | |

Objective: To use maxima and minima to solve practical problems. | |||

29 | Polynomials | Methods of Approximating Roots. | |

Objective: Methods of approximating roots. | |||

30 | Polynomials | Newton’s Method of Approximation. | |

Objective: Newton’s method of approximation. | |||

31 | Calculus part 2 | Antidifferentiation – Primitive Function. | |

Objective: To find primitive functions using antidifferentiation. | |||

32 | Calculus part 2 | Computation of Areas. | |

Objective: To calculate areas under curves using integration. | |||

33 | Calculus part 2 | The Trapezoidal rule and Simpson’s rule | |

Objective: To use Simpson’s rule to determine area under a curve. | |||

34 | Calculus part 2 | Computation of Volumes of Revolution. | |

Objective: To calculate the volume of a solid using integration. | |||

35 | Exam | Exam – Grade 8-12 Calculus | |

Objective: Exam |

### HSEE - Stats-Data-Probability Mathematics

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

1 | Study Plan | Study plan – HSEE – Stats-Data-Probability | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Graphs – Basic | Column Graphs | |

Objective: To read and interpret column graphs | |||

3 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

4 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

5 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

6 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

7 | Statistics part 1 | Relative Frequency | |

Objective: To extend the frequency distribution table to include a relative frequency column | |||

8 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

9 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

10 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

11 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

12 | Statistics part 1 | Cumulative Frequency | |

Objective: To construct cumulative frequency columns, histograms and polygons | |||

13 | Statistics part 1 | Calculating the Mean from a Frequency Distribution | |

Objective: To determine averages (mean, median and mode) from cumulative frequency polygons | |||

14 | Probability | Simple events | |

15 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

16 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

17 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

18 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

19 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

20 | Exam | Exam – HSEE – Stats-Data-Probability | |

Objective: Exam |

### HSEE - Number Sense Mathematics

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

1 | Study Plan | Study plan – HSEE – Number Sense | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Fractions | Comparing and ordering fractions | |

Objective: To compare and order fractions with the same and different numbers of equal parts | |||

3 | Fractions | Finding equivalent fractions | |

Objective: To reduce a fraction to its lowest form | |||

4 | Fractions | Mixed numerals | |

Objective: To name and recognise mixed numerals | |||

5 | Fractions | Improper fractions | |

Objective: To use diagrams and number lines to recognise and represent mixed numerals and improper fractions | |||

6 | Decimals | Adding decimals to two decimal places | |

Objective: To add decimals with the same number of decimal places (to two decimal Places) | |||

7 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

8 | Decimals | Using decimals – shopping problems | |

Objective: To read and interpret problems involving money | |||

9 | Decimals | Using decimals to record length | |

Objective: To interpret the everyday use of fractions and decimals | |||

10 | Decimals | Rounding Decimals | |

Objective: To round a number with one or two decimal places to the nearest whole number | |||

11 | Fractions | Subtracting fractions from whole numbers | |

Objective: To use a diagram and mental strategies to subtract fractions from whole numbers | |||

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

Objective: To add and subtract fractions with the same denominator | |||

13 | Fractions | Multiplying and dividing to obtain equivalent fractions. | |

Objective: To find equivalent fractions using multiplication or division. | |||

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

Objective: To reduce a fraction to its lowest form | |||

15 | Fractions | Comparing and ordering fractions greater than 1 | |

Objective: To use diagrams, number lines and equivalent fractions to compare and order fractions greater than 1 | |||

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

Objective: To add fractions with different denominators and the answer is less than 1 | |||

17 | Fractions | Multiplying fractions by whole numbers | |

Objective: To multiply common fractions by whole numbers | |||

18 | Fractions | Fractions of whole numbers | |

Objective: To find fractions of whole numbers | |||

19 | Decimals | Decimals to three decimal places | |

Objective: To express a number on a thousand as a decimal in thousandths | |||

20 | Decimals | Adding decimals with a different number of decimal places | |

Objective: To add decimal numbers with a different number of decimal places | |||

21 | Decimals | Subtracting decimals with a different number of places | |

Objective: To subtract decimals with a different number of decimal places | |||

22 | Decimals | Multiplying decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are multiplied by 10, 100 and 1000 | |||

23 | Decimals | Multiplying decimals by single-digit numbers | |

Objective: To multiply decimals by single-digit numbers | |||

24 | Decimals | Multiplication of decimals by decimals to two decimal places | |

Objective: To multiply decimals to two digits | |||

25 | Decimals | Dividing decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are divided by 10, 100 and 1000 | |||

26 | Decimals | Dividing decimals by whole numbers | |

Objective: To divide decimals by whole numbers | |||

27 | Decimals | Dividing numbers by decimals | |

Objective: To divide a whole number by a decimal fraction | |||

28 | Percentages | Understanding percentages | |

Objective: To recognise the percentage symbol and relate a common percentage to a fraction | |||

29 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

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

Objective: To change percentages to fractions and decimals | |||

31 | Fractions | Finding reciprocals of fractions and mixed numbers | |

Objective: To find the reciprocals of fractions and mixed numbers | |||

32 | Fractions | Dividing fractions | |

Objective: To divide fractions by other fractions | |||

33 | Fractions | Dividing mixed numbers | |

Objective: To divide mixed numbers | |||

34 | Fractions | Multiplying fractions | |

Objective: To multiply fractions and reduce the answer to its lowest form | |||

35 | Fractions | Multiplying mixed numbers | |

Objective: To multiply mixed numbers and reduce the answer to its lowest form | |||

36 | Problem solving | Sign Words | |

Objective: To recognise words and phrases that correspond to + – x and / | |||

37 | Problem solving | Problem Solving Strategies | |

Objective: To review problem solving words and an effective problem solving approach | |||

38 | Problem solving | Word Problems with Numbers | |

Objective: To solve number word problems using + – x and / | |||

39 | Problem solving | Word Problems with Money | |

Objective: To solve money word problems using + – x and / | |||

40 | Fractions | BODMAS | |

Objective: To calculate answers for fraction and mixed number questions using BODMAS | |||

41 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

42 | Algebra – Basic | Directed Numbers: Multiplication and Division | |

Objective: To multiply and divide directed numbers and evaluate powers of directed numbers | |||

43 | Standard/Scientific notation | Scientific notation with larger numbers | |

Objective: To write large numbers in standard or scientific notation | |||

44 | Standard/Scientific notation | Scientific notation with small numbers | |

Objective: To write small numbers in standard or scientific notation | |||

45 | Standard/Scientific notation | Changing scientific notation to numerals | |

Objective: To interpret scientific notation by writing in base 10 numerals | |||

46 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

47 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

48 | Indices/Exponents | Multiplying indices when raising a power to a power | |

Objective: To multiply indices when raising a power to a power | |||

49 | Indices/Exponents | Multiplying indices when raising to more than one term | |

Objective: To raise power products to a power | |||

50 | Indices/Exponents | Terms raised to the power of zero | |

Objective: To evaluate expressions where quantities are raised to the power 0 | |||

51 | Indices/Exponents | Negative Indices | |

Objective: To evaluate or simplify expressions containing negative indices | |||

52 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

53 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

54 | Percentages | Calculating Percentages and Fractions of Quantities | |

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

55 | Series and sequences part 2 | Compound Interest | |

Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n | |||

56 | Exam | Exam – HSEE – Number Sense | |

Objective: Exam |

### HSEE - Algebra and Functions Mathematics

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

1 | Study Plan | Study plan – HSEE – Algebra and Functions | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Algebra – Basic | Algebraic Expressions | |

Objective: To simplify numerical expressions and simplify and expand algebraic expressions | |||

3 | Algebra – Basic | Substitution into Algebraic Expressions | |

Objective: To evaluate simple algebraic expressions using whole numbers, fractions and decimals | |||

4 | Algebra – Basic | Inequalities | |

Objective: To solve algebraic inequalities requiring (at times) change of direction of inequality sign | |||

5 | Fractions | BODMAS | |

Objective: To calculate answers for fraction and mixed number questions using BODMAS | |||

6 | Algebra – Basic | Simplifying Algebraic Expressions: Adding Like Terms | |

Objective: To simplify numeric and algebraic addition expressions by collecting like terms | |||

7 | Algebra – Basic | Simplifying Algebraic Expressions: Subtracting Like Terms | |

Objective: To simplify algebraic subtractions by collecting like terms | |||

8 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

9 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

10 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

11 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

12 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

13 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

14 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

15 | Time | 24-hour time | |

Objective: To tell the time accurately using 24-hour time and change the time from am and pm time to 24-hour time | |||

16 | Time | Time Zones | |

Objective: To recognise and compare different time zones within Australia | |||

17 | Time | Average speed | |

Objective: To understand what is meant by the speed and average speed of an object and read the instantaneous speed of a vehicle on a speedometer | |||

18 | Graphs part 1 | The parabola: to describe properties of a parabola from its equation | |

Objective: To describe properties of a parabola from its equation and sketch the parabola | |||

19 | Graphs part 2 | Graphing cubic curves | |

Objective: To graph cubic curves whose equation is of the form y = (x – a)^3 + b or y = (a – x)^3 + b | |||

20 | Exam | Exam – HSEE – Algebra and Functions | |

Objective: Exam |

### HSEE - Measurement and Geometry Mathematics

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

1 | Study Plan | Study plan – HSEE – Measurement and Geometry | |

2 | Measurement – Length | Using the metre as a formal unit to measure perimeter | |

Objective: To calculate the perimeter of shapes whose measurements are given in metres | |||

3 | Measurement – Length | Using the formal unit of the centimetre to measure length and perimeter | |

Objective: To use a ruler to find lengths and perimeters in centimetres | |||

4 | Measurement – Length | Read and calculate distances on a map using the formal unit kilometre | |

Objective: To read distances (km) from a map and calculate total distances between locations | |||

5 | Measurement – Length | Compare and convert formal units of measurement | |

Objective: To change cm to mm and then convert mm, cm, m and km from one to another | |||

6 | Measurement – Area | Introduction to the square centimetre | |

Objective: To determine the area of a shape by counting the number of square centimetres | |||

7 | Measurement – Area | Larger Areas: Square Metre, Hectare, Square Kilometre | |

Objective: To calculate areas in square centimetres, square metres, square kilometres and hectares and convert one to another | |||

