yoursimply

THE SIMPLY ONLINE PROGRAMME

Designed to be built around each child’s specific strengths and weaknesses.

Simply Online is available in maths, English and reading for children between the ages of 4 and 18 years old, based on their current strengths and weaknesses.

Simply Online mathematics and English programmes have been fully aligned to the English National Curriculum.

Simply Online covers work required by students in Key Stage 1, Key Stage 2, Key Stage 3 and Key Stage 4. Whatever level your children are working at, you can rest assured that Simply Online will complement and work hand-in-hand with their current schoolwork.

Additionally, there is a range of GCSE revision courses for each of the major Examination Boards (AQA, Edexcel OCR and WJEC), depending on what your student is studying.

For those schools that offer the International Baccalaureate or Cambridge International Examinations curricula, these are also available within Simply Online as part of its standard curriculum library.

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

Find out what each stage of Simply Online covers

Simply Online Mathematics

KS1 – Maths – Reception Mathematics

# 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
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.
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.
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.
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.
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.
7 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.
8 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.
9 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.


KS1 – Maths – Year 1 Mathematics

# TOPIC TITLE
1 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.
2 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.
3 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.
4 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.
5 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.
6 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.
7 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.
8 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.
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.
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.
11 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.
12 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.
13 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.
14 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.
15 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.
16 Weight/mass Introducing the concept of mass
Objective: On completion of the lesson the student will understand the concepts of mass.
17 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.
18 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.
19 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.
20 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.
21 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.
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.


KS1 – Maths – Year 2 Mathematics

# TOPIC TITLE
1 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.
2 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.
3 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.
4 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.
5 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.
6 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.
7 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.
8 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.
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.
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.
11 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.
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.
13 Calculation-grouping Multiplication using equal groups
Objective: On completion of the lesson the student will be able to write about equal groups and rows and will understand how to count them.
14 Calculation-grouping Multiplication using repeated addition
Objective: On completion of the lesson the student will be able to write about equal groups and rows using another method and also learn different ways to count them.
15 Calculation-multiplication The multiplication sign
Objective: on completion of the lesson the student will be able to multiply single numbers to solve multiplication problems.
16 Calculation-multiples Multiples of 10 up to 100
Objective: On completion of the lesson the student will be able to read, write, rename and add multiples of ten.
17 Multiplication Multiplication – important facts.
Objective: On completion of the lesson the student will know the connection between multiplication and division and recognise the strategies to help solve multiplication number sentences.
18 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.
19 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.
20 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.
21 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.
22 Length Compare length by using informal units of measurement
Objective: On completion of the lesson the student will be able to measure objects around the student’s home and compare their length to each other. The student will also be able to compare the different ways the student measured the same object.
23 Length Using the metre as a formal unit to measure perimeter
Objective: On completion of the lesson the student will be able to calculate the perimeter of different shapes in metres.
24 Length Using the formal unit of the centimetre to measure length and perimeter
Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.
25 Weight/mass Introducing the concept of mass
Objective: On completion of the lesson the student will understand the concepts of mass.
26 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.
27 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.
28 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.
29 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.
30 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.
31 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.
32 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’.
33 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.
34 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.
35 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.
36 Data Pictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
37 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.


KS2 – Maths – Year 3 Mathematics

# 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.
2 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.
3 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.
4 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.
5 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
6 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.
7 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.
8 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.
9 Multiplication Multiplication using extended algorithms.
Objective: On completion of the lesson the student will have understood multiplication using extended algorithms.
10 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.
11 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.
12 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.
13 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.
14 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.
15 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.
16 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.
17 Fractions Adding and subtracting fractions with the same denominator
Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator.
18 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.
19 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.
20 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.
21 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.
22 Weight/mass Introducing the concept of mass
Objective: On completion of the lesson the student will understand the concepts of mass.
23 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.
24 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.
25 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.
26 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.
27 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.
28 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.
29 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.
30 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’.
31 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.
32 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.
33 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.
34 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.
35 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.
36 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.
37 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.
38 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.
39 Data Pictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
40 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.


KS2 – Maths – Year 4 Mathematics

# 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.
2 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.
3 Counting and numeration The numbers 10 000 to 99 999
Objective: On completion of the lesson the student will be able to count to 99 999 and use place value to read the value of the numerals within the larger numbers.
4 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.
5 Addition Addition up to the number 999
Objective: On completion of the lesson the student will be able to use place value to solve and record addition problems with three digit numbers.
6 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.
7 Subtraction Subtraction with borrowing
Objective: On completion of the lesson the student will be able to record subtraction number sentences and will understand the need to trade between place value columns using the renaming method
8 Subtraction Subtraction up to the number 999 using the renaming method
Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers.
9 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.
10 Multiplication Multiplication using extended algorithms.
Objective: On completion of the lesson the student will have understood multiplication using extended algorithms.
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.
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.
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.
14 Division Division with and without a remainder.
Objective: On completion of the lesson the student will understand division with and without a Remainder.
15 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.
16 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.
17 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.
18 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.
19 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.
20 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.
21 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.
22 Decimals Introduction to decimals
Objective: On completion of the lesson the student will be able to represent decimals to two decimal places.
23 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.
24 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.
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.
26 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.
27 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.
28 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.
29 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.
30 Weight/mass Introducing the concept of mass
Objective: On completion of the lesson the student will understand the concepts of mass.
31 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.
32 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.
33 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.
34 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.
35 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.
36 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.
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.
38 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.
39 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.
40 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.
41 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.
42 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.
43 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.
44 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.
45 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.
46 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.
47 Geometry-quadrilaterals Quadrilaterals
Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.
48 Geometry-quadrilaterals Classifying Quadrilaterals
Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals.
49 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.
50 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.
51 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.
52 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.
53 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.
54 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.
55 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.
56 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.
57 Data Pictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
58 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
59 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.


