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Mathematics

Literacy





Mathematics

Early Stage 1 - Kindergarten Mathematics

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# TOPIC TITLE
1 Using and applying number The numbers 1 to 5

Objective: On completion of the lesson the student will be able to read, write and identify the words and numerals for the numbers 1 to 5

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2 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.

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3 The number system Ordinal numbers 1 to 9

Objective: On completion of the lesson the student will be able to match ordinal words and numbers with groups of 1-9 objects.

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4 Using and applying number Zero and counting numbers 1 to 9

Objective: On completion of the lesson the student will be able to recognise, write and match the numeral and word for the number zero.

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5 Using and applying number The number 10

Objective: On completion of the lesson the student will be able to write the numeral and word for the number 10, count up to 10 objects and to match a group of objects to the correct number.

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6 Using and applying number Numbers 11 to 20

Objective: On completion of the lesson the student will be able to write the numeral and word for the numbers 11 to 20, count up to 20 and match a group of objects to the correct number.

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7 Using and applying number Using place value to order numbers up to 20

Objective: On completion of the lesson the student will be able to use place value to order numbers up to the value of 20.

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8 Reasoning Simple addition up to the number 10

Objective: On completion of the lesson the student will be able to write simple number sentences that show numbers adding up to another number.

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9 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.

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10 Time, days of week Days of the week

Objective: On completion of the lesson the student will be able to: name the days of the week in order, recognise them in a written form, be able to answer questions about the days of the week, and have an understanding of a diary.

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11 Time, duration Duration

Objective: On completion of the lesson the student will be able to estimate and measure the duration of an event using informal units, and compare and order the duration of an event using informal units.

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Stage 1 - Year 1 Mathematics

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# TOPIC TITLE
1 Using and applying number The numbers 1 to 5

Objective: On completion of the lesson the student will be able to read, write and identify the words and numerals for the numbers 1 to 5

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2 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.

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3 The number system Ordinal numbers 1 to 9

Objective: On completion of the lesson the student will be able to match ordinal words and numbers with groups of 1-9 objects.

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4 Using and applying number Zero and counting numbers 1 to 9

Objective: On completion of the lesson the student will be able to recognise, write and match the numeral and word for the number zero.

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5 Using and applying number The number 10

Objective: On completion of the lesson the student will be able to write the numeral and word for the number 10, count up to 10 objects and to match a group of objects to the correct number.

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6 Using and applying number Numbers 11 to 20

Objective: On completion of the lesson the student will be able to write the numeral and word for the numbers 11 to 20, count up to 20 and match a group of objects to the correct number.

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7 Using and applying number Using place value to order numbers up to 20

Objective: On completion of the lesson the student will be able to use place value to order numbers up to the value of 20.

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8 Reasoning Simple addition up to the number 10

Objective: On completion of the lesson the student will be able to write simple number sentences that show numbers adding up to another number.

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9 Reasoning Simple addition up to the number 20

Objective: On completion of the lesson the student will be able to write simple number sentences and also write addition in a vertical format using numbers up to 20.

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10 Calculations Subtraction by Comparison

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

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11 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.

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12 Calculations Subtraction up to the number 20 and beyond

Objective: On completion of the lesson the student will be capable of subtraction using tens and units and calculating the answer to take away or subtraction number sentences.

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13 Calculation-grouping Multiplication using equal groups

Objective: On completion of the lesson the student will be able to write about equal groups and rows and will understand how to count them.

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14 Calculation-grouping Multiplication using repeated addition

Objective: On completion of the lesson the student will be able to write about equal groups and rows using another method and also learn different ways to count them.

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15 Calculation-multiplication The multiplication sign

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

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16 Calculation sharing/division Strategies for division

Objective: On completion of the lesson the student will be able to share objects equally and will also learn how to write about them.

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17 Length Compare length by using informal units of measurement

Objective: On completion of the lesson the student will be able to measure objects around the student’s home and compare their length to each other. The student will also be able to compare the different ways the student measured the same object.

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18 Weight/mass Introducing the concept of mass

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

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19 Time, days of week Days of the week

Objective: On completion of the lesson the student will be able to: name the days of the week in order, recognise them in a written form, be able to answer questions about the days of the week, and have an understanding of a diary.

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20 Time, duration Duration

Objective: On completion of the lesson the student will be able to estimate and measure the duration of an event using informal units, and compare and order the duration of an event using informal units.

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21 Time, months Months and seasons of the year

Objective: On completion of the lesson the student will be able to: name and order the months of the year, know the number of days in each month, name the seasons in order, and know the number of months in each season.

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22 Time, quarter to, past Quarter past and quarter to

Objective: On completion of the lesson the student will be able to associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes, and use the terms ‘quarter to’ and ‘quarter past’.

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23 Time, analogue O’clock and half past on the analogue clock

Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock.

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Stage 1 - Year 2 Mathematics

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# TOPIC TITLE
1 Reasoning Simple addition up to the number 20

Objective: On completion of the lesson the student will be able to write simple number sentences and also write addition in a vertical format using numbers up to 20.

See the sample lesson in action here
2 Calculations Subtraction by Comparison

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

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3 Calculations Subtraction up to the number 20 and beyond

Objective: On completion of the lesson the student will be capable of subtraction using tens and units and calculating the answer to take away or subtraction number sentences.

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4 Calculation-grouping Multiplication using equal groups

Objective: On completion of the lesson the student will be able to write about equal groups and rows and will understand how to count them.

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5 Calculation-grouping Multiplication using repeated addition

Objective: On completion of the lesson the student will be able to write about equal groups and rows using another method and also learn different ways to count them.

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6 Calculation-multiplication The multiplication sign

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

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7 Calculation sharing/division Strategies for division

Objective: On completion of the lesson the student will be able to share objects equally and will also learn how to write about them.

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8 Calculation-multiples Multiples of 10 up to 100

Objective: On completion of the lesson the student will be able to read, write, rename and add multiples of ten.

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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.

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10 Calculation 10-100 Counting by 1, 2, 5, and 10 to 100

Objective: On completion of the lesson the student will be able to skip count to one hundred and show that one hundred equals ten times ten.

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11 Addition Addition to 99

Objective: On completion of the lesson the student will be able to use place value to add two 2-digit numbers together up to a total of 99.

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12 Subtraction Subtraction up to the number 99

Objective: On completion of the lesson the student will know how to find the answer to take away number sentences with bigger numbers and will also know how to write these number sentences.

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13 Time, months Months and seasons of the year

Objective: On completion of the lesson the student will be able to: name and order the months of the year, know the number of days in each month, name the seasons in order, and know the number of months in each season.

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14 Time, quarter to, past Quarter past and quarter to

Objective: On completion of the lesson the student will be able to associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes, and use the terms ‘quarter to’ and ‘quarter past’.

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15 Time, analogue O’clock and half past on the analogue clock

Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock.

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16 Lines and angles Describing position.

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

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17 Data Pictograms

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

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18 Data Bar Charts

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

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19 Length Compare length by using informal units of measurement

Objective: On completion of the lesson the student will be able to measure objects around the student’s home and compare their length to each other. The student will also be able to compare the different ways the student measured the same object.

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20 Length Using the metre as a formal unit to measure perimeter

Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.

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

Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.

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22 Volume Introduction to volume. using the cubic centimetre as a standard unit

Objective: On completion of the lesson the student will be able to: recognise the need for a formal unit to measure volume, use the abbreviation for cubic centimetre, construct three dimensional objects using cubic centimetre blocks, and use counting to determine vo

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23 Weight/mass Introducing the concept of mass

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

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Stage 1 - Year 3 Mathematics

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# TOPIC TITLE
1 Calculation-multiples Multiples of 10 up to 100

Objective: On completion of the lesson the student will be able to read, write, rename and add multiples of ten.

See the sample lesson in action here
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.

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3 Calculation 10-100 Counting by 1, 2, 5, and 10 to 100

Objective: On completion of the lesson the student will be able to skip count to one hundred and show that one hundred equals ten times ten.

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4 Addition Addition to 99

Objective: On completion of the lesson the student will be able to use place value to add two 2-digit numbers together up to a total of 99.

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5 Calculation-larger numbers The numbers 100 to 999

Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999.

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6 Subtraction Subtraction up to the number 99

Objective: On completion of the lesson the student will know how to find the answer to take away number sentences with bigger numbers and will also know how to write these number sentences.

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7 Subtraction Subtraction with borrowing

Objective: On completion of the lesson the student will be able to record subtraction number sentences and will understand the need to trade between place value columns using the renaming method

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8 Subtraction Subtraction of two-digit numbers Involving comparison.

Objective: On completion of the lesson the student will know how to solve and record the answer to word problems and will understand how estimation helps to find out if an answer is correct.

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9 Calculation sharing/division Strategies for division

Objective: On completion of the lesson the student will be able to share objects equally and will also learn how to write about them.

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10 Problems Solve and record division using known facts and sharing

Objective: On completion of the lesson the student will be able to use sharing concepts to solve and record division problems.

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11 Length Using the metre as a formal unit to measure perimeter

Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.

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

Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.

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13 Area Introduction to the square centimetre.

Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly.

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14 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.

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15 Volume Introduction to volume. using the cubic centimetre as a standard unit

Objective: On completion of the lesson the student will be able to: recognise the need for a formal unit to measure volume, use the abbreviation for cubic centimetre, construct three dimensional objects using cubic centimetre blocks, and use counting to determine vo

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16 Weight/mass Introducing the concept of mass

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

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17 3-D shapes Constructing models.

Objective: On completion of the lesson the student will be able to: Construct rectangular prisms using cubic centimetre blocks and counting to determine volume. Explain the advantages of using a cube to measure volume. Construct different rectangular prisms.

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18 Capacity Using the cubic cm and displacement to measure volume and capacity

Objective: On completion of the lesson the student will know a way to find volume and capacity.

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19 Weight/mass The kilogram

Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales.

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20 2-D shapes Using the prefix to determine polygons

Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides.

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21 2-D shapes Spatial properties of quadrilaterals

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

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22 Lines and angles Describing position.

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

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23 Lines and angles Mapping and grid references

Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places.

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24 Data Pictograms

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

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25 Data Bar Charts

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

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26 Time, minutes Analogue – Telling time – minutes in the hour

Objective: On completion of the lesson the student will be able to recognize the coordinated movements of the hands on an analogue clock.

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27 Time, units Units of time

Objective: On completion of the lesson the student will be able to convert units of time and read and interpret simple timetables, timelines and calendars.

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28 Time, quarter to, past Quarter past and quarter to

Objective: On completion of the lesson the student will be able to associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes, and use the terms ‘quarter to’ and ‘quarter past’.

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29 Time, minutes to the hour Minutes to

Objective: On completion of the lesson the student will be able to understand and read the minutes to the hour on an analogue clock.

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30 Time, minutes past the hour Minutes past

Objective: On completion of the lesson the student will be able to understand and read the minutes past the hour on an analogue clock.

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31 Time, digital, analogue Comparing analogue and digital time

Objective: On completion of the lesson the student will be able to: read analogue and digital clocks to the minute, be familiar with the recording of digital time, and tell the same time using both analogue and digital clocks.

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32 Time, digital O’clock and half past using digital time

Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on a digital clock.

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33 Time, analogue O’clock and half past on the analogue clock

Objective: On completion of the lesson the student will be able to use the terms ‘o’clock’ and ‘half past’, and read hour and half-hour time on an analogue clock.

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

Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole.

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

Objective: On completion of the lesson the student will be able to use the fractions to describe equal parts of a collection of objects.

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36 Fractions Comparing and ordering fractions

Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts.

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Stage 1 - Year 4 Mathematics

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# TOPIC TITLE
1 Calculation-larger numbers The numbers 100 to 999

Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999.

See the sample lesson in action here
2 Subtraction Subtraction with borrowing

Objective: On completion of the lesson the student will be able to record subtraction number sentences and will understand the need to trade between place value columns using the renaming method

See the sample lesson in action here
3 Subtraction Subtraction of two-digit numbers Involving comparison.

Objective: On completion of the lesson the student will know how to solve and record the answer to word problems and will understand how estimation helps to find out if an answer is correct.

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4 Multiplication Multiplication – important facts.

Objective: On completion of the lesson the student will know the connection between multiplication and division and recognise the strategies to help solve multiplication number sentences.

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5 Place value The numbers 1000 to 9999

Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999.

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6 Addition Addition up to the number 999

Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers.

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

Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers.

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8 Division Divide whole numbers by a 2 digit divisor

Objective: On completion of the lesson the student will be able to solve and record division problems with whole numbers using a two-digit divisor and show any remainders as a fraction.

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9 Problems Solve and record division using known facts and sharing

Objective: On completion of the lesson the student will be able to use sharing concepts to solve and record division problems.

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10 Division Division with and without a remainder.

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

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11 Length Using the metre as a formal unit to measure perimeter

Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.

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

Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.

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13 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.

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14 Length Compare and convert formal units of measurement

Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert.

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15 Area Introduction to the square centimetre.

Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly.

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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.

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17 Weight/mass The kilogram

Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales.

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18 Weight/mass The gram and net mass

Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams.

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19 2-D shapes Using the prefix to determine polygons

Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides.

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20 2-D shapes Spatial properties of quadrilaterals

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

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21 Angles Measure and classify angles

Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle.

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22 2-D shapes Recognise and name triangles

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

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23 3-D shapes Recognise and name pyramids according to spatial properties

Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties.

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24 Tessellating 2-D shapes Use grids to enlarge/reduce 2D shapes

Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate.

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25 3-D shapes Recognise and name prisms according to spatial properties

Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties.

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

Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre.

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27 Capacity Using the cubic cm and displacement to measure volume and capacity

Objective: On completion of the lesson the student will know a way to find volume and capacity.

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

Objective: On completion of the lesson the student will understand what a cubic centimetre is and how it can be used to find out the volume and capacity of a three dimensional shape.

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29 Capacity Converting between volume and capacity using kilolitres and litres

Objective: On completion of the lesson the student will know the formal units of measurement for volume and capacity for bigger objects. The student will also be able to use the knowledge of volume to work out capacity.

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30 Capacity Estimate, measure and compare the capacity of containers

Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it.

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31 Capacity Converting between volume and capacity using millilitres and litres

Objective: On completion of the lesson the student will be able to convert between units of capacity.

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32 Lines and angles Mapping and grid references

Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places.

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33 Lines and angles Main and intermediate compass points

Objective: On completion of the lesson the student will be able to use main and intermediate compass points to specify location.

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34 Lines and angles Informal coordinate system

Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper.

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35 Data Pictograms

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

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36 Data Bar Charts

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

See the sample lesson in action here
37 Time, minutes Analogue – Telling time – minutes in the hour

Objective: On completion of the lesson the student will be able to recognize the coordinated movements of the hands on an analogue clock.

See the sample lesson in action here
38 Time, quarter to, past Quarter past and quarter to

Objective: On completion of the lesson the student will be able to associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes, and use the terms ‘quarter to’ and ‘quarter past’.

See the sample lesson in action here
39 Time, digital, analogue Comparing analogue and digital time

Objective: On completion of the lesson the student will be able to: read analogue and digital clocks to the minute, be familiar with the recording of digital time, and tell the same time using both analogue and digital clocks.

See the sample lesson in action here
40 Time, units Units of time

Objective: On completion of the lesson the student will be able to convert units of time and read and interpret simple timetables, timelines and calendars.

See the sample lesson in action here
41 Time, minutes to the hour Minutes to

Objective: On completion of the lesson the student will be able to understand and read the minutes to the hour on an analogue clock.

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42 Time, minutes past the hour Minutes past

Objective: On completion of the lesson the student will be able to understand and read the minutes past the hour on an analogue clock.

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43 Time, a.m. p.m. AM and PM time

Objective: On completion of the lesson the student will be able to talk about am and pm time and use the correct notation for am and pm time.

See the sample lesson in action here
44 Decimals Introduction to decimals

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

See the sample lesson in action here
45 Decimals Comparing and ordering decimals to two decimal places

Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places.

See the sample lesson in action here
46 Decimals Decimals with whole numbers 10th and 100th

Objective: On completion of the lesson the student will be able to use and understand place value to show whole numbers, tenths and hundredths as decimals.

See the sample lesson in action here
47 Decimals Adding decimals to two decimal places

Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places)

See the sample lesson in action here
48 Decimals Subtracting decimals to two decimal places

Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places)

See the sample lesson in action here
49 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.

See the sample lesson in action here
50 Decimals Using decimals to record length

Objective: On completion of the lesson the student will be able to interpret the everyday use of fractions and decimals and use their knowledge of decimals to record measurements.

See the sample lesson in action here
51 Decimals Rounding decimals

Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.

See the sample lesson in action here
52 Fractions Using fractions 1/2, 1/4, 1/8 to describe part of a whole

Objective: On completion of the lesson the student will be able to: name fractions, and use fractions to describe equal parts of a whole.

See the sample lesson in action here
53 Fractions Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection

Objective: On completion of the lesson the student will be able to use the fractions to describe equal parts of a collection of objects.

See the sample lesson in action here
54 Fractions Comparing and ordering fractions

Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts.

See the sample lesson in action here
55 Fractions Finding equivalent fractions

Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.

See the sample lesson in action here
56 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.

See the sample lesson in action here
57 Fractions Fractions 1/5, 1/10, 1/100

Objective: On completion of the lesson the student will be able to: compare fractions with the denominators 5, 10, 100, and represent fractions with the denominator 5, 10, 100.

See the sample lesson in action here
58 Percentages Introduction to percentages, including relating common fractions to percentages

Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage.

See the sample lesson in action here
59 Percentages Changing fractions and decimals to percentages using tenths and hundredths

Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.

See the sample lesson in action here
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Stage 1 - Year 5 Mathematics

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# TOPIC TITLE
1 Place value The numbers 1000 to 9999

Objective: On completion of the lesson the student will be able to count to 999, skip count by 10s and 100s to 999 and use pictures or objects to represent the numbers 100 to 999.

See the sample lesson in action here
2 Addition Addition up to the number 999

Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers.

See the sample lesson in action here
3 Subtraction Subtraction up to the number 999 using the renaming method

Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers.

See the sample lesson in action here
4 Counting and numeration The numbers 10 000 to 99 999

Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers.

See the sample lesson in action here
5 Counting and numeration Addition to 9999 and beyond

Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems.

See the sample lesson in action here
6 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.

See the sample lesson in action here
7 Multiplication Multiples and factors of whole numbers

Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers.

See the sample lesson in action here
8 Multiplication Multiplication using extended algorithms.

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

See the sample lesson in action here
9 Division Division with and without a remainder.

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

See the sample lesson in action here
10 Division Dividing two and three digit numbers by a single digit number.

Objective: On completion of the lesson the student will understand dividing two and three digit numbers by a single digit number.

See the sample lesson in action here
11 Multiplication Multiplication by 2 and 3 digits

Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form.

See the sample lesson in action here
12 Multiplication Multiplying 2-digit numbers by multiple of 10

Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication.

See the sample lesson in action here
13 Multiplication Multiplying 3 and 4-digit numbers by multiples of 100

Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication.

See the sample lesson in action here
14 Time, a.m. p.m. AM and PM time

Objective: On completion of the lesson the student will be able to talk about am and pm time and use the correct notation for am and pm time.

See the sample lesson in action here
15 Time, 24-hour 24 hour time

Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time.

See the sample lesson in action here
16 Time zones Time zones

Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions.

See the sample lesson in action here
17 Time, distance, speed Average speed

Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object.

