Maths Workout · 2016. 8. 11. · aimed at Maths lessons covering NQF Levels 1 and 2. Maths Workout is versatile and simple to use. Teachers can teach a skill using Maths Workout

Maths Workout

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Introduction

Maths Workout is a set of maths exercises that can be used for starters, main lessons and plenaries. It is aimed at Maths lessons covering NQF Levels 1 and 2.

Maths Workout is versatile and simple to use. Teachers can teach a skill using Maths Workout to demonstrate it on an interactive whiteboard, then students can practise the skills individually on exactly the same exercises, but with new questions regenerated at the same level of differentiation.

Topics, Targets & Tasks The content is split into Topics, Targets and Tasks…

A Topic is a broad area of maths, broken down into between 1 and 5 targets. Topics are accessed

directly at www.mathsworkout.co.uk after logging in.

A Target is a specific attainment outcome, which should be achievable in one sitting. Targets are

accessed through the tabs at the top of the screen.

A Task is an individual exercise which forms part of a target. Each task is accessed through the slider bar at the bottom of each screen.

Topics can be tackled in any order. The time required to complete a topic will vary between about 20 minutes and 2 hours, depending on the topic and the ability of the student. Students can revisit each topic any number of times without repetition as the ‘Next Go’ button or ‘Reset’ button randomly generates new questions at the same level of differentiation.

Targets in each topic usually become progressively more challenging. Completion of a target is indicated by a sound and by a ‘Target Complete’ trophy. Students may attempt the tasks in any order, however it is better to attempt the tasks in numerical order, as where they naturally vary in difficulty, they have been carefully differentiated to ensure continuity of

learning. Completion of a task is indicated by a sound and the task number turning green with a tick showing above it. Some tasks can be attempted mentally, however students are advised to work with a pencil and paper where necessary, then enter their answers on screen. Where possible, it is better to use speakers or headphones to use this product, as it will be much more engaging.

These are the approximate levels for the various frameworks supported by our Maths and Numeracy product range. Each product has multiple uses and none of our products is guaranteed to cover all the content of any

course, specification, level or framework.

Framework Numeracy Warm Up

Numeracy Workout

Maths Workout

Key Stages 1 2 3 - 4

GCSE Grades - 3 - 1 9 - 2

Numeracy Certificate Entry Entry & Level 1 Level 2

Functional Skills Entry Entry & Level 1 Level 2

Scotland National 1 National 3 - 1 National 5 - 3

Age Range All Ages All Ages All Ages

All products are available to view as samples at: www.numeracywarmup.co.uk www.numeracyworkout.co.uk www.mathsworkout.co.uk

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Maths Workout


Number Tasks

Topics Target 1 Target 2 Target 3 Target 4 Target 5 Total

1 Arithmetic 8 8 10 8 4 38

2 Money 8 6 5 10 10 39

3 Time 6 4 9 10 4 33

4 Place Value 8 3 10 10 3 34

5 Decimals 10 8 4 6 6 34

6 Integers 3 5 10 12 8 38

7 Factors 4 7 3 5 2 21

8 Primes 6 7 4 17

9 Multiples 11 11 11 10 11 54

10 Powers 8 3 5 5 8 29

11 Order of Operations 7 4 4 15

12 Rounding & Estimation 2 12 12 12 5 43

13 Number Machines 9 10 10 9 10 48

14 Number Problems & Puzzles 10 10 6 2 2 30

15 Language Tasks & Quizzes 1 10 5 5 10 1 31

16 Using a Calculator 4 4 5 3 3 19

17 Fractions 1 10 9 8 8 6 41

18 Fractions 2 8 8 10 10 15 51

19 Percentages 1 14 6 10 6 10 46

20 Percentages 2 8 8 10 8 13 47

21 Ratio 11 5 10 8 3 37

22 Proportion 1 7 8 3 12 11 41

23 Indices 1 6 8 8 6 5 33

24 Surds 1 10 10 12 12 10 54

25 Surds 2 10 10 8 7 10 45

26 Standard Form 11 6 4 7 6 34


Total Number of Tasks 983

Maths Workout


Geometry & Measures Tasks

Topic Target 1 Target 2 Target 3 Target 4 Target 5 Total

1 Measurement 1 6 6 9 8 10 39

2 Measurement 2 3 12 10 7 12 44

3 Line Symmetry 11 11 11 10 11 54

4 Rotational Symmetry 7 6 6 6 25

5 Plane Symmetry 3 4 7 14

6 Shapes 5 6 2 13

7 Solids 5 10 7 8 7 37

8 Angles 11 7 9 10 37

9 Angles in a Polygon 6 7 5 18

10 Perimeter 6 6 12

11 Area 4 10 6 7 10 37

12 Capacity & Volume 14 4 10 3 10 41

13 Volume 5 4 3 5 17

14 Surface Area 4 4 2 5 15


16 Scale Drawings 4 6 7 7 6 30

17 Loci 4 4 4 12

18 Speed, Distance & Time 12 7 8 10 8 45

19 Transformations 1 6 11 9 12 14 52

20 Transformations 2 14 9 12 12 12 59

21 Similarity 9 9 14 7 7 46

22 Pythagoras 8 7 7 11 9 42

23 Trigonometry 1 6 12 12 12 6 48

24 Trigonometry 2 10 8 9 9 10 46

25 Circle Geometry 6 7 10 12 12 47



Maths Workout


Statistics & Probability Tasks


1 Tables & Diagrams 1 12 12 9 12 11 56

2 Tables & Diagrams 2 13 12 12 9 10 56

3 Mean, Median, Mode & Range 7 6 10 8 12 43

4 Pictograms 5 5 5 7 22

5 Bar Charts 10 5 7 7 5 34

6 Line Graphs 8 10 10 4 8 40

7 Scatter Graphs 3 3 2 8

8 Pie Charts 4 7 10 10 7 38

9 Stem & Leaf Diagrams 7 3 10

10 Introduction to Probability 7 12 7 11 7 44

11 Probability Lab 1 2 1 5 12 21


13 Data Handling Theory 8 8 7 10 3 36

14 Frequency Tables 10 5 8 5 10 38

15 Frequency Charts & Polygons 3 6 6 6 6 27

16 Histograms 5 12 8 10 12 47

17 Measures of Spread 1 8 6 10 10 10 44

18 Measures of Spread 2 12 10 8 10 8 48

19 Probability 1 10 7 10 6 7 40

20 Probability 2 10 12 7 7 12 48



Maths Workout


Algebra & Problem Solving Tasks


1 Writing Algebra 1 7 6 5 7 10 35

2 Writing Algebra 2 10 8 9 10 8 45

3 Like Terms 9 12 9 8 12 50

4 Expanding Brackets 10 10 10 7 10 47

5 Factorising 10 10 10 6 8 44

6 Solving Equations 1 11 7 6 4 8 36

7 Algebraic Modelling 5 4 5 3 7 24

8 Substitution 5 4 5 3 17

9 Formulae 7 5 5 5 7 29

10 Problem Solving Theory 1 1 1 1 4

11 Spotting Patterns 7 10 12 5 12 46

12 Problems & Puzzles 1 10 10 9 12 8 49


14 Sequences 1 4 6 10 6 6 32

15 Sequences 2 6 7 5 3 5 26

16 Solving Equations 2 10 8 11 12 8 49

17 Straight Lines 1 7 7 5 6 11 36

18 Straight Lines 2 7 3 4 4 5 23

19 Simultaneous Equations 10 8 8 11 11 48

20 Changing the Subject of a Formula 8 7 7 5 5 32

21 Quadratics 1 7 7 5 5 7 31

22 Quadratics 2 7 9 8 8 4 36

23 Indices 2 4 6 8 6 7 31

24 Algebraic Fractions 5 7 6 7 25

25 Inequalities 8 5 7 2 22

26 Proportion 2 4 5 4 4 17

27 Problems & Puzzles 2 10 11 9 9 8 47



Total Number of Tasks Currently in Maths Workout 3640

Maths Workout - Number


Number Topics

Topic Target 1 Target 2 Target 3 Target 4 Target 5

1 Arithmetic

Quick response task: simple

addition

Add two 3 or 4 digit whole

numbers

Puzzle: magic squares


subtraction and addition

Subtract two 3 or 4 digit

whole numbers

Puzzle: number triangles


multiplication

Recall multiplication facts up

to 13 x 13

Multiply up to a 4-digit by a

3-digit whole number


division

Recall division facts up to

169/13 = 13

Short and long division, no

remainder

Quick response task: mixed

questions on whole numbers

Mixed questions in context

2 Money

Find the total of a set of

coins

Solve problems with coin

totals

Identify a missing coin from

a total

Identify the coins required to

make a total

Calculate the change from a

given bill

Calculate a simple bill and

the change

Solve shopping problems

3 Time Convert between minutes

and seconds

Convert between hours,

minutes and seconds

Convert between fractional

hours, minutes and seconds

Calculate duration, start and

finish times: 12h clock

Calculate duration, start and

finish times: 12h and 24h

clock

4 Place Value

Convert numbers in words to

digits

Convert numbers in digits to words

Identify the place value of

digits in whole numbers and

decimals

Sort whole numbers up to

10000 and numbers with up

to 3 decimal places

Multiply and divide whole

and decimal numbers by 10,

100 and 1000

Solve problems using place

value: guess the number in

as few clues as possible

5 Decimals

Add and subtract numbers with up to 3 decimal places

Multiply a whole number by a number with up to 2

decimal places

Multiply a whole number by a number with up to 3

decimal places

Multiply numbers with up to 3 decimal places

Divide a number with up to 3 decimal places by a whole

number and by a number

with up to 2 decimal places;

exact answers

6 Integers

Sort positive and negative

temperatures on

thermometers


numbers with and without

context

Calculate original

temperature, final

temperature and change in

temperature

Add & subtract negative

numbers

Puzzles: magic squares and

number triangles

Use four rules with negative

numbers, positive and

negative decimals

Quick response task:

negative numbers

7 Factors List the factors of a number

by identifying factor pairs

List the factors of a number

by identifying factor pairs or

otherwise

Identify common factors and

the HCF of 2 or 3 numbers

Identify common factors and

the HCF of 2 or 3 numbers

Find the HCF of 2 or 3

numbers

8 Primes

Understand that a prime

number has exactly 2 distinct factors; Identify and

list prime numbers up to 100

Express a number as a

product of its prime factors

Express a number as a

product of its prime factors

9 Multiples Recognise patterns of

multiples in a 10 x 10

number grid

Enter missing numbers in

lists of multiples of 2 to 12

Quick response task: identify

multiples of 2 to 12

Identify non-multiples,

multiples and common

multiples of 2 or 3 numbers

Identify the LCM of 2 or 3

numbers

10 Powers

Calculate and identify

squares

Calculate and identify square

roots and squares

Calculate and identify cubes

and cube roots

Solve problems

Calculate and identify cubes

and cube roots

Solve problems

Write, expand and calculate

positive, whole powers

11 Order of Operations Understand and use the

order of operations with two

operations

Evaluate calculations with 2

or 3 operations with brackets

and powers

Evaluate calculations with 3

or more operations with

brackets and powers



Number Topics


12 Rounding & Estimation

Distinguish between exact

and approximate numbers

Round numbers up to

100,000.00 to the nearest whole number, 10, 100 and

1000

Round numbers up to

100.00000 to 1, 2, 3 and 4 decimal places

Round large and small

numbers to 1, 2 and 3 significant figures

Estimate by rounding to 1sf

and otherwise

Estimate by educated guess

13 Number Machines

Complete input and output

values for a number

machine; positive integers

Complete missing elements

in a number machine;