KS2 – Maths – Year 5 Mathematics

# 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.
2 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.
3 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.
4 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.
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.
6 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.
7 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.
8 Multiplication Multiplying 4-digit numbers by 4-digit number
Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication.
9 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.
10 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.
11 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.
12 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.
13 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.
14 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.
15 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
16 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.
17 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.
18 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.
19 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.
20 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.
21 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.
22 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.
23 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.
24 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.
25 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.
26 Money Problems involving money
Objective: On completion of the lesson the student will be able to solve problems with money.
27 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.
28 Fractions mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to: name and recognise mixed numbers (mixed numerals), count by halves and quarters, and use a number line to represent halves and quarters beyond one.
29 Fractions Improper fractions
Objective: 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.
30 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.
31 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.
32 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.
33 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.
34 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.
35 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
36 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.
37 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.
38 Decimals Introduction to decimals
Objective: On completion of the lesson the student will be able to represent decimals to two decimal places.
39 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.
40 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.
41 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)
42 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)
43 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.
44 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.
45 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.
46 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.
47 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.
48 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.
49 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.
50 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.
51 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.
52 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.
53 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.
54 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.
55 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
56 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.
57 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.
58 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.
59 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.
60 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.
61 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.
62 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.
63 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.
64 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.
65 Length Problems with length.
Objective: On completion of the lesson the student will be able to solve problems with length.
66 Mass Problems with mass.
Objective: On completion of the lesson the student will be able to solve problems with mass.
67 Area Problems with area.
Objective: On completion of the lesson the student will be able to solve problems with area.
68 Volume/capacity Problems with volume/capacity.
Objective: Problem Solving: problems involving volume/capacity
69 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.
70 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.
71 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.
72 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.
73 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.
74 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.
75 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.
76 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.
77 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.
78 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.
79 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.
80 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.
81 Geometry-quadrilaterals Classifying Quadrilaterals
Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals.
82 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.
83 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.
84 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.
85 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.
86 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.
87 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.
88 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.
89 Data Pictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
90 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
91 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.


KS2 – Maths – Year 6 Mathematics

# 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.
2 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.
3 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.
4 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.
5 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.
6 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.
7 Multiplication Multiplying 4-digit numbers by 4-digit number
Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication.
8 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.
9 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.
10 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.
11 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.
12 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
13 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.
14 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.
15 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.
16 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.
17 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.
18 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.
19 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.
20 Money Problems involving money
Objective: On completion of the lesson the student will be able to solve problems with money.
21 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.
22 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.
23 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.
24 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.
25 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.
26 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.
27 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.
28 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
29 Fractions Adding and subtracting fractions with the same denominator
Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator.
30 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.
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.
32 Fractions Fractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
33 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.
34 Fractions Dividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
35 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.
36 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.
37 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.
38 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.
39 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.
40 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.
41 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.
42 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.
43 Decimals Multiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
44 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.
45 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
46 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.
47 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.
48 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.
49 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.
50 Length Problems with length.
Objective: On completion of the lesson the student will be able to solve problems with length.
51 Mass Problems with mass.
Objective: On completion of the lesson the student will be able to solve problems with mass.
52 Area Problems with area.
Objective: On completion of the lesson the student will be able to solve problems with area.
53 Volume/capacity Problems with volume/capacity.
Objective: Problem Solving: problems involving volume/capacity
54 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.
55 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.
56 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.
57 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.
58 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.
59 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.
60 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.
61 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.
62 Geometry-quadrilaterals Classifying Quadrilaterals
Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals.
63 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.
64 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.
65 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.
66 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.
67 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.
68 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.
69 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.
70 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.
71 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.
72 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.
73 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.
74 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.
75 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.
76 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.
77 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.
78 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.
79 Trig complementary angles Complementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
80 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
81 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.
82 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.


KS3 – Maths – Year 7 Mathematics

# TOPIC TITLE
1 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.
2 Subtraction Subtraction involving four digit numbers and beyond using the renaming method.
Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers.
3 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.
4 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.
5 Multiplication Multiplying 4-digit numbers by 4-digit number
Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication.
6 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
7 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.
8 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.
9 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.
10 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.
11 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.
12 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.
13 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)
14 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)
15 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.
16 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.
17 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.
18 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.
19 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.
20 Decimals Multiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
21 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.
22 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.
23 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.
24 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.
25 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.
26 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.
27 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.
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.
29 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.
30 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.
31 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.
32 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.
33 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.
34 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
35 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.
36 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.
37 Fractions Multiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
38 Fractions Fractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
39 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
40 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.
41 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.
42 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.
43 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.
44 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.
45 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.
46 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.
47 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.
48 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.
49 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.
50 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.
51 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.
52 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.
53 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.
54 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.
55 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
56 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.
57 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.
58 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
59 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.
60 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.
61 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.
62 Geometry-angles Measuring angles
Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.
63 Geometry-angles Adjacent angles
Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.
64 Geometry-angles Complementary and supplementary angles
Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.
65 Geometry-angles Vertically opposite angles
Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.
66 Geometry-angles Angles at a Point.
Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.
67 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
68 Geometry-problems Additional questions involving parallel lines
Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.
69 Geometry-triangles Angle sum of a triangle
Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.
70 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.
71 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.
72 Geometry-quadrilaterals Classifying Quadrilaterals
Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals.
73 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.
74 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.
75 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.
76 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.
77 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.
78 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.
79 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
80 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.
81 Transformations Special transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
82 Translations Transformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.
83 Geometric transformations Geometry transformations without matrices: reflection (Stage 2)
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.
84 Geometric transformations Geometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.
85 Geometric transformations Geometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.
86 Geometric transformations Geometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.
87 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.
88 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.
89 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.
90 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.
91 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.
92 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.
93 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.
94 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.
95 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.
96 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.
97 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.
98 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.
99 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.
100 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.
101 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.
102 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.
103 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.
104 Algebraic expressions Expanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
105 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.
106 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.
107 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.
108 Algebraic equations Solving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
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.
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.
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.
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
113 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
114 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
115 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
116 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.
117 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
118 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
119 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.