See the sample lesson in action here
18 Angles Measure and classify angles

Objective: On completion of the lesson the student will be able to recognise, measure and classify angles and measure the angles in a triangle.

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19 2-D shapes Recognise and name triangles

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

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20 3-D shapes Recognise and name pyramids according to spatial properties

Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties.

See the sample lesson in action here
21 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.

See the sample lesson in action here
22 Lines and angles Mapping and grid references

Objective: On completion of the lesson the student will be able to identify specific places on a map and use regions on a grid to locate objects or places.

See the sample lesson in action here
23 3-D shapes Recognise nets for prisms, pyramids, cubes and cones

Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones.

See the sample lesson in action here
24 Tessellating 2-D shapes Use grids to enlarge/reduce 2D shapes

Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate.

See the sample lesson in action here
25 3-D shapes Viewing 3-D shapes.

Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles.

See the sample lesson in action here
26 Lines and angles Main and intermediate compass points

Objective: On completion of the lesson the student will be able to use main and intermediate compass points to specify location.

See the sample lesson in action here
27 Lines and angles Informal coordinate system

Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper.

See the sample lesson in action here
28 Data Pictograms

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

See the sample lesson in action here
29 Data Bar Charts

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

See the sample lesson in action here
30 Data Line graphs.

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

See the sample lesson in action here
31 Data Pie and bar graphs.

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

See the sample lesson in action here
32 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.

See the sample lesson in action here
33 Length Compare and convert formal units of measurement

Objective: On completion of the lesson the student will be able to use the formal units millimetre, centimetre, metre and kilometre to measure and convert.

See the sample lesson in action here
34 Area Introduction to the square centimetre.

Objective: On completion of the lesson the student will be able to calculate the area in square centimetres of surfaces or objects and record their results correctly.

See the sample lesson in action here
35 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.

See the sample lesson in action here
36 Area Larger areas: square metre, hectare, square kilometre.

Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit.

See the sample lesson in action here
37 Volume Using the cubic centimetre to measure volume.

Objective: On completion of the lesson the student will be able to: recognise the relationship between the length, breadth, height and volume of a rectangular prism, calculate the volume of rectangular prisms, and find the volume of rectangular prisms by counting.

See the sample lesson in action here
38 Capacity The relationship between the common units of capacity, the litre and the millilitre

Objective: On completion of the lesson the student will understand the relationship between the two common units of capacity, the litre and millilitre.

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39 Capacity Using the cubic cm and displacement to measure volume and capacity

Objective: On completion of the lesson the student will know a way to find volume and capacity.

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

Objective: On completion of the lesson the student will understand what a cubic centimetre is and how it can be used to find out the volume and capacity of a three dimensional shape.

See the sample lesson in action here
41 Capacity Converting between volume and capacity using kilolitres and litres

Objective: On completion of the lesson the student will know the formal units of measurement for volume and capacity for bigger objects. The student will also be able to use the knowledge of volume to work out capacity.

See the sample lesson in action here
42 Capacity Estimate, measure and compare the capacity of containers

Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it.

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43 Weight/mass The kilogram

Objective: On completion of the lesson the student will know: how to use the kilogram as a measure of mass., and how to weigh items accurately using scales.

See the sample lesson in action here
44 Weight/mass The gram and net mass

Objective: On completion of the lesson the student will understand: why there’s a zero button on digital scales, how to zero some other types of scales, and also how to measure mass in grams.

See the sample lesson in action here
45 Decimals Introduction to decimals

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

See the sample lesson in action here
46 Decimals Comparing and ordering decimals to two decimal places

Objective: On completion of the lesson the student will be able to compare and order decimals to two decimal places and understand decimal notation to two places.

See the sample lesson in action here
47 Decimals Decimals with whole numbers 10th and 100th

Objective: On completion of the lesson the student will be able to use and understand place value to show whole numbers, tenths and hundredths as decimals.

See the sample lesson in action here
48 Decimals Adding decimals to two decimal places

Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places)

See the sample lesson in action here
49 Decimals Subtracting decimals to two decimal places

Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places)

See the sample lesson in action here
50 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.

See the sample lesson in action here
51 Decimals Using decimals to record length

Objective: On completion of the lesson the student will be able to interpret the everyday use of fractions and decimals and use their knowledge of decimals to record measurements.

See the sample lesson in action here
52 Decimals Rounding decimals

Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.

See the sample lesson in action here
53 Decimals Adding decimals with a different number of decimal places

Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places.

See the sample lesson in action here
54 Decimals Subtracting decimals with a different number of places

Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places.

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55 Decimals Multiplying decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.

See the sample lesson in action here
56 Decimals Multiplying decimals by whole numbers

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

See the sample lesson in action here
57 Decimals Dividing decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.

See the sample lesson in action here
58 Decimals Dividing decimal fractions by whole numbers

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

See the sample lesson in action here
59 Fractions Finding equivalent fractions

Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.

See the sample lesson in action here
60 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.

See the sample lesson in action here
61 Fractions Fractions 1/5, 1/10, 1/100

Objective: On completion of the lesson the student will be able to: compare fractions with the denominators 5, 10, 100, and represent fractions with the denominator 5, 10, 100.

See the sample lesson in action here
62 Fractions Subtracting fractions from whole numbers

Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from

See the sample lesson in action here
63 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.

See the sample lesson in action here
64 Percentages Introduction to percentages, including relating common fractions to percentages

Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage.

See the sample lesson in action here
65 Percentages Changing fractions and decimals to percentages using tenths and hundredths

Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.

See the sample lesson in action here
66 Sign word problems Solving Word Problems by recognising Sign Words

Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division.

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67 Equations Problem solving strategies

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

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68 Number problems Problems with numbers.

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

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69 Money Problems involving money

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

See the sample lesson in action here
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Stage 1 - Year 6 Mathematics

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# TOPIC TITLE
1 Counting and numeration The numbers 10 000 to 99 999

Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers.

See the sample lesson in action here
2 Counting and numeration Addition to 9999 and beyond

Objective: On completion of the lesson the student will be able to use the student’s knowledge of place value to solve addition problems with 3, 4 and 5 digit numbers and word problems.

See the sample lesson in action here
3 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.

See the sample lesson in action here
4 Counting and numeration Seven digit numbers

Objective: On completion of the lesson the student will be able to use place value knowledge to read and write seven digit whole numbers.

See the sample lesson in action here
5 Multiplication Multiples and factors of whole numbers

Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers.

See the sample lesson in action here
6 Multiplication Multiplication using extended algorithms.

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

See the sample lesson in action here
7 Division Division with and without a remainder.

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

See the sample lesson in action here
8 Division Dividing two and three digit numbers by a single digit number.

Objective: On completion of the lesson the student will understand dividing two and three digit numbers by a single digit number.

See the sample lesson in action here
9 Multiplication Multiplication by 2 and 3 digits

Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form.

See the sample lesson in action here
10 Division Divide whole numbers by a 2 digit divisor

Objective: On completion of the lesson the student will be able to solve and record division problems with whole numbers using a two-digit divisor and show any remainders as a fraction.

See the sample lesson in action here
11 Multiplication Multiplying 2-digit numbers by multiple of 10

Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any multiple of 10 using the process of long multiplication.

See the sample lesson in action here
12 Multiplication Multiplying 3 and 4-digit numbers by multiples of 100

Objective: On completion of the lesson the student will be able to multiply any 3 or 4 digit numbers by any multiple of 100 using long multiplication.

See the sample lesson in action here
13 Multiplication Multiplying 2-digit numbers by 2-digit numbers

Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number.

See the sample lesson in action here
14 Multiplication Multiplying 4-digit numbers by 3-digit numbers

Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication.

See the sample lesson in action here
15 Division/repeat subtraction Repeated subtraction with divisors less than 20 with no remainders

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 20.

See the sample lesson in action here
16 Division/repeat subtraction Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 with divisors less than 20 and no remainders.

See the sample lesson in action here
17 Division/repeat subtraction Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 2,3,4 where divisors are greater than 20 and there are no remainders.

See the sample lesson in action here
18 Division/repeat subtraction Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 1,2,3 where the divisors are less than 20 and there are remainders.

See the sample lesson in action here
19 Division/repeat subtraction Repeated subtraction by multiples of 10 with divisors less than 20 with remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 where the divisors are greater than 12 and less than 20, and the dividend is any 3 digit number, and there are remainders.

See the sample lesson in action here
20 Division/repeat subtraction Repeated subtraction with divisors greater than 20 with remainders as fractions

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions

See the sample lesson in action here
21 Division/repeat subtraction Repeated subtraction with divisors less than 35 with some remainders

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders.

See the sample lesson in action here
22 Division/repeat subtraction Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders.

See the sample lesson in action here
23 Division/repeat subtraction Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders

Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders.

See the sample lesson in action here
24 Division/repeat subtraction Using divide, multiply and subtraction in the bring down method

Objective: On completion of the lesson the student will be able to use Long Division using the Divide, Multiply, Subtract and Bring Down method.

See the sample lesson in action here
25 3-D shapes Recognise and name pyramids according to spatial properties

Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties.

See the sample lesson in action here
26 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.

See the sample lesson in action here
27 Area Introducing the rules for finding the area of a rectangle and a parallelogram.

Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides.

See the sample lesson in action here
28 Area Larger areas: square metre, hectare, square kilometre.

Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit.

See the sample lesson in action here
29 Volume Introducing the formula for volume.

Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula.

See the sample lesson in action here
30 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

See the sample lesson in action here
31 Volume Solving Problems about Volume – Part 1.

Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms.

See the sample lesson in action here
32 Volume Solving Problems about Volume – Part 2.

Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit.

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33 Capacity Converting between volume and capacity using millilitres and litres

Objective: On completion of the lesson the student will be able to convert between units of capacity.

See the sample lesson in action here
34 Weight/mass The tonne – converting units and problems

Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another.

See the sample lesson in action here
35 Geometry-angles Measuring angles

Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.

See the sample lesson in action here
36 Data Bar Charts

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

See the sample lesson in action here
37 Data Line graphs.

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

See the sample lesson in action here
38 Data Pie and bar graphs.

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

See the sample lesson in action here
39 Time, 24-hour 24 hour time

Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time.

See the sample lesson in action here
40 Time zones Time zones

Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions.

See the sample lesson in action here
41 Time, distance, speed Average speed

Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object.

See the sample lesson in action here
42 3-D shapes Recognise nets for prisms, pyramids, cubes and cones

Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones.

See the sample lesson in action here
43 Tessellating 2-D shapes Use grids to enlarge/reduce 2D shapes

Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate.

See the sample lesson in action here
44 3-D shapes Viewing 3-D shapes.

Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles.

See the sample lesson in action here
45 Lines and angles Main and intermediate compass points

Objective: On completion of the lesson the student will be able to use main and intermediate compass points to specify location.

See the sample lesson in action here
46 Lines and angles Informal coordinate system

Objective: On completion of the lesson the student will be able to use an informal coordinate system to specify location, and locate coordinate points on grid paper.

See the sample lesson in action here
47 Decimals Rounding decimals

Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.

See the sample lesson in action here
48 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.

See the sample lesson in action here
49 Decimals Adding decimals with a different number of decimal places

Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places.

See the sample lesson in action here
50 Decimals Subtracting decimals with a different number of places

Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places.

See the sample lesson in action here
51 Decimals Multiplying decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.

See the sample lesson in action here
52 Decimals Multiplying decimals by whole numbers

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

See the sample lesson in action here
53 Decimals Dividing decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.

See the sample lesson in action here
54 Decimals Dividing decimal fractions by whole numbers

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

See the sample lesson in action here
55 Decimals Dividing numbers by a decimal fraction

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

See the sample lesson in action here
56 Percentages Introduction to percentages, including relating common fractions to percentages

Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage.

See the sample lesson in action here
57 Percentages Changing fractions and decimals to percentages using tenths and hundredths

Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.

See the sample lesson in action here
58 Percentages Changing percentages to fractions and decimals

Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.

See the sample lesson in action here
59 Fractions Finding equivalent fractions

Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.

See the sample lesson in action here
60 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.

See the sample lesson in action here
61 Fractions Improper fractions

Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.

See the sample lesson in action here
62 Fractions Subtracting fractions from whole numbers

Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from

See the sample lesson in action here
63 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.

See the sample lesson in action here
64 Fractions Multiplying and dividing to obtain equivalent fractions

Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.

See the sample lesson in action here
65 Fractions Reducing fractions to lowest equivalent form

Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.

See the sample lesson in action here
66 Fractions Comparing and ordering fractions greater than (>) 1

Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one.

See the sample lesson in action here
67 Fractions Multiplying fractions by whole numbers

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

See the sample lesson in action here
68 Fractions Fractions of whole numbers

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

See the sample lesson in action here
69 Sign word problems Solving Word Problems by recognising Sign Words

Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division.

See the sample lesson in action here
70 Equations Problem solving strategies

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

See the sample lesson in action here
71 Number problems Problems with numbers.

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

See the sample lesson in action here
72 Money Problems involving money

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

See the sample lesson in action here
73 Length Problems with length.

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

See the sample lesson in action here
74 Mass Problems with mass.

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

See the sample lesson in action here
75 Area Problems with area.

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

See the sample lesson in action here
76 Volume/capacity Problems with volume/capacity.

Objective: Problem Solving: problems involving volume/capacity

See the sample lesson in action here
Go to top

Stage 4 - Year 7 leading to Stage 5.2 Mathematics

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# TOPIC TITLE
1 Multiplication Multiplying 2-digit numbers by 2-digit numbers

Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number.

See the sample lesson in action here
2 Multiplication Multiplying 4-digit numbers by 3-digit numbers

Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication.

See the sample lesson in action here
3 Division/repeat subtraction Repeated subtraction with divisors less than 20 with no remainders

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 20.

See the sample lesson in action here
4 Division/repeat subtraction Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 with divisors less than 20 and no remainders.

See the sample lesson in action here
5 Division/repeat subtraction Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 2,3,4 where divisors are greater than 20 and there are no remainders.

See the sample lesson in action here
6 Division/repeat subtraction Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 1,2,3 where the divisors are less than 20 and there are remainders.

See the sample lesson in action here
7 Division/repeat subtraction Repeated subtraction by multiples of 10 with divisors less than 20 with remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 where the divisors are greater than 12 and less than 20, and the dividend is any 3 digit number, and there are remainders.

See the sample lesson in action here
8 Division/repeat subtraction Repeated subtraction with divisors greater than 20 with remainders as fractions

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions

See the sample lesson in action here
9 Division/repeat subtraction Repeated subtraction with divisors less than 35 with some remainders

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders.

See the sample lesson in action here
10 Division/repeat subtraction Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders.

See the sample lesson in action here
11 Division/repeat subtraction Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders

Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders.

See the sample lesson in action here
12 Division/repeat subtraction Using divide, multiply and subtraction in the bring down method

Objective: On completion of the lesson the student will be able to use Long Division using the Divide, Multiply, Subtract and Bring Down method.

See the sample lesson in action here
13 Decimals Rounding decimals

Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.

See the sample lesson in action here
14 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.

See the sample lesson in action here
15 Decimals Adding decimals with a different number of decimal places

Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places.

See the sample lesson in action here
16 Decimals Subtracting decimals with a different number of places

Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places.

See the sample lesson in action here
17 Decimals Multiplying decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.

See the sample lesson in action here
18 Decimals Multiplying decimals by whole numbers

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

See the sample lesson in action here
19 Decimals Dividing decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.

See the sample lesson in action here
20 Decimals Dividing decimal fractions by whole numbers

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

See the sample lesson in action here
21 Decimals Dividing numbers by a decimal fraction

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

See the sample lesson in action here
22 Percentages Changing fractions and decimals to percentages using tenths and hundredths

Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.

See the sample lesson in action here
23 Percentages Changing percentages to fractions and decimals

Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.

See the sample lesson in action here
24 Percentages One quantity as a percentage of another

Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.

See the sample lesson in action here
25 Percentages Calculating Percentages and Fractions of Quantities

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

See the sample lesson in action here
26 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.

See the sample lesson in action here
27 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.

See the sample lesson in action here
28 Fractions Improper fractions

Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.

See the sample lesson in action here
29 Fractions Comparing and ordering fractions greater than (>) 1

Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one.

See the sample lesson in action here
30 Fractions Adding and subtracting fractions with different denominators

Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.

See the sample lesson in action here
31 Fractions Multiplying fractions by whole numbers

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

See the sample lesson in action here
32 Fractions Fractions of whole numbers

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

See the sample lesson in action here
33 Fractions Multiplying and dividing to obtain equivalent fractions

Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.

See the sample lesson in action here
34 Fractions Reducing fractions to lowest equivalent form

Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.

See the sample lesson in action here
35 Fractions Finding reciprocals of fractions and mixed numbers (mixed numerals)

Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).

See the sample lesson in action here
36 Fractions Dividing fractions

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

See the sample lesson in action here
37 Fractions Dividing mixed numbers (mixed numerals)

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

See the sample lesson in action here
38 Fractions Multiplying fractions

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

See the sample lesson in action here
39 Fractions Multiplying mixed numbers (mixed numerals)

Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.

See the sample lesson in action here
40 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.

See the sample lesson in action here
41 Area Introducing the rules for finding the area of a rectangle and a parallelogram.

Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides.

See the sample lesson in action here
42 Area Finding the area of a triangle and other composite shapes.

Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas.

See the sample lesson in action here
43 Area Larger areas: square metre, hectare, square kilometre.

Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit.

See the sample lesson in action here
44 Volume Introducing the formula for volume.

Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula.

See the sample lesson in action here
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

See the sample lesson in action here
46 Volume Solving Problems about Volume – Part 1.

Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms.

See the sample lesson in action here
47 Volume Solving Problems about Volume – Part 2.

Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit.

See the sample lesson in action here
48 Capacity Converting between volume and capacity using millilitres and litres

Objective: On completion of the lesson the student will be able to convert between units of capacity.

See the sample lesson in action here
49 Weight/mass The tonne – converting units and problems

Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another.

See the sample lesson in action here
50 Data Bar Charts

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

See the sample lesson in action here
51 Data Line graphs.

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

See the sample lesson in action here
52 Data Pie and bar graphs.

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

See the sample lesson in action here
53 Algebraic expressions Algebraic expressions.

Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.

See the sample lesson in action here
54 Algebraic expressions Substitution into algebraic expressions.

Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.

See the sample lesson in action here
55 Algebraic expressions Directed numbers: addition and subtraction.

Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.

See the sample lesson in action here
56 Algebraic expressions Directed numbers: multiplication and division.

Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.

See the sample lesson in action here
57 Algebraic expressions Simplifying algebraic expressions: adding like terms.

Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.

See the sample lesson in action here
58 Algebraic expressions Simplifying algebraic Expressions: subtracting like terms.

Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.

See the sample lesson in action here
59 Algebraic expressions Simplifying Algebraic expressions: combining addition and subtraction.

Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.

See the sample lesson in action here
60 Algebraic expressions Simplifying algebraic expressions: multiplication

Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form.

See the sample lesson in action here
61 Algebraic expressions Simplifying algebraic expressions: division

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

See the sample lesson in action here
62 Algebraic expressions Expanding algebraic expressions: multiplication

Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.

See the sample lesson in action here
63 Algebraic expressions Expanding algebraic expressions: negative multiplier

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

See the sample lesson in action here
64 Algebraic expressions Expanding and simplifying algebraic expressions

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

See the sample lesson in action here
65 Algebraic equations Solving equations containing addition and subtraction

Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.