positive integers

Solve problems with positive

integers


in a number machine;

integers

Solve problems with integers

Complete input and output

values for a number

machine, including

multiply/dividing by a

negative


in a number machine,

including multiply/dividing

by a negative


14 Number Problems & Puzzles

Solve mixed questions on

the properties of number in

the form of a bingo game

Solve a magic square

Solve a problem in a magic

square

Solve number problems and

puzzles


puzzles


puzzles

15 Language Tasks & Quizzes 1 Match number terms to their

definitions

Engage with the language of

number through wordsearch

puzzles

Engage with the language of

number through crossword

puzzles

Enter missing words in

statements concerning

number terms

Quizzes: Mixed questions in

context on Topics 1 to 9

16 Using a Calculator

Use a calculator to do a

single stage calculation on

numbers with 1 decimal place

Use a calculator to do a

single stage calculation on

numbers with 2 decimal places

Use a calculator to solve

single stage problems in

word form including some contexts

Use a calculator to solve 2-

stage and multi-stage

problems including some in context; follow order of

operations

Use a calculator to solve

multi-stage problems

involving brackets and indices; follow order of

operations

17 Fractions 1

Identify the fraction of a

shape which is coloured;

simplest form not required

Colour the given fraction of

a shape

Complete equivalent

fractions

Compare the value of

fractions

Identify equivalent fractions

Reduce a fraction to its

simplest form

Convert between a mixed

number and an improper

fraction

Calculate fractional part of

a value

18 Fractions 2

Convert between a fraction

and a decimal; compare

fractions and decimals

Convert between a

recurring decimal and a

fraction in simplest form

Add fractions and mixed

numbers, expressing in

simplest form

Subtract fractions and

mixed numbers, expressing

in simplest form

Multiply & divide fractions

and mixed numbers,

expressing in simplest

form; Solve mixed

problems involving fractions

19 Percentages 1

Convert between fractions,

decimals and percentages; Compare the value of

fractions, decimals &

percentages

Identify the percentage of a

shape which is shaded; Shade in the correct

percentage of a given

shape

Calculate a percentage of a

quantity without a calculator

Calculate a percentage of

quantity using a calculator

Calculate simple interest

20 Percentages 2

Express one quantity as a

percentage of another

Calculate the actual change

and new value for a

percentage change

Calculate the percentage

change given original and

new value

Calculate the original value

after a percentage change

(reverse percentages)

Calculate compound

interest year-by-year and

by using a multiplying

factor

21 Ratio Simplify a ratio Identify the ratio of shaded

area to unshaded area in a

shape

Share an amount in a given

ratio

Solve mixed ratio questions

in context

Use a map scale to

calculate real and map

distances



Number Topics


22 Proportion 1

Solve simple direct

proportion questions

Interpret and draw line

graphs of direct proportion

Solve simple indirect

proportion questions

Distinguish between direct

and indirect proportion

Solve questions on rates

and best buys

Convert between different

quantities using conversion factors and graphs

including currency

exchange rates

23 Indices 1

Express in index form

(whole number indices);

expand and evaluate whole

number indices


(negative indices); evaluate

the reciprocal and other

negative indices


(fractional and negative

indices); evaluate fractional

and negative indices

Use the rules of indices to

multiply, divide & simplify

Use the rules of indices to

add, subtract & simplify

24 Surds 1

Revise square numbers

Express a whole number as

a product of 2 factors with

1 factor being square

Understand a surd

Simplify a surd

Express a surd expression

as a single surd

Simplify a product of surds Simplify a sum or difference

of surds

Expand and simplify a surd

expression in brackets

25 Surds 2 Simplify an expression with

a surd in the denominator

Rationalise the denominator Simplify an expression by

rationalising the

denominator

Simplify an expression by

rationalising the

denominator

Simplify an expression by

rationalising the

denominator

26 Standard Form Convert numbers greater

than 1 between ordinary notation and standard form

Convert numbers less than

1 from ordinary notation to standard form

Convert numbers less than

1 from standard form to ordinary notation

Multiply and divide

numbers in standard form without a calculator

Add and subtract numbers

in standard form without a calculator

27 Language Tasks & Quizzes 2

Match number terms to

their definitions

Engage with the language

of number through

wordsearch puzzles


of number through

crossword puzzles


statements concerning

number terms

Quizzes: Mixed questions

on Topics 1 to 9



Topic 1 - Arithmetic

Target 1 Target 2 Target 3 Target 4 Target 5

Quick response task: simple addition

Add two 3 or 4 digit whole numbers

Puzzle: magic squares


subtraction and addition

Subtract two 3 or 4 digit whole

numbers

Puzzle: number triangles


multiplication

Recall multiplication facts up to 13 x

13

Multiply up to a 4-digit by a 3-digit

whole number

Quick response task: simple division

Recall division facts up to 169/13 = 13

Short and long division, no remainder

Quick response task: mixed questions

on whole numbers

Mixed questions in context

1. Speed response; identify sums that

equal 10,12,15 or 20

1. Speed response; identify

subtractions that equal 5, 10, 15 or

20

1. Speed response; identify the

multiplications that equal 24


divisions that equal 2

1. Speed response; complete

questions involving 4 rules with whole

numbers

2. Speed response; identify sums that

equal 13,14,16,17,18 or 19


subtractions that equal

4,6,7,8,9,11,12,13,14,16,17,18,19





2. Speed response; complete missing

elements in questions involving 4

rules

3. Speed response; identify sums

from 21 to 49


subtractions from 21 to 30





3. Complete questions in context

involving 4 rules

4. Add a 2-digit whole number or a 3-

digit whole number to a 3-d whole

number

4. Subtract a 2-digit whole number

from a 3-digit whole number

4. Complete a grid of simple

multiplications up to 12x12

4. Complete a grid of simple divisions

from up to the 10 times table


involving 4 rules, including one puzzle

5. Add two 4-digit whole numbers 5. Subtract a 3-digit whole number

from a 4-digit whole number

5. Complete a grid of simple

multiplications up to 13x13

5. Complete a grid of simple divisions

from up to the 13 times table

6. Complete 3 x 3 magic squares

given the total

6. Complete number triangles; 3 base

numbers, all < 10

6. Complete a multiplication grid;

10x10; standard layout

6. Divide a 3-digit number by a

single-digit number; whole answer

7. Complete 3 x 3 magic squares 7. Complete number triangles; 3 base numbers, all < 25

7. Complete a multiplication grid; 10x10; random layout

7. Divide a 3-digit number by a 2-digit number; whole answer

8. Complete 4 x 4 magic squares 8. Complete number triangles; 4 base numbers, all < 50

8. Multiply a single-digit number or a 2-digit number by a 3-digit number

8. Divide a 3 or 4-digit number by a 2-digit number; whole answer

9. Multiply a single-digit number or a 2-digit number by a 4-digit number

10. Multiply a 3-digit number by a 4-

digit number



Topic 2 - Money


Find the total of a set of coins

Solve problems with coin totals

Identify a missing coin from a total Identify the coins required to make a

total

Calculate the change from a given bill Calculate a simple bill and the change

Solve shopping problems

1. Speed response: Find the total of 3

coins in pence

1. Identify a missing coin from a total 1. Speed response: Identify the coins

required to make a total

1. Calculate the correct change from

20p

1. Calculate the total cost in pence

and the correct change from £1


coins in pence



2. Speed response: Identify an amount and the correct change from

20p




coins in pence




50p




coins in £’s

4. Identify one or two missing coins

from a total

4. Speed response: Identify the coins


4. Speed response: Identify an

amount and the correct change from

50p




coins in £’s

5. Identify one or two missing coins

from a total

5. Speed response: Identify the coins



£1



6. Solve problems on coin totals 6. Identify one or two missing coins

from a total


£1

6. Solve problems on total cost and

change given

7. Solve problems on coin totals 7. Calculate the correct change from

£2


change given

8. Solve problems on coin totals 8. Speed response: Identify an amount and the correct change from

£2


change given


£5


change given


£5


change given



Topic 3 - Time


Convert between minutes and seconds Convert between hours, minutes and

seconds

Convert between fractional hours,

minutes and seconds

Calculate duration, start and finish

times: 12h clock

Calculate duration, start and finish

times: 12h and 24h clock

1. Convert minutes to seconds 1. Convert between hours and

minutes

1. Convert decimal fractions of a

minute to seconds

1. Calculate finish time given start

time and duration: all am

1. Complete a table of finish times,

durations and start times: 24h clock,

same day start and finish

2. Convert seconds to minutes 2. Convert between minutes & hours

and minutes

2. Convert seconds to decimal

fractions of a minute

2. Calculate duration given start time

and finish time: all am


durations and start times: 24h clock

3. Convert between minutes and

seconds

3. Convert hours, minutes and

seconds to seconds

3. Convert between decimal fractions

of a minute and seconds

3. Calculate start time given duration

and finish time: all am

3. Solve problems on start times,

finish times and duration

4. Convert minutes and seconds to

seconds

4. Convert between seconds and

hours, minutes and seconds

4. Convert fractions of a minute to

seconds


durations and start times: all am

4. Solve problems on start times,


5. Convert seconds to minutes and

seconds

5. Convert seconds to fractions of a

minute

5. Calculate finish time given start

time and duration

6. Convert between seconds &

minutes and seconds

6. Convert between fractions of a

minute and seconds

6. Calculate duration given start time

and finish time

7. Convert between fractions of an

hour and minutes

7. Calculate start time given duration

and finish time

8. Convert between decimals fractions

of an hour and minutes


durations and start times

9. Solve problems with fractions of

hours, minutes and seconds in context

9. Solve problems with start times,


10. Solve problems with fractions of hours and minutes, start times, finish

times and duration



Topic 4 - Place Value


Convert numbers in words to digits

Convert numbers in digits to words

Identify the place value of digits in

whole numbers and decimals

Sort whole numbers up to 10000 and

numbers with up to 3 decimal places

Multiply and divide whole and decimal

numbers by 10, 100 and 1000

Solve problems using place value:

guess the number in as few clues as possible

1. Write a 2-digit or 3-digit whole number in words as digits

1. Identify the place value of a digit in a whole number (up to 3-digits)

1. Sort positive integers up to 100 1. Multiply a single digit whole number by 10, 100 or 1000

1. Problem solving; identify a 3-digit whole number in as few clues as

possible

2. Write a 3-digit whole number in

words as digits (zero in tens column)

2. Identify the place value of a digit in

a whole number (up to 4-digits)

2. Sort positive integers up to 1000 2. Multiply a 2-digit whole number by

10, 100 or 1000

2. Problem solving; identify a 3-digit

whole number in as few clues as

possible


words as digits

3. Identify the place value of a digit in

a decimal number (up to 3 places of

decimals)

3. Sort positive integers up to 1000;

same 3 digits used throughout

3. Multiply a 3-digit whole number by

10, 100 or 1000

3. Problem solving; identify a 4 or 5-

digit whole number in as few clues as

possible


words as digits (zero in tens or

hundreds column)