KS3 – Maths – Year 8 Mathematics

# TOPIC TITLE
1 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.
2 Subtraction Subtraction involving four digit numbers and beyond using the renaming method.
Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers.
3 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.
4 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.
5 Multiplication Multiplying 4-digit numbers by 4-digit number
Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication.
6 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
7 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.
8 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.
9 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.
10 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.
11 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.
12 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.
13 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.
14 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.
15 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.
16 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.
17 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.
18 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
19 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.
20 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.
21 Fractions Multiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
22 Fractions Fractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
23 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.
24 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.
25 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).
26 Fractions Dividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
27 Fractions Dividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
28 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
29 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.
30 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.
31 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.
32 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.
33 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.
34 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.
35 Decimals Multiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
36 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.
37 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.
38 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.
39 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.
40 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.
41 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.
42 Area Comparing and ordering areas.
Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area.
43 Area 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.
44 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.
45 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.
46 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.
47 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
48 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.
49 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.
50 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.
51 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.
52 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.
53 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.
54 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.
55 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.
56 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.
57 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.
58 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.
59 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
60 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.
61 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.
62 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.
63 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.
64 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
65 Geometry-polygons Angles of regular polygons
Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees.
66 Trig complementary angles Complementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
67 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.
68 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.
69 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
70 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.
71 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.
72 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.
73 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.
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.
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.
76 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.
77 Transformations Special transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
78 Translations Transformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.
79 Geometric transformations Geometry transformations without matrices: reflection (Stage 2)
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.
80 Geometric transformations Geometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.
81 Geometric transformations Geometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.
82 Geometric transformations Geometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.
83 Geometric transformations The definition and concept of combined transformations resulting in an equivalent single transformation.
Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations.
84 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.
85 Number theory – equations Transformations that produce equivalent equations
Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations.
86 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.
87 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.
88 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.
89 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.
90 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.
91 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.
92 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.
93 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.
94 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.
95 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.
96 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.
97 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.
98 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.
99 Algebraic expressions Expanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
100 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.
101 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.
102 Algebraic equations Solving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
103 Algebraic equations Solving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
104 Algebraic equations Equations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
105 Algebraic equations Equations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
106 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.
107 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.
108 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.
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.
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.
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.
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
113 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.
114 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.
115 Statistics Stem and Leaf Plots along with Box and Whisker Plots
Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.
116 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
117 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
118 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.
119 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
120 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.
121 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
122 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
123 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.
124 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.


KS3 – Maths – Year 9 Mathematics

# TOPIC TITLE
1 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.
2 Money Problems involving money
Objective: On completion of the lesson the student will be able to solve problems with money.
3 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.
4 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.
5 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.
6 Fractions Multiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
7 Fractions Fractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
8 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.
9 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.
10 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).
11 Fractions Dividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
12 Fractions Dividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
13 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.
14 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.
15 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.
16 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.
17 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.
18 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.
19 Decimals Multiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
20 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.
21 Decimals Dividing decimal fractions by whole numbers
Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers.
22 Decimals Dividing numbers by a decimal fraction
Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction.
23 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
24 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.
25 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.
26 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.
27 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.
28 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.
29 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.
30 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.
31 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.
32 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.
33 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.
34 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.
35 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.
36 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.
37 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.
38 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.
39 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.
40 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.
41 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.
42 Fractional indices/exponents Fractional indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.
43 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.
44 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.
45 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.
46 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.
47 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.
48 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.
49 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.
50 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.
51 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
52 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.
53 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.
54 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
55 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.
56 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.
57 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.
58 Length Problems with length.
Objective: On completion of the lesson the student will be able to solve problems with length.
59 Mass Problems with mass.
Objective: On completion of the lesson the student will be able to solve problems with mass.
60 Area Problems with area.
Objective: On completion of the lesson the student will be able to solve problems with area.
61 Volume/capacity Problems with volume/capacity.
Objective: Problem Solving: problems involving volume/capacity
62 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.
63 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.
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.
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.
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.
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.
68 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
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.
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.
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.
72 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.
73 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
74 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.
75 Trig complementary angles Complementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
76 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.
77 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.
78 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.
79 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.
80 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.
81 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.
82 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.
83 Pythagoras Pythagorean triples
Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple.
84 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.
85 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.
86 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
87 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.
88 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.
89 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.
90 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.
91 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.
92 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.
93 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.
94 Transformations Special transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
95 Translations Transformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.
96 Geometric transformations Geometry transformations without matrices: reflection (Stage 2)
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.
97 Geometric transformations Geometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.
98 Geometric transformations Geometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.
99 Geometric transformations Geometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.
100 Geometric transformations The definition and concept of combined transformations resulting in an equivalent single transformation.
Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations.
101 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
102 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.
103 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.
104 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.
105 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.
106 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.
107 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.
108 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.
109 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.
110 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.
111 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.
112 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.
113 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.
114 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.
115 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.
116 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.
117 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.
118 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.
119 Algebraic expressions Expanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
120 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.
121 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.
122 Algebraic equations Solving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
123 Algebraic equations Solving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
124 Algebraic equations Equations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
125 Algebraic equations Equations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
126 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.
127 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.
128 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.
129 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.
130 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.
131 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.
132 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.
133 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.
134 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.
135 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.
136 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.
137 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.
138 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.
139 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.
140 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.
141 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
142 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.
143 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.
144 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
145 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.
146 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
147 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
148 Statistics Frequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
149 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
150 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.
151 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
152 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.
153 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
154 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
155 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.
156 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
157 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.
158 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.