8 | Measurement – Volume | Introducing the Formula for Volume | |

Objective: To calculate the volume of rectangular prisms using V=l x b x h | |||

9 | Measurement – Volume | Using the Cubic Metre to Measure Volume | |

Objective: To calculate the volume of rectangular prisms in cubic metres | |||

10 | Measurement – Capacity | Using the cubic cm and displacement to measure volume and capacity | |

Objective: To find volume and capacity using displacement | |||

11 | Measurement – Capacity | Using the Cubic cm as a Standard Unit of measurement for Volume and Capacity | |

Objective: To understand a cubic centimetre and how it can be used to find the volume and capacity of a three-dimensional shape | |||

12 | Measurement – Capacity | The relationship between the common units of capacity: the litre and the millilitre | |

Objective: To convert L to mL and vice versa using 1000 mL = 1 L | |||

13 | Measurement – Capacity | Converting between volume and capacity using kiloliters and liters | |

Objective: To know the formal units of measurement for volume and capacity for bigger objects | |||

14 | Measurement – Capacity | Estimate, measure and compare the capacity of containers | |

Objective: To understand estimation and a way to go about it | |||

15 | Measurement – Capacity | Converting between volume and capacity using milliliters and liters | |

Objective: To solve capacity problems involving mixed dimensional units | |||

16 | Measurement – Mass | Introducing the concept of mass | |

Objective: To distinguish between light and heavy objects | |||

17 | Measurement – Mass | The Kilogram | |

Objective: To recognise which of two (or more) objects has the greater mass | |||

18 | Measurement – Mass | The Gram | |

Objective: To calculate net mass in grams and solve shopping problems involving mass | |||

19 | Measurement – Mass | The Tonne | |

Objective: To convert kg to tonnes and solve problems involving heavy masses | |||

20 | Time | Average speed | |

Objective: To understand what is meant by the speed and average speed of an object and read the instantaneous speed of a vehicle on a speedometer | |||

21 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

22 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

23 | Measurement – Volume | Solving Problems about Volume Part 1 | |

Objective: To solve volume problems using same and mixed units of length | |||

24 | Measurement – Volume | Solving Problems about Volume Part 2 | |

Objective: To solve volume problems involving larger objects | |||

25 | Measurement – Advanced area | Area of a Trapezium | |

Objective: To calculate the area of trapezia using A=(h/2)(a+b) | |||

26 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

27 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

28 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

29 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

30 | Measurement – Advanced volume | Volume of Pyramids and Cones | |

Objective: To calculate the volumes of pyramids and cones | |||

31 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

32 | Surface area | Surface Area of a Triangular/Trapezoidal Prism | |

Objective: To calculate the surface area of triangular and trapezoidal prisms | |||

33 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

34 | Surface area | Surface Area of Pyramids | |

Objective: To calculate the surface area of pyramids | |||

35 | Surface area | Surface Area of Composite Solids | |

Objective: To calculate the surface area of composite solids | |||

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 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

38 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

39 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

40 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

41 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

42 | Pythagoras | Proofs of Pythagoras’ Theorem | |

Objective: To examine and complete proofs of Pythagoras’ Theorem | |||

43 | Geometry part 2 | Congruent triangles: Tests 1 and 2 | |

Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS | |||

44 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | |

Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS | |||

45 | Geometry part 2 | Proofs and Congruent Triangles | |

Objective: To use congruency in formal proofs in order to determine unknown angles and sides | |||

46 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

47 | Co-ordinate geometry part 2 | Transformations: Reflections | |

Objective: To identify reflections and to use isometric properties of reflections | |||

48 | Geometry transformations | Geometry Transformations without Matrices: Rotation | |

Objective: To determine rotation angle and to perform prescribed rotations | |||

49 | Exam | Exam – HSEE – Measurement and Geometry | |

Objective: Exam |

### HSEE - Mathematical Reasoning Mathematics

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

1 | Study Plan | Study plan – HSEE – Mathematical Reasoning | |

2 | Problem solving | Sign Words | |

Objective: To recognise words and phrases that correspond to + – x and / | |||

3 | Problem solving | Problem Solving Strategies | |

Objective: To review problem solving words and an effective problem solving approach | |||

4 | Problem solving | Word Problems with Numbers | |

Objective: To solve number word problems using + – x and / | |||

5 | Problem solving | Word Problems with Money | |

Objective: To solve money word problems using + – x and / | |||

6 | Problem solving | Word Problems with Length | |

Objective: To solve length word problems using + – x and / | |||

7 | Problem solving | Word Problems with Mass | |

Objective: To solve mass word problems using + – x and / | |||

8 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

9 | Problem solving | Word Problems with Volume/Capacity | |

Objective: To solve volume and capacity word problems using + – x and / | |||

10 | Measurement – Volume | Solving Problems about Volume Part 1 | |

Objective: To solve volume problems using same and mixed units of length | |||

11 | Measurement – Volume | Solving Problems about Volume Part 2 | |

Objective: To solve volume problems involving larger objects | |||

12 | Percentages | Calculating Percentages and Fractions of Quantities | |

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

13 | Algebra – Quadratic equations | Problem solving with quadratic equations | |

Objective: To solve problems which require finding the roots of a quadratic equation | |||

14 | Measurement – Capacity | Estimate, measure and compare the capacity of containers | |

Objective: To understand estimation and a way to go about it | |||

15 | Measurement – Mass | Introducing the concept of mass | |

Objective: To distinguish between light and heavy objects | |||

16 | Measurement – Mass | The Kilogram | |

Objective: To recognise which of two (or more) objects has the greater mass | |||

17 | Measurement – Mass | The Tonne | |

Objective: To convert kg to tonnes and solve problems involving heavy masses | |||

18 | Exam | Exam – HSEE – Mathematical Reasoning | |

Objective: Exam |

### HSEE - Algebra 1 Mathematics

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

1 | Study Plan | Study plan – HSEE – Algebra 1 | |

2 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

3 | Algebra – Basic | Directed Numbers: Multiplication and Division | |

Objective: To multiply and divide directed numbers and evaluate powers of directed numbers | |||

4 | Fractions | BODMAS | |

Objective: To calculate answers for fraction and mixed number questions using BODMAS | |||

5 | Fractions | Finding reciprocals of fractions and mixed numbers | |

Objective: To find the reciprocals of fractions and mixed numbers | |||

6 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

7 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

8 | Indices/Exponents | Multiplying indices when raising a power to a power | |

Objective: To multiply indices when raising a power to a power | |||

9 | Indices/Exponents | Multiplying indices when raising to more than one term | |

Objective: To raise power products to a power | |||

10 | Indices/Exponents | Terms raised to the power of zero | |

Objective: To evaluate expressions where quantities are raised to the power 0 | |||

11 | Indices/Exponents | Negative Indices | |

Objective: To evaluate or simplify expressions containing negative indices | |||

12 | Indices/Exponents | Fractional Indices | |

Objective: To evaluate or simplify expressions containing fractional indices | |||

13 | Indices/Exponents | Complex fractions as indices | |

Objective: To evaluate or simplify expressions containing complex fractional indices and radicals | |||

14 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

15 | Absolute value | Solving Absolute Value Equations | |

Objective: To solve equations involving absolute values | |||

16 | Absolute value | Solving and Graphing Inequalities | |

Objective: To graph the solution set of absolute value inequalities | |||

17 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

18 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

19 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

20 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

21 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

22 | Algebra – Basic | Equations involving Grouping Symbols | |

Objective: To solve equations containing grouping symbols on each side | |||

23 | Algebra – Basic | Equations involving fractions | |

Objective: To solve fraction equations with the unknown in either the numerator or denominator | |||

24 | Algebra – Basic | Inequalities | |

Objective: To solve algebraic inequalities requiring (at times) change of direction of inequality sign | |||

25 | Graphs part 1 | Graphing perfect squares: y=(a-x) squared | |

Objective: To describe and sketch parabolas of the form y = (x – a)^2 | |||

26 | Co-ordinate geometry part 1 | The Straight Line | |

Objective: To state the equation of lines parallel to the axes and to graph equations x = a and y = b | |||

27 | Co-ordinate geometry part 1 | Slope Intercept Form of a Line | |

Objective: To change equation to slope intercept form and graph it and to find equation given graph | |||

28 | Co-ordinate geometry part 2 | Inequalities on the Number Plane | |

Objective: To identify the graph which matches a given inequality | |||

29 | Co-ordinate geometry part 2 | Parallel Lines: identify equation of a line parallel to another | |

Objective: To change the standard form of a straight line equation to the y = mx + b form | |||

30 | Co-ordinate geometry part 2 | Perpendicular Lines | |

Objective: To identify the equation of a line that is perpendicular to a given linear equation | |||

31 | Co-ordinate geometry part 1 | The Gradient | |

Objective: To find the gradient of a line given its angle of inclination or given rise and run | |||

32 | Simultaneous equations | Simultaneous Equations | |

Objective: To solve simultaneous equations by substitution | |||

33 | Simultaneous equations | Elimination method | |

Objective: To solve simultaneous equations by elimination | |||

34 | Simultaneous equations | Elimination method part 2 | |

Objective: To solve more difficult simultaneous equations by elimination | |||

35 | Simultaneous equations | Applications of simultaneous equations | |

Objective: To solve problems using simultaneous equations | |||

36 | Algebra – Products and factors | Binomial Products | |

Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b) | |||

37 | Algebra – Products and factors | Binomial products with negative multiplier | |

Objective: To expand and simplify monic binomial products of the form (x – a)(x +/- b) | |||

38 | Algebra – Products and factors | Binomial Products (nonmonic) | |

Objective: To expand and simplify nonmonic binomial products | |||

39 | Algebra – Products and factors | Squaring a Binomial (monic) | |

Objective: To expand the square of a binomial by multiplication and by inspection | |||

40 | Algebra – Products and factors | Squaring a Binomial (nonmonic) | |

Objective: To expand the square of a nonmonic binomial by inspection | |||

41 | Algebra – Products and factors | Expansions Leading to the Difference of Two Squares | |

Objective: To expand the product of conjugate binomials leading to differences of squares | |||

42 | Algebra – Products and factors | Products in Simplification of Algebraic Expressions | |

Objective: To simplify algebraic expressions containing binomial products | |||

43 | Algebra – Products and factors | Larger Expansions | |

Objective: To expand and simplify the product of a binomial and a trinomial | |||

44 | Algebra – Products and factors | Highest Common Factor | |

Objective: To factorise an expression by identifying and extracting the highest common factor | |||