4. Sort positive integers up to 10000;

same 4 digits used throughout

4. Multiply a positive number < 1 with

1 dp by 10, 100 or 1000

5. Write a 2-digit or 3-digit whole

number in digits as words

5. Sort positive numbers with 1 dp up

to 10

5. Multiply a positive number < 1 with

1 to 3 places of decimals by 10, 100

or 1000


digits as words (zero in tens column)

6. Sort positive numbers with 1 dp up

to 100; same 3 digits used throughout

6. Divide a 2-digit whole number by

10 or 100


digits as words

7. Sort positive numbers with 2 places

of decimals up to 10

7. Divide a 2-digit whole number by

10, 100 or 1000


digits as words (zero in tens or hundreds column)

8. Sort positive numbers with 2 places

of decimals up to 10; same 3 digits used throughout

8. Divide a single-digit whole number

by 10, 100 or 1000

9. Sort positive numbers with 3 places of decimals up to 10; same 4 digits

used throughout

9. Divide a number < 1, with up to 2 places of decimals by 10, 100 or 1000

10. Sort positive numbers with up to 3

places of decimals up to 10; same

digit used throughout with zero

10. Divide and multiply a number <

10 with up to 3 places of decimals by

10, 100 or 1000



Topic 5 - Decimals


Add and subtract numbers with up to

3 decimal places

Multiply a whole number by a number

with up to 2 decimal places

Multiply a whole number by a number

with up to 3 decimal places

Multiply numbers with up to 3 decimal

places

Divide a number with up to 3 decimal

places by a whole number and by a number with up to 2 decimal places;

exact answers

1. Add 2 numbers < 100 with 1 dp 1. Multiply a single-digit whole

number by a number < 10 with 1 dp

1. Multiply a single digit whole

number by a number < 10 with 3

places of decimals

1. Multiply two numbers < 10 with 1

dp

1. Divide a number < 1000 with up to

4 digits and up to 2 places of decimals

by a whole number < 100

2. Add 2 numbers < 10 with 2 places

of decimals

2. Multiply a multiple of 10 by a

number < 10 with 1 dp


number < 10 with 3 places of

decimals

2. Multiply a number < 10 with 1 dp

by a number less than 10 with 2

places of decimals




3. Add 2 numbers < 10 with 3 places

of decimals


a number < 10 with 1 dp



decimals

3. Multiply two numbers < 10 with 2

dp




4. Subtract 2 numbers < 100 with 1

dp; positive answer


number < 10 with 1 dp

4. Mixed examples from tasks 1 to 3

and from Target 2; multiply a whole

number < 10000 by a number with up

to 3 places of decimals

4. Multiply a number < 10 with 1 dp

by a number less than 1 with 3 places

of decimals

4. Divide a number < 100 with up to 3

digits and 1 dp by a number < 10 with

1 dp

5. Subtract 2 numbers < 10 with 2

places of decimals; positive answer

5. Multiply a single digit whole

number by a number < 1 with 2 places of decimals

5. Multiply a number < 1 with 2

places of decimals by a number less than 1 with 3 places of decimals

5. Divide a number < 100 with up to 4

digits and 2 places of decimals by a number < 10 with 1 dp

6. Subtract 2 numbers < 10 with 3 places of decimals; positive answer

6. Multiply a multiple of 10 by a number < 10 with 2 places of

decimals

6. Mixed examples from tasks 1 to 5; multiply a number with up to 3

decimal places by a number with up

to 3 decimal places

6. Divide a number < 1000 with up to 4 digits and 5 places of decimals by a


decimals

7. Complete number squares; 3x3

positive numbers < 12 with 1 dp


a number < 1 with 2 places of

decimals

8. Complete number squares; 4x4

positive numbers < 12 with 1 dp


number < 1 with 2 places of decimals

9. Complete number triangles; 3

numbers along the base; positive

numbers < 20 with 1 dp

10. Complete number triangles; 4

numbers along the base; positive

numbers < 12 with 1 dp



Topic 6 - Integers



temperatures on thermometers

Sort positive and negative numbers

with and without context

Calculate original temperature, final

temperature and change in temperature

Add & subtract negative numbers

Puzzles: magic squares and number triangles

Use four rules with negative numbers,

positive and negative decimals

Quick response task: negative

numbers

1. Sort positive temperatures on a

thermometer

1. Sort positive and negative

temperatures involving zero, 2

negatives and 2 positives

1. Calculate the final temp. given the

original temp. and the rise (all

positive)

1. Subtract a positive 1-digit or 2-digit

integer from a positive 1- digit integer

1. Game: Identify calculations with

negative answers


temperatures on a thermometer


temperatures involving 3 negatives

and 2 positives

2. Calculate the rise given the original

temp. and the final temp. (all

positive)

2. Add a positive 1-digit integer to a

positive 1-digit or 2-digit integer

2. Complete missing entries in

additions and subtractions of integers

3. Sort commonly known

temperatures on a thermometer

3. Sort negative temperatures 3. Calculate the original temp. given

the rise and the final temp. (all

positive)

3. Subtract a 1-digit or 2-digit positive

integer from a 1-digit integer

3. Add and subtract positive and

negative numbers with 1 dp

4. Sort integers: 3 negatives and 2

positives and/or one positive and zero


original temp. and the rise (negative

start)


1-digit or 2-digit negative integer

4. Complete missing entries in

additions and subtractions of positive

and negative numbers with 1 dp

5. Sort integers: 4 negatives and 1

positives

5. Calculate the rise given the original

temp. and the final temp. (negative

start)

5. Add a negative single digit integer

to a negative single or 2-digit integer

5. Multiply 1-digit integers

6. Calculate the original temp. given

the rise and the final temp. (negative start)

6. Subtract a negative 1-digit or 2-

digit integer from a positive 1-digit integer

6. Divide 1-digit and 2-digit integers

by 1- digit integers


original temp. and the fall (positive or

negative start)


digit integer from a negative 1-digit

integer

7. Multiply integers by numbers with

up to 1 dp

8. Calculate the fall given the original

temp. and the final temp. (positive or

negative start)

8. Mixed additions and subtractions of

integers

8. Divide integers by numbers with up

to 1 dp; divide numbers with up to 1

dp by integers

9. Calculate the original temp. given

the fall and the final temp. (positive or

negative start)

9. Magic Square puzzles with integers

3 x 3

10. Calculate the rise or fall given the

original temp. and the final temp

(positive or negative start)

10. Magic Square puzzles with

integers 4 x 4

11. Number Triangle puzzles with

integers; 3 along base

12. Number Triangle puzzles with

integers; 4 along base



Topic 7 - Factors


List the factors of a number by

identifying factor pairs

List the factors of a number by

identifying factor pairs or otherwise

Identify common factors and the HCF

of 2 or 3 numbers

Identify common factors and the HCF

of 2 or 3 numbers

Find the HCF of 2 or 3 numbers

1. Identify and list the factors of 1,2,3

and 4 by identifying factor pairs

1. Identify and list the factors of 27,

29 and 30 by identifying factor pairs

1. Find the HCF of two numbers by

identifying the greatest factor in both lists of factors; 4 and 6; 6 and 8; 4

and 8

1. Complete a Venn diagram of factors

and thereby find the HCF of 20 and 24

1. Find the HCF of two numbers < 200

2. Identify and list the factors of 5,6,8


2. Identify and list the factors of 32,

33,40 and 43 by identifying factor

pairs


identifying the greatest factor in both

lists of factors; 8 and 12; 5 and 10; 6

and 9



2. Find the HCF of two 2-digit

numbers and up to two 3-digit

numbers

3. Identify and list the factors of

10,12,15 and 16 by identifying factor

pairs

3. Identify and list the factors of 36




lists of factors; 12 and 16; 10 and 15;

16 and 24



4. Identify and list the factors of

18,20,21 and 24 by identifying factor

pairs




and thereby find the HCF of 30, 32

and 48


by identifying factor pairs


and thereby find the HCF of 48, 64 and 72

6. Identify and list the factors of numbers up to 100

7. Identify and list the factors of 2-

digit or 3-digit numbers



Topic 8 - Primes

Target 1 Target 2 Target 3

Understand that a prime number has

exactly 2 distinct factors; Identify and list prime numbers up to 100

Express a number as a product of its

prime factors

Express a number as a product of its

prime factors

1. Identify and list the factors of 5,13,17 and 23 by identifying factor

pairs

1. Express 20 as a product of its prime factors, by completing a factor

tree

1. Express a single-digit and 2-digit number as a product of its prime

factors

2. Identify and list the prime numbers

< 100

2. Express 18 and 28 as a product of

their prime factors, by completing a

factor tree

2. Express a 2-digit and 3-digit

number as a product of its prime

factors

3. Speed response; distinguish

between prime numbers and non-

prime numbers; all numbers < 20



factor tree



factors






factor tree



factors (Choose number of factors)






factor tree




6. Express 120 and 200 as a product

of their prime factors, by completing a

factor tree

7. Express 216 and 1000 as a product of their prime factors, by completing a

factor tree



Topic 9 - Multiples


Recognise patterns of multiples in a

10 x 10 number grid

Enter missing numbers in lists of


Quick response task: identify


Identify non-multiples, multiples and

common multiples of 2 or 3 numbers

Identify the LCM of 2 or 3 numbers

1. Identify the multiples of 2 on a

10x10 multiplication grid

1. Enter missing numbers in a list of

multiples of 2

1. Quick response: Identify the

multiples of 2

1. Identify non-multiples and common

multiples of 2 and 3 by completing a Venn diagram

1. List the first 10 multiples of 1,2,3,5

and 10




multiples of 3


multiples of 2


multiples of 2 and 5 by completing a

Venn diagram

2. List the first 10 multiples of 4,6,7,8

and 9




multiples of 5


multiples of 3



Venn diagram

3. List the first 10 multiples of

11,12,15,20 and 50




multiples of 10


multiples of 4



Venn diagram

4. Identify the LCM by identifying the

smallest common entry in 2 lists of

multiples: 2,3 : 3,4 : 3,6




multiples of 4


multiples of 5



Venn diagram



multiples: 4,8 : 6,8 : 4,10




multiples of 6


multiples of 6



Venn diagram



multiples: 10,15 : 6,10 : 6,9




multiples of 7


multiples of 7


multiples of 2, 3 and 5 by completing a Venn diagram

7. Identify the LCM of 2 numbers < 12

8. Identify the multiples of 9 on a 10x10 multiplication grid

8. Enter missing numbers in a list of multiples of 8

8. Quick response: Identify the multiples of 8

8. Identify non-multiples and common multiples of 3, 4 and 5 by completing

a Venn diagram





multiples of 9


multiples of 9


multiples of 2, 3 and 7 by completing

a Venn diagram





multiples of 11


multiples of 10

10. Identify non-multiples and

common multiples of 3, 4 and 7 by

completing a Venn diagram

10. Identify the LCM of 2 single-digit

of 2-digit numbers (free choice or

lucky dip)




multiples of 12


multiples of 11

11. Identify the LCM of 3 single-digit

of 2-digit numbers (free choice or

lucky dip)


multiples of 12



Topic 10 - Powers


Calculate and identify squares Calculate and identify square roots

and squares

Calculate and identify cubes and cube

roots

Solve problems

Calculate and identify cubes and cube

roots

Solve problems

Write, expand and calculate positive,

whole powers

1. Enter the first ten squares numbers 1. Enter the first ten square roots 1. Enter the first ten cube numbers 1. Identify which numbers are both square and cube by completing a