KS4 – Maths – Foundation Mathematics

# TOPIC TITLE
1 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.
2 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.
3 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.
4 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.
5 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.
6 Multiplication Multiplying 4-digit numbers by 4-digit number
Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication.
7 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.
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
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.
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.
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.
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.
13 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.
14 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.
15 Number theory – equations Transformations that produce equivalent equations
Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations.
16 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.
17 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.
18 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)
19 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)
20 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.
21 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.
22 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.
23 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.
24 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.
25 Decimals Multiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
26 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.
27 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.
28 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.
29 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.
30 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.
31 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.
32 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.
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.
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.
35 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.
36 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
37 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.
38 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.
39 Fractions Multiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
40 Fractions Fractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
41 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.
42 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.
43 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).
44 Fractions Dividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
45 Fractions Dividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
46 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.
47 Money Problems involving money
Objective: On completion of the lesson the student will be able to solve problems with money.
48 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.
49 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.
50 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.
51 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.
52 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.
53 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.
54 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.
55 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.
56 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
57 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.
58 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.
59 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.
60 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.
61 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.
62 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.
63 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.
64 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.
65 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.
66 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.
67 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.
68 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.
69 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.
70 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.
71 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.
72 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.
73 Capacity Converting between volume and capacity using millilitres and litres
Objective: On completion of the lesson the student will be able to convert between units of capacity.
74 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.
75 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.
76 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.
77 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.
78 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.
79 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.
80 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.
81 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.
82 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.
83 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.
84 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.
85 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
86 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.
87 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.
88 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
89 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.
90 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.
91 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.
92 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.
93 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.
94 Length Problems with length.
Objective: On completion of the lesson the student will be able to solve problems with length.
95 Mass Problems with mass.
Objective: On completion of the lesson the student will be able to solve problems with mass.
96 Area Problems with area.
Objective: On completion of the lesson the student will be able to solve problems with area.
97 Volume/capacity Problems with volume/capacity.
Objective: Problem Solving: problems involving volume/capacity
98 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.
99 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.
100 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.
101 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.
102 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.
103 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.
104 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.
105 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.
106 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.
107 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.
108 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.
109 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.
110 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
111 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.
112 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.
113 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.
114 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.
115 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
116 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.
117 Trig complementary angles Complementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
118 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.
119 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
120 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.
121 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.
122 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.
123 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.
124 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.
125 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.
126 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.
127 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.
128 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.
129 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.
130 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.
131 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.
132 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.
133 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.
134 Transformations Special transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
135 Translations Transformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.
136 Geometric transformations Geometry transformations without matrices: reflection (Stage 2)
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.
137 Geometric transformations Geometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.
138 Geometric transformations Geometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.
139 Geometric transformations Geometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.
140 Geometric transformations The definition and concept of combined transformations resulting in an equivalent single transformation.
Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations.
141 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.
142 Pythagoras Pythagorean triples
Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple.
143 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.
144 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.
145 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.
146 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.
147 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.
148 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.
149 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.
150 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.
151 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.
152 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.
153 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.
154 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.
155 Algebraic expressions Expanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
156 Algebraic fractions Simplifying algebraic fractions using the index laws.
Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.
157 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.
158 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.
159 Algebraic equations Solving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
160 Algebraic equations Solving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
161 Algebraic equations Equations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
162 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.
163 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.
164 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.
165 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.
166 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.
167 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.
168 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.
169 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.
170 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.
171 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.
172 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.
173 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.
174 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.
175 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
176 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.
177 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.
178 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
179 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
180 Data Pictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
181 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.
182 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
183 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.
184 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.
185 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
186 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
187 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.
188 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
189 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.
190 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.


KS4 – Maths – Higher Mathematics

# TOPIC TITLE
1 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.
2 Multiplication Multiplying 4-digit numbers by 4-digit number
Objective: On completion of the lesson the student will be able to be able to multiply any 4 digit number by any other 4 digit number using long multiplication.
3 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.
4 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
5 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.
6 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.
7 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.
8 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.
9 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.
10 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.
11 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.
12 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.
13 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.
14 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.
15 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.
16 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.
17 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.
18 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.
19 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.
20 Decimals Multiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
21 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.
22 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.
23 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.
24 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.
25 Fractions Multiplying fractions by whole numbers
Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers.
26 Fractions Fractions of whole numbers
Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection.
27 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.
28 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.
29 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).
30 Fractions Dividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
31 Fractions Dividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
32 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.
33 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.
34 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.
35 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.
36 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.
37 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.
38 Fractional indices/exponents Fractional indices
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.
39 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.
40 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
41 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.
42 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.
43 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.
44 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.
45 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.
46 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.
47 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.
48 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.
49 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.
50 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.
51 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.
52 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.
53 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.
54 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
55 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.
56 Surds Expanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
57 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.
58 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.
59 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.
60 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.
61 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.
62 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.
63 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.
64 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.
65 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.
66 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.
67 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.
68 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.
69 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.
70 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.
71 Surface area Surface area of pyramids
Objective: On completion of the lesson the student will be able to find the surface areas of pyramids.
72 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
73 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.
74 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.
75 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
76 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.
77 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.
78 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.
79 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.
80 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.
81 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.
82 Length Problems with length.
Objective: On completion of the lesson the student will be able to solve problems with length.
83 Mass Problems with mass.
Objective: On completion of the lesson the student will be able to solve problems with mass.
84 Area Problems with area.
Objective: On completion of the lesson the student will be able to solve problems with area.
85 Volume/capacity Problems with volume/capacity.
Objective: Problem Solving: problems involving volume/capacity
86 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.
87 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.
88 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.
89 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.
90 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.
91 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.
92 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.
93 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.
94 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.
95 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.
96 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
97 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.
98 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.
99 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.
100 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.
101 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
102 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.
103 Trig complementary angles Complementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
104 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.
105 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
106 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’
107 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.
108 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.
109 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.
110 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.’
111 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.
112 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.
113 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.
114 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.
115 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.
116 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.
117 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
118 Circle Geometry-cyclic quads Theorem – If the opposite angles in a quadrilateral are supplementary then the quadrilateral is cyclic.
Objective: On completion of the lesson the student will be able to prove that a quadrilateral is cyclic using the supplementary angles theorem.
119 Circle Geometry-subtending Theorem – If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic.
Objective: On completion of the lesson the student will be able to prove that ‘ If an interval subtends equal angles at two points on the same side of it, then the end points of the interval and the two points are concyclic’, and use this result to complete the ques
120 Circle Geometry Theorem – When circles touch, the line of the centres passes through the point of contact.
Objective: On completion of the lesson the student will be able to prove that ‘ When two circles touch, the line of the centres passes through the point of contact’, and use this result to complete questions that require it.
121 Circle Geometry-non-collinear Theorem – Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points.
Objective: On completion of the lesson the student will be able to prove that ‘ Any three non-collinear points lie on a unique circle whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining these points’, and use this knowled
122 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
123 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.
124 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.
125 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.
126 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.
127 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.
128 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.
129 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.
130 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.
131 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.
132 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.
133 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.
134 Transformations Special transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
135 Translations Transformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.
136 Geometric transformations Geometry transformations without matrices: reflection (Stage 2)
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.
137 Geometric transformations Geometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.
138 Geometric transformations Geometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.
139 Geometric transformations Geometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.
140 Geometric transformations The definition and concept of combined transformations resulting in an equivalent single transformation.
Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations.
141 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.
142 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.
143 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.
144 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.
145 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.
146 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.
147 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.
148 Pythagoras Pythagorean triples
Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple.
149 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.
150 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.
151 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.
152 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.
153 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.
154 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.
155 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
156 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.
157 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.
158 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.
159 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.
160 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.
161 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.
162 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.
163 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.
164 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.
165 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.
166 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.
167 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.
168 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.
169 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.
170 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.
171 Trig-reciprocal ratios Reciprocal ratios.
Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios.
172 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.
173 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.
174 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.
175 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.
176 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.
177 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.
178 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.
179 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.
180 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.
181 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.
182 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.
183 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.
184 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.
185 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.
186 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.
187 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.
188 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.
189 Algebraic expressions Expanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
190 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.
191 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.
192 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.
193 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.
194 Algebraic expressions-larger expansions Algebraic Expressions – Larger expansions.
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.
195 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.
196 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.
197 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.
198 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.
199 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.
200 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.
201 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.
202 Algebraic equations Solving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
203 Algebraic equations Solving equations containing binomial expressions
Objective: On completion of the lesson the student will be able to move terms in binomial equations.
204 Algebraic equations Equations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
205 Algebraic equations Equations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
206 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.
207 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.
208 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.
209 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.
210 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.
211 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.
212 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.
213 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.
214 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.
215 Factorising quads Factorisation of non-monic quadratic trinomials
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
216 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.
217 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.
218 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.
219 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.
220 Algebra-factorising Simplifying easy algebraic fractions.
Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising.
221 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.
222 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.
223 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.
224 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.
225 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.
226 Quadratic equations Introduction to quadratic equations.
Objective: On completion of the lesson the student will understand simple quadratic equations.
227 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.
228 Quadratic equations Solving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
229 Quadratic equations The quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
230 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.
231 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..
232 Vectors Vectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.
233 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.
234 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.
235 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.
236 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
237 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.
238 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.
239 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.
240 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.
241 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
242 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.
243 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
244 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.
245 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
246 Statistics Frequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
247 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
248 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.
249 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
250 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
251 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.
252 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
253 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.
254 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.