45 | Algebra – Products and factors | Difference of Two Squares | |

Objective: To factorise differences of two squares | |||

46 | Algebra – Products and factors | Common factor and the difference of two squares | |

Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares. | |||

47 | Exam | Exam – HSEE – Algebra 1 | |

Objective: Exam |

### HSEE - complete Mathematics

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

1 | Study Plan | Study plan – HSEE – complete | |

2 | Fractions | Comparing and ordering fractions | |

Objective: To compare and order fractions with the same and different numbers of equal parts | |||

3 | Fractions | Finding equivalent fractions | |

Objective: To reduce a fraction to its lowest form | |||

4 | Fractions | Mixed numerals | |

Objective: To name and recognise mixed numerals | |||

5 | Fractions | Improper fractions | |

6 | Decimals | Adding decimals to two decimal places | |

Objective: To add decimals with the same number of decimal places (to two decimal Places) | |||

7 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

8 | Decimals | Using decimals – shopping problems | |

Objective: To read and interpret problems involving money | |||

9 | Decimals | Using decimals to record length | |

Objective: To interpret the everyday use of fractions and decimals | |||

10 | Decimals | Rounding Decimals | |

Objective: To round a number with one or two decimal places to the nearest whole number | |||

11 | Measurement – Length | Using the metre as a formal unit to measure perimeter | |

Objective: To calculate the perimeter of shapes whose measurements are given in metres | |||

12 | Measurement – Length | Using the formal unit of the centimetre to measure length and perimeter | |

Objective: To use a ruler to find lengths and perimeters in centimetres | |||

13 | Measurement – Length | Read and calculate distances on a map using the formal unit kilometre | |

Objective: To read distances (km) from a map and calculate total distances between locations | |||

14 | Measurement – Length | Compare and convert formal units of measurement | |

Objective: To change cm to mm and then convert mm, cm, m and km from one to another | |||

15 | Measurement – Area | Introduction to the square centimetre | |

Objective: To determine the area of a shape by counting the number of square centimetres | |||

16 | Measurement – Area | Larger Areas: Square Metre, Hectare, Square Kilometre | |

Objective: To calculate areas in square centimetres, square metres, square kilometres and hectares and convert one to another | |||

17 | Fractions | Subtracting fractions from whole numbers | |

Objective: To use a diagram and mental strategies to subtract fractions from whole numbers | |||

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

Objective: To add and subtract fractions with the same denominator | |||

19 | Fractions | Multiplying and dividing to obtain equivalent fractions. | |

Objective: To find equivalent fractions using multiplication or division. | |||

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

Objective: To reduce a fraction to its lowest form | |||

21 | Fractions | Comparing and ordering fractions greater than 1 | |

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

Objective: To add fractions with different denominators and the answer is less than 1 | |||

23 | Fractions | Multiplying fractions by whole numbers | |

Objective: To multiply common fractions by whole numbers | |||

24 | Fractions | Fractions of whole numbers | |

Objective: To find fractions of whole numbers | |||

25 | Decimals | Decimals to three decimal places | |

Objective: To express a number on a thousand as a decimal in thousandths | |||

26 | Decimals | Adding decimals with a different number of decimal places | |

Objective: To add decimal numbers with a different number of decimal places | |||

27 | Decimals | Subtracting decimals with a different number of places | |

Objective: To subtract decimals with a different number of decimal places | |||

28 | Decimals | Multiplying decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are multiplied by 10, 100 and 1000 | |||

29 | Decimals | Multiplying decimals by single-digit numbers | |

Objective: To multiply decimals by single-digit numbers | |||

30 | Graphs – Basic | Column Graphs | |

Objective: To read and interpret column graphs | |||

31 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

32 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

33 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

34 | Measurement – Volume | Using the Cubic Metre to Measure Volume | |

Objective: To calculate the volume of rectangular prisms in cubic metres | |||

35 | Measurement – Capacity | Using the cubic cm and displacement to measure volume and capacity | |

Objective: To find volume and capacity using displacement | |||

36 | Measurement – Capacity | Using the Cubic cm as a Standard Unit of measurement for Volume and Capacity | |

Objective: To understand a cubic centimetre and how it can be used to find the volume and capacity of a three-dimensional shape | |||

37 | Measurement – Capacity | The relationship between the common units of capacity: the litre and the millilitre | |

Objective: To convert L to mL and vice versa using 1000 mL = 1 L | |||

38 | Measurement – Volume | Introducing the Formula for Volume | |

Objective: To calculate the volume of rectangular prisms using V=l x b x h | |||

39 | Measurement – Capacity | Converting between volume and capacity using kiloliters and liters | |

Objective: To know the formal units of measurement for volume and capacity for bigger objects | |||

40 | Measurement – Capacity | Estimate, measure and compare the capacity of containers | |

Objective: To understand estimation and a way to go about it | |||

41 | Measurement – Capacity | Converting between volume and capacity using milliliters and liters | |

Objective: To solve capacity problems involving mixed dimensional units | |||

42 | Decimals | Multiplication of decimals by decimals to two decimal places | |

Objective: To multiply decimals to two digits | |||

43 | Decimals | Dividing decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are divided by 10, 100 and 1000 | |||

44 | Decimals | Dividing decimals by whole numbers | |

Objective: To divide decimals by whole numbers | |||

45 | Decimals | Dividing numbers by decimals | |

Objective: To divide a whole number by a decimal fraction | |||

46 | Measurement – Mass | Introducing the concept of mass | |

Objective: To distinguish between light and heavy objects | |||

47 | Measurement – Mass | The Kilogram | |

Objective: To recognise which of two (or more) objects has the greater mass | |||

48 | Measurement – Mass | The Gram | |

Objective: To calculate net mass in grams and solve shopping problems involving mass | |||

49 | Measurement – Mass | The Tonne | |

Objective: To convert kg to tonnes and solve problems involving heavy masses | |||

50 | Time | Average speed | |

51 | Time | Time Zones | |

Objective: To recognise and compare different time zones within Australia | |||

52 | Percentages | Understanding percentages | |

Objective: To recognise the percentage symbol and relate a common percentage to a fraction | |||

53 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

54 | Fractions | Finding reciprocals of fractions and mixed numbers | |

Objective: To find the reciprocals of fractions and mixed numbers | |||

55 | Fractions | Dividing fractions | |

Objective: To divide fractions by other fractions | |||

56 | Fractions | Dividing mixed numbers | |

Objective: To divide mixed numbers | |||

57 | Fractions | Multiplying fractions | |

Objective: To multiply fractions and reduce the answer to its lowest form | |||

58 | Fractions | Multiplying mixed numbers | |

Objective: To multiply mixed numbers and reduce the answer to its lowest form | |||

59 | Problem solving | Sign Words | |

Objective: To recognise words and phrases that correspond to + – x and / | |||

60 | Problem solving | Problem Solving Strategies | |

Objective: To review problem solving words and an effective problem solving approach | |||

61 | Problem solving | Word Problems with Numbers | |

Objective: To solve number word problems using + – x and / | |||

62 | Problem solving | Word Problems with Money | |

Objective: To solve money word problems using + – x and / | |||

63 | Problem solving | Word Problems with Length | |

Objective: To solve length word problems using + – x and / | |||

64 | Problem solving | Word Problems with Mass | |

Objective: To solve mass word problems using + – x and / | |||

65 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

66 | Problem solving | Word Problems with Volume/Capacity | |

Objective: To solve volume and capacity word problems using + – x and / | |||

67 | Algebra – Basic | Algebraic Expressions | |

Objective: To simplify numerical expressions and simplify and expand algebraic expressions | |||

68 | Algebra – Basic | Substitution into Algebraic Expressions | |

Objective: To evaluate simple algebraic expressions using whole numbers, fractions and decimals | |||

69 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

70 | Algebra – Basic | Directed Numbers: Multiplication and Division | |

Objective: To multiply and divide directed numbers and evaluate powers of directed numbers | |||

71 | Algebra – Basic | Simplifying Algebraic Expressions: Adding Like Terms | |

Objective: To simplify numeric and algebraic addition expressions by collecting like terms | |||

72 | Algebra – Basic | Simplifying Algebraic Expressions: Subtracting Like Terms | |

Objective: To simplify algebraic subtractions by collecting like terms | |||

73 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

74 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

75 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

76 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

77 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

78 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

79 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

80 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

81 | Measurement – Volume | Solving Problems about Volume Part 1 | |

Objective: To solve volume problems using same and mixed units of length | |||

82 | Measurement – Volume | Solving Problems about Volume Part 2 | |

Objective: To solve volume problems involving larger objects | |||

83 | Standard/Scientific notation | Scientific notation with larger numbers | |

Objective: To write large numbers in standard or scientific notation | |||

84 | Standard/Scientific notation | Scientific notation with small numbers | |

Objective: To write small numbers in standard or scientific notation | |||

85 | Standard/Scientific notation | Changing scientific notation to numerals | |

Objective: To interpret scientific notation by writing in base 10 numerals | |||

86 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

87 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

88 | Indices/Exponents | Multiplying indices when raising a power to a power | |

Objective: To multiply indices when raising a power to a power | |||

89 | Indices/Exponents | Multiplying indices when raising to more than one term | |

Objective: To raise power products to a power | |||

90 | Indices/Exponents | Terms raised to the power of zero | |

Objective: To evaluate expressions where quantities are raised to the power 0 | |||

91 | Indices/Exponents | Negative Indices | |

Objective: To evaluate or simplify expressions containing negative indices | |||

92 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

93 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

94 | Statistics part 1 | Relative Frequency | |

Objective: To extend the frequency distribution table to include a relative frequency column | |||

95 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

96 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

97 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

98 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

99 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

100 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

101 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

102 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

103 | Algebra – Basic | Equations involving Grouping Symbols | |

Objective: To solve equations containing grouping symbols on each side | |||

104 | Algebra – Basic | Equations involving fractions | |

Objective: To solve fraction equations with the unknown in either the numerator or denominator | |||

105 | Algebra – Basic | Inequalities | |

106 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

107 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

108 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

109 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

110 | Pythagoras | Proofs of Pythagoras’ Theorem | |

Objective: To examine and complete proofs of Pythagoras’ Theorem | |||

111 | Geometry part 2 | Congruent triangles: Tests 1 and 2 | |

Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS | |||

112 | Measurement – Advanced area | Area of a Trapezium | |

Objective: To calculate the area of trapezia using A=(h/2)(a+b) | |||

113 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | |

Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS | |||

114 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

115 | Geometry part 2 | Proofs and Congruent Triangles | |

Objective: To use congruency in formal proofs in order to determine unknown angles and sides | |||