Venn diagram of square and cube

numbers

1. Expand powers of 10: powers 2 to 7

2. Enter the missing numbers in

straightforward square number

calculations: 1-10


straightforward square root

calculations: 1-10


straightforward cube number

calculations: 1-10

2. Enter the first ten cube roots 2. Expand powers of 2: powers 2 to 7

3. Speed response: Identify the first

10 square numbers

3. Enter missing numbers in

calculations involving squares and

square roots: 1-10

3. Speed response: Identify the first

10 cube numbers


straightforward cube root calculations:

1-10

3. Expand powers of 3: powers 2 to 7


calculations involving square

numbers: 1-10


calculations involving cube numbers:

1-10


calculations involving squares, cubes,

square roots and cube roots: 1-10

4. Expand powers of 1 to 5 : powers 2

to 7

5. Enter the second ten squares

numbers: 11-20


calculations involving square and cube

numbers: 1-10


involving squares, cubes, square roots

and cube roots

5. Express expanded form in index

form: 1 to 6: powers 2 to 6


straightforward square number calculations: 11-20

6. Express expanded form in index

form: 2 to 9: powers 2 to 8

7. Speed response: Identify the

second 10 square numbers

7. Complete calculations involving

indices, square roots and cube roots


calculations involving square

numbers: 1-20


calculations involving indices, square

roots and cube roots



Topic 11 - Order of Operations


Understand and use the order of

operations with two operations

Evaluate calculations with 2 or 3

operations with brackets and powers

Evaluate calculations with 3 or more


1. Complete simple calculations with 2

operations (x or / and + or -)


operations with brackets


operations

2. Complete simple calculations with 2 operations (x or / and + or -)

2. Complete simple calculations with 2 operations with brackets and squares

2. Complete simple calculations with 3 operations

3. Complete simple calculations with 2 operations (x or / and + or -)

3. Complete simple calculations with 3 operations with brackets and powers

3. Complete simple calculations with 3 operations with brackets


operations (x or / and + or -)


operations with fractions




operations (+ or - and + or -)


operations (x or / and x or /)

7. Mixed examples of tasks 1 to 6



Topic 12 - Rounding & Estimation


Distinguish between exact and

approximate numbers

Round numbers up to 100,000.00 to

the nearest whole number, 10, 100 and 1000

Round numbers up to 100.00000 to 1,

2, 3 and 4 decimal places

Round large and small numbers to 1,

2 and 3 significant figures

Estimate by rounding to 1sf and

otherwise

Estimate by educated guess

1. Distinguish between exact and approximate numbers

1. Round numbers < 100 with 1 dp to the nearest whole number

1. Round numbers < 10 with 2 dp to 1 dp

1. Identify the 1st significant figure in a number

1. Estimate calculations by rounding to 1 sf: 1 operation

2. Distinguish between exact and

approximate numbers

2. Round numbers < 100 with 2 dp to

the nearest whole number


1 dp

2. Identify the 2nd significant figure in

a number

2. Estimate calculations by rounding

to 1 sf: 2 operations

3. Round numbers < 10000 with 1 dp

to the nearest whole number;

rounding causes knock-on place value

changes


to 1 dp ; rounding causes knock-on

place value changes

3. Identify the 3rd significant figure in

a number

3. Estimate calculations by rounding

to 1 sf: 2 operations; quiz style

4. Round whole numbers < 1000 to

the nearest 10


2 dp

4. Round a whole number < 100000

to 1 sf

4. Estimate values of commonplace

objects: quiz style


the nearest 10


to 2 dp

5. Round a number with up to 3 dp <

1000 to 1 sf

5. Estimate the number of shapes up

to 200


the nearest 10; rounding causes

knock-on place value changes


to 1 dp ; rounding causes knock-on

place value changes


1 to 1 sf


the nearest 100

7. Round numbers < 10 with 4 dp to 3

dp

7. Round a whole number < 100000

to 2 sf


the nearest 100


3 dp


100 to 2 sf

9. Round whole numbers < 1000000

to the nearest 100; rounding causes

knock-on place value changes

9. Round numbers < 10 with 4 dp to 3

dp ; rounding causes knock-on place

value changes


1 to 2 sf


to the nearest 1000


to 4 dp

10. Round a whole number <

1000000 to 3 sf


to the nearest 1000


to 4 dp

11. Round a number with up to 3 dp

< 1000 to 3 sf

12. Round whole numbers < 10000000 to the nearest 1000;

rounding causes knock-on place value

changes

12. Round numbers < 10 with 5 dp to 4 dp ; rounding causes knock-on

place value changes

12. Round a number with up to 6 dp < 1 to 3 sf



Topic 13 - Number Machines


Complete input and output values for

a number machine; positive integers

Complete missing elements in a

number machine; positive integers

Solve problems with positive integers


number machine; integers


Complete input and output values for

a number machine, including multiply/dividing by a negative


number machine, including multiply/dividing by a negative


1. Complete output values for a

number machine

1. Complete input and output values

for a number machine




number machine




number machine

2. Find a missing operation given the

input and output values of a number

machine



machine


number machine



machine


number machine



machine



machine


number machine



machine


number machine



machine



machine


number machine



machine


number machine

5. Complete input values for an

addition number machine




number machine




number machine

6. Complete missing elements in a

number machine


number machine


number machine


number machine


number machine

7. Solve problems with positive

integers

7. Solve problems with integers 7. Complete output values for a

number machine

7. Solve problems with integers


number machine


integers

8. Solve problems with integers 8. Complete output values for a

number machine





integers

9. Solve problems with integers 9. Complete input and output values




integers

10. Solve problems with integers 10. Solve problems with integers



Topic 14 - Number Problems & Puzzles


Solve mixed questions on the

properties of number in the form of a bingo game

Solve a magic square

Solve a problem in a magic square

Solve number problems and puzzles Solve number problems and puzzles Solve number problems and puzzles

1. Solve mixed questions on the properties of number in the form of a

bingo game

1. Solve a 3 x 3 magic square: total given

1. Complete a number puzzle by adding digits to a triangular grid

(totals: 9 and 10)

1. Complete a number puzzle by adding digits to calculations of four

rules

1. Complete a section of a 10 x 10 multiplication grid; 10 x 10 grid

available

2. Solve mixed questions on the

properties of number in the form of a

bingo game

2. Solve a 3 x 3 magic square 2. Complete a number puzzle by

adding digits to a triangular grid

(totals: 11 and 12)

2. Complete a number puzzle by

adding digits to calculations of four

rules

2. Complete a section of a 20 x 20

multiplication grid



bingo game

3. Solve a 3 x 3 magic square: no

individual entries marked



(totals: 19 and 20)



bingo game

4. Solve a 3 x 3 magic square

containing negative integers



(totals: 21 and 23)



bingo game

5. Solve a problem in a 3 x 3 magic

square


adding digits to a grid (totals: 12 and

13)



bingo game

6. Solve a problem in a 3 x 3 magic

square containing negative integers


adding digits to a grid (totals: 14 and

15)

7. Solve mixed questions on the properties of number in the form of a

bingo game

7. Solve a 4 x 4 magic square: total given



bingo game

8. Solve a 4 x 4 magic square:

individual entries not marked



bingo game


negative integers used



bingo game


negative integers used: individual

entries not marked



Topic 15 - Language Tasks & Quizzes 1


Engage with Maths language by

matching terms to their descriptions

Engage with Maths language through

wordsearch puzzles


crossword puzzles


completing sentences

Quiz: Mixed questions on Topics 1 to

13

1. Match terms to their descriptions 1. Complete a wordsearch 1. Complete a crossword 1. Enter missing words in sentences 1. Quiz: Mixed questions from Topics

1 to 13

2. Match terms to their descriptions 2. Complete a wordsearch 2. Complete a crossword 2. Enter missing words in sentences




6. Match terms to their descriptions 6. Enter missing words in sentences







Topic 16 - Using a Calculator


Use a calculator to do a single stage

calculation on numbers with 1 decimal place

Use a calculator to do a single stage

calculation on numbers with 2 decimal places

Use a calculator to solve single stage

problems in word form including some contexts

Use a calculator to solve 2-stage and

multi-stage problems including some in context; follow order of operations

Use a calculator to solve multi-stage

problems involving brackets and indices; follow order of operations

1. Use a calculator to calculate the sum of 2 numbers with 1 or 2 dp

1. Use a calculator to calculate the sum of 2 numbers with up to 3 dp

1. Use a calculator to solve a single stage problem in word form including

some contexts

1. Use a calculator to carry out a 2-stage calculation; requires correct use

of order of operations

1. Use a calculator to carry out a calculation involving 3 or more

stages; requires correct use of order

of operations

2. Use a calculator to calculate the

difference of 2 numbers with 1 or 2 dp


difference of 2 numbers with up to 3

dp

2. Use a calculator to solve a single

stage problem in word form including

some contexts

2. Use a calculator to carry out a 2-

stage calculation; requires correct use

of order of operations

2. Use a calculator to carry out a

calculation involving 3 or more

stages; requires correct use of order

of operations


product of 2 numbers with 1 or 2 dp


product of 2 numbers with up to 3 dp



some contexts

3. Use a calculator to solve a problem

involving 2 or more stages; requires

correct use of order of operations

3. Speed response; Use a calculator to

carry out a single stage calculation;

requires correct use of order of

operations


division of 2 numbers with 1 or 2 dp


division of 2 numbers with up to 3 dp



some contexts

5. Use a calculator to solve a single stage problem in word form including

some contexts



Topic 17 - Fractions 1


Identify the fraction of a shape which

is coloured; simplest form not required

Colour the given fraction of a shape

Complete equivalent fractions

Compare the value of fractions

Identify equivalent fractions

Reduce a fraction to its simplest form Convert between a mixed number and

an improper fraction

Calculate fractional part of a value

1. Identify the fraction of a shape that

is coloured (1/2:x/4:x/3:x/5)

1. Complete a list of equivalent

fractions (1/2:1/3) by entering the

numerator or denominator

1. Reduce a fraction to its simplest

form; a/b: b<15; common factor < 6

1. Convert an improper fraction to a

mixed number: a/b: b < 6: a < 3xb

1. Calculate a unitary fraction of a

value: 1/b of c: b < 5: c < 10


is coloured (x/4:x/6:x/5:x/6)


fractions (1/4:2/3) by entering the

numerator or denominator






value: 1/b of c: b < 6: c < 19


is coloured (x/6:x/7:x/9:x/9)


fractions (a/b: a<10:b<11: a<b) by

entering the numerator or

denominator






value: 1/b of c: b < 13: c < 201


is coloured (x/9:x/8:x/16:x/12):

optional motion for fun

4. Speed response: Identify fractions

that have a value = 1/2,1/3 or 1/4


form; a/b: b<200; common factor <

13

4. Convert a mixed number to an

improper fraction: M+a/b: b < 6: M <

3

4. Calculate a fraction of a value: a/b

of c: b < 6: c < 21


is coloured (x/10:x/12:x/16:x/32): optional motion for fun

5. Speed response: Identify fractions

that have a value < 1/2,1/3 or 1/4

5. Memory game: Identify a fraction

and its simplest form: a/b: b < 9

5. Convert a mixed number to an

improper fraction: M+a/b: b < 7: M < 5

5. Calculate a fraction of a value: a/b

of c: b < 8: c < 31

6. Colour the given fraction of a shape (x/4:1/2:x/3:x/5)

6. Speed response: Identify fractions that have a value > (1/2,1/3 or 1/4)

6. Memory game: Identify a fraction and its simplest form: a/b: b < 13

6. Convert a mixed number to an improper fraction: M+a/b: b < 13: M

< 10

6. Calculate a fraction of a value: a/b of c: b < 11: c < 71

7. Colour the given fraction of a shape

(x/4:x/6:x/5:x/6)