KS5 – Maths – Core Mathematics

# 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.
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.
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.
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.
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.
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.
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.
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.
9 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.
10 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.
11 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.
12 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
13 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.
14 Surds Expanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
15 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.
16 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.
17 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.
18 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.
19 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.
20 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.
21 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.
22 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.
23 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.
24 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.
25 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.
26 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.
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.
28 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.
29 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.
30 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.
31 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.
32 Factorising quads Factorisation of non-monic quadratic trinomials
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
33 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.
34 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.
35 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.
36 Quadratic equations Solving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
37 Quadratic equations Completing the square
Objective: On completion of the lesson the student will understand the process of completing the square.
38 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.
39 Quadratic equations The quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
40 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.
41 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..
42 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.
43 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.
44 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.
45 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.
46 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.
47 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.
48 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.
49 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.
50 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.
51 Algebra-polynomials Polynomials and long division.
Objective: On completion of the lesson the student will understand the long division process with polynomials.
52 Polynomial equations Polynomial equations
Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms.
53 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.
54 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.
55 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.
56 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.
57 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.
58 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.
59 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
60 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.
61 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.
62 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.
63 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.
64 Logic Inductive and deductive reasoning
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.
65 Logic Definition and use of counter examples
Objective: On completion of this lesson the student will be able to create counter examples to statements.
66 Logic Indirect proofs
Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved.
67 Logic Mathematical induction
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.
68 Logic Conditional statements (converse, inverse and contrapositive) (Stage 2)
Objective: On completion of the lesson the student will be able to form related conditional statements.
69 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.
70 Transformations Special transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
71 Translations Transformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.
72 Geometric transformations The definition and concept of combined transformations resulting in an equivalent single transformation.
Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations.
73 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.
74 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.
75 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.
76 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.
77 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.
78 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.
79 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.
80 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.
81 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.
82 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.
83 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.
84 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.
85 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.
86 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.
87 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.
88 Co-ordinate Geometry-Theorems Angles between two lines
Objective: On completion of the lesson the student will be able to calculate the angle between given lines and derive the equation of a line given its angle to another line.
89 Co-ordinate Geometry-Theorems Internal and external division of an interval
Objective: On completion of the lesson the student will be able to divide an interval according to a given ratio and to calculate what point divides an interval in a given ratio for both internal and external divisions.
90 Geometry – triangles Triangle inequality theorem
Objective: On completion of the lesson the student will understand and use the triangle inequality theorem.
91 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.
92 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.
93 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.
94 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.
95 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.
96 Graphing binomials Binomial products [non-monic].
Objective: On completion of the lesson, the student will have examined more complex examples with binomial products.
97 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.
98 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.
99 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.
100 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.
101 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.
102 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.
103 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.
104 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.
105 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.
106 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.
107 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.
108 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.
109 Calculus Limits
Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.
110 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.
111 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.
112 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.
113 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.
114 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.
115 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.
116 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
117 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.
118 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.
119 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.
120 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.
121 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.
122 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.
123 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).
124 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.
125 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.
126 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.
127 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.
128 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.
129 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.
130 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.
131 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.
132 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.
133 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.
134 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
135 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.
136 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.
137 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.
138 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.
139 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.
140 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.
141 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.
142 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.
143 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.
144 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.
145 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.
146 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.
147 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.
148 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.
149 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.
150 Trig-reciprocal ratios Reciprocal ratios.
Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios.
151 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.
152 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.
153 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.
154 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.
155 Trig equations Solving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.
156 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.
157 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.
158 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.
159 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.
160 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.
161 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.
162 Trigonometry Double angle formulas (Stage 2)
Objective: On completion of the lesson the student will derive and use the double angle trig identities.
163 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.
164 Trigonometry t Formulas (Stage 2)
Objective: On completion of the lesson the student will solve trig equations using the t substitution.
165 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.
166 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
167 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.
168 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.
169 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.
170 Logarithms-Log laws Laws of logarithms.
Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.
171 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.
172 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.
173 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.
174 Logarithms-Equations and logs Equations involving logarithms.
Objective: On completion of the lesson the student will be able to solve equations with log terms.
175 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.
176 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.
177 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.
178 Logarithms-Log curves Working with log curves.
Objective: On completion of the lesson the student will be able to solve problems with log curves
179 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.
180 Functions Notation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
181 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.
182 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.
183 Functions Evaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
184 Functions Functions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
185 Functions Composition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
186 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.
187 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.
188 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.
189 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.
190 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.
191 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.
192 Vectors Vectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.
193 Uniform motion Average speed
Objective: On completion of the lesson the student will be able to convert units for speed, distance and time.
194 Uniform motion Using subscripted variables
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, distance and time.
195 Uniform motion Uniform motion with equal distances
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, equal distances and time.
196 Uniform motion Uniform motion adding the distances
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, adding distances for total distance and time.
197 Uniform motion Uniform motion with unequal distances
Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, unequal distances and time.
198 Uniform motion Uniform motion of all types
Objective: On completion of the lesson the student will use all types of subscripted variables for calculations to determine speed, distance and time.
199 Motion under acceleration Motion under gravity – objects in vertical motion
Objective: On completion of the lesson the student will convert rates and use equations of motion that include uniform acceleration.
200 Motion under acceleration Introducing initial velocity
Objective: On completion of the lesson the student will use equations of motion that include uniform acceleration and an initial velocity.
201 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.
202 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.
203 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.
204 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.
205 Logarithms-Complex numbers Absolute value
Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers
206 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.
207 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.
208 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.
209 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.
210 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.
211 Matrices Basic concepts – Matrices
Objective: On completion of the lesson the student will have had an introduction to matrices
212 Matrices Addition and subtraction of matrices
Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations.
213 Matrices Scalar matrix multiplication
Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix.
214 Matrices Multiplication of one matrix by another matrix
Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication.
215 Matrices Translation in the number plane
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.
216 Matrices Translation by matrix multiplication
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane.
217 Simultaneous equations Number of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.
218 Vectors 2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.
219 Linear systems Optimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.
220 Linear systems Linear systems with matrices (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.
221 Linear systems Row-echelon form (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.
222 Linear systems Gauss Jordan elimination method (Stage 2)
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.
223 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.
224 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.
225 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.
226 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.
227 Conic sections Circles
Objective: On completion of the lesson the student will identify the radius of a circle given in standard form.
228 Conic sections Ellipses
Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse.
229 Conic sections Hyperbola
Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola.