116 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

117 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

118 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

119 | Measurement – Advanced volume | Volume of Pyramids and Cones | |

Objective: To calculate the volumes of pyramids and cones | |||

120 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

121 | Surface area | Surface Area of a Triangular/Trapezoidal Prism | |

Objective: To calculate the surface area of triangular and trapezoidal prisms | |||

122 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

123 | Surface area | Surface Area of Pyramids | |

Objective: To calculate the surface area of pyramids | |||

124 | Surface area | Surface Area of Composite Solids | |

Objective: To calculate the surface area of composite solids | |||

125 | 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. | |||

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

Objective: To change percentages to fractions and decimals | |||

127 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

128 | Percentages | Calculating Percentages and Fractions of Quantities | |

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

129 | Series and sequences part 2 | Compound Interest | |

Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n | |||

130 | Graphs part 1 | Graphing perfect squares: y=(a-x) squared | |

Objective: To describe and sketch parabolas of the form y = (x – a)^2 | |||

131 | Co-ordinate geometry part 1 | The Straight Line | |

Objective: To state the equation of lines parallel to the axes and to graph equations x = a and y = b | |||

132 | Co-ordinate geometry part 1 | Slope Intercept Form of a Line | |

Objective: To change equation to slope intercept form and graph it and to find equation given graph | |||

133 | Co-ordinate geometry part 2 | Inequalities on the Number Plane | |

Objective: To identify the graph which matches a given inequality | |||

134 | Co-ordinate geometry part 2 | Parallel Lines: identify equation of a line parallel to another | |

Objective: To change the standard form of a straight line equation to the y = mx + b form | |||

135 | Co-ordinate geometry part 2 | Perpendicular Lines | |

Objective: To identify the equation of a line that is perpendicular to a given linear equation | |||

136 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

137 | Absolute value | Solving Absolute Value Equations | |

Objective: To solve equations involving absolute values | |||

138 | Absolute value | Solving and Graphing Inequalities | |

Objective: To graph the solution set of absolute value inequalities | |||

139 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

140 | Co-ordinate geometry part 2 | Transformations: Reflections | |

Objective: To identify reflections and to use isometric properties of reflections | |||

141 | Geometry transformations | Geometry Transformations without Matrices: Rotation | |

Objective: To determine rotation angle and to perform prescribed rotations | |||

142 | Probability | Simple events | |

143 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

144 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

145 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

146 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

147 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots | |||

148 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

149 | Simultaneous equations | Simultaneous Equations | |

Objective: To solve simultaneous equations by substitution | |||

150 | Simultaneous equations | Elimination method | |

Objective: To solve simultaneous equations by elimination | |||

151 | Simultaneous equations | Elimination method part 2 | |

Objective: To solve more difficult simultaneous equations by elimination | |||

152 | Simultaneous equations | Applications of simultaneous equations | |

Objective: To solve problems using simultaneous equations | |||

153 | Algebra – Products and factors | Binomial Products | |

Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b) | |||

154 | Algebra – Products and factors | Binomial products with negative multiplier | |

Objective: To expand and simplify monic binomial products of the form (x – a)(x +/- b) | |||

155 | Algebra – Products and factors | Binomial Products (nonmonic) | |

Objective: To expand and simplify nonmonic binomial products | |||

156 | Algebra – Products and factors | Squaring a Binomial (monic) | |

Objective: To expand the square of a binomial by multiplication and by inspection | |||

157 | Algebra – Products and factors | Squaring a Binomial (nonmonic) | |

Objective: To expand the square of a nonmonic binomial by inspection | |||

158 | Algebra – Products and factors | Expansions Leading to the Difference of Two Squares | |

Objective: To expand the product of conjugate binomials leading to differences of squares | |||

159 | Algebra – Products and factors | Products in Simplification of Algebraic Expressions | |

Objective: To simplify algebraic expressions containing binomial products | |||

160 | Algebra – Products and factors | Larger Expansions | |

Objective: To expand and simplify the product of a binomial and a trinomial | |||

161 | Algebra – Products and factors | Highest Common Factor | |

Objective: To factorise an expression by identifying and extracting the highest common factor | |||

162 | Algebra – Products and factors | Difference of Two Squares | |

Objective: To factorise differences of two squares | |||

163 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 1 | |

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

164 | Graphs part 1 | The parabola: to describe properties of a parabola from its equation | |

Objective: To describe properties of a parabola from its equation and sketch the parabola | |||

165 | Graphs part 2 | Graphing cubic curves | |

Objective: To graph cubic curves whose equation is of the form y = (x – a)^3 + b or y = (a – x)^3 + b | |||

166 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

167 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

168 | Logic | Mathematical induction | |

Objective: To use proof by mathematical induction | |||

169 | Exam | Exam – HSEE – complete | |

Objective: Exam |

### SAT Trigonometry Mathematics

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

1 | Study Plan | Study plan – SAT Trigonometry | |

2 | Trigonometry part 1 | Trigonometric Ratios | |

Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle | |||

3 | Trigonometry part 1 | Using the Calculator | |

Objective: To determine trigonometric ratios using a calculator | |||

4 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 1 Sin] | |

Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle | |||

5 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | |

Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle | |||

6 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | |

Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle | |||

7 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | |

Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator | |||

8 | Trigonometry part 1 | Bearings: The Compass | |

Objective: To change from true bearings to compass bearings and vice versa | |||

9 | Trigonometry part 1 | Angles of Elevation and Depression | |

Objective: To identify and distinguish between angles of depression and elevation | |||

10 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | |

Objective: To solve problems involving bearings and angles of elevation and depression | |||

11 | Trigonometry part 1 | Using the Calculator to Find an Angle Given a Trigonometric Ratio | |

Objective: To find angles in right-angled triangles given trigonometric ratios | |||

12 | Trigonometry part 1 | Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle | |

Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems | |||

13 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | |

Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees | |||

14 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | |

Objective: To complete the cosine rule to find a subject side for given triangles | |||

15 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | |

Objective: To complete the cosine rule to find a subject angle for given triangles | |||

16 | Trigonometry part 1 | The Sine Rule: Finding a Side | |

Objective: To find an unknown side of a triangle using the sine rule | |||

17 | Trigonometry part 1 | The Sine Rule: Finding an Angle | |

Objective: To find an unknown angle of a triangle using the sine rule | |||

18 | Trigonometry part 1 | The Sine Area Formula for a Triangle | |

Objective: To use the sine formula for the area of a triangle to calculate area | |||

19 | Co-ordinate geometry part 1 | The Distance Formula | |

Objective: To use the distance formula to calculate the lengths of lines and distances | |||

20 | Co-ordinate geometry part 1 | The Mid-Point Formula | |

Objective: To determine the mid-point of an interval using the mid-point formula | |||

21 | Co-ordinate geometry part 1 | The Gradient | |

Objective: To find the gradient of a line given its angle of inclination or given rise and run | |||

22 | Co-ordinate geometry part 1 | The Gradient Formula | |

Objective: To use the gradient formula to find the gradient of straight lines | |||

23 | Trigonometry part 2 | Reciprocal Ratios | |

Objective: To find the trigonometric ratios for a given right-angled triangle | |||

24 | Trigonometry part 2 | Complementary Angle Results | |

Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality | |||

25 | Trigonometry part 2 | Trigonometric Identities | |

Objective: To simplify expressions using trigonometric equalities | |||

26 | Trigonometry part 2 | Angles of Any Magnitude | |

Objective: To assign angles to quadrants and to find trigonometric values for angles | |||

27 | Trigonometry part 2 | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |

Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees | |||

28 | Trigonometry part 2 | Graphing the Trigonometric Ratios I: Sine Curve | |

Objective: To recognise the sine curve and explore shifts of phase and amplitude | |||

29 | Trigonometry part 2 | Graphing the Trigonometric Ratios II: Cosine Curve | |

Objective: To recognise the cosine curve and explore shifts of phase and amplitude | |||

30 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | |

Objective: To recognise the tangent curve and explore shifts of phase and amplitude | |||

31 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | |

Objective: To graph the primary trigonometric functions and their inverses | |||

32 | Trigonometry part 2 | Using One Trig. Ratio to Find Another | |

Objective: To derive trig ratios complement from one given trig ratio + some other quadrant identifier. | |||

33 | Trigonometry part 2 | Solving Trigonometric Equations – Type I | |

Objective: To Solve trigonometric equations for angles from 0 to 360 degrees. | |||

34 | Trigonometry part 2 | Solving Trigonometric Equations – Type II | |

Objective: To solve trigonometric equations for angles from 0 to 360 degrees. | |||

35 | Trigonometry part 2 | Solving Trigonometric Equations – Type III | |

Objective: To solve trigonometric equations using tan? = sin?/cos?. | |||

36 | Polar coordinates | Polar Coordinates – Plotting and Converting | |

Objective: To plot polar points and convert polar coordinates to rectangular coordinates | |||

37 | Polar coordinates | Converting Rectangular Coordinates to Polar Form | |

Objective: To convert rectangular to polar coordinates | |||

38 | Polar coordinates | Graphing Polar Functions | |

Objective: To write the polar coordinates of a point for selected argument ranges | |||

39 | Trigonometry part 2 | Trigonometric Sum and Difference Identities | |

Objective: To evaluate trig functions of angles using sum and difference identities | |||

40 | Trigonometry part 2 | Double Angle Identities | |

Objective: To use double angle identities to evaluate trig. functions and solve trig equations | |||

41 | Trigonometry part 2 | Half-angle Identities | |

Objective: To evaluate trig. functions of angles using half-angle identities | |||

42 | Trigonometry part 2 | t Formulas | |

Objective: To write t-formulae for trig. functions. To solve equations using t-formulae | |||

43 | Exam | Exam – SAT Trigonometry | |

Objective: Exam |

### SAT Linear Algebra Mathematics

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

1 | Study Plan | Study plan – SAT Linear Algebra | |

2 | Matrices | Matrices: basic concepts | |

Objective: To write and state the order of a matrix and to identify square matrices | |||

3 | Matrices | Addition and Subtraction of Matrices | |

Objective: To add and subtract matrices | |||

4 | Matrices | Scalar matrix: multiplication | |

Objective: To multiply a matrix by a scalar | |||

5 | Matrices | Multiplication of one matrix by another matrix | |

Objective: To perform matrix multiplication and to recognise that AB is not equal to BA | |||