See the sample lesson in action here
66 Algebraic equations Solving equations containing multiplication and division

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

See the sample lesson in action here
67 Algebraic equations Solving two step equations

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

See the sample lesson in action here
68 Geometry-angles Measuring angles

Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.

See the sample lesson in action here
69 Geometry-angles Adjacent angles

Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.

See the sample lesson in action here
70 Geometry-angles Complementary and supplementary angles

Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.

See the sample lesson in action here
71 Geometry-angles Vertically opposite angles

Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.

See the sample lesson in action here
72 Geometry-angles Angles at a Point.

Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.

See the sample lesson in action here
73 Geometry-angles Parallel Lines.

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

See the sample lesson in action here
74 Geometry-problems Additional questions involving parallel lines

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.

See the sample lesson in action here
75 Geometry-triangles Angle sum of a triangle

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.

See the sample lesson in action here
76 Special triangles Special triangles

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.

See the sample lesson in action here
77 Geometry-quadrilaterals Quadrilaterals

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.

See the sample lesson in action here
78 Geometry-constructions Geometric constructions

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

See the sample lesson in action here
79 Sign word problems Solving Word Problems by recognising Sign Words

Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division.

See the sample lesson in action here
80 Equations Problem solving strategies

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

See the sample lesson in action here
81 Number problems Problems with numbers.

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

See the sample lesson in action here
82 Money Problems involving money

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

See the sample lesson in action here
83 Length Problems with length.

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

See the sample lesson in action here
84 Mass Problems with mass.

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

See the sample lesson in action here
85 Area Problems with area.

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

See the sample lesson in action here
86 Volume/capacity Problems with volume/capacity.

Objective: Problem Solving: problems involving volume/capacity

See the sample lesson in action here
Go to top

Stage 4 - Year 7 leading to Stage 5.3 Mathematics

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# TOPIC TITLE
1 Multiplication Multiplying 2-digit numbers by 2-digit numbers

Objective: On completion of the lesson the student will be able to multiply any 2 digit number by any other 2 digit number.

See the sample lesson in action here
2 Multiplication Multiplying 4-digit numbers by 3-digit numbers

Objective: On completion of the lesson the student will be able to multiply any 4 digit numbers by any 3 digit numbers using long multiplication.

See the sample lesson in action here
3 Division/repeat subtraction Repeated subtraction with divisors less than 20 with no remainders

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 20.

See the sample lesson in action here
4 Division/repeat subtraction Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 with divisors less than 20 and no remainders.

See the sample lesson in action here
5 Division/repeat subtraction Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 2,3,4 where divisors are greater than 20 and there are no remainders.

See the sample lesson in action here
6 Division/repeat subtraction Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 1,2,3 where the divisors are less than 20 and there are remainders.

See the sample lesson in action here
7 Division/repeat subtraction Repeated subtraction by multiples of 10 with divisors less than 20 with remainders

Objective: On completion of the lesson the student will be able to use long division with repeated subtraction by multiples of 10 where the divisors are greater than 12 and less than 20, and the dividend is any 3 digit number, and there are remainders.

See the sample lesson in action here
8 Division/repeat subtraction Repeated subtraction with divisors greater than 20 with remainders as fractions

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors greater than 20 and remainders expressed as fractions

See the sample lesson in action here
9 Division/repeat subtraction Repeated subtraction with divisors less than 35 with some remainders

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 35, with some remainders.

See the sample lesson in action here
10 Division/repeat subtraction Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders

Objective: On completion of the lesson the student will be able to use long division by repeated subtraction with divisors less than 55 and where dividends are 3 and 4 digit numbers, and there are some remainders.

See the sample lesson in action here
11 Division/repeat subtraction Repeated subtraction with divisors greater than 50 with dividends of thousands and some remainders

Objective: On completion of the lesson the student will able to use Long Division by repeated subtraction with divisors greater than 50 including division of thousands, and some remainders.

See the sample lesson in action here
12 Division/repeat subtraction Using divide, multiply and subtraction in the bring down method

Objective: On completion of the lesson the student will be able to use Long Division using the Divide, Multiply, Subtract and Bring Down method.

See the sample lesson in action here
13 Decimals Rounding decimals

Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.

See the sample lesson in action here
14 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.

See the sample lesson in action here
15 Decimals Adding decimals with a different number of decimal places

Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places.

See the sample lesson in action here
16 Decimals Subtracting decimals with a different number of places

Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places.

See the sample lesson in action here
17 Decimals Multiplying decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.

See the sample lesson in action here
18 Decimals Multiplying decimals by whole numbers

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

See the sample lesson in action here
19 Decimals Dividing decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.

See the sample lesson in action here
20 Decimals Dividing decimal fractions by whole numbers

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

See the sample lesson in action here
21 Decimals Dividing numbers by a decimal fraction

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

See the sample lesson in action here
22 Percentages Changing fractions and decimals to percentages using tenths and hundredths

Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.

See the sample lesson in action here
23 Percentages Changing percentages to fractions and decimals

Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.

See the sample lesson in action here
24 Percentages One quantity as a percentage of another

Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.

See the sample lesson in action here
25 Percentages Calculating Percentages and Fractions of Quantities

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

See the sample lesson in action here
26 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.

See the sample lesson in action here
27 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.

See the sample lesson in action here
28 Fractions Improper fractions

Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.

See the sample lesson in action here
29 Fractions Comparing and ordering fractions greater than (>) 1

Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one.

See the sample lesson in action here
30 Fractions Adding and subtracting fractions with different denominators

Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.

See the sample lesson in action here
31 Fractions Multiplying fractions by whole numbers

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

See the sample lesson in action here
32 Fractions Fractions of whole numbers

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

See the sample lesson in action here
33 Fractions Multiplying and dividing to obtain equivalent fractions

Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.

See the sample lesson in action here
34 Fractions Reducing fractions to lowest equivalent form

Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.

See the sample lesson in action here
35 Fractions Finding reciprocals of fractions and mixed numbers (mixed numerals)

Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).

See the sample lesson in action here
36 Fractions Dividing fractions

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

See the sample lesson in action here
37 Fractions Dividing mixed numbers (mixed numerals)

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

See the sample lesson in action here
38 Fractions Multiplying fractions

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

See the sample lesson in action here
39 Fractions Multiplying mixed numbers (mixed numerals)

Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.

See the sample lesson in action here
40 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.

See the sample lesson in action here
41 Area Introducing the rules for finding the area of a rectangle and a parallelogram.

Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides.

See the sample lesson in action here
42 Area Finding the area of a triangle and other composite shapes.

Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas.

See the sample lesson in action here
43 Area Larger areas: square metre, hectare, square kilometre.

Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit.

See the sample lesson in action here
44 Volume Introducing the formula for volume.

Objective: On completion of the lesson the student will be able to: derive the formula for the volume of prisms, and calculate the area of prisms using the volume formula.

See the sample lesson in action here
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

See the sample lesson in action here
46 Volume Solving Problems about Volume – Part 1.

Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms.

See the sample lesson in action here
47 Volume Solving Problems about Volume – Part 2.

Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit.

See the sample lesson in action here
48 Capacity Converting between volume and capacity using millilitres and litres

Objective: On completion of the lesson the student will be able to convert between units of capacity.

See the sample lesson in action here
49 Weight/mass The tonne – converting units and problems

Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another.

See the sample lesson in action here
50 Data Bar Charts

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

See the sample lesson in action here
51 Data Line graphs.

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

See the sample lesson in action here
52 Data Pie and bar graphs.

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

See the sample lesson in action here
53 Algebraic expressions Algebraic expressions.

Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.

See the sample lesson in action here
54 Algebraic expressions Substitution into algebraic expressions.

Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.

See the sample lesson in action here
55 Algebraic expressions Directed numbers: addition and subtraction.

Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.

See the sample lesson in action here
56 Algebraic expressions Directed numbers: multiplication and division.

Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.

See the sample lesson in action here
57 Algebraic expressions Simplifying algebraic expressions: adding like terms.

Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.

See the sample lesson in action here
58 Algebraic expressions Simplifying algebraic Expressions: subtracting like terms.

Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.

See the sample lesson in action here
59 Algebraic expressions Simplifying Algebraic expressions: combining addition and subtraction.

Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.

See the sample lesson in action here
60 Algebraic expressions Simplifying algebraic expressions: multiplication

Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form.

See the sample lesson in action here
61 Algebraic expressions Simplifying algebraic expressions: division

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

See the sample lesson in action here
62 Algebraic expressions Expanding algebraic expressions: multiplication

Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.

See the sample lesson in action here
63 Algebraic expressions Expanding algebraic expressions: negative multiplier

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

See the sample lesson in action here
64 Algebraic expressions Expanding and simplifying algebraic expressions

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

See the sample lesson in action here
65 Algebraic equations Solving equations containing addition and subtraction

Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.

See the sample lesson in action here
66 Algebraic equations Solving equations containing multiplication and division

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

See the sample lesson in action here
67 Algebraic equations Solving two step equations

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

See the sample lesson in action here
68 Sign word problems Solving Word Problems by recognising Sign Words

Objective: On completion of the lesson the student will be able to solve problems by recognising Sign Words that identify which operation to use: addition, subtraction, multiplication or division.

See the sample lesson in action here
69 Equations Problem solving strategies

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

See the sample lesson in action here
70 Number problems Problems with numbers.

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

See the sample lesson in action here
71 Money Problems involving money

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

See the sample lesson in action here
72 Length Problems with length.

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

See the sample lesson in action here
73 Mass Problems with mass.

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

See the sample lesson in action here
74 Area Problems with area.

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

See the sample lesson in action here
75 Volume/capacity Problems with volume/capacity.

Objective: Problem Solving: problems involving volume/capacity

See the sample lesson in action here
76 Algebraic equations Solving equations containing binomial expressions

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

See the sample lesson in action here
77 Algebraic equations Equations involving grouping symbols.

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

See the sample lesson in action here
78 Area Area of a circle.

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.

See the sample lesson in action here
79 Volume Finding the volume of prisms

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.

See the sample lesson in action here
80 Geometry-angles Measuring angles

Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.

See the sample lesson in action here
81 Geometry-angles Adjacent angles

Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.

See the sample lesson in action here
82 Geometry-angles Complementary and supplementary angles

Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.

See the sample lesson in action here
83 Geometry-angles Vertically opposite angles

Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.

See the sample lesson in action here
84 Geometry-angles Angles at a Point.

Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.

See the sample lesson in action here
85 Geometry-angles Parallel Lines.

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

See the sample lesson in action here
86 Geometry-problems Additional questions involving parallel lines

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.

See the sample lesson in action here
87 Geometry-triangles Angle sum of a triangle

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.

See the sample lesson in action here
88 Geometry-triangles Exterior angle theorem

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.

See the sample lesson in action here
89 Special triangles Special triangles

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.

See the sample lesson in action here
90 Geometry-quadrilaterals Quadrilaterals

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.

See the sample lesson in action here
91 Geometry-constructions Geometric constructions

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

See the sample lesson in action here
92 Geometry problems More difficult exercises involving parallel lines

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log

See the sample lesson in action here
93 Geometry-reasoning Further difficult exercises involving formal reasoning

Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.

See the sample lesson in action here
94 Similar triangles Similar triangles

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

See the sample lesson in action here
95 Pythagoras Find the hypotenuse

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

See the sample lesson in action here
96 Pythagoras Pythagorean triples

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

See the sample lesson in action here
97 Pythagoras Find the hypotenuse Part 2

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

See the sample lesson in action here
98 Pythagoras Calculating a leg of a right-angled triangle

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.

See the sample lesson in action here
99 Statistics Frequency distribution table

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.

See the sample lesson in action here
100 Statistics Frequency histograms and polygons

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

See the sample lesson in action here
101 Statistics Relative frequency

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

See the sample lesson in action here
102 Statistics The range.

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.

See the sample lesson in action here
103 Statistic-probability The mode

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.

See the sample lesson in action here
104 Statistic-probability The mean

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.

See the sample lesson in action here
105 Statistic-probability The median

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

See the sample lesson in action here
106 Statistic-probability Probability of Simple Events

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

See the sample lesson in action here
Go to top

Stage 4 - Year 8 leading to Stage 5.2 Mathematics

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# TOPIC TITLE
1 Decimals Multiplying decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.

See the sample lesson in action here
2 Decimals Multiplying decimals by whole numbers

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

See the sample lesson in action here
3 Decimals Dividing decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.

See the sample lesson in action here
4 Decimals Dividing decimal fractions by whole numbers

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

See the sample lesson in action here
5 Decimals Dividing numbers by a decimal fraction

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

See the sample lesson in action here
6 Fractions Multiplying fractions

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

See the sample lesson in action here
7 Fractions Multiplying mixed numbers (mixed numerals)

Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.

See the sample lesson in action here
8 Fractions Finding reciprocals of fractions and mixed numbers (mixed numerals)

Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).

See the sample lesson in action here
9 Fractions Dividing fractions

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

See the sample lesson in action here
10 Fractions Dividing mixed numbers (mixed numerals)

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

See the sample lesson in action here
11 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.

See the sample lesson in action here
12 Percentages Changing percentages to fractions and decimals

Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.

See the sample lesson in action here
13 Percentages One quantity as a percentage of another

Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.

See the sample lesson in action here
14 Percentages Calculating Percentages and Fractions of Quantities

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

See the sample lesson in action here
15 Algebraic expressions Algebraic expressions.

Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.

See the sample lesson in action here
16 Algebraic expressions Substitution into algebraic expressions.

Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.

See the sample lesson in action here
17 Algebraic expressions Directed numbers: addition and subtraction.

Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.

See the sample lesson in action here
18 Algebraic expressions Directed numbers: multiplication and division.

Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.

See the sample lesson in action here
19 Algebraic expressions Simplifying algebraic expressions: adding like terms.

Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.

See the sample lesson in action here
20 Algebraic expressions Simplifying algebraic Expressions: subtracting like terms.

Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.

See the sample lesson in action here
21 Algebraic expressions Simplifying Algebraic expressions: combining addition and subtraction.

Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.

See the sample lesson in action here
22 Algebraic expressions Simplifying algebraic expressions: multiplication

Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form.

See the sample lesson in action here
23 Algebraic expressions Simplifying algebraic expressions: division

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

See the sample lesson in action here
24 Algebraic expressions Expanding algebraic expressions: multiplication

Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.

See the sample lesson in action here
25 Algebraic expressions Expanding algebraic expressions: negative multiplier

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

See the sample lesson in action here
26 Algebraic expressions Expanding and simplifying algebraic expressions

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

See the sample lesson in action here
27 Algebra-highest common factor Highest common factor.

Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.

See the sample lesson in action here
28 Algebraic equations Solving equations containing addition and subtraction

Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.

See the sample lesson in action here
29 Algebraic equations Solving equations containing multiplication and division

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

See the sample lesson in action here
30 Algebraic equations Solving two step equations

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

See the sample lesson in action here
31 Algebraic equations Solving equations containing binomial expressions

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

See the sample lesson in action here
32 Algebraic equations Equations involving grouping symbols.

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

See the sample lesson in action here
33 Area Introducing the rules for finding the area of a rectangle and a parallelogram.

Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides.

See the sample lesson in action here
34 Area Finding the area of a triangle and other composite shapes.

Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas.

See the sample lesson in action here
35 Area Area of a circle.

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.

See the sample lesson in action here
36 Volume Finding the volume of prisms

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.

See the sample lesson in action here
37 Geometry-angles Measuring angles

Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.

See the sample lesson in action here
38 Geometry-angles Adjacent angles

Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.

See the sample lesson in action here
39 Geometry-angles Complementary and supplementary angles

Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.

See the sample lesson in action here
40 Geometry-angles Vertically opposite angles

Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.

See the sample lesson in action here
41 Geometry-angles Angles at a Point.

Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.

See the sample lesson in action here
42 Geometry-angles Parallel Lines.

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

See the sample lesson in action here
43 Geometry-problems Additional questions involving parallel lines

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.

See the sample lesson in action here
44 Geometry-triangles Angle sum of a triangle

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.

See the sample lesson in action here
45 Geometry-triangles Exterior angle theorem

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.

See the sample lesson in action here
46 Special triangles Special triangles

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.

See the sample lesson in action here
47 Geometry-quadrilaterals Quadrilaterals

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.

See the sample lesson in action here
48 Geometry-constructions Geometric constructions

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

See the sample lesson in action here
49 Geometry problems More difficult exercises involving parallel lines

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log

See the sample lesson in action here
50 Geometry-reasoning Further difficult exercises involving formal reasoning

Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.

See the sample lesson in action here
51 Similar triangles Similar triangles

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

See the sample lesson in action here
52 Pythagoras Find the hypotenuse

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

See the sample lesson in action here
53 Pythagoras Pythagorean triples

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

See the sample lesson in action here
54 Pythagoras Find the hypotenuse Part 2

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

See the sample lesson in action here
55 Pythagoras Calculating a leg of a right-angled triangle

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.

See the sample lesson in action here
56 Statistics Frequency distribution table

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.

See the sample lesson in action here
57 Statistics Frequency histograms and polygons

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

See the sample lesson in action here
58 Statistics Relative frequency

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

See the sample lesson in action here
59 Statistics The range.

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.

See the sample lesson in action here
60 Statistic-probability The mode

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.

See the sample lesson in action here
61 Statistic-probability The mean

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.

See the sample lesson in action here
62 Statistic-probability The median

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

See the sample lesson in action here
63 Statistic-probability Probability of Simple Events

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

See the sample lesson in action here
Go to top

Stage 5 - Year 8 leading to Stage 5.3 Mathematics

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# TOPIC TITLE
1 Decimals Multiplying decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.

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2 Decimals Multiplying decimals by whole numbers

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

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3 Decimals Dividing decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.

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4 Decimals Dividing decimal fractions by whole numbers

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

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5 Decimals Dividing numbers by a decimal fraction

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

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6 Fractions Finding reciprocals of fractions and mixed numbers (mixed numerals)

Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).

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7 Fractions Dividing fractions

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

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8 Fractions Dividing mixed numbers (mixed numerals)

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

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9 Fractions Multiplying fractions

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

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10 Fractions Multiplying mixed numbers (mixed numerals)

Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.

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11 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.

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12 Percentages Changing percentages to fractions and decimals

Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.

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13 Percentages One quantity as a percentage of another

Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.

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14 Percentages Calculating Percentages and Fractions of Quantities

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

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15 Algebraic expressions Algebraic expressions.

Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.

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16 Algebraic expressions Substitution into algebraic expressions.

Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.

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17 Algebraic expressions Directed numbers: addition and subtraction.

Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.

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18 Algebraic expressions Directed numbers: multiplication and division.

Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.

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19 Algebraic expressions Simplifying algebraic expressions: adding like terms.

Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.

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20 Algebraic expressions Simplifying algebraic Expressions: subtracting like terms.

Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.

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21 Algebraic expressions Simplifying Algebraic expressions: combining addition and subtraction.

Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.

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22 Algebraic expressions Simplifying algebraic expressions: multiplication

Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form.

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23 Algebraic expressions Simplifying algebraic expressions: division

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

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24 Algebraic expressions Expanding algebraic expressions: multiplication

Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.

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25 Algebraic expressions Expanding algebraic expressions: negative multiplier

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

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26 Algebraic expressions Expanding and simplifying algebraic expressions

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

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27 Area Introducing the rules for finding the area of a rectangle and a parallelogram.

Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides.

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28 Area Finding the area of a triangle and other composite shapes.

Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas.

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29 Area Area of a circle.

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.

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30 Geometry-angles Measuring angles

Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.

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31 Geometry-angles Adjacent angles

Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.

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32 Geometry-angles Complementary and supplementary angles

Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.