KS5 – Maths – Statistics Mathematics

# TOPIC TITLE
1 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
2 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.
3 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
4 Statistics Frequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
5 Statistics The range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
6 Statistic-probability The mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
7 Statistic-probability The mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
8 Statistic-probability The median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
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.
10 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.
11 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.
12 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.
13 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.
14 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
15 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.
16 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.
17 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
18 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
19 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.
20 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
21 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.
22 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.
23 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.
24 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.
25 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
26 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.
27 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.


EdExcel-GCSE Revision Foundation Mathematics

# TOPIC TITLE
1 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.
2 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.
3 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.
4 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.
5 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.
6 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.
7 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.
8 Decimals Multiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
9 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.
10 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.
11 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.
12 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.
13 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.
14 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.
15 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.
16 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.
17 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.
18 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.
19 Fractions Dividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
20 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.
21 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.
22 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.
23 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
24 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.
25 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.
26 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.
27 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.
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.
29 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.
30 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.
31 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.
32 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.
33 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.
34 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.
35 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.
36 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.
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.
38 Geometry-angles Adjacent angles
Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.
39 Geometry-angles Complementary and supplementary angles
Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.
40 Geometry-angles Vertically opposite angles
Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.
41 Geometry-angles Angles at a Point.
Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.
42 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
43 Geometry-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.
44 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.
45 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
46 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.
47 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.
48 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.
49 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.
50 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.
51 Transformations Special transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
52 Translations Transformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.
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.
54 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.
55 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.
56 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.
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.
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.
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.
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.
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.
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.
63 Algebraic expressions Expanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
64 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.
65 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.
66 Algebraic equations Solving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
67 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.
68 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.
69 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.
70 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.
71 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.
72 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.
73 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
74 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.
75 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.
76 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
77 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
78 Data Pictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
79 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.
80 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
81 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.
82 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.
83 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.



EdExcel-GCSE Revision Higher Mathematics

# TOPIC TITLE
1 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.
2 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.
3 Fractions Dividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
4 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.
5 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.
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.
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.
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.
9 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
10 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.
11 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.
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.
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.
14 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.
15 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.
16 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.
17 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.
18 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.
19 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.
20 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.
21 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.
22 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.
23 Surds Expanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
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.
25 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.
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.
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.
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.
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.
30 Surface area Surface area of pyramids
Objective: On completion of the lesson the student will be able to find the surface areas of pyramids.
31 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
32 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.
33 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.
34 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.
35 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.
36 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.
37 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
38 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.
39 Trig complementary angles Complementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
40 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.
41 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.
42 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.
43 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.’
44 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.
45 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.
46 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.
47 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.
48 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
49 Geometry-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.
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.
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.
52 Geometric transformations Geometry transformations without matrices: reflection (Stage 2)
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.
53 Geometric transformations Geometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.
54 Geometric transformations Geometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.
55 Geometric transformations Geometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.
56 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.
57 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.
58 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.
59 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.
60 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.
61 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.
62 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.
63 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.
64 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.
65 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.
66 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.
67 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.
68 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.
69 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.
70 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.
71 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.
72 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.
73 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.
74 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.
75 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.
76 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.
77 Algebraic expressions-larger expansions Algebraic Expressions – Larger expansions.
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.
78 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.
79 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.
80 Algebraic equations Equations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
81 Algebraic equations Equations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
82 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.
83 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.
84 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.
85 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.
86 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.
87 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.
88 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.
89 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.
90 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.
91 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.
92 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.
93 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.
94 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.
95 Quadratic equations Solving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
96 Quadratic equations The quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
97 Vectors Vectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.
98 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.
99 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.
100 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
101 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.
102 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
103 Statistics Frequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
104 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.
105 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
106 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.
107 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.


AQA-GCSE Revision Foundation Mathematics

# TOPIC TITLE
1 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.
2 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.
3 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.
4 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.
5 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.
6 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.
7 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.
8 Decimals Multiplying decimals by whole numbers
Objective: On completion of the lesson the student will be able to multiply decimals by whole numbers.
9 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.
10 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.
11 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.
12 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.
13 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.
14 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.
15 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.
16 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.
17 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.
18 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.
19 Fractions Dividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.
20 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.
21 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.
22 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.
23 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
24 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.
25 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.
26 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.
27 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.
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.
29 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.
30 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.
31 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.
32 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.
33 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.
34 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.
35 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.
36 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.
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.
38 Geometry-angles Adjacent angles
Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.
39 Geometry-angles Complementary and supplementary angles
Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.
40 Geometry-angles Vertically opposite angles
Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.
41 Geometry-angles Angles at a Point.
Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.
42 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
43 Geometry-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.
44 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.
45 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
46 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.
47 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.
48 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.
49 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.
50 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.
51 Transformations Special transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.
52 Translations Transformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.
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.
54 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.
55 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.
56 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.
57 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.
58 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.
59 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.
60 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.
61 Algebraic expressions Expanding and simplifying algebraic expressions
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.
62 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.
63 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.
64 Algebraic equations Solving two step equations
Objective: On completion of the lesson the student will be able to solve two step equations.
65 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.
66 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.
67 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.
68 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.
69 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.
70 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.
71 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
72 Data Bar Charts
Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs.
73 Data Line graphs.
Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs.
74 Data Pictograms
Objective: On completion of the lesson the student will be able to organise, read and summarise information in picture graphs.
75 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.
76 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
77 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.
78 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.
79 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.