6 | Matrices | Translation in the number plane | |

Objective: To use matrix addition to translate points | |||

7 | Matrices | Translation by matrix multiplication | |

Objective: To transform points and objects by matrix multiplication | |||

8 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | |

Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication | |||

9 | Matrices | Vectors | |

Objective: To use vectors to find resultant speeds and displacements | |||

10 | Matrices – Linear systems | Number of Solutions | |

Objective: To determine solutions to systems of equations | |||

11 | Matrices – Linear systems | Vector Addition in 2 and 3D | |

Objective: To represent, add, subtract and determine the direction of vectors | |||

12 | Matrices – Linear systems | Optimal Solutions | |

Objective: To use linear programming to maximise or minimise an objective function | |||

13 | Matrices – Linear systems | Linear Systems with Matrices | |

Objective: To identify and describe matrices and perform row operations in matrices | |||

14 | Matrices – Linear systems | Row Echelon Form | |

Objective: To identify and create matrices in row echelon form and to solve systems of equations | |||

15 | Matrices – Linear systems | Gauss Jordan Elimination | |

Objective: To use the Gauss Jordan Elimination Method to solve systems of linear equations | |||

16 | Exam | Exam – SAT Linear Algebra | |

Objective: Exam |

### SAT Analysis Mathematics

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

1 | Study Plan | Study plan – SAT Analysis | |

2 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

3 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

4 | Logic | Proof by Disproof of a Contradictory Statement | |

Objective: To prove that a statement is true by proving that the contradictory statement is false | |||

5 | Logic | Mathematical induction | |

Objective: To use proof by mathematical induction | |||

6 | Graphs part 2 | Graphing complex polynomials: quadratics with no real roots | |

Objective: To graph quadratics that have no real roots, hence don’t cut the x-axis | |||

7 | Graphs part 2 | General equation of a circle: determine and graph the equation | |

Objective: To determine and graph the equation of a circle with radius a and centre (h,k) | |||

8 | Graphs part 2 | Graphing cubic curves | |

9 | Graphs part 2 | Absolute Value Equations | |

Objective: To graph equations involving absolute values | |||

10 | Graphs part 2 | The Rectangular Hyperbola | |

Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x | |||

11 | Graphs part 2 | The Exponential Function | |

Objective: To graph exponential curves whose exponents are either positive or negative | |||

12 | Graphs part 2 | Logarithmic Functions | |

Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) | |||

13 | Conic sections | Introduction to Conic Sections and Their General Equation | |

Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2 | |||

14 | Conic sections | The Parabola | |

Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px | |||

15 | Conic sections | Circles | |

Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles | |||

16 | Conic sections | The Ellipsis | |

Objective: To identify ellipses of the form x^2/a^2 + y^2/b^2 = 1 and to find the equation of ellipses | |||

17 | Conic sections | The Hyperbola | |

Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation | |||

18 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

19 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

20 | Function | Selecting Appropriate Domain and Range | |

Objective: To determine appropriate domains for functions | |||

21 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

22 | Function | Evaluating and Graphing Piecewise Functions | |

Objective: To evaluate and graph piecewise functions | |||

23 | Function | Combining Functions | |

24 | Function | Simplifying Composite Functions | |

Objective: To simplify, evaluate and determine the domain of composite functions | |||

25 | Function | Inverse Functions | |

Objective: To find the inverse of a function and determine whether this inverse is itself a function | |||

26 | Function | Graphing Rational Functions Part 1 | |

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes | |||

27 | Function | Graphing Rational Functions Part 2 | |

Objective: To determine asymptotes and graph rational functions | |||

28 | Function | Parametric Equations | |

Objective: To interchange parametric and Cartesian equations and to identify graphs | |||

29 | Function | Polynomial Addition: in Combining and Simplifying Functions | |

Objective: To evaluate, simplify and graph rational functions | |||

30 | Function | Parametric Functions | |

Objective: To change Cartesian and parametric equations and to graph parametric functions | |||

31 | Polar coordinates | Polar Coordinates – Plotting and Converting | |

Objective: To plot polar points and convert polar coordinates to rectangular coordinates | |||

32 | Polar coordinates | Converting Rectangular Coordinates to Polar Form | |

Objective: To convert rectangular to polar coordinates | |||

33 | Polar coordinates | Graphing Polar Functions | |

Objective: To write the polar coordinates of a point for selected argument ranges | |||

34 | Trigonometry part 2 | Trigonometric Sum and Difference Identities | |

Objective: To evaluate trig functions of angles using sum and difference identities | |||

35 | Trigonometry part 2 | Double Angle Identities | |

Objective: To use double angle identities to evaluate trig. functions and solve trig equations | |||

36 | Trigonometry part 2 | Half-angle Identities | |

Objective: To evaluate trig. functions of angles using half-angle identities | |||

37 | Trigonometry part 2 | t Formulas | |

Objective: To write t-formulae for trig. functions. To solve equations using t-formulae | |||

38 | Complex numbers | Complex Numbers: Adding and Subtracting | |

Objective: To recognise and manipulate simple complex numbers and expressions | |||

39 | Complex numbers | Complex Numbers: Multiplying and Dividing | |

Objective: To perform multiplication and division of complex numbers | |||

40 | Complex numbers | Adding and Subtracting Complex Numbers using Vectors | |

Objective: To perform complex number operations graphically using vectors | |||

41 | Complex numbers | The Absolute Value of a Complex Number | |

Objective: To find the absolute value of a complex number | |||

42 | Complex numbers | Trigonometric Form of a Complex Number | |

Objective: To find the trigonometric form of a complex number | |||

43 | Complex numbers | Multiplication and Division of Complex Numbers in Trigonometric Form | |

Objective: To multiply and divide complex numbers using DeMoivre’s Theorem | |||

44 | Complex numbers | DeMoivre’s theorem | |

Objective: To find powers of complex numbers using DeMoivre’s theorem | |||

45 | Complex numbers | The nth Root of Real and Complex Numbers | |

Objective: To find the roots of a complex function using DeMoivre’s theorem | |||

46 | Complex numbers | Fundamental Theorem of Algebra | |

Objective: To find the nth zeros of a polynomial function both real and complex | |||

47 | Calculus part 1 | Limits | |

Objective: To find the limit value of a function as x approaches n | |||

48 | Calculus part 1 | Differentiation from First Principles | |

Objective: To differentiate functions from first principles | |||

49 | Calculus part 1 | Differentiation of y = x to the power of n | |

Objective: To differentiate algebraic functions using the laws of differentiation | |||

50 | Calculus part 1 | Meaning of dy over dx – Equations of Tangents and Normals | |

Objective: To find and use the slope of tangents and normals | |||

51 | Series and sequences part 2 | Geometric Means | |

Objective: To find geometric means of a and b and insert geometric means between 2 endpoints | |||

52 | Series and sequences part 2 | The sum to n terms of a G.P. | |

Objective: To find the sum of n terms of a sequence | |||

53 | Series and sequences part 2 | Sigma notation | |

Objective: To evaluate progressions using sigma notation | |||

54 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | |

Objective: To find the limiting sum of a sequence | |||

55 | Exam | Exam – SAT Analysis | |

Objective: Exam |

### SAT Advanced Probability - Statistics Mathematics

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

1 | Study Plan | Study plan – SAT Advanced Probability | |

2 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

3 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

4 | Statistics part 1 | Relative Frequency | |

Objective: To extend the frequency distribution table to include a relative frequency column | |||

5 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

6 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

7 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

8 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

9 | Statistics part 1 | Cumulative Frequency | |

Objective: To construct cumulative frequency columns, histograms and polygons | |||

10 | Statistics part 1 | Calculating the Mean from a Frequency Distribution | |

Objective: To determine averages (mean, median and mode) from cumulative frequency polygons | |||

11 | Probability | The Binomial Theorem and Binomial Coefficients | |

Objective: To calculate binomial coefficients and expand binomial powers. | |||

12 | Probability | Simple events | |

13 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

14 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

15 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

16 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

17 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

18 | Probability | P[A or B] When A and B are NOT mutually exclusive | |

Objective: To calculate the probability of non exclusive events using P(A or B) = P(A)+P(B) | |||

19 | Probability | Binomial probabilities using the Binomial Theorem | |

Objective: To calculate the binomial probability of a given number of successful trials | |||

20 | Probability | Counting techniques and ordered selections | |

Objective: To use counting techniques in probability | |||

21 | Probability | Unordered selections – combinations | |

Objective: To use the nCr formula to solve problems where unordered selections occur | |||

22 | Statistics part 2 | Calculating mean, mode and median from grouped data | |

Objective: To identify class centres, get frequency counts and determine mean, mode and median values | |||

23 | Statistics part 2 | Using the Calculator for Statistics | |

Objective: To find a mean, using a data set or a frequency distribution table and calculator. | |||

24 | Statistics part 2 | Measures of Spread | |

Objective: To determine a range and use it in decision making | |||

25 | Statistics part 2 | Standard deviation applications | |

Objective: To find a standard deviation, using a data set or a frequency distribution table and calculator | |||

26 | Statistics part 2 | Applications of Standard Deviation | |

Objective: To use standard deviation as a measure of deviation from a mean | |||

27 | Statistics part 2 | The Normal Distribution | |

Objective: To use the standard deviation of a normal distribution to find a percentage of scores within ranges | |||

28 | Statistics part 2 | Measures of Spread: the interquartile range | |

Objective: To find the upper and lower quartiles and the interquartile range | |||

29 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots | |||

30 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

31 | Exam | Exam – SAT Advanced Probability | |

Objective: Exam |

### SAT Extension Mathematics

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

1 | Study Plan | Study plan – SAT Extension | |

2 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

3 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

4 | Logic | Proof by Disproof of a Contradictory Statement | |

Objective: To prove that a statement is true by proving that the contradictory statement is false | |||

5 | Logic | Mathematical induction | |

Objective: To use proof by mathematical induction | |||

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 | Trigonometry part 1 | Trigonometric Ratios | |

Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle | |||

8 | Trigonometry part 1 | Using the Calculator | |

Objective: To determine trigonometric ratios using a calculator | |||

9 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 1 Sin] | |

Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle | |||

10 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | |

Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle | |||

11 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | |

Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle | |||

12 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | |

13 | Trigonometry part 1 | Bearings: The Compass | |

Objective: To change from true bearings to compass bearings and vice versa | |||

14 | Trigonometry part 1 | Angles of Elevation and Depression | |

Objective: To identify and distinguish between angles of depression and elevation | |||