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33 Geometry-angles Vertically opposite angles

Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.

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34 Geometry-angles Angles at a Point.

Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.

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35 Geometry-angles Parallel Lines.

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

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36 Geometry-problems Additional questions involving parallel lines

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.

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37 Geometry-triangles Angle sum of a triangle

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.

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38 Geometry-triangles Exterior angle theorem

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.

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39 Special triangles Special triangles

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.

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40 Geometry-quadrilaterals Quadrilaterals

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.

See the sample lesson in action here
41 Geometry-constructions Geometric constructions

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

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42 Geometry problems More difficult exercises involving parallel lines

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log

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43 Geometry-reasoning Further difficult exercises involving formal reasoning

Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.

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44 Similar triangles Similar triangles

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

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45 Pythagoras Find the hypotenuse

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

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46 Pythagoras Pythagorean triples

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

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47 Pythagoras Find the hypotenuse Part 2

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

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48 Pythagoras Calculating a leg of a right-angled triangle

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.

See the sample lesson in action here
49 Statistics Frequency distribution table

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.

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50 Statistics Frequency histograms and polygons

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

See the sample lesson in action here
51 Statistics Relative frequency

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

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52 Statistics The range.

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.

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53 Statistic-probability The mode

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.

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54 Statistic-probability The mean

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.

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55 Statistic-probability The median

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

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56 Statistic-probability Probability of Simple Events

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

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57 Algebra-highest common factor Highest common factor.

Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.

See the sample lesson in action here
58 Algebraic equations Solving equations containing addition and subtraction

Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.

See the sample lesson in action here
59 Algebraic equations Solving equations containing multiplication and division

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

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60 Algebraic equations Solving two step equations

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

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61 Algebraic equations Solving equations containing binomial expressions

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

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62 Algebraic equations Equations involving grouping symbols.

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

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63 Algebraic equations Equations involving fractions.

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

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64 Algebra-factorising Simplifying easy algebraic fractions.

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

See the sample lesson in action here
65 Algebraic fractions Simplifying algebraic fractions using the index laws.

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.

See the sample lesson in action here
66 Rules for indices/exponents Adding indices when multiplying terms with the same base

Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.

See the sample lesson in action here
67 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.

See the sample lesson in action here
68 Rules for indices/exponents Multiplying indices when raising a power to a power

Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.

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69 Area Area of a trapezium.

Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula.

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70 Area Area of a rhombus.

Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems.

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71 Area Area of regular polygons and composite figures.

Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula.

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72 Surface area Surface area of a cube/rectangular prism.

Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.

See the sample lesson in action here
73 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.

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74 Surface area Surface area of a cylinder and sphere.

Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.

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75 Volume Finding the volume of prisms

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.

See the sample lesson in action here
76 Volume Volume of a cylinder and sphere.

Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.

See the sample lesson in action here
Go to top

Stage 5 - Year 9 leading to Stage 5.2 Mathematics

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# TOPIC TITLE
1 Algebraic expressions Expanding algebraic expressions: multiplication

Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.

See the sample lesson in action here
2 Algebraic expressions Expanding algebraic expressions: negative multiplier

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

See the sample lesson in action here
3 Algebraic expressions Expanding and simplifying algebraic expressions

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

See the sample lesson in action here
4 Algebra-highest common factor Highest common factor.

Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.

See the sample lesson in action here
5 Algebraic equations Solving equations containing addition and subtraction

Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.

See the sample lesson in action here
6 Algebraic equations Solving equations containing multiplication and division

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

See the sample lesson in action here
7 Algebraic equations Solving two step equations

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

See the sample lesson in action here
8 Algebraic equations Solving equations containing binomial expressions

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

See the sample lesson in action here
9 Algebraic equations Equations involving grouping symbols.

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

See the sample lesson in action here
10 Algebra-factorising Simplifying easy algebraic fractions.

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

See the sample lesson in action here
11 Rules for indices/exponents Adding indices when multiplying terms with the same base

Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.

See the sample lesson in action here
12 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.

See the sample lesson in action here
13 Rules for indices/exponents Multiplying indices when raising a power to a power

Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.

See the sample lesson in action here
14 Rules for indices/exponents Multiplying indices when raising to more than one term

Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.

See the sample lesson in action here
15 Rules for indices/exponents Terms raised to the power of zero

Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.

See the sample lesson in action here
16 Rules for indices/exponents Negative Indices

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

See the sample lesson in action here
17 Algebraic fractions Simplifying algebraic fractions using the index laws.

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.

See the sample lesson in action here
18 Scientific notation Scientific notation with larger numbers

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

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19 Scientific notation Scientific notation with small numbers

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.

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20 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.

See the sample lesson in action here
21 Area Area of a circle.

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.

See the sample lesson in action here
22 Area Area of a trapezium.

Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula.

See the sample lesson in action here
23 Area Area of a rhombus.

Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems.

See the sample lesson in action here
24 Area Area of regular polygons and composite figures.

Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula.

See the sample lesson in action here
25 Surface area Surface area of a cube/rectangular prism.

Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.

See the sample lesson in action here
26 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.

See the sample lesson in action here
27 Surface area Surface area of a cylinder and sphere.

Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.

See the sample lesson in action here
28 Volume Finding the volume of prisms

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.

See the sample lesson in action here
29 Volume Volume of a cylinder and sphere.

Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.

See the sample lesson in action here
30 Statistics Frequency distribution table

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.

See the sample lesson in action here
31 Statistics Frequency histograms and polygons

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

See the sample lesson in action here
32 Statistics Relative frequency

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

See the sample lesson in action here
33 Statistics The range.

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.

See the sample lesson in action here
34 Statistic-probability The mode

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.

See the sample lesson in action here
35 Statistic-probability The mean

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.

See the sample lesson in action here
36 Statistic-probability The median

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

See the sample lesson in action here
37 Geometry-problems Additional questions involving parallel lines

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.

See the sample lesson in action here
38 Geometry-triangles Angle sum of a triangle

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.

See the sample lesson in action here
39 Geometry-triangles Exterior angle theorem

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.

See the sample lesson in action here
40 Special triangles Special triangles

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.

See the sample lesson in action here
41 Geometry-quadrilaterals Quadrilaterals

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.

See the sample lesson in action here
42 Geometry-constructions Geometric constructions

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

See the sample lesson in action here
43 Geometry problems More difficult exercises involving parallel lines

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log

See the sample lesson in action here
44 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.

See the sample lesson in action here
45 Geometry-congruence Congruent triangles, Test 3 and 4

Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.

See the sample lesson in action here
46 Pythagoras Find the hypotenuse

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

See the sample lesson in action here
47 Pythagoras Pythagorean triples

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

See the sample lesson in action here
48 Pythagoras Find the hypotenuse Part 2

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

See the sample lesson in action here
49 Pythagoras Calculating a leg of a right-angled triangle

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.

See the sample lesson in action here
50 Trigonometry-ratios Trigonometric ratios.

Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op

See the sample lesson in action here
51 Trigonometry-ratios Using the calculator.

Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.

See the sample lesson in action here
52 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.

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53 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 2 Cosine].

Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.

See the sample lesson in action here
54 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].

Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.

See the sample lesson in action here
55 Trigonometry-ratios Unknown in the denominator. [Case 4].

Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.

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56 Trigonometry-compass Bearings – the compass.

Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.

See the sample lesson in action here
57 Trigonometry-elevation Angles of elevation and depression.

Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.

See the sample lesson in action here
58 Statistic-probability Probability of Simple Events

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

See the sample lesson in action here
Go to top

Stage 5 - Year 9 leading to Stage 5.3 Mathematics

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# TOPIC TITLE
1 Algebraic expressions Expanding algebraic expressions: multiplication

Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.

See the sample lesson in action here
2 Algebraic expressions Expanding algebraic expressions: negative multiplier

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

See the sample lesson in action here
3 Algebraic expressions Expanding and simplifying algebraic expressions

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

See the sample lesson in action here
4 Algebra-highest common factor Highest common factor.

Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.

See the sample lesson in action here
5 Algebraic equations Solving equations containing addition and subtraction

Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.

See the sample lesson in action here
6 Algebraic equations Solving equations containing multiplication and division

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

See the sample lesson in action here
7 Algebraic equations Solving two step equations

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

See the sample lesson in action here
8 Algebraic equations Solving equations containing binomial expressions

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

See the sample lesson in action here
9 Algebraic equations Equations involving grouping symbols.

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

See the sample lesson in action here
10 Algebraic equations Equations involving fractions.

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

See the sample lesson in action here
11 Algebra-factorising Simplifying easy algebraic fractions.

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

See the sample lesson in action here
12 Algebraic fractions Simplifying algebraic fractions using the index laws.

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.

See the sample lesson in action here
13 Rules for indices/exponents Adding indices when multiplying terms with the same base

Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.

See the sample lesson in action here
14 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.

See the sample lesson in action here
15 Rules for indices/exponents Multiplying indices when raising a power to a power

Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.

See the sample lesson in action here
16 Rules for indices/exponents Multiplying indices when raising to more than one term

Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.

See the sample lesson in action here
17 Rules for indices/exponents Terms raised to the power of zero

Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.

See the sample lesson in action here
18 Rules for indices/exponents Negative Indices

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

See the sample lesson in action here
19 Fractional indices/exponents Fractional indices

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

See the sample lesson in action here
20 Scientific notation Scientific notation with larger numbers

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

See the sample lesson in action here
21 Scientific notation Scientific notation with small numbers

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.

See the sample lesson in action here
22 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.

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23 Area Area of a circle.

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.

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24 Area Area of a trapezium.

Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula.

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25 Area Area of a rhombus.

Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems.

See the sample lesson in action here
26 Area Area of regular polygons and composite figures.

Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula.

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27 Surface area Surface area of a cube/rectangular prism.

Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.

See the sample lesson in action here
28 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.

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29 Surface area Surface area of a cylinder and sphere.

Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.

See the sample lesson in action here
30 Volume Finding the volume of prisms

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.

See the sample lesson in action here
31 Volume Volume of a cylinder and sphere.

Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.

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32 Statistics Frequency distribution table

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.

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33 Statistics Frequency histograms and polygons

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

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34 Statistics Relative frequency

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

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35 Statistics The range.

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.

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36 Statistic-probability The mode

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.

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37 Statistic-probability The mean

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.

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38 Statistic-probability The median

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

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39 Geometry-problems Additional questions involving parallel lines

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.

See the sample lesson in action here
40 Geometry-triangles Angle sum of a triangle

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.

See the sample lesson in action here
41 Geometry-triangles Exterior angle theorem

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.

See the sample lesson in action here
42 Special triangles Special triangles

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.

See the sample lesson in action here
43 Geometry-quadrilaterals Quadrilaterals

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.

See the sample lesson in action here
44 Geometry-constructions Geometric constructions

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

See the sample lesson in action here
45 Geometry problems More difficult exercises involving parallel lines

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log

See the sample lesson in action here
46 Geometry-reasoning Further difficult exercises involving formal reasoning

Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.

See the sample lesson in action here
47 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.

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48 Geometry-congruence Congruent triangles, Test 3 and 4

Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.

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49 Geometry-congruence Proofs and congruent triangles.

Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent.

See the sample lesson in action here
50 Similar triangles Similar triangles

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

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51 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.

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52 Overlapping triangles Examples involving overlapping triangles

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

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53 Pythagoras Find the hypotenuse

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

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54 Pythagoras Pythagorean triples

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

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55 Pythagoras Find the hypotenuse Part 2

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

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56 Pythagoras Calculating a leg of a right-angled triangle

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.

See the sample lesson in action here
57 Trigonometry-ratios Trigonometric ratios.

Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op

See the sample lesson in action here
58 Trigonometry-ratios Using the calculator.

Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.

See the sample lesson in action here
59 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 1 Sine].

Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.

See the sample lesson in action here
60 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 2 Cosine].

Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.

See the sample lesson in action here
61 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].

Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.

See the sample lesson in action here
62 Trigonometry-ratios Unknown in the denominator. [Case 4].

Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.

See the sample lesson in action here
63 Trigonometry-compass Bearings – the compass.

Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.

See the sample lesson in action here
64 Trigonometry-elevation Angles of elevation and depression.

Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.

See the sample lesson in action here
65 Statistic-probability Probability of Simple Events

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

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66 Statistic-probability Rolling a pair of dice

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.

See the sample lesson in action here
Go to top

Stage 5.2 - Year 10 leading to Stage 5.2 Mathematics

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# TOPIC TITLE
1 Fractions Comparing and ordering fractions

Objective: On completion of the lesson the student will be able to compare and order fractions with the same number of equal parts, and compare and order fractions with a different number of equal parts.

See the sample lesson in action here
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.

See the sample lesson in action here
3 Fractions Improper fractions

Objective: On completion of the lesson the student will be able to: use diagrams and number lines to recognise and represent mixed numbers and improper fractions, and develop strategies for changing improper fractions to mixed numbers and vice versa, mentally.

See the sample lesson in action here
4 Fractions Fractions 1/5, 1/10, 1/100

Objective: On completion of the lesson the student will be able to: compare fractions with the denominators 5, 10, 100, and represent fractions with the denominator 5, 10, 100.

See the sample lesson in action here
5 Fractions Finding equivalent fractions

Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines.

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6 Fractions Multiplying and dividing to obtain equivalent fractions

Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.

See the sample lesson in action here
7 Fractions Reducing fractions to lowest equivalent form

Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.

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8 Fractions Comparing and ordering fractions greater than (>) 1

Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one.

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9 Fractions Subtracting fractions from whole numbers

Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from

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10 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.

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11 Fractions Adding and subtracting fractions with different denominators

Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.

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12 Fractions Multiplying fractions by whole numbers

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

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13 Fractions Fractions of whole numbers

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

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14 Fractions Multiplying fractions

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

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15 Fractions Multiplying mixed numbers (mixed numerals)

Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.

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16 Fractions Finding reciprocals of fractions and mixed numbers (mixed numerals)

Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).

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17 Fractions Dividing fractions

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

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18 Fractions Dividing mixed numbers (mixed numerals)

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

See the sample lesson in action here
19 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.

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20 Percentages Calculating Percentages and Fractions of Quantities

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

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21 Algebraic equations Solving two step equations

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

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22 Algebraic equations Solving equations containing binomial expressions

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

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23 Decimals Adding decimals to two decimal places

Objective: On completion of the lesson the student will be able to add decimals with the same number of decimal places (to two decimal places)

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24 Decimals Subtracting decimals to two decimal places

Objective: On completion of the lesson the student will be able to subtract decimals with the same number of decimal places (to two decimal places)

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25 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.

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26 Decimals Using decimals to record length

Objective: On completion of the lesson the student will be able to interpret the everyday use of fractions and decimals and use their knowledge of decimals to record measurements.

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27 Decimals Rounding decimals

Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number.

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28 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.

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29 Decimals Adding decimals with a different number of decimal places

Objective: On completion of the lesson the student will be able to add decimal numbers with different numbers of decimal places.

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30 Decimals Subtracting decimals with a different number of places

Objective: On completion of the lesson the student will be able to subtract decimals with different numbers of decimal places.

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31 Decimals Multiplying decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to multiply decimal numbers by one hundred and recognise the pattern formed when decimals are multiplied by ten, one hundred and one thousand.

See the sample lesson in action here
32 Decimals Multiplying decimals by whole numbers

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

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33 Decimals Multiplication of decimals by decimals to two decimal places

Objective: On completion of the lesson the student will be able to multiply decimals to two digits.

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34 Decimals Dividing decimals by 10, 100 and 1000

Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.

See the sample lesson in action here
35 Decimals Dividing decimal fractions by whole numbers

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

See the sample lesson in action here
36 Decimals Dividing numbers by a decimal fraction

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

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37 Percentages Introduction to percentages, including relating common fractions to percentages

Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage.

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38 Percentages Changing fractions and decimals to percentages using tenths and hundredths

Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion.

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39 Percentages Changing percentages to fractions and decimals

Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals.

See the sample lesson in action here
40 Percentages One quantity as a percentage of another

Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.

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41 Algebraic equations Equations involving grouping symbols.

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

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42 Algebraic equations Equations involving fractions.

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

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43 Algebra-inequalities Solving Inequalities.

Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.

See the sample lesson in action here
44 Algebra-factorising Simplifying easy algebraic fractions.

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

See the sample lesson in action here
45 Rules for indices/exponents Adding indices when multiplying terms with the same base

Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.

See the sample lesson in action here
46 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.

See the sample lesson in action here
47 Rules for indices/exponents Multiplying indices when raising a power to a power

Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.

See the sample lesson in action here
48 Rules for indices/exponents Multiplying indices when raising to more than one term

Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.

See the sample lesson in action here
49 Rules for indices/exponents Terms raised to the power of zero

Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.

See the sample lesson in action here
50 Rules for indices/exponents Negative Indices

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

See the sample lesson in action here
51 Algebraic fractions Simplifying algebraic fractions using the index laws.

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.

See the sample lesson in action here
52 Fractional indices/exponents Fractional indices

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

See the sample lesson in action here
53 Scientific notation Scientific notation with larger numbers

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

See the sample lesson in action here
54 Scientific notation Scientific notation with small numbers

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.

See the sample lesson in action here
55 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.

See the sample lesson in action here
56 Significant figures Significant figures

Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures.

See the sample lesson in action here
57 Trigonometry-ratios Trigonometric ratios.

Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op

See the sample lesson in action here
58 Trigonometry-ratios Using the calculator.

Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.

See the sample lesson in action here
59 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 1 Sine].

Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances.

See the sample lesson in action here
60 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 2 Cosine].

Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.

See the sample lesson in action here
61 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].

Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.

See the sample lesson in action here
62 Trigonometry-ratios Unknown in the denominator. [Case 4].

Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.

See the sample lesson in action here
63 Trigonometry-compass Bearings – the compass.

Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.

See the sample lesson in action here
64 Trigonometry-elevation Angles of elevation and depression.

Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.

See the sample lesson in action here
65 Trigonometry-practical Trigonometric ratios in practical situations.

Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.

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66 Trigonometry- ratios Using the trigonometric ratios to find an angle in a right-angled triangle.

Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.

See the sample lesson in action here
67 Trigonometry-ratios Using the calculator to find an angle given a trigonometric ratio.

Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.

See the sample lesson in action here
68 Geometry-problems Additional questions involving parallel lines

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.

See the sample lesson in action here
69 Geometry-triangles Angle sum of a triangle

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.

See the sample lesson in action here
70 Geometry-triangles Exterior angle theorem

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.

See the sample lesson in action here
71 Special triangles Special triangles

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.

See the sample lesson in action here
72 Geometry-quadrilaterals Quadrilaterals

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.

See the sample lesson in action here
73 Geometry-constructions Geometric constructions

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

See the sample lesson in action here
74 Geometry problems More difficult exercises involving parallel lines

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log

See the sample lesson in action here
75 Geometry-reasoning Further difficult exercises involving formal reasoning

Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.

See the sample lesson in action here
76 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.

See the sample lesson in action here
77 Geometry-congruence Congruent triangles, Test 3 and 4

Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.

See the sample lesson in action here
78 Geometry-congruence Proofs and congruent triangles.

Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent.

See the sample lesson in action here
79 Similar triangles Similar triangles

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

See the sample lesson in action here
80 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.

See the sample lesson in action here
81 Overlapping triangles Examples involving overlapping triangles

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

See the sample lesson in action here
82 Geometry – triangles Triangle inequality theorem

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

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83 Area Area of a trapezium.

Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula.

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84 Area Area of a rhombus.

Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems.

See the sample lesson in action here
85 Area Area of a circle.

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.