AQA-GCSE Revision Higher Mathematics

# TOPIC TITLE
1 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.
2 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.
3 Fractions Dividing mixed numbers (mixed numerals)
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).
4 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.
5 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.
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.
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.
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.
9 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentages
10 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.
11 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.
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.
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.
14 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.
15 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.
16 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.
17 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.
18 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.
19 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.
20 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.
21 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.
22 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.
23 Surds Expanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.
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.
25 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.
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.
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.
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.
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.
30 Surface area Surface area of pyramids
Objective: On completion of the lesson the student will be able to find the surface areas of pyramids.
31 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
32 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.
33 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.
34 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.
35 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.
36 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.
37 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
38 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.
39 Trig complementary angles Complementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
40 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.
41 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.
42 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.
43 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.’
44 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.
45 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.
46 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.
47 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.
48 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
49 Geometry-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.
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.
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.
52 Geometric transformations Geometry transformations without matrices: reflection (Stage 2)
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.
53 Geometric transformations Geometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.
54 Geometric transformations Geometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.
55 Geometric transformations Geometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.
56 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.
57 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.
58 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.
59 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.
60 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.
61 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.
62 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.
63 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.
64 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.
65 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.
66 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.
67 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.
68 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.
69 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.
70 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.
71 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.
72 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.
73 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.
74 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.
75 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.
76 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.
77 Algebraic expressions-larger expansions Algebraic Expressions – Larger expansions.
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.
78 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.
79 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.
80 Algebraic equations Equations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols
81 Algebraic equations Equations involving fractions.
Objective: On completion of the lesson the student will know how to solve equations using fractions.
82 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.
83 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.
84 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.
85 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.
86 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.
87 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.
88 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.
89 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.
90 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.
91 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.
92 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.
93 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.
94 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.
95 Quadratic equations Solving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
96 Quadratic equations Completing the square
Objective: On completion of the lesson the student will understand the process of completing the square.
97 Quadratic equations The quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
98 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.
99 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.
100 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
101 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.
102 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
103 Statistics Frequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
104 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.
105 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
106 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.
107 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.


OCR-GCSE Revision Foundation Mathematics

# TOPIC TITLE
1 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
2 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
3 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
4 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
5 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
6 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
7 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
8 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
9 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.See the sample lesson in action here
10 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
11 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
12 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
13 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
14 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
15 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
16 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
17 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
18 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
19 Fractions Dividing fractions
Objective: On completion of the lesson the student will be able to divide fractions.See the sample lesson in action here
20 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
21 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
22 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
23 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentagesSee the sample lesson in action here
24 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
25 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
26 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
27 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
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.See the sample lesson in action here
29 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
30 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
31 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
32 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
33 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.See the sample lesson in action here
34 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
35 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
36 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
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-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
44 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
45 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
46 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.See the sample lesson in action here
47 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.See the sample lesson in action here
48 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
49 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.See the sample lesson in action here
50 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
51 Transformations Special transformations – reflections, rotations and enlargements.
Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable.See the sample lesson in action here
52 Translations Transformations – reflections
Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection.See the sample lesson in action here
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.See the sample lesson in action here
54 Sequences and Series General sequences.
Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.See the sample lesson in action here
55 Sequences and Series Finding Tn given Sn.
Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.See the sample lesson in action here
56 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
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 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
64 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
65 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
66 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
67 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.See the sample lesson in action here
68 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
69 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
70 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
71 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
72 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
73 Statistic-probability The median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scoresSee the sample lesson in action here
74 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
75 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
76 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
77 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
78 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.See the sample lesson in action here
79 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
80 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
81 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