15 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | |

Objective: To solve problems involving bearings and angles of elevation and depression | |||

16 | Trigonometry part 1 | Using the Calculator to Find an Angle Given a Trigonometric Ratio | |

Objective: To find angles in right-angled triangles given trigonometric ratios | |||

17 | Trigonometry part 1 | Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle | |

Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems | |||

18 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | |

Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees | |||

19 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | |

Objective: To complete the cosine rule to find a subject side for given triangles | |||

20 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | |

Objective: To complete the cosine rule to find a subject angle for given triangles | |||

21 | Trigonometry part 1 | The Sine Rule: Finding a Side | |

Objective: To find an unknown side of a triangle using the sine rule | |||

22 | Trigonometry part 1 | The Sine Rule: Finding an Angle | |

Objective: To find an unknown angle of a triangle using the sine rule | |||

23 | Trigonometry part 1 | The Sine Area Formula for a Triangle | |

Objective: To use the sine formula for the area of a triangle to calculate area | |||

24 | Co-ordinate geometry part 1 | The Gradient | |

Objective: To find the gradient of a line given its angle of inclination or given rise and run | |||

25 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

26 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

27 | Statistics part 1 | Relative Frequency | |

Objective: To extend the frequency distribution table to include a relative frequency column | |||

28 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

29 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

30 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

31 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

32 | Statistics part 1 | Cumulative Frequency | |

Objective: To construct cumulative frequency columns, histograms and polygons | |||

33 | Statistics part 1 | Calculating the Mean from a Frequency Distribution | |

Objective: To determine averages (mean, median and mode) from cumulative frequency polygons | |||

34 | Probability | The Binomial Theorem and Binomial Coefficients | |

Objective: To calculate binomial coefficients and expand binomial powers. | |||

35 | Probability | Simple events | |

36 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

37 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

38 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

39 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

40 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

41 | Probability | P[A or B] When A and B are NOT mutually exclusive | |

Objective: To calculate the probability of non exclusive events using P(A or B) = P(A)+P(B) | |||

42 | Probability | Binomial probabilities using the Binomial Theorem | |

Objective: To calculate the binomial probability of a given number of successful trials | |||

43 | Probability | Counting techniques and ordered selections | |

Objective: To use counting techniques in probability | |||

44 | Probability | Unordered selections – combinations | |

Objective: To use the nCr formula to solve problems where unordered selections occur | |||

45 | Matrices | Matrices: basic concepts | |

Objective: To write and state the order of a matrix and to identify square matrices | |||

46 | Matrices | Addition and Subtraction of Matrices | |

Objective: To add and subtract matrices | |||

47 | Matrices | Scalar matrix: multiplication | |

Objective: To multiply a matrix by a scalar | |||

48 | Matrices | Multiplication of one matrix by another matrix | |

Objective: To perform matrix multiplication and to recognise that AB is not equal to BA | |||

49 | Matrices | Translation in the number plane | |

Objective: To use matrix addition to translate points | |||

50 | Matrices | Translation by matrix multiplication | |

Objective: To transform points and objects by matrix multiplication | |||

51 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | |

Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication | |||

52 | Matrices | Vectors | |

Objective: To use vectors to find resultant speeds and displacements | |||

53 | Matrices – Linear systems | Number of Solutions | |

Objective: To determine solutions to systems of equations | |||

54 | Matrices – Linear systems | Vector Addition in 2 and 3D | |

Objective: To represent, add, subtract and determine the direction of vectors | |||

55 | Matrices – Linear systems | Optimal Solutions | |

Objective: To use linear programming to maximise or minimise an objective function | |||

56 | Matrices – Linear systems | Linear Systems with Matrices | |

Objective: To identify and describe matrices and perform row operations in matrices | |||

57 | Matrices – Linear systems | Row Echelon Form | |

Objective: To identify and create matrices in row echelon form and to solve systems of equations | |||

58 | Matrices – Linear systems | Gauss Jordan Elimination | |

Objective: To use the Gauss Jordan Elimination Method to solve systems of linear equations | |||

59 | Graphs part 2 | Graphing complex polynomials: quadratics with no real roots | |

Objective: To graph quadratics that have no real roots, hence don’t cut the x-axis | |||

60 | Graphs part 2 | General equation of a circle: determine and graph the equation | |

Objective: To determine and graph the equation of a circle with radius a and centre (h,k) | |||

61 | Graphs part 2 | Graphing cubic curves | |

62 | Graphs part 2 | Absolute Value Equations | |

Objective: To graph equations involving absolute values | |||

63 | Graphs part 2 | The Rectangular Hyperbola | |

Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x | |||

64 | Graphs part 2 | The Exponential Function | |

Objective: To graph exponential curves whose exponents are either positive or negative | |||

65 | Graphs part 2 | Logarithmic Functions | |

Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) | |||

66 | Conic sections | Introduction to Conic Sections and Their General Equation | |

Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2 | |||

67 | Conic sections | The Parabola | |

Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px | |||

68 | Conic sections | Circles | |

69 | Conic sections | The Ellipsis | |

70 | Conic sections | The Hyperbola | |

71 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

72 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

73 | Function | Selecting Appropriate Domain and Range | |

Objective: To determine appropriate domains for functions | |||

74 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

75 | Function | Evaluating and Graphing Piecewise Functions | |

Objective: To evaluate and graph piecewise functions | |||

76 | Function | Combining Functions | |

77 | Function | Simplifying Composite Functions | |

Objective: To simplify, evaluate and determine the domain of composite functions | |||

78 | Function | Inverse Functions | |

Objective: To find the inverse of a function and determine whether this inverse is itself a function | |||

79 | Function | Graphing Rational Functions Part 1 | |

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes | |||

80 | Function | Graphing Rational Functions Part 2 | |

Objective: To determine asymptotes and graph rational functions | |||

81 | Function | Parametric Equations | |

Objective: To interchange parametric and Cartesian equations and to identify graphs | |||

82 | Function | Polynomial Addition: in Combining and Simplifying Functions | |

Objective: To evaluate, simplify and graph rational functions | |||

83 | Function | Parametric Functions | |

Objective: To change Cartesian and parametric equations and to graph parametric functions | |||

84 | Statistics part 2 | Calculating mean, mode and median from grouped data | |

85 | Statistics part 2 | Using the Calculator for Statistics | |

Objective: To find a mean, using a data set or a frequency distribution table and calculator. | |||

86 | Statistics part 2 | Measures of Spread | |

Objective: To determine a range and use it in decision making | |||

87 | Statistics part 2 | Standard deviation applications | |

88 | Statistics part 2 | Applications of Standard Deviation | |

Objective: To use standard deviation as a measure of deviation from a mean | |||

89 | Statistics part 2 | The Normal Distribution | |

90 | Statistics part 2 | Measures of Spread: the interquartile range | |

Objective: To find the upper and lower quartiles and the interquartile range | |||

91 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots | |||

92 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

93 | Trigonometry part 2 | Reciprocal Ratios | |

Objective: To find the trigonometric ratios for a given right-angled triangle | |||

94 | Trigonometry part 2 | Complementary Angle Results | |

Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality | |||

95 | Trigonometry part 2 | Trigonometric Identities | |

Objective: To simplify expressions using trigonometric equalities | |||

96 | Trigonometry part 2 | Angles of Any Magnitude | |

Objective: To assign angles to quadrants and to find trigonometric values for angles | |||

97 | Trigonometry part 2 | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |

Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees | |||

98 | Trigonometry part 2 | Graphing the Trigonometric Ratios I: Sine Curve | |

Objective: To recognise the sine curve and explore shifts of phase and amplitude | |||

99 | Trigonometry part 2 | Graphing the Trigonometric Ratios II: Cosine Curve | |

Objective: To recognise the cosine curve and explore shifts of phase and amplitude | |||

100 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | |

Objective: To recognise the tangent curve and explore shifts of phase and amplitude | |||

101 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | |

Objective: To graph the primary trigonometric functions and their inverses | |||

102 | Trigonometry part 2 | Using One Trig. Ratio to Find Another | |

Objective: To derive trig ratios complement from one given trig ratio + some other quadrant identifier. | |||

103 | Trigonometry part 2 | Solving Trigonometric Equations – Type I | |

Objective: To Solve trigonometric equations for angles from 0 to 360 degrees. | |||

104 | Trigonometry part 2 | Solving Trigonometric Equations – Type II | |

Objective: To solve trigonometric equations for angles from 0 to 360 degrees. | |||

105 | Trigonometry part 2 | Solving Trigonometric Equations – Type III | |

Objective: To solve trigonometric equations using tan? = sin?/cos?. | |||

106 | Polar coordinates | Polar Coordinates – Plotting and Converting | |

Objective: To plot polar points and convert polar coordinates to rectangular coordinates | |||

107 | Polar coordinates | Converting Rectangular Coordinates to Polar Form | |

Objective: To convert rectangular to polar coordinates | |||

108 | Polar coordinates | Graphing Polar Functions | |

Objective: To write the polar coordinates of a point for selected argument ranges | |||

109 | Trigonometry part 2 | Trigonometric Sum and Difference Identities | |

Objective: To evaluate trig functions of angles using sum and difference identities | |||

110 | Trigonometry part 2 | Double Angle Identities | |

Objective: To use double angle identities to evaluate trig. functions and solve trig equations | |||

111 | Trigonometry part 2 | Half-angle Identities | |

Objective: To evaluate trig. functions of angles using half-angle identities | |||

112 | Trigonometry part 2 | t Formulas | |

Objective: To write t-formulae for trig. functions. To solve equations using t-formulae | |||

113 | Logarithms | The Graph of the Logarithmic Curve | |

Objective: To solve problems involving logarithmic curves | |||

114 | Complex numbers | Complex Numbers: Adding and Subtracting | |

Objective: To recognise and manipulate simple complex numbers and expressions | |||

115 | Complex numbers | Complex Numbers: Multiplying and Dividing | |

Objective: To perform multiplication and division of complex numbers | |||

116 | Complex numbers | Adding and Subtracting Complex Numbers using Vectors | |

Objective: To perform complex number operations graphically using vectors | |||

117 | Complex numbers | The Absolute Value of a Complex Number | |

Objective: To find the absolute value of a complex number | |||

118 | Complex numbers | Trigonometric Form of a Complex Number | |

Objective: To find the trigonometric form of a complex number | |||

119 | Complex numbers | Multiplication and Division of Complex Numbers in Trigonometric Form | |