7. Speed response: Identify a fraction

equivalent to a given unitary fraction

7. Speed response: Match fractions

with their simplest form; unitary

fractions

7. Memory game: Identify an

improper fraction and equivalent

mixed number: M+a/b: b < 6: M < 3


(x/6:x/7:x/9:x/9)

8. Speed response: Identify a fraction

equivalent to a given fraction

8. Speed response: Match fractions

with their simplest form; simple

fractions

8. Memory game: Identify an

improper fraction and equivalent

mixed number: M+a/b: b < 10: M < 5


(x/9:x/8:x/16:x/12): optional motion

for fun

9. Memory game: Identify two

equivalent fractions

10. Colour the given fraction of a

shape (x/8:x/12:x/16:x/32): optional

motion for fun



Topic 18 - Fractions 2


Convert between a fraction and a

decimal; compare fractions and decimals

Convert between a recurring decimal

and a fraction in simplest form

Add fractions and mixed numbers,

expressing in simplest form

Subtract fractions and mixed

numbers, expressing in simplest form

Multiply & divide fractions and mixed

numbers, expressing in simplest form; Solve mixed problems involving

fractions

1. Convert between a fraction and a

decimal (tenth)

1. Write a recurring decimals with 1

dp as a fraction

1. Add 2 fractions with same

denominator; no simplifying required

1. Subtract 2 fractions with same

denominator; no simplifying required

1. Multiply two unitary fractions using

‘of’ as the operator


decimal (quarter, eighth)


dp (recurring sequence length 2) as a

fraction

2. Add 2 fractions with same

denominator

2. Subtract 2 fractions with same

denominator

2. Multiply a unitary fraction by a

fraction using ‘of’ as the operator


decimal (third, fifth)



fraction

3. Add 2 fractions with one

denominator a constant multiple of

the other

3. Subtract 2 fractions with one


the other

3. Multiply 2 fractions


and decimal of equivalent value

(quarter, half, tenth)



fraction

4. Add 2 fractions with one


the other; answer less than 1

4. Subtract 2 fractions with one


the other

4. Multiply 2 fractions; larger

denominators



(quarter, half, tenth, fifth, eighth)

5. Mixed questions from tasks 1 to 4 5. Add 2 fractions with different

denominators; answers include mixed

numbers

5. Subtract 2 fractions with different


numbers

5. Multiply a mixed number by a

fraction



(eighth, hundredth)

6. Write 1/3s and 1/9s as recurring

decimals

6. Add 2 fractions with different


numbers; larger denominators

6. Subtract 2 fractions with different


numbers; larger denominators

6. Multiply a mixed number by a

fraction; larger denominators

7. Sort fractions and decimals 7. Write 1/33s and 1/99s as recurring decimals

7. Add a mixed number to a fraction 7. Subtract a fraction from a mixed number

7. Multiply a mixed number by a mixed number

8. Sort fractions and decimals; extension

8. Write 1/333s and 1/999s as recurring decimals

8. Add a mixed number to a fraction and; larger denominators

8. Subtract a fraction from a mixed number with 1 as the whole number

8. Multiply a mixed number by a mixed number; larger denominator

9. Add 2 mixed numbers 9. Subtract 2 mixed numbers 9. Divide a fraction by a fraction with guidance

10. Add 2 mixed numbers; larger

denominators;

10. Subtract 2 mixed numbers and;

larger denominators

10. Divide a fraction by a fraction

11. Divide a fraction by a fraction;

larger denominators

12. Divide a mixed number by a

fraction; divide a fraction by a mixed

number

13. Divide a mixed number by a

mixed number

14. Solve fractions questions in context

15. Solve fractions questions in context



Topic 19 - Percentages 1


Convert between fractions, decimals

and percentages; Compare the value of fractions, decimals & percentages

Identify the percentage of a shape

which is shaded; Shade in the correct percentage of a given shape

Calculate a percentage of a quantity

without a calculator

Calculate a percentage of quantity

using a calculator

Calculate simple interest

1. Convert between a decimal and a percentage (1/10)

1. Identify the percentage of a shape that is coloured (1/2:x/4:x/10:x/5)

1. Calculate a percentage of a quantity; 10,25,75,100

1. Calculate a whole number percentage of a quantity

1. Calculate simple interest with assistance; whole number interest

rate; whole pounds

2. Convert between a decimal and a

percentage (1/4,1/8)

2. Identify the percentage of a shape

that is coloured (x/4:x/3:x/5:x/8)

2. Calculate a percentage of a

quantity; 10,25,75,100; larger

numbers

2. Calculate a whole number

percentage of a quantity; larger

numbers

2. Calculate simple interest with

assistance; whole number interest

3. Convert between a decimal and a


3. Identify the percentage of a shape

that is coloured (x/20:x/40:x/50)


quantity; 5,10,20,30,40; whole

number answers

3. Calculate a fractional percentage of

a quantity


assistance; fractional interest rate;

multiples of 10


percentage (1/10)


(1/2:x/4:x/10:x/5)


quantity; 5,10,20,30,40


a quantity; multiples of 100


assistance; fractional interest rate




(x/4:x/3:x/5:x/8)


quantity; 5,10,15,20,30,40


a quantity; large whole numbers

5. Calculate simple interest; whole

number interest rate




(x/20:x/40:x/50); optional motion


quantity; 5,10,15,20,30,35,40

6. Calculate a whole number

percentage > 100 of a quantity

6. Calculate simple interest; fractional

interest rate; multiples of 10

7. Convert between a fraction,

decimal and percentage

(1/4,1/5,1/10)


quantity; 0.5,1,1.5,2,3.5

7. Calculate simple interest; fractional

interest rate; halves of years

8. Convert between a fraction,


(1/3,1/8,1/100)


quantity; 0.5,1,1.5,2,98,99,99.5

8. Calculate simple interest; table form;

whole number interest rate; whole

years

9. Memory game: Identify a decimal

and percentage of equivalent value (1/2,1/4,1/10)


quantity; x12.5

9. Complete missing entries in a table

of simple interest calculations; whole number interest rate

10. Memory game: Identify a decimal

and percentage of equivalent value

(1/3,1/8,1/100)


quantity; mixed examples from tasks

1 to 9

10. Complete missing entries in a

table of simple interest calculations;

fractional interest rate



(1/2,1/4,1/10)



(1/4,1/5,1/8,1/10)

13. Sort fractions, decimals and

percentages

14. Sort fractions, decimals and

percentages; extension



Topic 20 - Percentages 2


Express one quantity as a percentage

of another

Calculate the actual change and new

value for a percentage change

Calculate the percentage change

given original and new value

Calculate the original value after a

percentage change (reverse percentages)

Calculate compound interest year-by-

year and by using a multiplying factor

1. Express a number as a % of a greater number < 11 with assistance

1. Calculate the actual change and the new value in a % increase < 100%;

with assistance

1. Calculate the % increase given the original amount and the actual

change; with assistance

1. Calculate the original value after a % increase; with assistance

1. Calculate compound interest year-by-year over 2 years; with assistance

2. Express a number as a % of a

greater number < 41 with assistance

2. Calculate the actual change and the

new value in a % increase < 100%;

with assistance

2. Calculate the % increase given the

original and final amount; with

assistance

2. Calculate the original value after a

% increase; with assistance

2. Calculate compound interest year-

by-year over 2 years; with assistance


greater number < 11

3. Increase a value by a percentage <

100%

3. Calculate the % decrease given the

original amount and the actual

change; with assistance


% decrease; with assistance




greater number < 51

4. Increase a value by a % > 100% 4. Calculate the % decrease given the

original and final amount; assistance


% decrease; with assistance




greater number < 100


new value in a % decrease; with

assistance

5. Calculate the % change given the

original and final amount


% change


by-year over 2 or 3 years


lesser number < 100


new value in a % decrease; with

assistance

6. Calculate the % change given the

original and final amount; larger

numbers

6. Complete a table of original values

given the % change and whole final

values

6. Complete a table of values of

compound interest calculated year-by-

year over 2 to 4 years

7. Express an amount in pence as a %

of a greater amount in whole pounds

7. Mixed questions on increasing or

decreasing a value by a % < 100%

7. Complete a table of actual and %

changes; whole final value

7. Complete a table of original values

given the % change and fractional final values

7. Identify the multiplying factor for a

% increase < 100%

8. Express an amount in pence as a % of a greater amount

8. Complete a table of % increases and decreases

8. Complete a table of actual and % changes; fractional final value

8. Complete a table of original values given the % increase > 100% and

final values

8. Identify the multiplying factor for a % increase > 100%

9. Complete a table of actual

increases and % increases > 100%;

whole final value

9. Calculate compound interest over 2

years using a multiplying factor; with

assistance

10. Complete a table of actual

increases and % increases > 100%;

fractional final value

10. Calculate compound interest over

3 years using a multiplying factor;

with assistance


4 years using a multiplying factor;

with assistance


2 to 4 years using a multiplying factor

13. Complete a table of compound

interest over 2 to 11 years using a

multiplying factor



Topic 21 - Ratio


Simplify a ratio Identify the ratio of shaded area to

unshaded area in a shape

Share an amount in a given ratio Solve mixed ratio questions in context Use a map scale to calculate real and

map distances

1. Simplify a ratio; 2 part ratio 1. Identify the ratio of shaded area to

unshaded area in a shape (parts: 2,3,4,5)

1. Divide an amount in a given ratio;

whole pounds; 2 part ratio

1. Complete a table of values for

mixing 2 paint colours in a given ratio

1. Calculate the real distance given

the scale and the map distance

2. Simplify a ratio; 2 part ratio;

greater common factors

2. Identify the ratio of shaded area to

unshaded area in a shape (parts:

4,5,6)


whole kg; 2 part ratio

2. Complete a table of values for

mixing 2 paint colours in a given ratio

2. Calculate the map distance given

the scale and the real distance





6,7,9)


whole pounds; larger ratio values; 2

part ratio

3. Calculate the correct amount of

paint for a mixture made from a given

ratio of 2 different colours

3. Calculate the real or map distance

given the map or real distance and

the scale

4. Simplify a ratio; 3 part ratio 4. Identify the ratio of shaded area to


9,8,12,16)


pounds and pence; 2 part ratio

4. Calculate the correct amount of

paint for a mixture made from a given

ratio of 2 different colours





10,12,16,32)