OCR-GCSE Revision Higher Mathematics

# TOPIC TITLE
1 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
2 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
3 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
4 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
5 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
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.See the sample lesson in action here
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.See the sample lesson in action here
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.See the sample lesson in action here
9 Percentages Calculating Percentages and Fractions of Quantities
Objective: To find percentages and fractions of quantities and solve problems with percentagesSee the sample lesson in action here
10 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
11 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
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 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
15 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
16 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
17 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
18 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
19 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
20 Surds Introducing surds
Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.See the sample lesson in action here
21 Surds Some rules for the operations with surds
Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds.See the sample lesson in action here
22 Surds Simplifying surds
Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication.See the sample lesson in action here
23 Surds Expanding surds
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.See the sample lesson in action here
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.See the sample lesson in action here
25 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
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.See the sample lesson in action here
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.See the sample lesson in action here
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 Surface area Surface area of pyramids
Objective: On completion of the lesson the student will be able to find the surface areas of pyramids.See the sample lesson in action here
31 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 perpendiculSee the sample lesson in action here
32 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
33 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
34 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.See the sample lesson in action here
35 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.See the sample lesson in action here
36 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
37 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 logSee the sample lesson in action here
38 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.See the sample lesson in action here
39 Trig complementary angles Complementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.See the sample lesson in action here
40 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
41 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.See the sample lesson in action here
42 Circle Geometry Theorem – Angles in the same segment of a circle are equal.
Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.See the sample lesson in action here
43 Circle Geometry Theorem – The angle of a semi-circle is a right angle.
Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’See the sample lesson in action here
44 Circle Geometry Theorem – The opposite angles of a cyclic quadrilateral are supplementary.
Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.See the sample lesson in action here
45 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.See the sample lesson in action here
46 Circle Geometry Theorem – Tangents to a circle from an external point are equal.
Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.See the sample lesson in action here
47 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.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-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.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.See the sample lesson in action here
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.See the sample lesson in action here
52 Geometric transformations Geometry transformations without matrices: reflection (Stage 2)
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.See the sample lesson in action here
53 Geometric transformations Geometry transformations without matrices: translation (Stage 2)
Objective: On completion of this lesson the student will perform translations in a number plane.See the sample lesson in action here
54 Geometric transformations Geometry transformations without matrices: rotation (Stage 2)
Objective: On completion of this lesson the student will perform and construct rotations.See the sample lesson in action here
55 Geometric transformations Geometry transformations without matrices: dilation or enlargement (Stage 2)
Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor.See the sample lesson in action here
56 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
57 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
58 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
59 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
60 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
61 Graph sine Graphing the trigonometric ratios – I Sine curve.
Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period.See the sample lesson in action here
62 Graph cosine Graphing the trigonometric ratios – II Cosine curve.
Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period.See the sample lesson in action here
63 Graphs tan curve Graphing the trigonometric ratios – III Tangent curve.
Objective: On completion of the lesson the student will know how to recognise and draw the tan curve.See the sample lesson in action here
64 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
65 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
66 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
67 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
68 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
69 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
70 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
71 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
72 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
73 Trigonometry-areas The area formula
Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle.See the sample lesson in action here
74 Sequences and Series General sequences.
Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.See the sample lesson in action here
75 Sequences and Series Finding Tn given Sn.
Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.See the sample lesson in action here
76 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.See the sample lesson in action here
77 Algebraic expressions-larger expansions Algebraic Expressions – Larger expansions.
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.See the sample lesson in action here
78 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.See the sample lesson in action here
79 Functions and graphs Quadratic polynomials of the form y = ax. + bx + c.
Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.See the sample lesson in action here
80 Algebraic equations Equations involving grouping symbols.
Objective: On completion of the lesson the student will be able to solve equations using grouping symbolsSee the sample lesson in action here
81 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
82 Simultaneous equns Elimination method
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method.See the sample lesson in action here
83 Simultaneous equns Elimination method part 2
Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method.See the sample lesson in action here
84 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.See the sample lesson in action here
85 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.See the sample lesson in action here
86 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.See the sample lesson in action here
87 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.See the sample lesson in action here
88 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.See the sample lesson in action here
89 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
90 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.See the sample lesson in action here
91 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.See the sample lesson in action here
92 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
93 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.See the sample lesson in action here
94 Quadratic equations Quadratic equations with factorisation.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.See the sample lesson in action here
95 Quadratic equations Solving quadratic equations.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.See the sample lesson in action here
96 Quadratic equations Completing the square
Objective: On completion of the lesson the student will understand the process of completing the square.See the sample lesson in action here
97 Quadratic equations The quadratic formula
Objective: On completion of the lesson the student will be familiar with the quadratic formula.See the sample lesson in action here
98 Statistic-probability Calculating the median from a frequency distribution
Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon.See the sample lesson in action here
99 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
100 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.See the sample lesson in action here
101 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
102 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.See the sample lesson in action here
103 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
104 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
105 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.See the sample lesson in action here
106 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
107 Statistic-probability Tree diagrams – depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.See the sample lesson in action here


 

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Example 4 – Private tutors have always been a popular choice for parents. The cost for a private tutor varies quite considerably but, depending where you live, on average tutors can cost between £20-£30 per hour, per subject, per child. So with this example, a family with 2 school age children, requiring help with both maths & English subjects, would be spending a minimum of £320 per month or £73.84 per week. This amounts to £3,840 per year, every year, to provide a tutor for their children for 1 hour per week, per subject. Once again, This family could of course choose to only use a tutor for one of their children or only pay for only 1 subject, which would reduce the cost.

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Example 3Centre based tuition. In this example, a family, with 2 school age children, could choose an alternative centre based tuition option where their children attend for between 60-90 mins per week, which currently costs approx. £45.00 per month, per child, per subject. This family would therefore be spending approx. £180 per month or £41.53 per week. This amounts to £2,160 per year, every year, to provide this form of tuition for their children. They could of course choose to only send one of their children to the centre or only pay for only 1 subject, which would reduce the cost.

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Example 2Simply Online. The average size UK family, with two or more children, currently spends £2900.00 on their Simply Online programme, making it £60.42 a month or £13.94 per week. So when you consider that on this basis, the example 2 programme would belong to the family and can be used by multiple children at no extra cost and as often as they need to use it. This would provide the children with a solid foundation, in both maths and English subjects, that would support their learning right throughout their schooling. This represents exceptional value for money compared to all other tuition alternatives for the equivalent level of support.

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Example 1Simply Online. Subject to their particular circumstances, a family ‘could’ purchase a basic Simply Online programme outright from as little as £1790.00. This would cover the equivalent of a key stage but would be dependant on a number of factors. To make the programme as affordable as possible to everyone, and because it is a long term learning course design to supplement and support school, it is possible to spread these payments over time, making it £8.36 per week.

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Full Topic List for Grammar

Adjectives
Advanced Dictionary Use
Adverbs
Antonyms and Synonyms
Apostrophe – Possession
Auxiliary Verbs
Basic Dictionary Use
Capitalisation
Case – Nouns and Pronouns
Clauses
Colons and Semi-Colons
Commas 2
Common Errors
Common Nouns
Conjunctions – Sentences
Contractions
English Grammar – Level 1
English Grammar – Level 2
English Grammar – Level 3
English Grammar – Level 4
English Grammar – Level 5
Essay Writing 1
Essay Writing 2
Figurative Language
Gerunds
Homonyms – Homophones and Homographs
Interjections
Letter Writing
Mass and Count Nouns
Mnemonics
Modal Verbs
Nouns
Participles – as Verbs and Adjectives
Parts of Speech Part a
Parts of Speech Part b
Parts of Speech Part h
Phrases
Plurals
Plurals of Foreign Nouns
Prefixes
Pronouns
Punctuation
Punctuation Skills Part b
Regular and Irregular Verbs
Review of Figures of Speech
Sentence Improvement
Sentence Structure Part a
Sentences
Similes and Metaphors
Simple and Compound Verbs
Spelling
Spelling Skills
Subject-Verb Agreement
Suffixes
Transitive and Intransitive Verbs
Variety of Expression
Verb tense – Compound
Verbs
Verbs – Active and Passive voice
Verbs – Infinitives
Vocabulary Development
Vowels
Vowels and Consonants

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