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86 Area Area of regular polygons and composite figures.

Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula.

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87 Surface area Surface area of a cube/rectangular prism.

Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.

See the sample lesson in action here
88 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.

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89 Surface area Surface area of a cylinder and sphere.

Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.

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90 Surface area Surface area of pyramids

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

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91 Surface area Surface area of cones

Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul

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92 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.

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93 Volume Finding the volume of prisms

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.

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94 Volume Volume of a cylinder and sphere.

Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.

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95 Volume Volume of pyramids and cones.

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones.

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96 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.

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97 Coordinate Geometry-the plane Distance formula.

Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results.

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98 Coordinate Geometry-midpoint, slope Mid-point formula

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

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99 Coordinate Geometry-gradient Gradient

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.

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100 Coordinate Geometry-gradient Gradient formula.

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.

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101 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.

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102 Coordinate Geometry-slope, etc. Lines through the origin.

Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.

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

Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.

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104 Coordinate Geometry-intercept Slope intercept form of a line.

Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.

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105 Coordinate Geometry-point slope Point slope form of a line

Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line.

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106 Statistics Frequency distribution table

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.

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107 Statistics Frequency histograms and polygons

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

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108 Statistics Relative frequency

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

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109 Statistics The range.

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.

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110 Statistic-probability The mode

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.

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111 Statistic-probability The mean

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.

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112 Statistic-probability The median

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

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113 Statistic-probability Cumulative frequency

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

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114 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.

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115 Statistic-probability Probability of Simple Events

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

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116 Statistic-probability Tree diagrams – depending on previous outcomes

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.

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117 Statistic-probability The complementary result ..

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.

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Go to top

Stage 5.3 - Year 10 Leading to Stage 5.3 Mathematics

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# TOPIC TITLE
1 Surds Introducing surds

Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.

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2 Surds Some rules for the operations with surds

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

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3 Surds Simplifying surds

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

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4 Surds Creating entire surds

Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds

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5 Surds Adding and subtracting like surds

Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.

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6 Surds Expanding surds

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

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7 Surds Binomial expansions

Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.

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8 Surds Conjugate binomials with surds

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

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9 Surds Rationalising the denominator

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

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10 Surds Rationalising binomial denominators

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

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11 Rules for indices/exponents Negative Indices

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

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12 Fractional indices/exponents Fractional indices

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

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13 Fractional indices/exponents Complex fractions as indices

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

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14 Scientific notation Scientific notation with larger numbers

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

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15 Scientific notation Scientific notation with small numbers

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.

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16 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.

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17 Significant figures Significant figures

Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures.

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18 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.

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19 Logarithms-Equations and logs Equations of type log x to the base 3 = 4.

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.

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20 Logarithms-Equations and logs Equations of type log 32 to the base x = 5.

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.

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21 Logarithms-Log laws Laws of logarithms.

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

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22 Logarithms-Log laws expansion Using the log laws to expand logarithmic expressions.

Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.

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23 Logarithms-Log laws simplifying Using the log laws to simplify expressions involving logarithms.

Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.

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24 Logarithms-Log laws numbers Using the log laws to find the logarithms of numbers.

Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples.

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25 Logarithms-Equations and logs Equations involving logarithms.

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

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26 Logarithms-Logs to solve equations Using logarithms to solve equations.

Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.

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27 Algebra- formulae Equations resulting from substitution into formulae.

Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations.

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28 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.

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29 Algebra-inequalities Solving Inequalities.

Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.

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30 Algebra-negative indices Algebraic fractions resulting in negative indices.

Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.

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31 Factorisation Factorisation of algebraic fractions including binomials.

Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods.

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32 Algebraic fractions-binomial Cancelling binomial factors in algebraic fractions.

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

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33 Graphing binomials Binomial products.

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

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34 Graphing binomials Binomial products with negative multiplier

Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products.

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35 Graphing binomials Binomial products [non-monic].

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

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36 Squaring binomial Squaring a binomial. [monic]

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

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37 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.

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38 Factorising Expansions leading to the difference of two squares

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

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39 Algebraic expressions-products Products in simplification of algebraic expressions

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

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40 Algebraic expressions-larger expansions Algebraic Expressions – Larger expansions.

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

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41 Algebra-highest common factor Highest common factor.

Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.

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42 Factors by grouping Factors by grouping.

Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.

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43 Difference of 2 squares Difference of two squares

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

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44 Common fact and diff Common factor and the difference of two squares

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

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45 Quadratic trinomials Quadratic trinomials [monic] – Case 1.

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

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46 Factorising quads Factorising quadratic trinomials [monic] – Case 2.

Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.

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47 Factorising quads Factorising quadratic trinomials [monic] – Case 3.

Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.

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48 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.

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49 Factorising quads Factorisation of non-monic quadratic trinomials

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

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50 Factorising quads Factorisation of non-monic quadratic trinomials – moon method

Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.

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51 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.

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52 Simultaneous equns Simultaneous equations

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

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53 Simultaneous equns Elimination method

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

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54 Simultaneous equns Elimination method part 2

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

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55 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.

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56 Quadratic equations Introduction to quadratic equations.

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

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57 Quadratic equations Quadratic equations with factorisation.

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

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58 Quadratic equations Solving quadratic equations.

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

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59 Quadratic equations Completing the square

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

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60 Quadratic equations Solving quadratic equations by completing the square

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

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61 Quadratic equations The quadratic formula

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

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62 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.

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63 Quadratic equations Solving simultaneous quadratic equations graphically

Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..

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64 Geometry-circles The equation of a circle: to find radii of circles

Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius.

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65 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.

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66 Functions and graphs Quadratic polynomials of the form y = ax. + bx + c.

Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.

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67 Functions and graphs Graphing perfect squares: y=(a-x) squared

Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.

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68 Co-ordinate Geometry-Two point formula Two point formula: equation of a line which joins a pair of points.

Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.

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69 Co-ordinate Geometry-Intercept form Intercept form of a straight line: find the equation when given x and y

Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.

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70 Co-ordinate Geometry-Parallel lines equations Parallel lines: identify equation of a line parallel to another

Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.

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71 Co-ordinate Geometry-Perpendicular lines Perpendicular lines.

Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line.

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72 Co-ordinate Geometry-Inequalities Inequalities on the number plane.

Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.

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73 Trigonometry-exact ratios Trigonometric ratios of 30., 45. and 60. – exact ratios.

Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.

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74 Trigonometry-cosine rule The cosine rule to find an unknown side. [Case 1 SAS].

Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.

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75 Trigonometry-cosine rule The cosine rule to find an unknown angle. [Case 2 SSS].

Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.

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76 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.

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77 Trigonometry-sine rule The sine rule to find an unknown angle. Case 2.

Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.

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78 Trigonometry-areas The area formula

Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.

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79 Statistics – grouped data Calculating mean, mode and median from grouped data

Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.

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80 Statistics – Range and dispersion Range as a measure of dispersion

Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.

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81 Statistics – Spread Measures of spread

Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.

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82 Statistics – Standard deviation Normal distribution

Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.

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83 Statistics – Interquartile range Measures of spread: the interquartile range

Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range

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84 Statistics Stem and Leaf Plots along with Box and Whisker Plots

Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.

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85 Statistics Scatter Diagrams

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

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86 Statistic-probability Probability of Simple Events

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

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87 Statistic-probability Rolling a pair of dice

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.

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88 Statistic-probability Experimental probability

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

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89 Statistic-probability Tree diagrams – not depending on previous outcomes

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.

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90 Statistic-probability Tree diagrams – depending on previous outcomes

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.

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91 Statistic-probability The complementary result ..

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.

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92 Statistic-probability P[A or B] When A and B are both mutually and NOT mutually exclusive

Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.

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93 Geometry problems More difficult exercises involving parallel lines

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log

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94 Geometry-reasoning Further difficult exercises involving formal reasoning

Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.

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95 Geometry-polygons Angles of regular polygons

Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees.

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96 Pythagoras Find the hypotenuse

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

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97 Pythagoras Pythagorean triples

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

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98 Pythagoras Find the hypotenuse Part 2

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

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99 Pythagoras Calculating a leg of a right-angled triangle

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.

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100 Pythagoras Proofs of Pythagoras theorem

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

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101 Circle Geometry Theorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs.

Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro

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102 Circle Geometry Theorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord.

Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’

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103 Circle Geometry Theorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal.

Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre.

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104 Circle Geometry Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc.

Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.

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105 Circle Geometry Theorem – Angles in the same segment of a circle are equal.

Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.

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106 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.’

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107 Circle Geometry Theorem – The opposite angles of a cyclic quadrilateral are supplementary.

Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.

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108 Circle Geometry Theorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle.

Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite.

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109 Circle Geometry Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.

Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact.

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110 Circle Geometry Theorem – Tangents to a circle from an external point are equal.

Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.

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111 Circle Geometry Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

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Stage 6 - General Mathematics Preliminary (Year 11) Mathematics

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# TOPIC TITLE
1 Statistics Frequency distribution table

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.

See the sample lesson in action here
2 Statistics Frequency histograms and polygons

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

See the sample lesson in action here
3 Statistics Relative frequency

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

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4 Statistics The range.

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.

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5 Statistic-probability The mode

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.

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6 Statistic-probability The mean

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.

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7 Statistic-probability The median

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

See the sample lesson in action here
8 Statistic-probability Cumulative frequency

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

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9 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.

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10 Statistics Stem and Leaf Plots along with Box and Whisker Plots

Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.

See the sample lesson in action here
11 Area Finding the area of a triangle and other composite shapes.

Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas.

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12 Area Larger areas: square metre, hectare, square kilometre.

Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit.

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13 Area Area of a trapezium.

Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula.

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14 Area Area of a rhombus.

Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems.

See the sample lesson in action here
15 Area Area of a circle.

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.

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16 Surface area Surface area of a cube/rectangular prism.

Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.

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17 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.

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18 Surface area Surface area of pyramids

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

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19 Capacity Converting between volume and capacity using millilitres and litres

Objective: On completion of the lesson the student will be able to convert between units of capacity.

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20 Weight/mass The tonne – converting units and problems

Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another.

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21 Volume Finding the volume of prisms

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.

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22 Volume Volume of a cylinder and sphere.

Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.

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23 Volume Volume of pyramids and cones.

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones.

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24 Pythagoras Find the hypotenuse

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

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25 Pythagoras Pythagorean triples

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

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26 Pythagoras Find the hypotenuse Part 2

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

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27 Pythagoras Calculating a leg of a right-angled triangle

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.

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28 Trigonometry-ratios Trigonometric ratios.

Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op

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29 Trigonometry-ratios Using the calculator.

Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.

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30 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.

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31 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 2 Cosine].

Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.

See the sample lesson in action here
32 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].

Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.

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33 Trigonometry-ratios Unknown in the denominator. [Case 4].

Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.

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34 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.

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35 Trigonometry-elevation Angles of elevation and depression.

Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.

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36 Trigonometry-practical Trigonometric ratios in practical situations.

Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.

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37 Trigonometry-ratios Using the calculator to find an angle given a trigonometric ratio.

Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.

See the sample lesson in action here
38 Trigonometry- ratios Using the trigonometric ratios to find an angle in a right-angled triangle.

Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.

See the sample lesson in action here
39 Trigonometry-exact ratios Trigonometric ratios of 30., 45. and 60. – exact ratios.

Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.

See the sample lesson in action here
40 Scientific notation Scientific notation with larger numbers

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

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41 Scientific notation Scientific notation with small numbers

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.

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42 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.

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43 Significant figures Significant figures

Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures.

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44 Algebraic expressions Expanding algebraic expressions: negative multiplier

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

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45 Algebraic expressions Expanding and simplifying algebraic expressions

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

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46 Algebraic expressions-products Products in simplification of algebraic expressions

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

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47 Algebraic equations Solving two step equations

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

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48 Algebraic equations Solving equations containing binomial expressions

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

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49 Algebraic equations Equations involving grouping symbols.

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

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50 Algebraic equations Equations involving fractions.

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

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51 Algebra-factorising Simplifying easy algebraic fractions.

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

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52 Algebraic fractions Simplifying algebraic fractions using the index laws.

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.

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53 Algebra- formulae Equations resulting from substitution into formulae.

Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations.

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54 Simultaneous equns Simultaneous equations

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

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55 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.

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56 Coordinate Geometry-slope, etc. Lines through the origin.

Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.

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57 Coordinate Geometry-intercept Slope intercept form of a line.

Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.

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58 Co-ordinate Geometry-Intercept form Intercept form of a straight line: find the equation when given x and y

Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.

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59 Similar triangles Similar triangles

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

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60 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.

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61 Overlapping triangles Examples involving overlapping triangles

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

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62 Statistic-probability Probability of Simple Events

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

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63 Statistic-probability Rolling a pair of dice

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.

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64 Statistic-probability Experimental probability

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

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65 Statistic-probability The complementary result ..

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.

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66 Statistic-probability P[A or B] When A and B are both mutually and NOT mutually exclusive

Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.

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67 Sequences and Series-Compound interest Compound interest

Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.

See the sample lesson in action here
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Stage 6 - General Mathematics HSC (Year 12) Mathematics

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# TOPIC TITLE
1 Statistics – grouped data Calculating mean, mode and median from grouped data

Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.

See the sample lesson in action here
2 Statistics – Range and dispersion Range as a measure of dispersion

Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.

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3 Statistics – Spread Measures of spread

Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.

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4 Statistics – Standard deviation Standard deviation applications

Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.

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5 Statistics – Standard deviation Normal distribution

Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.

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6 Statistics – Interquartile range Measures of spread: the interquartile range

Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range

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7 Statistics Scatter Diagrams

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

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8 Area Area of regular polygons and composite figures.

Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula.

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9 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.

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10 Surface area Surface area of a cylinder and sphere.

Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.

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11 Surface area Surface area of cones

Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul

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12 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.

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13 Trigonometry-cosine rule The cosine rule to find an unknown side. [Case 1 SAS].

Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.

See the sample lesson in action here
14 Trigonometry-cosine rule The cosine rule to find an unknown angle. [Case 2 SSS].

Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.

See the sample lesson in action here
15 Trigonometry-sine rule The sine rule to find an unknown side. Case 1.

Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.

See the sample lesson in action here
16 Trigonometry-sine rule The sine rule to find an unknown angle. Case 2.

Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.

See the sample lesson in action here
17 Trigonometry-areas The area formula

Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.

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18 Statistic-probability Tree diagrams – not depending on previous outcomes

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.

See the sample lesson in action here
19 Statistic-probability Tree diagrams – depending on previous outcomes

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.

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20 Statistic-probability Counting techniques and ordered selections – permutations

Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability.

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21 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.

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22 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.

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23 Coordinate geometry Solve by graphing

Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.

See the sample lesson in action here
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Stage 6 - Mathematics Preliminary (Year 11 - 2 Unit) Mathematics

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# TOPIC TITLE
1 Rules for indices/exponents Adding indices when multiplying terms with the same base

Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.

See the sample lesson in action here
2 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.

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3 Rules for indices/exponents Multiplying indices when raising a power to a power

Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.

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4 Rules for indices/exponents Multiplying indices when raising to more than one term

Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.

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5 Rules for indices/exponents Terms raised to the power of zero

Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.

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6 Rules for indices/exponents Negative Indices

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

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7 Fractional indices/exponents Fractional indices

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

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8 Fractional indices/exponents Complex fractions as indices

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

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9 Scientific notation Scientific notation with larger numbers

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

See the sample lesson in action here
10 Scientific notation Scientific notation with small numbers

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.

See the sample lesson in action here
11 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.

See the sample lesson in action here
12 Significant figures Significant figures

Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures.

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13 Surds Introducing surds

Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.

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14 Surds Some rules for the operations with surds

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

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15 Surds Simplifying surds

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

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16 Surds Creating entire surds

Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds

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17 Surds Adding and subtracting like surds

Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.

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18 Surds Expanding surds

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

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19 Surds Binomial expansions

Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.

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20 Surds Conjugate binomials with surds

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

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21 Surds Rationalising the denominator

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

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22 Surds Rationalising binomial denominators

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

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23 Algebra-factorising Simplifying easy algebraic fractions.

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

See the sample lesson in action here
24 Algebraic fractions Simplifying algebraic fractions using the index laws.

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.

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25 Algebra-negative indices Algebraic fractions resulting in negative indices.

Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.

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26 Factorisation Factorisation of algebraic fractions including binomials.

Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods.

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27 Algebraic fractions-binomial Cancelling binomial factors in algebraic fractions.

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

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28 Absolute value or modulus Simplifying absolute values

Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.

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29 Absolute value or modulus Solving for the variable

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

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30 Absolute value or modulus Solving and graphing inequalities

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

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31 Graphing binomials Binomial products.

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

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32 Graphing binomials Binomial products with negative multiplier

Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products.

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33 Graphing binomials Binomial products [non-monic].

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

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34 Squaring binomial Squaring a binomial. [monic]

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

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35 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.

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36 Factorising Expansions leading to the difference of two squares

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

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37 Algebraic expressions-products Products in simplification of algebraic expressions

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

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38 Algebraic expressions-larger expansions Algebraic Expressions – Larger expansions.

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

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39 Algebra-highest common factor Highest common factor.

Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.

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40 Factors by grouping Factors by grouping.

Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.

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41 Difference of 2 squares Difference of two squares

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

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42 Common fact and diff Common factor and the difference of two squares

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

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43 Quadratic trinomials Quadratic trinomials [monic] – Case 1.

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

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44 Factorising quads Factorising quadratic trinomials [monic] – Case 2.

Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.

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45 Factorising quads Factorising quadratic trinomials [monic] – Case 3.

Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.

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46 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.

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47 Factorising quads Factorisation of non-monic quadratic trinomials

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

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48 Factorising quads Factorisation of non-monic quadratic trinomials – moon method

Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.

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49 Sum/diff 2 cubes Sum and difference of two cubes.

Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them.

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50 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.

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51 Simultaneous equns Simultaneous equations

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

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52 Simultaneous equns Elimination method

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

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53 Simultaneous equns Elimination method part 2

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

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54 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.

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55 Coordinate geometry Solve by graphing

Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.

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56 Quadratic equations Introduction to quadratic equations.

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

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57 Quadratic equations Quadratic equations with factorisation.

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

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58 Quadratic equations Solving quadratic equations.

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

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59 Quadratic equations Completing the square

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

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60 Quadratic equations Solving quadratic equations by completing the square

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

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61 Quadratic equations The quadratic formula

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

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62 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.

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63 Quadratic equations Solving simultaneous quadratic equations graphically

Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..

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64 Geometry-angles Adjacent angles

Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.

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65 Geometry-angles Complementary and supplementary angles

Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.

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66 Geometry-angles Vertically opposite angles

Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.

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67 Geometry-angles Angles at a Point.

Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.

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68 Geometry-angles Parallel Lines.

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

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69 Geometry-problems Additional questions involving parallel lines

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.

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70 Geometry-triangles Angle sum of a triangle

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.

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71 Geometry-triangles Exterior angle theorem

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.

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72 Special triangles Special triangles

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.

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73 Geometry-quadrilaterals Quadrilaterals

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.

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74 Geometry To identify collinear points, coplanar lines and points in 2 and 3 dimensions

Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays.

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75 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.

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76 Geometry problems More difficult exercises involving parallel lines

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log

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77 Geometry-reasoning Further difficult exercises involving formal reasoning

Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.

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78 Geometry-constructions Angle bisector construction and its properties (Stage 2)

Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge.

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79 Geometry-constructions Circumcentre and incentre (Stage 2)

Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values.

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80 Geometry-constructions Orthocentre and centroids (Stage 2)

Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values.

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81 Geometry-quadrilaterals Midsegments of Triangles

Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.