Objective: To multiply and divide complex numbers using DeMoivre’s Theorem | |||

120 | Complex numbers | DeMoivre’s theorem | |

Objective: To find powers of complex numbers using DeMoivre’s theorem | |||

121 | Complex numbers | The nth Root of Real and Complex Numbers | |

Objective: To find the roots of a complex function using DeMoivre’s theorem | |||

122 | Complex numbers | Fundamental Theorem of Algebra | |

Objective: To find the nth zeros of a polynomial function both real and complex | |||

123 | Polynomials | Introduction to polynomials | |

Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic | |||

124 | Polynomials | The Sum, Difference and Product of Two Polynomials | |

Objective: To add, subtract and multiply polynomials | |||

125 | Polynomials | Polynomials and Long Division | |

Objective: To perform long division of polynomials, finding quotient and remainder | |||

126 | Polynomials | The Remainder Theorem | |

Objective: To determine a remainder when a first polynomial is divided by a second | |||

127 | Polynomials | More on Remainder Theorem | |

Objective: To determine polynomial coefficients given a divisor and remainder | |||

128 | Polynomials | The factor theorem | |

Objective: To use the factor theorem to show that (x-a) is a factor of P(x) | |||

129 | Polynomials | More on the factor theorem | |

Objective: To use the factor theorem to find algebraic variables in polynomials | |||

130 | Polynomials | Complete factorisations using the factor theorem | |

Objective: To use the factor theorem to derive factors of a polynomial | |||

131 | Polynomials | Polynomial equations | |

Objective: To practise solving polynomial equations | |||

132 | Polynomials | Graphs of polynomials | |

Objective: To derive graphs of polynomials by factorising | |||

133 | Polynomials | The Sum and Product of the Roots of Quadratic Equations. | |

Objective: Sum and product of roots of quadratic equations. | |||

134 | Polynomials | The Sum and Product of the Roots of Cubic and Quartic Equations. | |

Objective: Sum and product of toots of cubic and quartic equations. | |||

135 | Polynomials | Methods of Approximating Roots. | |

Objective: Methods of approximating roots. | |||

136 | Polynomials | Newton’s Method of Approximation. | |

Objective: Newton’s method of approximation. | |||

137 | Calculus part 1 | Limits | |

Objective: To find the limit value of a function as x approaches n | |||

138 | Calculus part 1 | Differentiation from First Principles | |

Objective: To differentiate functions from first principles | |||

139 | Calculus part 1 | Differentiation of y = x to the power of n | |

Objective: To differentiate algebraic functions using the laws of differentiation | |||

140 | Calculus part 1 | Meaning of dy over dx – Equations of Tangents and Normals | |

Objective: To find and use the slope of tangents and normals | |||

141 | Calculus part 1 | Function of a Function Rule, Product Rule, Quotient Rule. | |

Objective: To differentiate functions using the product, quotient and chain rules. | |||

142 | Calculus part 1 | Increasing, Decreasing and Stationary Functions. | |

Objective: To determine values of x for which f(x) is increasing, decreasing or stationary. | |||

143 | Calculus part 1 | The Second Derivative – Concavity. | |

Objective: To determine concavity of a curve at a point using the second derivative. | |||

144 | Calculus part 1 | Classification of Stationary Points. | |

Objective: To Locate and describe stationary points and points of inflection using differention. | |||

145 | Series and sequences part 2 | Geometric Means | |

Objective: To find geometric means of a and b and insert geometric means between 2 endpoints | |||

146 | Series and sequences part 2 | The sum to n terms of a G.P. | |

Objective: To find the sum of n terms of a sequence | |||

147 | Series and sequences part 2 | Sigma notation | |

Objective: To evaluate progressions using sigma notation | |||

148 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | |

Objective: To find the limiting sum of a sequence | |||

149 | Series and sequences part 2 | Recurring Decimals and the Infinite G.P. | |

Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction | |||

150 | Series and sequences part 2 | Compound Interest | |

Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n | |||

151 | Series and sequences part 2 | Superannuation | |

Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time | |||

152 | Series and sequences part 2 | Time Payments | |

Objective: To calculate the payments required to pay off a loan | |||

153 | Calculus part 2 | Curve Sketching. | |

Objective: To practice curve sketching of polynomials using calculus techniques. | |||

154 | Calculus part 2 | Practical Applications of Maxima and Minima. | |

Objective: To use maxima and minima to solve practical problems. | |||

155 | Calculus part 2 | Antidifferentiation – Primitive Function. | |

Objective: To find primitive functions using antidifferentiation. | |||

156 | Calculus part 2 | Computation of Areas. | |

Objective: To calculate areas under curves using integration. | |||

157 | Calculus part 2 | Computation of Volumes of Revolution. | |

Objective: To calculate the volume of a solid using integration. | |||

158 | Calculus part 2 | The Trapezoidal rule and Simpson’s rule | |

Objective: To use Simpson’s rule to determine area under a curve. | |||

159 | Exam | Exam – SAT Extension | |

Objective: Exam |

### SAT All Lessons Mathematics

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

1 | Study Plan | Study plan – SAT All Lessons | |

2 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

3 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

4 | Logic | Proof by Disproof of a Contradictory Statement | |

Objective: To prove that a statement is true by proving that the contradictory statement is false | |||

5 | Logic | Mathematical induction | |

Objective: To use proof by mathematical induction | |||

6 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 1 Sin] | |

Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle | |||

7 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | |

Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle | |||

8 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | |

Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle | |||

9 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | |

10 | Trigonometry part 1 | Bearings: The Compass | |

Objective: To change from true bearings to compass bearings and vice versa | |||

11 | Trigonometry part 1 | Angles of Elevation and Depression | |

Objective: To identify and distinguish between angles of depression and elevation | |||

12 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | |

Objective: To solve problems involving bearings and angles of elevation and depression | |||

13 | Trigonometry part 1 | Using the Calculator to Find an Angle Given a Trigonometric Ratio | |

Objective: To find angles in right-angled triangles given trigonometric ratios | |||

14 | Trigonometry part 1 | Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle | |

Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems | |||

15 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | |

Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees | |||

16 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | |

Objective: To complete the cosine rule to find a subject side for given triangles | |||

17 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | |

Objective: To complete the cosine rule to find a subject angle for given triangles | |||

18 | Trigonometry part 1 | The Sine Rule: Finding a Side | |

Objective: To find an unknown side of a triangle using the sine rule | |||

19 | Trigonometry part 1 | The Sine Rule: Finding an Angle | |

Objective: To find an unknown angle of a triangle using the sine rule | |||

20 | Trigonometry part 1 | The Sine Area Formula for a Triangle | |

Objective: To use the sine formula for the area of a triangle to calculate area | |||

21 | Co-ordinate geometry part 1 | The Gradient | |

Objective: To find the gradient of a line given its angle of inclination or given rise and run | |||

22 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

23 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

24 | Statistics part 1 | Relative Frequency | |

Objective: To extend the frequency distribution table to include a relative frequency column | |||

25 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

26 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

27 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

28 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

29 | Statistics part 1 | Cumulative Frequency | |

Objective: To construct cumulative frequency columns, histograms and polygons | |||

30 | Statistics part 1 | Calculating the Mean from a Frequency Distribution | |

Objective: To determine averages (mean, median and mode) from cumulative frequency polygons | |||

31 | Probability | The Binomial Theorem and Binomial Coefficients | |

Objective: To calculate binomial coefficients and expand binomial powers. | |||

32 | Probability | Simple events | |

33 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

34 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

35 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

36 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

37 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

38 | Probability | P[A or B] When A and B are NOT mutually exclusive | |

Objective: To calculate the probability of non exclusive events using P(A or B) = P(A)+P(B) | |||

39 | Probability | Binomial probabilities using the Binomial Theorem | |

Objective: To calculate the binomial probability of a given number of successful trials | |||

40 | Probability | Counting techniques and ordered selections | |

Objective: To use counting techniques in probability | |||

41 | Probability | Unordered selections – combinations | |

Objective: To use the nCr formula to solve problems where unordered selections occur | |||

42 | Matrices | Matrices: basic concepts | |

Objective: To write and state the order of a matrix and to identify square matrices | |||

43 | Matrices | Addition and Subtraction of Matrices | |

Objective: To add and subtract matrices | |||

44 | Matrices | Scalar matrix: multiplication | |

Objective: To multiply a matrix by a scalar | |||

45 | Matrices | Multiplication of one matrix by another matrix | |

Objective: To perform matrix multiplication and to recognise that AB is not equal to BA | |||

46 | Matrices | Translation in the number plane | |

Objective: To use matrix addition to translate points | |||

47 | Matrices | Translation by matrix multiplication | |

Objective: To transform points and objects by matrix multiplication | |||

48 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | |

Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication | |||

49 | Matrices | Vectors | |

Objective: To use vectors to find resultant speeds and displacements | |||

50 | Matrices – Linear systems | Number of Solutions | |

Objective: To determine solutions to systems of equations | |||

51 | Matrices – Linear systems | Vector Addition in 2 and 3D | |

Objective: To represent, add, subtract and determine the direction of vectors | |||

52 | Matrices – Linear systems | Optimal Solutions | |

Objective: To use linear programming to maximise or minimise an objective function | |||

53 | Matrices – Linear systems | Linear Systems with Matrices | |

Objective: To identify and describe matrices and perform row operations in matrices | |||

54 | Matrices – Linear systems | Row Echelon Form | |

Objective: To identify and create matrices in row echelon form and to solve systems of equations | |||

55 | Matrices – Linear systems | Gauss Jordan Elimination | |

Objective: To use the Gauss Jordan Elimination Method to solve systems of linear equations | |||

56 | Graphs part 2 | Graphing complex polynomials: quadratics with no real roots | |

Objective: To graph quadratics that have no real roots, hence don’t cut the x-axis | |||

57 | Graphs part 2 | General equation of a circle: determine and graph the equation | |

Objective: To determine and graph the equation of a circle with radius a and centre (h,k) | |||

58 | Graphs part 2 | Graphing cubic curves | |

59 | Graphs part 2 | Absolute Value Equations | |

Objective: To graph equations involving absolute values | |||

60 | Graphs part 2 | The Rectangular Hyperbola | |

Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x | |||

61 | Graphs part 2 | The Exponential Function | |

Objective: To graph exponential curves whose exponents are either positive or negative | |||

62 | Graphs part 2 | Logarithmic Functions | |

Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) | |||

63 | Conic sections | Introduction to Conic Sections and Their General Equation | |

Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2 | |||

64 | Conic sections | The Parabola | |

Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px | |||

65 | Conic sections | Circles | |

66 | Conic sections | The Ellipsis | |

67 | Conic sections | The Hyperbola | |

68 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

69 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

70 | Function | Selecting Appropriate Domain and Range | |

Objective: To determine appropriate domains for functions | |||

71 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

72 | Function | Evaluating and Graphing Piecewise Functions | |

Objective: To evaluate and graph piecewise functions | |||

73 | Function | Combining Functions | |

74 | Function | Simplifying Composite Functions | |

Objective: To simplify, evaluate and determine the domain of composite functions | |||

75 | Function | Inverse Functions | |

Objective: To find the inverse of a function and determine whether this inverse is itself a function | |||

76 | Function | Graphing Rational Functions Part 1 | |

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes | |||

77 | Function | Graphing Rational Functions Part 2 | |

Objective: To determine asymptotes and graph rational functions | |||

78 | Function | Parametric Equations | |

Objective: To interchange parametric and Cartesian equations and to identify graphs | |||

79 | Function | Polynomial Addition: in Combining and Simplifying Functions | |

Objective: To evaluate, simplify and graph rational functions | |||

80 | Function | Parametric Functions | |

Objective: To change Cartesian and parametric equations and to graph parametric functions | |||

81 | Statistics part 2 | Calculating mean, mode and median from grouped data | |

82 | Statistics part 2 | Using the Calculator for Statistics | |

Objective: To find a mean, using a data set or a frequency distribution table and calculator. | |||

83 | Statistics part 2 | Measures of Spread | |

Objective: To determine a range and use it in decision making | |||

84 | Statistics part 2 | Standard deviation applications | |

85 | Statistics part 2 | Applications of Standard Deviation | |

Objective: To use standard deviation as a measure of deviation from a mean | |||

86 | Statistics part 2 | The Normal Distribution | |

87 | Statistics part 2 | Measures of Spread: the interquartile range | |

Objective: To find the upper and lower quartiles and the interquartile range | |||

88 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots | |||

89 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

90 | Trigonometry part 2 | Reciprocal Ratios | |

Objective: To find the trigonometric ratios for a given right-angled triangle | |||

91 | Trigonometry part 2 | Complementary Angle Results | |

Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality | |||

92 | Trigonometry part 2 | Trigonometric Identities | |

Objective: To simplify expressions using trigonometric equalities | |||

93 | Trigonometry part 2 | Angles of Any Magnitude | |

Objective: To assign angles to quadrants and to find trigonometric values for angles | |||

94 | Trigonometry part 2 | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |

Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees | |||

95 | Trigonometry part 2 | Graphing the Trigonometric Ratios I: Sine Curve | |

Objective: To recognise the sine curve and explore shifts of phase and amplitude | |||

96 | Trigonometry part 2 | Graphing the Trigonometric Ratios II: Cosine Curve | |

Objective: To recognise the cosine curve and explore shifts of phase and amplitude | |||

97 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | |

Objective: To recognise the tangent curve and explore shifts of phase and amplitude | |||

98 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | |

Objective: To graph the primary trigonometric functions and their inverses | |||

99 | Trigonometry part 2 | Solving Trigonometric Equations – Type I | |

Objective: To Solve trigonometric equations for angles from 0 to 360 degrees. | |||

100 | Trigonometry part 2 | Solving Trigonometric Equations – Type II | |

Objective: To solve trigonometric equations for angles from 0 to 360 degrees. | |||

101 | Trigonometry part 2 | Solving Trigonometric Equations – Type III | |

Objective: To solve trigonometric equations using tan? = sin?/cos?. | |||

102 | Polar coordinates | Polar Coordinates – Plotting and Converting | |

Objective: To plot polar points and convert polar coordinates to rectangular coordinates | |||

103 | Polar coordinates | Converting Rectangular Coordinates to Polar Form | |

Objective: To convert rectangular to polar coordinates | |||

104 | Polar coordinates | Graphing Polar Functions | |

Objective: To write the polar coordinates of a point for selected argument ranges | |||

105 | Trigonometry part 2 | Trigonometric Sum and Difference Identities | |

Objective: To evaluate trig functions of angles using sum and difference identities | |||

106 | Trigonometry part 2 | Double Angle Identities | |

Objective: To use double angle identities to evaluate trig. functions and solve trig equations | |||

107 | Trigonometry part 2 | Half-angle Identities | |

Objective: To evaluate trig. functions of angles using half-angle identities | |||

108 | Trigonometry part 2 | t Formulas | |

Objective: To write t-formulae for trig. functions. To solve equations using t-formulae | |||

109 | Complex numbers | Complex Numbers: Adding and Subtracting | |

Objective: To recognise and manipulate simple complex numbers and expressions | |||

110 | Complex numbers | Complex Numbers: Multiplying and Dividing | |

Objective: To perform multiplication and division of complex numbers | |||

111 | Complex numbers | Adding and Subtracting Complex Numbers using Vectors | |

Objective: To perform complex number operations graphically using vectors | |||

112 | Complex numbers | The Absolute Value of a Complex Number | |

Objective: To find the absolute value of a complex number | |||

113 | Complex numbers | Trigonometric Form of a Complex Number | |

Objective: To find the trigonometric form of a complex number | |||

114 | Complex numbers | Multiplication and Division of Complex Numbers in Trigonometric Form | |

Objective: To multiply and divide complex numbers using DeMoivre’s Theorem | |||

115 | Complex numbers | DeMoivre’s theorem | |

Objective: To find powers of complex numbers using DeMoivre’s theorem | |||

116 | Complex numbers | The nth Root of Real and Complex Numbers | |

Objective: To find the roots of a complex function using DeMoivre’s theorem | |||

117 | Complex numbers | Fundamental Theorem of Algebra | |

Objective: To find the nth zeros of a polynomial function both real and complex | |||

118 | Polynomials | Introduction to polynomials | |

Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic | |||

119 | Polynomials | The Sum, Difference and Product of Two Polynomials | |

Objective: To add, subtract and multiply polynomials | |||

120 | Polynomials | Polynomials and Long Division | |

Objective: To perform long division of polynomials, finding quotient and remainder | |||

121 | Polynomials | The Remainder Theorem | |

Objective: To determine a remainder when a first polynomial is divided by a second | |||

122 | Polynomials | More on Remainder Theorem | |

Objective: To determine polynomial coefficients given a divisor and remainder | |||

123 | Polynomials | The factor theorem | |

Objective: To use the factor theorem to show that (x-a) is a factor of P(x) | |||

124 | Polynomials | More on the factor theorem | |

Objective: To use the factor theorem to find algebraic variables in polynomials | |||

125 | Polynomials | Complete factorisations using the factor theorem | |

Objective: To use the factor theorem to derive factors of a polynomial | |||

126 | Polynomials | Polynomial equations | |

Objective: To practise solving polynomial equations | |||

127 | Polynomials | Graphs of polynomials | |

Objective: To derive graphs of polynomials by factorising | |||

128 | Polynomials | The Sum and Product of the Roots of Quadratic Equations. | |

Objective: Sum and product of roots of quadratic equations. | |||

129 | Polynomials | The Sum and Product of the Roots of Cubic and Quartic Equations. | |

Objective: Sum and product of toots of cubic and quartic equations. | |||

130 | Polynomials | Methods of Approximating Roots. | |

Objective: Methods of approximating roots. | |||

131 | Polynomials | Newton’s Method of Approximation. | |

Objective: Newton’s method of approximation. | |||

132 | Calculus part 1 | Limits | |

Objective: To find the limit value of a function as x approaches n | |||

133 | Calculus part 1 | Differentiation from First Principles | |

Objective: To differentiate functions from first principles | |||

134 | Calculus part 1 | Differentiation of y = x to the power of n | |

Objective: To differentiate algebraic functions using the laws of differentiation | |||

135 | Calculus part 1 | Meaning of dy over dx – Equations of Tangents and Normals | |

Objective: To find and use the slope of tangents and normals | |||

136 | Calculus part 1 | Function of a Function Rule, Product Rule, Quotient Rule. | |

Objective: To differentiate functions using the product, quotient and chain rules. | |||

137 | Calculus part 1 | Increasing, Decreasing and Stationary Functions. | |

Objective: To determine values of x for which f(x) is increasing, decreasing or stationary. | |||

138 | Calculus part 1 | The Second Derivative – Concavity. | |

Objective: To determine concavity of a curve at a point using the second derivative. | |||

139 | Calculus part 1 | Classification of Stationary Points. | |

Objective: To Locate and describe stationary points and points of inflection using differention. | |||

140 | Series and sequences part 2 | Geometric Means | |

Objective: To find geometric means of a and b and insert geometric means between 2 endpoints | |||

141 | Series and sequences part 2 | The sum to n terms of a G.P. | |

Objective: To find the sum of n terms of a sequence | |||

142 | Series and sequences part 2 | Sigma notation | |

Objective: To evaluate progressions using sigma notation | |||

143 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | |

Objective: To find the limiting sum of a sequence | |||

144 | Series and sequences part 2 | Recurring Decimals and the Infinite G.P. | |

Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction | |||

145 | Series and sequences part 2 | Compound Interest | |

Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n | |||

146 | Series and sequences part 2 | Superannuation | |

Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time | |||

147 | Series and sequences part 2 | Time Payments | |

Objective: To calculate the payments required to pay off a loan | |||

148 | Calculus part 2 | Curve Sketching. | |

Objective: To practice curve sketching of polynomials using calculus techniques. | |||

149 | Calculus part 2 | Practical Applications of Maxima and Minima. | |

Objective: To use maxima and minima to solve practical problems. | |||

150 | Calculus part 2 | Antidifferentiation – Primitive Function. | |

Objective: To find primitive functions using antidifferentiation. | |||

151 | Calculus part 2 | Computation of Areas. | |

Objective: To calculate areas under curves using integration. | |||

152 | Calculus part 2 | Computation of Volumes of Revolution. | |

Objective: To calculate the volume of a solid using integration. | |||

153 | Calculus part 2 | The Trapezoidal rule and Simpson’s rule | |

Objective: To use Simpson’s rule to determine area under a curve. | |||

154 | Exam | Exam – SAT All Lessons | |

Objective: Exam |

### 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. |

### 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. |

### 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. |

### 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. |

### 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. |

### 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. |

### 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. |

### 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. |

### 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. |