5. Complete a table of ratios dividing

an amount in a given ratio; whole

answers; 2 part ratio

5. Calculate a ratio from a fraction

6. Simplify a ratio of quantities

expressed in different units; with

assistance


whole pounds; 3 part ratio

6. Calculate a fraction from a ratio

7. Simplify a ratio of quantities

expressed in different units; with assistance


whole pounds; 3 part ratio; larger ratio values

7. Calculate a ratio from information

in context

8. Express a ratio in simplest form from information in context

8. Divide an amount in a given ratio; pounds and pence; 3 part ratio

8. Calculate a ratio from information in context

9. Memory game; identify a ratio and its simplest form

9. Find the angles of a triangle given their ratio

10. Speed response; match ratios

with their simplest form; unitary

ratios

10. Find the angles of a quadrilateral

given their ratio

11. Speed response; match ratios

with their simplest form



Topic 22 - Proportion 1


Solve a simple direct proportion

question

Read, interpret and draw a line graph

of direct proportion

Solve a simple indirect proportion

question

Distinguish between direct and

indirect proportion

Solve questions on rates and best

buys

Convert between different quantities

using a conversion factor and graph

Calculate currency exchange

1. Calculate the cost of n items given

the cost of 1

1. Read and interpret a line graph of

direct proportion

1. Solve an indirect proportion

question

1. Calculate the rate for 1 item given

the rate for n items

1. Convert between miles and

kilometres; whole numbers

2. Calculate the rate for n items given

the rate for 1


direct proportion

2. Solve an indirect proportion

question

2. Calculate the best buy of 2 items

by comparing rates


kilometres

3. Calculate the cost of 1 item given

the cost of n


direct proportion

3. Solve a mixture of direct and

indirect proportion questions


by comparing rates

3. Construct a conversion graph

between miles and kilometres from a

table of information

4. Calculate the rate for 1 item given

the rate for n


direct proportion


by comparing rates

4. Read and interpret a conversion

graph between miles and kilometres


the rate for m

5. Construct a straight line graph of

direct proportion from a table of

information


by comparing rates




the rate for m


direct proportion from a table of

information


by comparing rates




the rate for m


direct proportion from a single piece

of information


by comparing rates

7. Convert between £ and $ using an

exchange rate in terms of £1


direct proportion from a single piece of information


by comparing rates

8. Convert between £ and $ using an

exchange rate in terms of $1

9. Calculate the best buy of 2 items by comparing rates

9. Construct a conversion graph between £ and $ using an exchange

rate in terms of £1


by comparing rates


graph between £’s and $’s

11. Solve a problem involving

combined rates


graph between £’s and $’s

12. Solve a problem involving

combined rates



Topic 23 - Indices 1


Express in index form (whole number

indices); expand and evaluate whole number indices

Express in index form (negative

indices); evaluate the reciprocal and other negative indices

Express in index form (fractional and

negative indices); evaluate fractional and negative indices

Use the rules of indices to multiply,

divide & simplify

Use the rules of indices to add,

subtract & simplify

1. Write a sequence of multiplications in index form

1. Evaluate the reciprocal of a whole number in fraction form with

assistance

1. Express a root in index form 1. Multiply in index form; both positive indices; with assistance

1. Simplify index form raised to an index; both positive indices; with

assistance

2. Expand index form and evaluate 2. Evaluate negative indices in

fraction form with assistance

2. Express fractional index form as a

root; with assistance

2. Multiply in index form; 1 or 2

negative indices

2. Simplify index form raised to an

index; 1 or 2 negative indices

3. Complete mixed calculations

involving index form and square and

cube roots

3. Evaluate negative indices in

fraction form

3. Evaluate fractional index form, by

expressing as a root, and evaluating;

with assistance

3. Complete missing elements in

multiplications in index form

3. Evaluate index form raised to an

index; 1 or 2 negative indices

4. Complete missing elements in

mixed calculations involving index

form and square and cube roots

4. Express a unitary fraction in index

form with assistance

4. Evaluate negative fractional index

form, by expressing as a root, and

evaluating; with assistance

4. Divide in index form; both positive

indices; with assistance

4. Simplify expressions in index form

5. Speed response; identify a value in

index form and its expanded value

5. Express a unitary fraction in index

form in 2 equivalent ways with

assistance

5. Express roots and reciprocals in

positive index form

5. Divide in index form; 1 or 2

negative indices

5. Simplify and evaluate expressions

in index form


index form and its expanded value


negative index form and its expanded

value as a fraction

6. Evaluate index form 6. Complete missing elements in

divisions in index form


negative index form and its expanded value as a fraction


fractional index form and its expanded value

8. Evaluate the reciprocal of a fraction 8. Speed response; identify a value in negative fractional index form and its

expanded value as a fraction



Topic 24 - Surds 1


Revise square numbers

Express a whole number as a product of 2 factors with 1 factor being square

Understand a surd

Simplify a surd

Express a surd expression as a single

surd

Simplify a product of surds Simplify a sum or difference of surds Expand and simplify a surd expression

in brackets

1. Revision: Identify square numbers

up to 100

1. Demo: Understand a surd

Distinguish between a surd and a non-

surd

1. Demo: Simplify a surd expression

of the form √a x √b

1. Demo: Simplify an expression of

the form √ab ± √ac

1. Demo: Expand and simplify an

expression in brackets of the form

√a(n ± √a), √a(√b ± m√c)


up to 100

2. Demo: Simplify a surd of the form

√ab

2. Simplify a surd expression of the

form √a x √b

2. Simplify an expression of the form

√ab ± √ac

2. Expand and simplify an expression

in brackets of the form √a(n ± √a)

3. Revision: Match whole numbers

and their square up to 100

3. Simplify a surd of the form √ab

with assistance


form √a x √b


√ab ± √ac


in brackets of the form √a(√a ± √b)


from 121 to 400

4. Simplify a surd of the form √ab 4. Speed Response: Match a surd

expression and its simplified form


√ab ± n√ac


in brackets of the form √ab(√ac ±

√ad)


from 121 to 400

5. Simplify a surd of the form √ab 5. Demo: Simplify a surd expression

of the form √a x n√b x √c


m√ab ± n√ac

5. Demo: Expand and simplify an

expression in brackets of the form (n

± m√a) (p ± q√b)

6. Revision: Match whole numbers

and their square from 121 to 400

6. Speed Response: Match a surd and

its simplified form


form √a x n√b x √c

6. Demo: Simplify an expression of

the form √ab ± n√ac ± √ad


in brackets of the form (1 ±n √a)

(n√a ±1)

7. Express a whole number as a

product of 2 factors with 1 factor being square

7. Express a surd expression as a

single surd


form √a x n√b x √c


√ab ± √ac ± √ad


in brackets of the form (n ± m√a) (√a ± p)

8. Express a whole number as a product of 2 factors with 1 factor

being square

8. Express a surd expression as a single surd

8. Simplify a surd expression of the form √a x n√b x √c

8. Simplify an expression of the form √ab ± n√ac ± √ad

8. Expand and simplify an expression in brackets of the form (a ± √b) (c±

√d)


product of 2 factors with 1 factor

being square

9. Speed Response: Match a surd and

its simplified form

9. Demo: Simplify a surd expression

in index form


m√ab ± n√ac ± √ad

9. Expand and simplify miscellaneous

expressions in brackets


product of 2 factors with 1 factor

being square

10. Memory Task: Match a surd and

its simplified form

10. Simplify a surd expression in

index form

10. Demo: Simplify an expression

including sums or differences of surds

in index form

10. Expand and simplify miscellaneous

expressions in brackets


index form

11. Simplify an expression including

sums or differences of surds in index

form


index form

12. Simplify an expression including

sums or differences of surds in index

form



Topic 25 - Surds 2


Simplify an expression with a surd in

the denominator

Rationalise the denominator Simplify an expression by rationalising

the denominator

Simplify an expression by rationalising

the denominator

Simplify an expression by rationalising

the denominator

1. Demo: Use the rule of surds: √a/b

= √a/√b to simplify an expression

1. Demo: Rationalise the

denominator: a/√b

1. Demo: Simplify an expression by

rationalising the denominator: √a/√b x √c, √a x √b/√c


rationalising the denominator: (n√a±b)/√c

1. Demo: Know simple surd,

compound surd, conjugate surd


√a/√b which simplifies to a simple

surd

2. Rationalise the denominator: a/√b

and with assistance

2. Simplify an expression: √a/√b x

√c, √a x √b/√c

2. Simplify an expression: (√a±b)/√c 2. Demo: Multiply a compound surd

by its conjugate

3. Speed Response: Match a surd

fraction and its simplification

3. Rationalise the denominator: a/√b 3. Simplify an expression: n√a/√b x

√c, n√a x √b/m√c

3. Simplify an expression:

(n√a±b)/√c

3. Multiply a compound surd by its

conjugate


fraction and its simplification


expression and its form after

rationalisation of the denominator

4. Simplify an expression: n√a x

√b/m√c x √d


(n√a±b)/√c


rationalising the denominator:

a/(b±√c), √a/( b±√c)


(√a±√b )/√c with assistance


expression and its form after

rationalisation of the denominator

5. Simplify an expression: n√a x

√b/m√c x √d


(n√a±b)/√c

5. Simplify an expression by


a/(b±√c)



6. Demo: Rationalise the denominator

and simplify: 1/√a and √a/√b


rationalising the denominators: a/b√c

+ d/e√f


(n√a±b)/√c


rationalising the denominator: √a/(

b±√c)



7. Rationalise the denominator and

simplify: 1/√a and n√a/√b

7. Simplify an expression: a/b√c +

d/e√f


(n√a±b)/√c



a/(√b±c), a/(√b±√c)




simplify: n/√a and m√a/√b

8. Simplify an expression: a/b√c +

d/e√f


rationalising the denominator: a/(√b±c), a/(b√c±d), a/(√b±√c),

√a/(√b±√c)







(a±b√c)/(√d±e), (a±b√c)/ (√d±√e)

10. Simplify a miscellaneous fractional

expression





(a±b√c)/(√d±e), (a±b√c)/(√d±√e)