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82 Geometry-quadrilaterals Classifying Quadrilaterals

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

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83 Geometry-quadrilaterals Using the Properties of a Parallelogram

Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram.

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84 Geometry-quadrilaterals Proving a Shape is a Parallelogram

Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram.

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85 Geometry-quadrilaterals Properties of the Rectangle, Square and Rhombus

Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values.

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86 Geometry-quadrilaterals Properties of the Trapezium and Kite

Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values.

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87 Geometry-locus Constructions and loci – single condition

Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition.

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88 Geometry-locus Constructions and loci – multiple conditions

Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane.

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89 Geometry-polygons Angles of regular polygons

Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees.

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90 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.

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91 Geometry-congruence Congruent triangles, Test 3 and 4

Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.

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92 Geometry-congruence Proofs and congruent triangles.

Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent.

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93 Similar triangles Similar triangles

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

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94 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.

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95 Overlapping triangles Examples involving overlapping triangles

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

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96 Geometry – triangles Triangle inequality theorem

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

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97 Pythagoras Find the hypotenuse

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

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98 Pythagoras Pythagorean triples

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

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99 Pythagoras Find the hypotenuse Part 2

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

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100 Pythagoras Calculating a leg of a right-angled triangle

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.

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101 Coordinate Geometry-the plane Distance formula.

Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results.

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102 Coordinate Geometry-midpoint, slope Mid-point formula

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

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103 Coordinate Geometry-gradient Gradient

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.

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104 Coordinate Geometry-gradient Gradient formula.

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.

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105 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.

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106 Coordinate Geometry-slope, etc. Lines through the origin.

Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.

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

Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.

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108 Coordinate Geometry-intercept Slope intercept form of a line.

Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.

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109 Coordinate Geometry-point slope Point slope form of a line

Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line.

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110 Co-ordinate Geometry-Two point formula Two point formula: equation of a line which joins a pair of points.

Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.

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111 Co-ordinate Geometry-Intercept form Intercept form of a straight line: find the equation when given x and y

Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.

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112 Co-ordinate Geometry-Parallel lines equations Parallel lines: identify equation of a line parallel to another

Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.

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113 Co-ordinate Geometry-Perpendicular lines Perpendicular lines.

Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line.

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114 Co-ordinate Geometry-Theorems Perpendicular distance

Objective: On completion of the lesson the student will be able to derive the formula to calculate the distance between a given point and a given line. The student will also be able to calculate the distance between parallel lines.

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115 Co-ordinate Geometry-Theorems Line through intersection of two given lines

Objective: On completion of the lesson the student will be able to calculate the equation of a line which goes through the intersection of two given lines and also through another named point or satisfies some other specified condition.

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116 Co-ordinate Geometry-Inequalities Inequalities on the number plane.

Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.

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117 Trigonometry-ratios Trigonometric ratios.

Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op

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118 Trigonometry-ratios Using the calculator.

Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.

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119 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.

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120 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 2 Cosine].

Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.

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121 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].

Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.

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122 Trigonometry-ratios Unknown in the denominator. [Case 4].

Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.

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123 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.

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124 Trigonometry-elevation Angles of elevation and depression.

Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.

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125 Trigonometry-practical Trigonometric ratios in practical situations.

Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.

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126 Trigonometry-ratios Using the calculator to find an angle given a trigonometric ratio.

Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.

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127 Trigonometry- ratios Using the trigonometric ratios to find an angle in a right-angled triangle.

Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.

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128 Trigonometry-exact ratios Trigonometric ratios of 30., 45. and 60. – exact ratios.

Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.

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129 Trigonometry-cosine rule The cosine rule to find an unknown side. [Case 1 SAS].

Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.

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130 Trigonometry-cosine rule The cosine rule to find an unknown angle. [Case 2 SSS].

Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.

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131 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.

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132 Trigonometry-sine rule The sine rule to find an unknown angle. Case 2.

Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.

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133 Trigonometry-areas The area formula

Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.

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134 Trig larger angles Angles of any magnitude

Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle.

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135 Trig larger angles Trigonometric ratios of 0°, 90°, 180°, 270° and 360°

Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees.

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136 Trig identities Trigonometric identities

Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities.

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137 Geometry-circles The equation of a circle: to find radii of circles

Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius.

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138 Geometry-circles The semicircle: to select the equation given the semi circle and vice versa

Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle.

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139 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.

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140 Functions and graphs Quadratic polynomials of the form y = ax. + bx + c.

Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.

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141 Functions and graphs Graphing perfect squares: y=(a-x) squared

Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.

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142 Graphing roots Graphing irrational roots

Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.

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143 Graphing-polynomials Graphing complex polynomials: quadratics with no real roots

Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it.

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144 Graphing-polynomials General equation of a circle: determine and graph the equation

Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning.

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145 Graphing-cubic curves Graphing cubic curves

Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information.

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146 Absolute value equations Absolute value equations

Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio

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147 Rect.hyperbola The rectangular hyperbola.

Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features.

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148 Conic sections The parabola x. = 4ay

Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form.

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149 Conic sections Circles

Objective: On completion of the lesson the student will identify the radius of a circle given in standard form.

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150 Functions Definition, domain and range

Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.

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151 Functions Notation and evaluations

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

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152 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.

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153 Functions Domain and range from graphical representations

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.

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154 Functions Evaluating and graphing piecewise functions

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

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155 Functions Functions combinations

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

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156 Calculus Limits

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.

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157 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.

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158 Calculus=1st prin Differentiation of y = x to the power of n.

Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.

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159 Calculus-differential, integ Meaning of dy over dx – equations of tangents and normals.

Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.

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Stage 6 - Mathematics HSC (Year 12 - 2 Unit) Mathematics

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# TOPIC TITLE
1 Functions Rational functions Part 1

Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes.

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2 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.

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3 Geometry-quadrilaterals Midsegments of Triangles

Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.

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4 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.

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5 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.

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6 Logarithms-Equations and logs Equations of type log x to the base 3 = 4.

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.

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7 Logarithms-Equations and logs Equations of type log 32 to the base x = 5.

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.

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8 Logarithms-Log laws Laws of logarithms.

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

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9 Logarithms-Log laws expansion Using the log laws to expand logarithmic expressions.

Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.

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10 Logarithms-Log laws simplifying Using the log laws to simplify expressions involving logarithms.

Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.

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11 Logarithms-Log laws numbers Using the log laws to find the logarithms of numbers.

Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples.

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12 Logarithms-Equations and logs Equations involving logarithms.

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

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13 Logarithms-Logs to solve equations Using logarithms to solve equations.

Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.

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14 Logarithms-Change base formula Change of base formula

Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base.

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15 Exponential function The exponential function.

Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1.

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16 Log functions Logarithmic functions.

Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit

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17 Logarithms-Graph-log curve The graph of the logarithmic curve

Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves.

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18 Logarithms-Log curves Working with log curves.

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

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19 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.

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20 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.

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21 Graphs tan curve Graphing the trigonometric ratios – III Tangent curve.

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

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22 Graph reciprocals Graphing the trigonometric ratios – IV Reciprocal ratios.

Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.

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23 Trig larger angles Using one ratio to find another.

Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude.

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24 Trig equations Solving trigonometric equations – Type I.

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

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25 Trig equations Solving trigonometric equations – Type II.

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

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26 Trig equations Solving trigonometric equations – Type III.

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

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27 Sequences and Series General sequences.

Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.

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28 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.

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29 Arithmetic Progression The arithmetic progression

Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.

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30 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.

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31 Arithmetic Progression Given two terms of A.P., find the sequence.

Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms

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32 Arithmetic Progression Arithmetic means

Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.

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33 Arithmetic Progression The sum to n terms of an A.P.

Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.

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34 Geometric Progression The geometric progression.

Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.

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35 Geometric Progression Finding the position of a term in a G.P.

Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.

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36 Geometric Progression Given two terms of G.P., find the sequence.

Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.

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37 Sequences and Series-Geometric means Geometric means.

Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.

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38 Sequences and Series-Sum of gp The sum to n terms of a G.P.

Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P).

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39 Sequences and Series-Sigma notation Sigma notation

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

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40 Sequences and Series-Sum-infinity Limiting sum or sum to infinity.

Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems.

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41 Sequences and Series-Recurring decimal infinity Recurring decimals and the infinite G.P.

Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number.

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42 Calculus Limits

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.

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43 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.

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44 Calculus=1st prin Differentiation of y = x to the power of n.

Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.

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45 Calculus-differential, integ Meaning of dy over dx – equations of tangents and normals.

Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.

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46 Calculus-differential, integ Function of a function rule, product rule, quotient rule.

Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule.

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47 Calculus-differential, integ Increasing, decreasing and stationary functions.

Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.

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48 Calculus-2nd derivative The second derivative – concavity.

Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.

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49 Calculus First Derivative – turning points and curve sketching

Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve.

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50 Calculus – Curve sketching Curve sketching

Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve.

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51 Calculus – Maxima minima Practical applications of maxima and minima

Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems.

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52 Calculus – Integration Integration – anti-differentiation, primitive function

Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions.

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53 Calculus – Computation area Computation of an area

Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area.

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54 Calculus – Computation volumes Computation of volumes of revolution

Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy.

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55 Calculus – Trapezoidal and Simpson’s rules The Trapezium rule and Simpson’s rule

Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve.

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56 Sequences and Series-Compound interest Compound interest

Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.

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57 Sequences and Series-Superannuation Superannuation.

Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.

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58 Sequences and Series-Time payments Time payments.

Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.

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59 Sequences and Series Applications of arithmetic sequences

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

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60 Statistic-probability Probability of Simple Events

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

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61 Statistic-probability Rolling a pair of dice

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.

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62 Statistic-probability Experimental probability

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

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63 Statistic-probability Tree diagrams – not depending on previous outcomes

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.

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64 Statistic-probability Tree diagrams – depending on previous outcomes

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.

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65 Statistic-probability The complementary result ..

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.

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66 Statistic-probability P[A or B] When A and B are both mutually and NOT mutually exclusive

Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.

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67 Geometry-locus Constructions and loci – single condition

Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition.

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68 Geometry-locus Constructions and loci – multiple conditions

Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane.

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Go to top

Stage 6 - Mathematics with Extension 1 Preliminary (Year 11 - 3 Unit) Mathematics

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# TOPIC TITLE
1 Rules for indices/exponents Adding indices when multiplying terms with the same base

Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.

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2 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.

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3 Rules for indices/exponents Multiplying indices when raising a power to a power

Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.

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4 Rules for indices/exponents Multiplying indices when raising to more than one term

Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.

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5 Rules for indices/exponents Terms raised to the power of zero

Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.

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6 Rules for indices/exponents Negative Indices

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

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7 Fractional indices/exponents Fractional indices

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

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8 Fractional indices/exponents Complex fractions as indices

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

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9 Scientific notation Scientific notation with larger numbers

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

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10 Scientific notation Scientific notation with small numbers

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.

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11 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.

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12 Significant figures Significant figures

Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures.

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13 Surds Introducing surds

Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.

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14 Surds Some rules for the operations with surds

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

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15 Surds Simplifying surds

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

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16 Surds Creating entire surds

Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds

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17 Surds Adding and subtracting like surds

Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.

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18 Surds Expanding surds

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

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19 Surds Binomial expansions

Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.

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20 Surds Conjugate binomials with surds

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

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21 Surds Rationalising the denominator

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

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22 Surds Rationalising binomial denominators

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

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23 Algebra-factorising Simplifying easy algebraic fractions.

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

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24 Algebraic fractions Simplifying algebraic fractions using the index laws.

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.

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25 Algebra-negative indices Algebraic fractions resulting in negative indices.

Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.

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26 Factorisation Factorisation of algebraic fractions including binomials.

Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods.

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27 Algebraic fractions-binomial Cancelling binomial factors in algebraic fractions.

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

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28 Absolute value or modulus Simplifying absolute values

Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.

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29 Absolute value or modulus Solving for the variable

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

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30 Absolute value or modulus Solving and graphing inequalities

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

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31 Graphing binomials Binomial products.

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

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32 Graphing binomials Binomial products with negative multiplier

Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products.

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33 Graphing binomials Binomial products [non-monic].

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

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34 Squaring binomial Squaring a binomial. [monic]

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

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35 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.

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36 Factorising Expansions leading to the difference of two squares

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

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37 Algebraic expressions-products Products in simplification of algebraic expressions

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

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38 Algebraic expressions-larger expansions Algebraic Expressions – Larger expansions.

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

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39 Algebra-highest common factor Highest common factor.

Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.

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40 Factors by grouping Factors by grouping.

Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.

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41 Difference of 2 squares Difference of two squares

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

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42 Common fact and diff Common factor and the difference of two squares

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

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43 Quadratic trinomials Quadratic trinomials [monic] – Case 1.

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

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44 Factorising quads Factorising quadratic trinomials [monic] – Case 2.

Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.

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45 Factorising quads Factorising quadratic trinomials [monic] – Case 3.

Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.

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46 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.

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47 Factorising quads Factorisation of non-monic quadratic trinomials

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

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48 Factorising quads Factorisation of non-monic quadratic trinomials – moon method

Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.

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49 Sum/diff 2 cubes Sum and difference of two cubes.

Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them.

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50 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.

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51 Simultaneous equns Simultaneous equations

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

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52 Simultaneous equns Elimination method

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

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53 Simultaneous equns Elimination method part 2

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

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54 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.

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55 Coordinate geometry Solve by graphing

Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.

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56 Quadratic equations Introduction to quadratic equations.

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

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57 Quadratic equations Quadratic equations with factorisation.

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

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58 Quadratic equations Solving quadratic equations.

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

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59 Quadratic equations Completing the square

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

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60 Quadratic equations Solving quadratic equations by completing the square

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

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61 Quadratic equations The quadratic formula

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

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62 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.

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63 Quadratic equations Solving simultaneous quadratic equations graphically

Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..

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64 Geometry-angles Adjacent angles

Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.

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65 Geometry-angles Complementary and supplementary angles

Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.

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66 Geometry-angles Vertically opposite angles

Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.

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67 Geometry-angles Angles at a Point.

Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.

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68 Geometry-angles Parallel Lines.

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

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69 Geometry-problems Additional questions involving parallel lines

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.

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70 Geometry-triangles Angle sum of a triangle

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.

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71 Geometry-triangles Exterior angle theorem

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.

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72 Special triangles Special triangles

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.

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73 Geometry-quadrilaterals Quadrilaterals

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.

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74 Geometry To identify collinear points, coplanar lines and points in 2 and 3 dimensions

Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays.

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75 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.

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76 Geometry problems More difficult exercises involving parallel lines

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log

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77 Geometry-reasoning Further difficult exercises involving formal reasoning

Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.

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78 Geometry-quadrilaterals Classifying Quadrilaterals

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

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79 Geometry-quadrilaterals Using the Properties of a Parallelogram

Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram.

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80 Geometry-quadrilaterals Proving a Shape is a Parallelogram

Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram.

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81 Geometry-quadrilaterals Properties of the Rectangle, Square and Rhombus

Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values.

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82 Geometry-quadrilaterals Properties of the Trapezium and Kite

Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values.

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83 Geometry-polygons Angles of regular polygons

Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees.

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84 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.

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85 Geometry-congruence Congruent triangles, Test 3 and 4

Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.

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86 Geometry-congruence Proofs and congruent triangles.

Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent.

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87 Similar triangles Similar triangles

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

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88 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.

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89 Overlapping triangles Examples involving overlapping triangles

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

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90 Geometry – triangles Triangle inequality theorem

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

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91 Pythagoras Find the hypotenuse

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

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92 Pythagoras Pythagorean triples

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

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93 Pythagoras Find the hypotenuse Part 2

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

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94 Pythagoras Calculating a leg of a right-angled triangle

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.

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95 Coordinate Geometry-the plane Distance formula.

Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results.

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96 Coordinate Geometry-midpoint, slope Mid-point formula

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

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97 Coordinate Geometry-gradient Gradient

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.

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98 Coordinate Geometry-gradient Gradient formula.

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.

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99 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.

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100 Coordinate Geometry-slope, etc. Lines through the origin.

Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.

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

Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.

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102 Coordinate Geometry-intercept Slope intercept form of a line.

Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.

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103 Coordinate Geometry-point slope Point slope form of a line

Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line.

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104 Trigonometry-ratios Trigonometric ratios.

Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op

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105 Trigonometry-ratios Using the calculator.

Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles.

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106 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.

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107 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 2 Cosine].

Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle.

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108 Trigonometry-ratios Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio].

Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle.

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109 Trigonometry-ratios Unknown in the denominator. [Case 4].

Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown.

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110 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.

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111 Trigonometry-elevation Angles of elevation and depression.

Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them.

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112 Trigonometry-practical Trigonometric ratios in practical situations.

Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.

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113 Trigonometry-ratios Using the calculator to find an angle given a trigonometric ratio.

Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio.

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114 Trigonometry- ratios Using the trigonometric ratios to find an angle in a right-angled triangle.

Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides.

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115 Trigonometry-exact ratios Trigonometric ratios of 30., 45. and 60. – exact ratios.

Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.

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116 Trigonometry-cosine rule The cosine rule to find an unknown side. [Case 1 SAS].

Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle.

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117 Trigonometry-cosine rule The cosine rule to find an unknown angle. [Case 2 SSS].

Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides.

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118 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.

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119 Trigonometry-sine rule The sine rule to find an unknown angle. Case 2.

Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle.

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120 Trigonometry-areas The area formula

Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.

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121 Trig larger angles Angles of any magnitude

Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle.

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122 Trig larger angles Trigonometric ratios of 0°, 90°, 180°, 270° and 360°

Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees.

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123 Trig identities Trigonometric identities

Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities.

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124 Trigonometry Sin(A+B) etc sum and difference identities (Stage 2)

Objective: On completion of the lesson the student will be using the reference triangles for 30, 45 and 60 degrees with the sum and difference of angles to find additional exact values of trigonometric ratios.

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125 Trigonometry Double angle formulas (Stage 2)

Objective: On completion of the lesson the student will derive and use the double angle trig identities.

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126 Trigonometry Half angle identities (Stage 2)

Objective: On completion of the lesson the student will derive and use the power reducing formulas and the half angle trig identities.

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127 Trigonometry t Formulas (Stage 2)

Objective: On completion of the lesson the student will solve trig equations using the t substitution.

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128 Geometry-circles The equation of a circle: to find radii of circles

Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius.

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129 Geometry-circles The semicircle: to select the equation given the semi circle and vice versa

Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle.

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130 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.

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131 Functions and graphs Quadratic polynomials of the form y = ax. + bx + c.

Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.

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132 Functions and graphs Graphing perfect squares: y=(a-x) squared

Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.

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133 Graphing roots Graphing irrational roots

Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.

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134 Graphing-polynomials Graphing complex polynomials: quadratics with no real roots

Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it.

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135 Graphing-polynomials General equation of a circle: determine and graph the equation

Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning.

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136 Graphing-cubic curves Graphing cubic curves

Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information.

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137 Absolute value equations Absolute value equations

Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio

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138 Rect.hyperbola The rectangular hyperbola.

Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features.

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139 Conic sections The parabola x. = 4ay

Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form.

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140 Functions Parametric equations (Stage 2)

Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range.

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141 Conic sections Circles

Objective: On completion of the lesson the student will identify the radius of a circle given in standard form.

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142 Functions Definition, domain and range

Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.

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143 Functions Notation and evaluations

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

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144 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.

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145 Functions Domain and range from graphical representations

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.

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146 Functions Evaluating and graphing piecewise functions

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

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147 Calculus Limits

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.

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148 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.

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149 Calculus=1st prin Differentiation of y = x to the power of n.

Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.

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150 Calculus-differential, integ Meaning of dy over dx – equations of tangents and normals.

Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.

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151 Circle Geometry Theorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs.

Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro

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152 Circle Geometry Theorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord.

Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’

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153 Circle Geometry Theorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal.

Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre.

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154 Circle Geometry Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc.

Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.

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155 Circle Geometry Theorem – Angles in the same segment of a circle are equal.

Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.

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156 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.’

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157 Circle Geometry Theorem – The opposite angles of a cyclic quadrilateral are supplementary.

Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.

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158 Circle Geometry Theorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle.

Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite.

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159 Circle Geometry Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.

Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact.

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160 Circle Geometry Theorem – Tangents to a circle from an external point are equal.

Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.

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161 Circle Geometry Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

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162 Circle Geometry-chords Theorem – The products of the intercepts of two intersecting chords are equal.

Objective: On completion of the lesson the student will be able to prove that ‘The product of the intercepts of two intersecting chords are equal.’, and use this result to complete questions that require this knowledge.

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163 Circle Geometry-tangents Theorem – The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point. [Including Alternate Proof]

Objective: On completion of the lesson the student will be able to prove and apply ‘The square of the length of the tangent from an external point is equal to the product of the intercepts of the secant passing through this point ‘, and use this result to complete q

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164 Geometry-constructions Angle bisector construction and its properties (Stage 2)

Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge.

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165 Geometry-constructions Circumcentre and incentre (Stage 2)

Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values.

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166 Geometry-constructions Orthocentre and centroids (Stage 2)

Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values.

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167 Algebra-polynomials Introduction to polynomials

Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not.

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168 Algebra-polynomials The sum, difference and product of two polynomials.

Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers.

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169 Algebra-polynomials Polynomials and long division.

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

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170 Remainder theorem The remainder theorem.

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

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171 Remainder theorem More on remainder theorem

Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials.

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172 Factor theorem The factor theorem

Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial.

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173 Factor theorem More on the factor theorem

Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials.

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174 Factor theorem Complete factorisations using the factor theorem

Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros.

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175 Polynomial equations Polynomial equations

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

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176 Graphs, polynomials Graphs of polynomials

Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves.

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177 Roots quad equations Sum and product of roots of quadratic equations

Objective: On completion of the lesson the student will understand the formulas for the sum and product of roots of quadratic polynomials and how to use them. The student will understand how to form a quadratic equation given its roots.

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178 Roots quad equations Sum and product of roots of cubic and quartic equations

Objective: On completion of the lesson the student will be able to do problems on the sum and products of roots of cubic and quartic equations.

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Stage 6 - Mathematics with Extension 1 HSC (Year 12 - 3 Unit) Mathematics

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# TOPIC TITLE
1 Functions Rational functions Part 1

Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes.

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2 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.

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3 Geometry-quadrilaterals Midsegments of Triangles

Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.

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4 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.

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5 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.

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6 Logarithms-Equations and logs Equations of type log x to the base 3 = 4.

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.

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7 Logarithms-Equations and logs Equations of type log 32 to the base x = 5.

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.

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8 Logarithms-Log laws Laws of logarithms.

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

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9 Logarithms-Log laws expansion Using the log laws to expand logarithmic expressions.

Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.

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10 Logarithms-Log laws simplifying Using the log laws to simplify expressions involving logarithms.

Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.

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11 Logarithms-Log laws numbers Using the log laws to find the logarithms of numbers.

Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples.

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12 Logarithms-Equations and logs Equations involving logarithms.

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

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13 Logarithms-Logs to solve equations Using logarithms to solve equations.

Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.

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14 Logarithms-Change base formula Change of base formula

Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base.

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15 Exponential function The exponential function.

Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1.

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16 Log functions Logarithmic functions.

Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit

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17 Logarithms-Graph-log curve The graph of the logarithmic curve

Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves.

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18 Logarithms-Log curves Working with log curves.

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

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19 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.

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20 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.

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21 Graphs tan curve Graphing the trigonometric ratios – III Tangent curve.

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

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22 Graph reciprocals Graphing the trigonometric ratios – IV Reciprocal ratios.

Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.

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23 Trig larger angles Using one ratio to find another.

Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude.

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24 Trig equations Solving trigonometric equations – Type I.

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

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25 Trig equations Solving trigonometric equations – Type II.

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

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26 Trig equations Solving trigonometric equations – Type III.

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

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27 Functions Composition of functions

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

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28 Functions Inverse functions

Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used.

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29 Sequences and Series General sequences.

Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.

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30 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.

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31 Arithmetic Progression The arithmetic progression

Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.

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32 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.

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33 Arithmetic Progression Given two terms of A.P., find the sequence.

Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms

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34 Arithmetic Progression Arithmetic means

Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.

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35 Arithmetic Progression The sum to n terms of an A.P.

Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.

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36 Geometric Progression The geometric progression.

Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.

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37 Geometric Progression Finding the position of a term in a G.P.

Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.

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38 Geometric Progression Given two terms of G.P., find the sequence.

Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.

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39 Sequences and Series-Geometric means Geometric means.

Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.

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40 Sequences and Series-Sum of gp The sum to n terms of a G.P.

Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P).

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41 Sequences and Series-Sigma notation Sigma notation

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

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42 Sequences and Series-Sum-infinity Limiting sum or sum to infinity.

Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems.

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43 Sequences and Series-Recurring decimal infinity Recurring decimals and the infinite G.P.

Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number.

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44 Calculus Limits

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.

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45 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.

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46 Calculus=1st prin Differentiation of y = x to the power of n.

Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.

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47 Calculus-differential, integ Meaning of dy over dx – equations of tangents and normals.

Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.

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48 Calculus-differential, integ Function of a function rule, product rule, quotient rule.

Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule.

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49 Calculus-differential, integ Increasing, decreasing and stationary functions.

Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.

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50 Calculus-2nd derivative The second derivative – concavity.

Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.

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51 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.

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52 Calculus – Curve sketching Curve sketching

Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve.

See the sample lesson in action here
53 Calculus – Maxima minima Practical applications of maxima and minima

Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems.

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54 Calculus – Integration Integration – anti-differentiation, primitive function

Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions.

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55 Calculus – Computation area Computation of an area

Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area.

See the sample lesson in action here
56 Calculus – Computation volumes Computation of volumes of revolution

Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy.

See the sample lesson in action here
57 Calculus – Trapezoidal and Simpson’s rules The Trapezium rule and Simpson’s rule

Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve.

See the sample lesson in action here
58 Sequences and Series-Compound interest Compound interest

Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.

See the sample lesson in action here
59 Sequences and Series-Superannuation Superannuation.

Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.

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60 Sequences and Series-Time payments Time payments.

Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.

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61 Sequences and Series Applications of arithmetic sequences

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

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62 Logic Mathematical induction

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

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63 Statistic-probability Probability of Simple Events

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

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64 Statistic-probability Rolling a pair of dice

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.

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65 Statistic-probability Experimental probability

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

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66 Statistic-probability Tree diagrams – not depending on previous outcomes

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.

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67 Statistic-probability Tree diagrams – depending on previous outcomes

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.

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68 Statistic-probability The complementary result ..

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.

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69 Statistic-probability P[A or B] When A and B are both mutually and NOT mutually exclusive

Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.

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70 Statistic-probability Binomial Theorem – Pascal’s Triangle

Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.

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71 Statistic-probability Binomial probabilities using the Binomial Theorem

Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem

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72 Statistic-probability Counting techniques and ordered selections – permutations

Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability.

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73 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.

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74 Geometry-locus Constructions and loci – single condition

Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition.

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75 Geometry-locus Constructions and loci – multiple conditions

Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane.

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76 Approx roots Methods of approximating roots

Objective: On completion of the lesson the student will be capable of finding approximate roots of polynomial equations using half the interval method. The student will be able to make a number of applications of this rule within the one question.

See the sample lesson in action here
77 Newton’s approx Newton’s method of approximation

Objective: On completion of the lesson the student will be able to use Newton’s method in finding approximate roots of polynomial equations and be capable of more than one application of this method.

See the sample lesson in action here
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Stage 6 - Mathematics Extension 2 HSC (Year 12) Mathematics

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# TOPIC TITLE
1 Number theory – sets Number sets and their members

Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system.

See the sample lesson in action here
2 Logarithms-Complex numbers Imaginary numbers and standard form

Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction.

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3 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.

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4 Logarithms-Complex numbers Plotting complex number and graphical representation

Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers.

See the sample lesson in action here
5 Logarithms-Complex numbers Absolute value

Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers

See the sample lesson in action here
6 Logarithms-Complex numbers Trigonometric form of a complex number

Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form.

See the sample lesson in action here
7 Logarithms-Complex numbers Multiplication and division of complex numbers in trig form (Stage 2)

Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division.

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8 Logarithms-Complex numbers DeMoivre’s theorem (Stage 2)

Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form.

See the sample lesson in action here
9 Logarithms-Complex numbers The nth root of real and complex numbers (Stage 2)

Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form.

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10 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.

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11 Polar coordinates Plotting polar coordinates and converting polar to rectangular

Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system.

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12 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.

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13 Polar coordinates Write and graph points in polar form with negative vectors (Stage 2)

Objective: On completion of the lesson the student will be using negative angles and negative vector lengths.

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14 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.

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15 Conic sections Ellipses

Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse.

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16 Conic sections Hyperbola

Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola.

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17 Functions Polynomial addition etc in combining and simplifying functions (Stage 2)

Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra.

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18 Functions Parametric functions (Stage 2)

Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion.

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Literacy

Australian National Curriculum Foundation - Kindergarten Literacy

# TOPIC TITLE
1 It’s time to learn your A B C! The Alphabet!

Objective: Students will practise reading the letters of the alphabet and practise recognition of: a, b, c, d, e, f.
2 It’s time to learn your A B C! 1 2 3 – It’s A B C!

Objective: Students will hear and practise saying the alphabet and the numbers 1-11.
3 It’s time to learn your A B C! How do you spell that?

Objective: Students will develop their letter recognition skills by listening to a conversation. They will be able to identify the letters by name.
4 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.
5 It’s time to learn your A B C! What time is it?

Objective: Students will develop their comprehension skills by listening to a conversation about asking and telling the time. They will practise using the key sentences.
6 It’s time to learn your A B C! ‘A’ sounds like …!

Objective: Students will listen to, discriminate between and practise the sounds of the letters a, b, c, d, e, f.
7 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.
8 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.
9 Eight Purple Stars! Ten Little Pandas

Objective: Students will read a picture story and practise the numbers 1-10.
10 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 …’.
11 Fun at School Close the door, please!

Objective: Students will develop their listening and speaking skills. They will read and hear a picture story, and practise classroom instructions.
12 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 …’.
13 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?’.
14 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 …?’.
15 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.
16 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.
17 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’.
18 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’.
19 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’.
20 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.
21 Animal Mania! What animal is that?

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.
22 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.
23 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.
24 We like to play games. What’s your favourite?

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.
25 Do you like hamburgers? At a Café

Objective: Students will develop their comprehension skills by reading a picture story about food preferences.
26 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.
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Australian National Curriculum Year 1 Literacy

# TOPIC TITLE
1 Punctuation Sentence Endings

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
2 Sentences The Sentence

Objective: To identify and use complete sentences.
3 Capitalisation Capital Letters 1

Objective: To use capital letters correctly: to begin sentences, for proper nouns.
4 Punctuation Commas 1

Objective: To use commas: to list, to make meaning clear, and when writing the date.
5 Common Nouns Common Nouns

Objective: To show a common noun names an object or thing.
6 Sentences The Sentence

Objective: To identify and use complete sentences.
7 Parts of Speech Part h Articles and Demonstratives

Objective: To identify and use articles and demonstratives correctly.
8 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.
9 Common Nouns Common Nouns

Objective: To show a common noun names an object or thing.
10 Pronouns Pronouns

Objective: To show a pronoun is used in place of a noun.
11 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.
12 Adjectives Adjectives

Objective: To show an adjective is a word that describes a noun.
13 Adverbs Adverbs

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
14 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.
15 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’.
16 School and Play I have lots of subjects!

Objective: Students will practise reading, and saying words and simple sentences to describe school subjects and the days of the week.
17 School and Play On the Weekend

Objective: Students will practise reading and recognising simple sentences about weekend activities.
18 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.
19 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.
20 I walk in the summer. The Seasons

Objective: Students will develop their reading skills and practise new words to describe the seasons.
21 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.
22 What’s the weather like today? Have you got a ‘W’?

Objective: Students will develop their comprehension skills by reading a text in which ‘have got’ is used. They will also revise the letters of the alphabet and learn some new ones.
23 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.
24 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.
25 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.
26 They’re usually in the lounge room. Hide and Seek

Objective: Students will develop their comprehension skills by reading a story about finding people.
27 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.
28 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.
29 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.
30 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.
31 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.
32 Sentences The Sentence

Objective: To identify and use complete sentences.
33 Common Errors Common Errors in spelling and punctuation

Objective: To identify and eliminate common errors.
34 Spelling Spelling

Objective: To use the ‘Look, Say, Write’ method for learning spelling. Plus 300 spelling words.
35 Basic Dictionary Use Basic Dictionary Use

Objective: To find words arranged alphabetically and identify word meanings in dictionaries.
36 Capitalisation Capital Letters 1

Objective: To use capital letters correctly: to begin sentences, for proper nouns.
37 Punctuation Sentence Endings

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
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Australian National Curriculum Year 2 Literacy

# TOPIC TITLE
1 Punctuation Commas 1

Objective: To use commas: to list, to make meaning clear, and when writing the date.
2 Capitalisation Capital Letters 1

Objective: To use capital letters correctly: to begin sentences, for proper nouns.
3 Nouns Proper Nouns

Objective: To show a proper noun is used to name a person, place or a title.
4 Parts of Speech Part b Conjunctions

Objective: To identify and use conjunctions correctly.
5 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
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 Nouns Collective and Abstract Nouns

Objective: To identify and use collective and abstract nouns.
9 Capitalisation Capital Letters 1

Objective: To use capital letters correctly: to begin sentences, for proper nouns.
10 Spelling Spelling

Objective: To use the ‘Look, Say, Write’ method for learning spelling. Plus 300 spelling words.
11 Spelling Skills Syllabification

Objective: To improve spelling by dividing words correctly into syllables.
12 Prefixes Prefixes

Objective: The identify and use prefixes.
13 Suffixes Suffixes

Objective: The identify and use suffixes.
14 Spelling Spelling

Objective: To use the ‘Look, Say, Write’ method for learning spelling. Plus 300 spelling words.
15 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’.
16 We’re very busy. On the farm

Objective: Students will increase their vocabulary and develop their reading skills by reading, in which the present continuous tense is used.
17 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.
18 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.
19 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.
20 Can I look at your new kite? I’ve got a secret!

Objective: Students will increase their vocabulary and develop their reading skills by reading a text in which ‘has’ and ‘have got’ are used to talk about possessions.
21 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.
22 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.
23 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.
24 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.
25 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.
26 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.
27 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.
28 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.
29 We need to take a metal pan. What’s it made of?

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.
30 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’.
31 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’.
32 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.
33 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.
34 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.
35 Punctuation Sentence Endings

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
36 Basic Dictionary Use Basic Dictionary Use

Objective: To find words arranged alphabetically and identify word meanings in dictionaries.
37 Capitalisation Capital Letters 1

Objective: To use capital letters correctly: to begin sentences, for proper nouns.
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Australian National Curriculum Year 3 Literacy

# TOPIC TITLE
1 Modal Verbs Modal Verbs

Objective: To identify and use modal verbs with the appropriate form of the main verb.
2 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.
3 Adverbs Adverbs

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
4 Common Nouns Common Nouns

Objective: To show a common noun names an object or thing.
5 Nouns Proper Nouns

Objective: To show a proper noun is used to name a person, place or a title.
6 Nouns Collective and Abstract Nouns

Objective: To identify and use collective and abstract nouns.
7 Let’s hit the beach! Modals of obligation

Objective: Learn about modals of obligation.
8 Let’s hit the beach! Imperatives

Objective: Learn how to use imperatives.
9 Contractions Contractions

Objective: To identify and use contractions.
10 Apostrophe – Possession Apostrophe – Possession

Objective: To use the apostrophe of possession correctly.
11 Clauses Clauses

Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
12 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.
13 Thanks and goodbye Time clauses

Objective: Learn how to use time clauses.
14 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.
15 Verbs Verbs – Tense

Objective: To identify and use the correct tense of verbs: past, present and future.
16 Simple and Compound Verbs Simple and Compound Verbs

Objective: To identify and use simple and compound verbs.
17 Auxiliary Verbs Auxiliary Verbs

Objective: To identify and use auxiliary verbs within compound verbs.
18 Regular and Irregular Verbs Regular and Irregular Verbs

Objective: To identify and use regular and irregular verbs in the present and past tense.
19 Verbs – Infinitives Verbs – Infinitives

Objective: To identify and use the infinitive form of the verb.
20 What’s Homestay? Simple Present

Objective: Learn the correct structure for the simple present.
21 Setting off Present perfect

Objective: Learn the correct structure for the present perfect.
22 Amazing Aussie animals Present continuous

Objective: Learn about the present continuous tense.
23 Amazing Aussie animals Past continuous

Objective: Learn about the past continuous tense.
24 Big day out! The future with ‘will’ and ‘going to’

Objective: Learn the uses of ‘will’ and ‘going to’ to talk about the future.
25 Modal Verbs Modal Verbs

Objective: To identify and use modal verbs with the appropriate form of the main verb.
26 Adverbs Adverbs

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
27 Amazing Aussie animals Giving facts and opinions

Objective: Present phrases that ask for and give opinions.
28 Thanks and goodbye Talking about feelings

Objective: Present constructions for talking about feelings.
29 What do you like to do? Adverbs of frequency

Objective: Learn about the past continuous tense.
30 Spelling Skills Spelling

Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’.
31 Vowels and Consonants Vowels and Consonants

Objective: To identify and use vowels and consonants.
32 Vowels Vowels – Long and Short

Objective: To identify long and short vowel sounds, and their use.
33 Plurals Plurals 1 – simple

Objective: To form plurals (more than one) by adding ‘s’ and ‘es’ correctly.
34 Plurals Plurals 2 – special rules

Objective: To form plurals with special rules: words ending in ‘y’ and ‘f’.
35 Homonyms – Homophones and Homographs Homonyms – Homophones and Homographs

Objective: To identify and use correctly homonyms, both homophones and homographs.
36 Spelling Skills Spelling

Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’.
37 What do you like to do? Expressing likes and dislikes

Objective: Present phrases used to express likes and dislikes.
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 Commas 2 Commas 2

Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech.
41 Colons and Semi-Colons Colons and Semi-Colons

Objective: To use colons and semi-colons correctly.
42 Homonyms – Homophones and Homographs Homonyms – Homophones and Homographs

Objective: To identify and use correctly homonyms, both homophones and homographs.
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Australian National Curriculum Year 4 Literacy

# TOPIC TITLE
1 Advanced Dictionary Use Advanced Dictionary Use

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
2 Plurals of Foreign Nouns Plurals 5 – Foreign

Objective: To form plurals of foreign nouns.
3 Amazing Aussie animals Giving facts and opinions

Objective: Present phrases that ask for and give opinions.
4 Thanks and goodbye Talking about feelings

Objective: Present constructions for talking about feelings.
5 Pronouns Pronouns

Objective: To show a pronoun is used in place of a noun.
6 Pronouns Pronouns 2

Objective: To recognise and use personal, possessive and relative pronouns.
7 Parts of Speech Part b Conjunctions

Objective: To identify and use conjunctions correctly.
8 Phrases Phrases

Objective: To identify and use phrases including adjectival and adverbial phrases.
9 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
10 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
11 BBQ Party! Sequence markers

Objective: Learn the words used in sequences or ordering.
12 Punctuation Skills Part b Quotation Marks

Objective: To use quotation marks for direct speech.
13 Parts of Speech Part a Prepositions

Objective: To identify and use prepositions correctly.
14 Adverbs Adverbs

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
15 Phrases Phrases

Objective: To identify and use phrases including adjectival and adverbial phrases.
16 Adjectives Adjectives

Objective: To show an adjective is a word that describes a noun.
17 A new home Prepositions of location

Objective: Learn about prepositions of location.
18 Here we are! Adjectives

Objective: Learn the use of adjectives.
19 Punctuation Skills Part b Quotation Marks

Objective: To use quotation marks for direct speech.
20 Parts of Speech Part a Prepositions

Objective: To identify and use prepositions correctly.
21 Adverbs Adverbs

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
22 Phrases Phrases

Objective: To identify and use phrases including adjectival and adverbial phrases.
23 A new home Prepositions of location

Objective: Learn about prepositions of location.
24 Plurals of Foreign Nouns Plurals 5 – Foreign

Objective: To form plurals of foreign nouns.
25 Advanced Dictionary Use Advanced Dictionary Use

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
26 Vowels Vowels – Long and Short

Objective: To identify long and short vowel sounds, and their use.
27 Homonyms – Homophones and Homographs Homonyms – Homophones and Homographs

Objective: To identify and use correctly homonyms, both homophones and homographs.
28 Common Errors Common Errors in spelling and punctuation

Objective: To identify and eliminate common errors.
29 Adjectives Adjectives

Objective: To show an adjective is a word that describes a noun.
30 Adverbs Adverbs

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
31 Adjectives Adjectives – from Nouns and Verbs

Objective: To create adjectives from nouns and verbs. E.g. China – Chinese
32 Adjectives Adjectives – Comparatives and Superlatives

Objective: To identify and use comparative and superlative adjectives.
33 Here we are! Comparatives and superlatives

Objective: Learn how to use comparatives and superlatives in English.
34 Setting off Questions

Objective: Learn the correct structure for forming yes/no questions. Learn the correct structure for forming wh questions.
35 Here we are! Asking for repetition

Objective: Learn how to ask someone to repeat something in English.
36 A new home Offers and requests

Objective: Present the phrases used to make offers and requests.
37 Amazing Aussie animals Giving facts and opinions

Objective: Present phrases that ask for and give opinions.
38 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’.
39 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 …’.
40 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.
41 It couldn’t be mine! The Riding Lesson

Objective: Students will build vocabulary, answer comprehension questions and practise using possessive pronouns and adjectives.
42 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’.
43 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’.
44 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’.
45 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.
46 What’s the problem? What’s the matter?

Objective: Students will read and comprehend a passage in which words are used to describe feelings.
47 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’.
48 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’.
49 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.
50 Space and Time We’ve done our research.

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.
51 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.
52 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.
53 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.
54 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.
55 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.
56 Class Camp Dear Parents, …

Objective: Students will develop their comprehension skills by reading a letter which uses a variety of verb tenses.
57 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.
58 Commas 2 Commas 2

Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech.
59 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
60 Vocabulary Development Vocabulary

Objective: To identify and use better words than ‘got’ and ‘said’.
61 Parts of Speech Part a Prepositions

Objective: To identify and use prepositions correctly.
62 Adverbs Adverbs

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
63 Phrases Phrases

Objective: To identify and use phrases including adjectival and adverbial phrases.
64 Adjectives Adjectives

Objective: To show an adjective is a word that describes a noun.
65 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
66 Spelling Skills Word Usage

Objective: To correctly choose words with similar spelling, sound and meaning.
67 Colons and Semi-Colons Colons and Semi-Colons

Objective: To use colons and semi-colons correctly.
68 Capitalisation Capital Letters 1

Objective: To use capital letters correctly: to begin sentences, for proper nouns.
69 Punctuation Sentence Endings

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
70 Capitalisation Capital Letters 2

Objective: To use capital letters correctly: in titles and letters.
71 Punctuation Commas 1

Objective: To use commas: to list, to make meaning clear, and when writing the date.
72 Common Errors Common Errors in spelling and punctuation

Objective: To identify and eliminate common errors.
73 Common Errors Common Errors in writing

Objective: To identify and eliminate common errors.
74 Common Errors Common Errors in verb usage, spelling and punctuation

Objective: To identify and eliminate common errors.
75 Spelling Skills Word Usage

Objective: To correctly choose words with similar spelling, sound and meaning.
76 Vocabulary Development Vocabulary

Objective: To identify and use better words than ‘got’ and ‘said’.
77 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
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Australian National Curriculum Year 5 Literacy

# TOPIC TITLE
1 Advanced Dictionary Use Advanced Dictionary Use

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
2 Nouns Proper Nouns

Objective: To show a proper noun is used to name a person, place or a title.
3 Apostrophe – Possession Apostrophe – Possession

Objective: To use the apostrophe of possession correctly.
4 Clauses Clauses

Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
5 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
6 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
7 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.
8 Adjectives Adjectives

Objective: To show an adjective is a word that describes a noun.
9 Phrases Phrases

Objective: To identify and use phrases including adjectival and adverbial phrases.
10 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
11 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
12 Thanks and goodbye Adjectives

Objective: Learn the use of adjectives.
13 Prefixes Prefixes

Objective: The identify and use prefixes.
14 Suffixes Suffixes

Objective: The identify and use suffixes.
15 Advanced Dictionary Use Advanced Dictionary Use

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
16 Plurals Plurals 3 – Unusual

Objective: To create unusual plurals: for words ending in ‘o’; by changing the vowels or by adding letters.
17 Plurals Plurals 4 – Unusual

Objective: To use nouns whose singular and plural forms are the same. To use compound noun plurals.
18 Plurals of Foreign Nouns Plurals 5 – Foreign

Objective: To form plurals of foreign nouns.
19 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
20 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
21 Figurative Language Onomatopoeia, Assonance and Alliteration

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
22 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
23 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
24 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
25 Figurative Language Onomatopoeia, Assonance and Alliteration

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
26 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
27 Verbs – Active and Passive voice Verbs – Active and Passive voice

Objective: To identify and use active and passive voice.
28 There’s a … It’s famous!

Objective: Students will increase their vocabulary, develop their reading skills and practise using the verb ‘to be’.
29 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 …’.
30 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.
31 Hobbies and Festivals My favourite festival

Objective: Students will build vocabulary; begin to use conjunctions ‘and’, ‘but’ or ‘because’.
32 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’.
33 What can you do? Have you got everything?

Objective: Students will read and comprehend a written text using ‘have’, ‘haven’t got’, ‘but’ or ‘and’.
34 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.
35 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’.
36 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.
37 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.
38 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’.
39 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.
40 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.
41 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.
42 To Australia and Back! Getting There!

Objective: Students will develop their comprehension skills by reading a text about travel plans. They will also learn about coordinate conjunctions.
43 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.
44 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.
45 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.
46 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.
47 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.
48 Mnemonics Spelling – Mnemonics

Objective: To identify and use mnemonics to assist in correct spelling.
49 Essay Writing 2 Essay Writing 2

Objective: To develop and write essays.
50 Capitalisation Capital Letters 1

Objective: To use capital letters correctly: to begin sentences, for proper nouns.
51 Punctuation Sentence Endings

Objective: To use full-stops, question marks, exclamation marks and capital letters correctly.
52 Capitalisation Capital Letters 2

Objective: To use capital letters correctly: in titles and letters.
53 Punctuation Commas 1

Objective: To use commas: to list, to make meaning clear, and when writing the date.
54 Common Errors Common Errors in spelling and punctuation

Objective: To identify and eliminate common errors.
55 Common Errors Common Errors in writing

Objective: To identify and eliminate common errors.
56 Common Errors Common Errors in verb usage, spelling and punctuation

Objective: To identify and eliminate common errors.
57 Spelling Skills Word Usage

Objective: To correctly choose words with similar spelling, sound and meaning.
58 Vocabulary Development Vocabulary

Objective: To identify and use better words than ‘got’ and ‘said’.
59 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
60 Commas 2 Commas 2

Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech.
61 Parts of Speech Part b Conjunctions

Objective: To identify and use conjunctions correctly.
62 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
63 Verbs – Active and Passive voice Verbs – Active and Passive voice

Objective: To identify and use active and passive voice.
64 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
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Australian National Curriculum Year 6 Literacy

# TOPIC TITLE
1 Pronouns Pronouns

Objective: To show a pronoun is used in place of a noun.
2 Pronouns Pronouns 2

Objective: To recognise and use personal, possessive and relative pronouns.
3 Punctuation Commas 1

Objective: To use commas: to list, to make meaning clear, and when writing the date.
4 Commas 2 Commas 2

Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech.
5 Clauses Clauses

Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
6 Mass and Count Nouns Determiners

Objective: To identify and use determiners correctly with mass and count nouns.
7 Verbs Verbs – Tense

Objective: To identify and use the correct tense of verbs: past, present and future.
8 Verb tense – Compound Verb tense – Compound

Objective: To identify and use ‘to be’ and ‘to have’ with the appropriate participle of the main verb.
9 Spelling Skills Spelling

Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’.
10 Advanced Dictionary Use Advanced Dictionary Use

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
11 Prefixes Prefixes

Objective: The identify and use prefixes.
12 Suffixes Suffixes

Objective: The identify and use suffixes.
13 Mnemonics Spelling – Mnemonics

Objective: To identify and use mnemonics to assist in correct spelling.
14 Spelling Skills Syllabification

Objective: To improve spelling by dividing words correctly into syllables.
15 Adjectives Adjectives

Objective: To show an adjective is a word that describes a noun.
16 Adverbs Adverbs

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
17 Modal Verbs Modal Verbs

Objective: To identify and use modal verbs with the appropriate form of the main verb.
18 Verbs – Active and Passive voice Verbs – Active and Passive voice

Objective: To identify and use active and passive voice.
19 Gerunds Gerunds

Objective: To identify and use gerunds.
20 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
21 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.
22 Verbs – Active and Passive voice Verbs – Active and Passive voice

Objective: To identify and use active and passive voice.
23 Mnemonics Spelling – Mnemonics

Objective: To identify and use mnemonics to assist in correct spelling.
24 Essay Writing 2 Essay Writing 2

Objective: To develop and write essays.
25 Adjectives Adjectives

Objective: To show an adjective is a word that describes a noun.
26 Adverbs Adverbs

Objective: To identify and use adverbs. To understand an adverb tells something about (modifies) a verb.
27 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
28 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
29 Figurative Language Onomatopoeia, Assonance and Alliteration

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
30 Spelling Skills Word Usage

Objective: To correctly choose words with similar spelling, sound and meaning.
31 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
32 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.
33 Have you met? The world in a classroom!

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.
34 Modal Verbs Modal Verbs

Objective: To identify and use modal verbs with the appropriate form of the main verb.
35 Transitive and Intransitive Verbs Transitive and Intransitive Verbs

Objective: To identify and use transitive and intransitive verbs.
36 Case – Nouns and Pronouns Case – Nouns, Pronouns and Possessive Adjectives

Objective: To identify the case of nouns and pronouns.
37 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.
38 Verbs Verbs – Tense

Objective: To identify and use the correct tense of verbs: past, present and future.
39 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
40 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
41 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
42 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
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Australian National Curriculum Year 7 Literacy

# TOPIC TITLE
1 Mnemonics Spelling – Mnemonics

Objective: To identify and use mnemonics to assist in correct spelling.
2 Essay Writing 2 Essay Writing 2

Objective: To develop and write essays.
3 Phrases Phrases

Objective: To identify and use phrases including adjectival and adverbial phrases.
4 Clauses Clauses

Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
5 Parts of Speech Part a Prepositions

Objective: To identify and use prepositions correctly.
6 Parts of Speech Part b Conjunctions

Objective: To identify and use conjunctions correctly.
7 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
8 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
9 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
10 Commas 2 Commas 2

Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech.
11 Punctuation Skills Part b Quotation Marks

Objective: To use quotation marks for direct speech.
12 Colons and Semi-Colons Colons and Semi-Colons

Objective: To use colons and semi-colons correctly.
13 Apostrophe – Possession Apostrophe – Possession

Objective: To use the apostrophe of possession correctly.
14 Punctuation Punctuation – Various

Objective: To use hyphens, dashes, apostrophes, quotation marks, parentheses and brackets correctly.
15 Interjections Interjections

Objective: To identify and use interjections correctly.
16 Clauses Clauses

Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
17 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.
18 Modal Verbs Modal Verbs

Objective: To identify and use modal verbs with the appropriate form of the main verb.
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 Big day out! First and second conditionals

Objective: Learn the use of first conditionals. Learn the use of second conditionals.
22 Let’s hit the beach! Modals of obligation

Objective: Learn about modals of obligation.
23 Let’s hit the beach! Imperatives

Objective: Learn how to use imperatives.
24 Spelling Skills Spelling

Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’.
25 Prefixes Prefixes

Objective: The identify and use prefixes.
26 Suffixes Suffixes

Objective: The identify and use suffixes.
27 Advanced Dictionary Use Advanced Dictionary Use

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
28 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
29 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
30 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
31 Verbs Verbs – Tense

Objective: To identify and use the correct tense of verbs: past, present and future.
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Australian National Curriculum Year 8 Literacy

# TOPIC TITLE
1 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
2 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
3 Transitive and Intransitive Verbs Transitive and Intransitive Verbs

Objective: To identify and use transitive and intransitive verbs.
4 Case – Nouns and Pronouns Case – Nouns, Pronouns and Possessive Adjectives

Objective: To identify the case of nouns and pronouns.
5 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
6 Punctuation Punctuation – Various

Objective: To use hyphens, dashes, apostrophes, quotation marks, parentheses and brackets correctly.
7 Colons and Semi-Colons Colons and Semi-Colons

Objective: To use colons and semi-colons correctly.
8 Punctuation Punctuation – Various

Objective: To use hyphens, dashes, apostrophes, quotation marks, parentheses and brackets correctly.
9 Commas 2 Commas 2

Objective: To use commas: to separate places, to separate clauses within sentences, and when using direct speech.
10 Punctuation Skills Part b Quotation Marks

Objective: To use quotation marks for direct speech.
11 Phrases Phrases

Objective: To identify and use phrases including adjectival and adverbial phrases.
12 Clauses Clauses

Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
13 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
14 Transitive and Intransitive Verbs Transitive and Intransitive Verbs

Objective: To identify and use transitive and intransitive verbs.
15 Case – Nouns and Pronouns Case – Nouns, Pronouns and Possessive Adjectives

Objective: To identify the case of nouns and pronouns.
16 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
17 Verbs – Active and Passive voice Verbs – Active and Passive voice

Objective: To identify and use active and passive voice.
18 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
19 Advanced Dictionary Use Advanced Dictionary Use

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
20 Plurals Plurals 1 – simple

Objective: To form plurals (more than one) by adding ‘s’ and ‘es’ correctly.
21 Plurals Plurals 2 – special rules

Objective: To form plurals with special rules: words ending in ‘y’ and ‘f’.
22 Plurals Plurals 3 – Unusual

Objective: To create unusual plurals: for words ending in ‘o’; by changing the vowels or by adding letters.
23 Plurals Plurals 4 – Unusual

Objective: To use nouns whose singular and plural forms are the same. To use compound noun plurals.
24 Plurals of Foreign Nouns Plurals 5 – Foreign

Objective: To form plurals of foreign nouns.
25 Spelling Skills Spelling

Objective: To correctly spell words after adding suffixes: ‘ing’, ‘ed’, ‘er’, ‘est’.
26 Prefixes Prefixes

Objective: The identify and use prefixes.
27 Suffixes Suffixes

Objective: The identify and use suffixes.
28 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
29 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
30 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
31 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
32 Figurative Language Onomatopoeia, Assonance and Alliteration

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
33 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
34 Advanced Dictionary Use Advanced Dictionary Use

Objective: To use dictionaries by identifying all the information provided. To use a thesaurus.
35 Antonyms and Synonyms Antonyms and Synonyms

Objective: To identify and use antonyms and synonyms.
36 Essay Writing 2 Essay Writing 2

Objective: To develop and write essays.
37 Verbs Verbs – Tense

Objective: To identify and use the correct tense of verbs: past, present and future.
38 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
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Australian National Curriculum Year 9 Literacy

# TOPIC TITLE
1 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
2 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
3 Figurative Language Onomatopoeia, Assonance and Alliteration

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
4 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
5 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
6 Big day out! First and second conditionals

Objective: Learn the use of first conditionals. Learn the use of second conditionals.
7 BBQ Party! Sequence markers

Objective: Learn the words used in sequences or ordering.
8 Mass and Count Nouns Determiners

Objective: To identify and use determiners correctly with mass and count nouns.
9 Let’s hit the beach! Modals of obligation

Objective: Learn about modals of obligation.
10 Let’s hit the beach! Imperatives

Objective: Learn how to use imperatives.
11 Colons and Semi-Colons Colons and Semi-Colons

Objective: To use colons and semi-colons correctly.
12 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
13 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
14 Clauses Clauses

Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
15 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
16 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
17 Figurative Language Onomatopoeia, Assonance and Alliteration

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
18 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
19 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
20 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
21 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
22 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
23 Figurative Language Onomatopoeia, Assonance and Alliteration

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
24 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
25 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
26 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
27 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
28 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
29 Essay Writing 2 Essay Writing 2

Objective: To develop and write essays.
30 Verbs Verbs – Tense

Objective: To identify and use the correct tense of verbs: past, present and future.
31 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
32 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
33 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
34 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
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Australian National Curriculum Year 10 Literacy

# TOPIC TITLE
1 Pronouns Pronouns 2

Objective: To recognise and use personal, possessive and relative pronouns.
2 Essay Writing 2 Essay Writing 2

Objective: To develop and write essays.
3 Verbs – Active and Passive voice Verbs – Active and Passive voice

Objective: To identify and use active and passive voice.
4 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
5 Clauses Clauses

Objective: To identify and use clauses including adjectival, adverbial and noun clauses.
6 Nouns Collective and Abstract Nouns

Objective: To identify and use collective and abstract nouns.
7 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
8 Similes and Metaphors Similes and Metaphors

Objective: To identify and use similes and metaphors.
9 Figurative Language Symbolism and Personification

Objective: To identify, and make use of, symbolism and personification.
10 Figurative Language Onomatopoeia, Assonance and Alliteration

Objective: To identify, and make use of, onomatopoeia, assonance, and alliteration.
11 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
12 Essay Writing 2 Essay Writing 2

Objective: To develop and write essays.
13 Essay Writing 2 Essay Writing 2

Objective: To develop and write essays.
14 Verbs Verbs – Tense

Objective: To identify and use the correct tense of verbs: past, present and future.
15 Conjunctions – Sentences Conjunctions – Sentences

Objective: To use conjunctions to increase the variety of sentence structure in written expression.
16 Sentence Improvement Sentence Improvement

Objective: To construct expressive sentences by using adjectives, adverbs, phrases and clauses.
17 Variety of Expression Sentence Construction

Objective: To construct expressive and precise sentences to improve meaning.
18 Review of Figures of Speech Review of Figures of Speech

Objective: To identify multiple uses of figures of speech within writing.
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