Topic 26 - Standard Form


Convert numbers greater than 1

between ordinary notation and standard form

Express numbers less than 1 in

standard form

Expand standard form to ordinary

notation; numbers < 1

Multiply and divide numbers in

standard form without a calculator

Add and subtract numbers in standard

form without a calculator

1. Engage with the pattern of indices by expressing a sequence of multiples

of 10 in index form

1. Engage with the pattern of indices by expressing a sequence of decimal

fractions in index form

1. Expand standard form for negative indices; single digit whole numbers

1. Multiply 2 numbers in standard form; (a x 10n) x (b x 10m): a x b <

10

1. Add 2 numbers in standard form with the same index; (a x 10n) + (b x

10m): a + b < 10

2. Express a number > 1 with a single

non-zero digit in standard form; with

assistance

2. Express a number < 1 with a single

non-zero digit in standard form; with

assistance

2. Expand standard form for negative

indices; 2-digit numbers with 1 dp

2. Convert a number in scientific

notation to correct standard form

2. Add 2 numbers in standard form

with the same index; (a x 10n) + (b x

10m): a + b maybe >= 10

3. Express a number < 1 with 2 non-

zero digits in standard form; with

assistance

3. Express a number < 1 with 2 non-

zero digits in standard form; with

assistance

3. Expand standard form for negative

indices; 3-digit numbers with 2 dp;

includes zero as middle digit

3. Multiply 2 numbers in standard

form; (a x 10n) x (b x 10m): a x b

maybe > 10

3. Add 2 numbers in standard form;

(a x 10n) + (b x 10m): a + b maybe

>= 10; |n-m| = 1

4. Express a number > 1with 2 non-

zero digits in standard form

4. Express a number < 1with 2 non-

zero digits in standard form

4. Express standard form as

thousands, millions, billions, etc

4. Multiply 2 numbers in standard

form; (a x 10n) x (b x 10m): a x b

maybe > 10; a or b has 1 dp

4. Add 2 numbers in standard form;

(a x 10n) + (b x 10m): a + b maybe

>= 10; |n-m| = 2

5. Express a number > 1 with 2 or 3

non-zero digits in standard form

5. Express a number < 1 with 2 or 3

non-zero digits in standard form

5. Raise a number in standard form to

a power and rewrite in standard form

5. Subtract 2 numbers in standard

form with the same index; (a x 10n) -

(b x 10m): a - b > 0

6. Express a large number given as

thousands, millions, billions in

standard form

6. Express a small number given as

thousandths, millionths, billionths in

standard form

6. Divide 2 numbers in standard form;

(a x 10n) / (b x 10m): a / b > 1

6. Subtract 2 numbers in standard

form with the same index; (a x 10n) -

(b x 10m): a - b > 0; |n-m| < 3

7. Expand standard form; single digit whole numbers >= 1

7. Divide 2 numbers in standard form; (a x 10n) / (b x 10m): a / b maybe <=

1

8. Expand standard form; 2-digit

numbers with 1 dp > 1

9. Expand standard form; 2 or 3-digit

numbers with 1 or 2 dp > 1

10. Express standard form as

thousands, millions, billions, etc

11. Convert between standard form

and ordinary form in context








wordsearch puzzles


crossword puzzles



Quizzes: Mixed questions on Topics 15

to 24; Differentiated from 1 to 2


15 to 24

2. Match terms to their descriptions 2. Complete a wordsearch 2. Complete a crossword 2. Enter missing words in sentences 2. Quiz: Mixed questions from Topics 15 to 24








10. Match terms to their descriptions

Maths Workout - Geometry & Measures


Geometry & Measures Topics


1 Measurement 1 Measure a distance using a

slider and fixed scale

Measure a distance using a

moveable ruler

Complete missing numbers

along a linear scale

Read a linear scale using

interpolation

Read a circular scale using

interpolation

2 Measurement 2

Engage with units of

measure and their symbols

Convert between metric

units of length


units of mass

Know approximate

equivalences between Imperial and metric units

Convert between Imperial

and metric units

Identify and calculate with

upper and lower bounds

3 Line Symmetry

Complete a single colour

pattern of squares with one

line of symmetry

Complete a multi-coloured

pattern of squares with one

line of symmetry

Complete a line pattern

with one line of symmetry

Identify the number of lines

of symmetry on a shape or

pattern

Complete a pattern of

squares with two lines of

symmetry

Distinguish between shapes

with and without line

symmetry

Identify and attach one or

two lines of symmetry to a

shape or pattern

4 Rotational Symmetry

Engage with rotational

symmetry in nature,

geometry, patterns and kaleidoscopes

Identify the order of

rotational symmetry

Complete a pattern with

rotational symmetry

Complete a pattern with

rotational symmetry

5 Plane Symmetry

Engage with plane symmetry

Identify the number of planes of symmetry

Identify the number of planes of symmetry

6 Shapes

Recognise and explore facts

about triangles,

quadrilaterals and regular

polygons

Recognise and explore facts

about triangles,

quadrilaterals and regular

polygons

Calculate the exterior and

interior angles of a regular

polygon

Calculate the sum of the

interior angles of a polygon

Solve problems and puzzles

with shapes

7 Solids

Identify the number of

faces, edges and vertices

on a range of solids










Investigate Euler’s formula

Solve problems and puzzles

with solids

8 Angles

Work with angle types and

sizes

Estimate and measure

angles

Estimate by drawing

Calculate angles along a

straight line, at a vertex

and around a point

Calculate angles in triangles

and quadrilaterals

Calculate angles created by

parallel lines and a

transverse and other

quadrilaterals

Calculate angles in diagrams

involving regular polygons

9 Perimeter

Calculate the perimeter of a

simple rectilinear shape

Calculate the circumference

of a circle and the perimeter

of a complex shape with

circular elements

10 Area

Estimate the area of shapes

by counting squares and

half-squares

Calculate the area of a

square, rectangle and

complex shape


units of area


triangle and complex

shapes with triangular

elements


circle and complex shapes

with circular elements

Calculate the area of a kite,

rhombus, trapezium,

parallelogram and complex

shape





11 Capacity & Volume

Understand and convert

between units of capacity and volume

Read a scale using

interpolation to find the amount of liquid in a

container

Find the volume of a solid

by counting cubes and half-cubes

Calculate the volume of a

cube and cuboid

Calculate the capacity of a

cuboid container and the amount of liquid it contains

12 Volume Calculate the volume of a

cube, cuboid and complex

solid


prism


cylinder and complex solid

with cylindrical elements


pyramid, cone, sphere and

complex solid

13 Surface Area

Calculate the surface area

of a cube, cuboid and

complex solid


of a cylinder and complex

solids with cylindrical

elements


of a cone


of a sphere and complex

solids

14 Language Tasks & Quizzes 1 Match maths terms to their

definitions


of SSM through wordsearch

puzzles


of SSM through crossword

puzzles


statements concerning SSM

terms


of SSM through hangman

game

15 Scale Drawings

Understand and measure

angles of elevation &

depression

Use a scale to calculate real

and map distances

Read and measure a 3-

figure bearing

Locate a point and the

relative position of 2 points

on a scale drawing given a

bearing and a distance

Construct a triangle

Solve a scale drawing

problem with bearings

16 Loci Construct the locus of a point with a simple path

Construct the locus of a point with a simple or

complex path

Construct the locus of a point with a simple or

complex path

17 Speed, Distance & Time

Calculate distance, speed,

time and average speed

Read and interpret a

distance-time graph

Calculate speed


distance-time graph

Calculate speed and average speed

Construct a distance-time

graph to solve a problem

Construct a distance-time

graph to solve a problem

Calculate average speed

18 Transformations 1 Identify the image of a

reflection

Perform a simple reflection

by drawing the image of an

object reflected in a line

Perform and describe a

translation: non-vector

instructions


simple rotation about a

point: multiples of 15O


simple enlargement: no

point of enlargement

19 Transformations 2


reflection on a coordinate

grid


translation on a coordinate

grid using vector notation


rotation about a point on a

coordinate grid

Perform and describe an

enlargement on a

coordinate grid with a

centre of enlargement:

whole positive scale factor

Perform and describe an

enlargement on a

coordinate grid with a

centre of enlargement:

fractional and negative integer scale factor

20 Similarity

Understand similarity and

congruence

Identify corresponding

sides and angles

Prove similarity for two

triangles

Calculate lengths on similar

shapes using ratio of

corresponding sides

Calculate length and area

using the linear scale factor

and area scale factor

Calculate length, area,

surface area, volume and

capacity using the linear,

area and volume scale factors

Solve problems with similar

shapes and solids


on Topics 1 to 10;

differentiated from 1 to 7

21 Pythagoras Investigate, know and prove Pythagoras

Calculate the hypotenuse in a right angled triangle

Calculate a shorter side in a right angled triangle

Solve mixed problems using Pythagoras

Apply Pythagoras in 3D





22 Trigonometry 1

Engage with trigonometric nomenclature and

SOHCAHTOA

Calculate an angle using sin, cos and tan

Calculate a side using sin, cos and tan; required side

is the numerator

Calculate a side using sin, cos and tan; required side

is the denominator

Know the formula triangles from SOHCAHTOA

Calculate any side and any

angle

23 Trigonometry 2

Calculate any side and any

angle using trigonometry

Solve problems using trigonometry and

Pythagoras

Use the formula: area of a

triangle = ½ absinC

Calculate sides and angles

with the sine rule

Calculate sides and angles

with the cosine rule

Solve mixed trigonometry

problems

24 Circle Geometry

Calculate the circumference

of a circle and the perimeter of a complex

shape


circle and a complex shape

Calculate the length of an

arc, the area of a sector and the area of a segment

Know and use circle

theorems that do not involve tangents

Know and use circle

theorems that involve tangents


Engage with Maths

language by matching

terms to their descriptions

Engage with Maths

language through

wordsearch puzzles

Engage with Maths

language through

crossword puzzles

Engage with Maths

language by completing

sentences

Engage with Maths

language through Hangman


on Topics 1 to 10;

Differentiated from 1 to 7



Topic 1 - Measurement 1


Measure a distance using a slider and

fixed scale

Measure a distance using a moveable

ruler

Complete missing numbers along a

linear scale

Read a linear scale using interpolation Read a circular scale using

interpolation

1. Use a vertical slider to measure the

length of a line to the nearest millimetre

1. Use a ruler to measure the length

of a line to the nearest millimetre

1. Complete missing numbers along a

linear scale; whole numbers; scale progresses by 1

1. Read a horizontal linear scale; large

intervals multiples of 10; 10 small divisions

1. Read a static circular speedometer;

large intervals multiples of 10; 10 small divisions


length of an image to the nearest

millimetre


of an image to the nearest millimetre


linear scale; whole numbers; scale

progresses by 2


intervals multiples of 10; interpolation

required - 5 small divisions

2. Read a static circular speedometer;

large intervals multiples of 10;

interpolation required - 5 small

divisions


length of an image to the nearest

millimetre


of an image to the nearest millimetre



progresses by 5


intervals multiples of 100; 10 small

divisions

3. Read a circular dial; large intervals

multiples of 1,10, 100,1000; 10 small

divisions

4. Use a horizontal slider to measure

the height of an image to the nearest

millimetre

4. Use a ruler to measure the height

and width of an image to the nearest

millimetre



progresses by 4, 5 and 6


intervals multiples of 100;


divisions

4. Read a circular dial; large intervals

multiples of 1,10, 100,1000;


divisions


the height of an image to the nearest

millimetre


and width of an image to the nearest

millimetre



progresses by 7, 8 and 9


intervals whole numbers; 10 small

divisions

5. Read a circular scale; large

intervals multiples of 10; 10 small

divisions


the height of an image to the nearest millimetre; work out the average of 5

heights


and width of an image to the nearest millimetre; work out the average of 5

heights


linear scale; decimals; 1dp; scale progresses by 0.1, 0.2 and 0.5


intervals whole numbers; interpolation required - 5 small divisions


intervals multiples of 1; interpolation required; 5 small divisions

Large intervals multiples of 100; 10

small divisions


linear scale; decimals; 1dp; scale

progresses by 0.3, 0.4 and 0.6

7. Read a vertical linear scale; varied

large and small intervals;

interpolation required


intervals multiples of 10; interpolation

required; 5 small divisions



progresses by 0.01, 0.02 and 0.05

8. Read a vertical linear scale; varied

large and small intervals;

interpolation required


intervals multiples of 1,100;

interpolation required; 5 small

divisions



progresses by 0.01 to 0.09


intervals multiples of 0.1,0.01;

interpolation required; 5 small

divisions


intervals multiples of 0.001,0.001; interpolation required; 5 small

divisions



Topic 2 - Measurement 2


Engage with units of measure and

their symbols

Convert between metric units of

length

Convert between metric units of mass Know approximate equivalences

between Imperial and metric units

Convert between Imperial and metric

units

Identify and calculate with upper and

lower bounds

1. Speed response; identify a unit of

measure and its symbol

1. Convert between metres and

centimetres; metres to 1 dp

1. Convert between kilograms and

grams; kilograms to 1 dp

1. Know approximate equivalences

between imperial and metric units

1. Understand upper and lower

bounds

2. Speed response; identify a unit of

measure and its symbol

2. Convert between metres and

centimetres; metres to 2 dp

2. Convert between kilograms and

grams; kilograms to 3 dp


kilometres, using 5 miles = 8

kilometre

2. Calculate upper and lower bounds

for measurements: nearest whole unit


between units of length, area, mass

and capacity & volume

3. Convert between centimetres and

millimetres; whole centimetres

3. Convert between grams and

milligrams; grams to 2 dp


kilometres, using 1 mile = 1.6 km


for measurements: nearest 10 units

4. Convert between centimetres and

millimetres; centimetres to 1 dp

4. Convert between grams and

milligrams; grams to 3 dp

4. Convert between feet and inches,

and metres, using 1 inch = 2.54cm


for measurements: nearest 100 units

5. Convert between kilometres and

metres; kilometres to 1 dp

5. Convert between tonnes and

kilograms; tonnes to 3 dp

5. Convert between pounds and

kilograms, using 1kg = 2.2lb


for measurements: nearest ½ of a

unit

6. Convert between kilometres and

metres; kilometres to 3 dp

6. Solve problems in context involving

conversion between metric units of

mass

6. Convert between pounds and

kilograms, using 1kg = 2.2lb


for measurements: nearest tenth of a

unit


conversion between metric units of length


conversion between metric units of mass

7. Problem solving; convert between

combined rates


for measurements: nearest hundredth of a unit

8. Solve problems in context involving conversion between metric units of

length

8. Speed response; identify 2 equal masses expressed in different units

8. Calculate the greatest and least perimeter of a rectangle;

measurements: nearest whole unit

9. Speed response; identify 2 equal

lengths expressed in different units


masses expressed in different units

9. Calculate the greatest and least

area of a rectangle; measurements:

nearest whole unit




masses expressed in different units


perimeter of a rectangle;

measurements: nearest tenth of a

unit




value of a single stage calculation;

measurements: various accuracy




value of a multi-stage calculation;

measurements: various accuracy



Topic 3 - Line Symmetry


Complete a single colour pattern of

squares with one line of symmetry

Complete a multi-coloured pattern of

squares with one line of symmetry

Complete a line pattern with one line

of symmetry

Identify the number of lines of

symmetry on a shape or pattern

Complete a pattern of squares with

two lines of symmetry

Distinguish between shapes with and

without line symmetry; identify the number of lines of symmetry; add 1

or 2 lines of symmetry to a pattern

1. Complete a single colour pattern

with one vertical line of symmetry; 24

squares

1. Complete a multi-colour pattern


squares

1. Complete a line pattern with one

slant line of symmetry, adding 2 lines

1. Identify the number of lines of

symmetry on a geometric shape

1. Distinguish between capital letters

with and without line symmetry


with one horizontal line of symmetry;

24 squares



24 squares




symmetry on a geometric shape

2. Distinguish between capital letters

with and without line symmetry;

letters rotated



squares



squares




symmetry on a design


symmetry on capital letters



40 squares



40 squares



4. Engage with patterns with 2 lines of

symmetry by drawing a pattern which

automatically has 2 lines of symmetry


symmetry on capital letters; letters

rotated



squares



squares



5. Draw a pattern with 2 lines of

symmetry; 48 squares

5. Distinguish between road signs with

and without line symmetry


with one horizontal line of symmetry; 60 squares


with one horizontal line of symmetry; 60 squares





6. Add a line of symmetry to a single

colour pattern


with one slant line of symmetry; 24

squares



squares

7. Complete a line pattern on

isometric dotted grid with one vertical

line of symmetry



7. Add a line of symmetry to a multi-

colour pattern



squares



squares



line of symmetry



8. Add 2 lines of symmetry to a single

colour pattern



squares



squares



line of symmetry


symmetry; 96 squares; optional

motion

9. Add 2 lines of symmetry to a multi-

colour pattern



squares



squares



line of symmetry


symmetry; 192 squares; optional

motion

10. Add 2 lines of symmetry to a

multi-colour pattern



squares



squares



line of symmetry

11. Add 2 lines of symmetry to a

multi-colour pattern



Topic 4 - Rotational Symmetry

Target 1 Target 2 Target 3 Target 4

Engage with rotational symmetry in

nature, geometry, patterns and kaleidoscopes

Identify the order of rotational

symmetry

Complete a pattern with rotational

symmetry

Complete a pattern with rotational

symmetry

1. Engage with rotational symmetry in nature

1. Identify the order of rotational symmetry for a polygon

1. Engage with a pattern with rotational symmetry order 2

1. Complete a multi-colour line pattern with rotational symmetry

order 3

2. Engage with rotational symmetry in

nature

2. Identify the order of rotational

symmetry for a polygon


with rotational symmetry order 2

2. Complete a single colour line

pattern with rotational symmetry

order 3

3. Engage with rotational symmetry

by observing a simplified snowflake

rotate around its centre


symmetry for a polygon





4. Engage with rotational symmetry by

observing a regular pentagon rotate


symmetry for geometric shape






by observing a regular octagon rotate

around its centre





5. Complete a multi-colour line


order 6


by observing a design rotate around

its centre





6. Complete a single colour line


order 6


by changing criteria on a kaleidoscope



Topic 5 - Plane Symmetry


Engage with plane symmetry

Identify the number of planes of

symmetry

Identify the number of planes of

symmetry

1. Understand plane symmetry 1. Identify the number of symmetry

planes of a cube

1. Identify the number of symmetry

planes of a pentagonal prism

2. Observe plane symmetry in nature 2. Identify the number of symmetry planes of a cuboid with no square

faces

2. Identify the number of symmetry planes of a hexagonal prism

3. Distinguish between solids with and

without plane symmetry


planes of a cuboid with a square

cross-section


planes of a cone


planes of a cylinder


planes of a square prism


planes of an equilateral triangular

prism


planes of an isosceles triangular prism


planes of a scalene triangular prism



Topic 6 - Shapes


Recognise and explore facts about

triangles, quadrilaterals and regular polygons

Recognise and explore facts about

triangles, quadrilaterals and regular polygons

Solve problems and puzzles with

shapes

1. Know the properties of equilateral, Isosceles, right-angled and scalene

triangles

1. Identify the names of triangles and quadrilaterals

1. Problem Solving: Recognise a shape from a limited view

2. Know the properties of a square,

rectangle, kite, parallelogram,

rhombus and trapezium

2. Identify the names of quadrilaterals

and polygons

2. Problem Solving: Recognise a

shape from clues

3. Know the properties of regular

polygons: equilateral triangle, square,

pentagon, hexagon, octagon and

decagon

3. Identify the names of polygons, a

semicircle and an ellipse

4. Engage with the concept of a

regular polygon tending to a circle

4. Match the name of a polygon with

the correct number of sides; 3 - 10

5. Know the properties of a circle 5. Match the name of a polygon with

the correct number of sides; 10 - 100

6. Quiz: Enter the name of the shape



Topic 7 - Solids


Identify the number of faces, edges

and vertices on a range of solids







Investigate Euler’s formula

Solve problems and puzzles with

solids

1. Observe a range of solids Tasks 1-10. Enter the number of vertices, edges and faces for a...

1. Cube

Tasks 1-7. Enter the number of vertices, edges and faces for a...

1. Hexahedron

Tasks 1-8. Enter the number of vertices, edges and faces for a...

1. Decagonal prism

1. Problem Solving: Recognise the nets of a cube

2. Observe a range of solids; click to

see a close-up and name

2. Cuboid 2. Octahedron 2. Dodecagonal prism 2. Engage with the 11 nets of a cube;

observe them fold up

3. Identify the names of solids 3. Triangular prism 3. Octagonal-based pyramid 3. Dodecagonal prism 3. Distinguish between a proper net

and a false net

4. Identify the names of solids 4. Triangular-based pyramid

4. Decagonal-based pyramid 4. Cone 4. Distinguish between a proper net

and a false net

5. Identify the names of solids 5. Tetrahedron 5. Dodecagonal-based pyramid 5. Cylinder 5. Name a solid from its net

6. Square-based pyramid 6. Hexagonal prism 6. Dodecahedron 6. Problem Solving: Recognise a solid

from a limited view

7. Pentagonal-based pyramid 7. Octagonal prism 7. Icosahedron 7. Problem Solving: Recognise a solid

from clues

8. Pentagonal-based prism 8. Investigate Euler’s formula

9. Hexagonal-based pyramid

10. Hexagonal-based prism



Topic 8 - Angles


Work with angle types and sizes

Estimate and measure angles

Estimation an angle drawing

Calculate angles along a straight line,

at a vertex and around a point

Calculate angles in triangles and

quadrilaterals

Calculate angles created by parallel

lines and a transverse and other quadrilaterals

1. Identify all the right angles in a picture

1. Calculate angles along a straight line; horizontal

1. Calculate angles in a triangle 1. Calculate alternate angles

2. Distinguish between right angles

and non-right angles

2. Calculate angles along a straight

line

2. Calculate angles in a triangle 2. Calculate alternate angles

3. Know acute, right, obtuse, straight,

reflex and complete turn

3. Calculate angles along a straight

line; includes right angles

3. Calculate angles in a right-angled

triangle

3. Calculate complementary angles

4. Identify the names of angles:

acute, right, obtuse, straight, reflex,

complete turn

4. Calculate vertically opposite angles 4. Calculate angles in an isosceles

triangle

4. Calculate complementary angles

5. Identify an angle: acute, right,

obtuse, straight, reflex or complete

turn

5. Calculate angles around a point 5. Calculate angles in an isosceles

triangle

5. Calculate angles in a parallelogram

6. Speed response: separate angles

into: acute, right, obtuse, straight,

reflex or complete turn

6. Calculate angles around a point 6. Calculate angles in mixed diagrams 6. Calculate angles in a rhombus

7. Estimate and measure the size of

an acute angle

7. Calculate angles around a point;

includes right angles

7. Calculate angles in a quadrilateral

with at least one right angle

7. Calculate angles in a trapezium


an obtuse angle

8. Calculate angles in a quadrilateral 8. Calculate angles in varied diagrams


an acute or obtuse angle

9. Calculate angles in a kite 9. Calculate angles in varied diagrams


an acute or obtuse angle; inside scale

of protractor

10. Calculate angles in varied

diagrams

11. Estimate an acute or obtuse angle

by drawing



Topic 9 - Angles in a Polygon


Calculate the exterior and interior

angles of a regular polygon

Calculate the sum of the interior

angles of a polygon

Calculate angles in diagrams involving

regular polygons

1. Understand how external angles

are drawn on an irregular polygon

1. Understand that the external and

internal angles add up to 180o

1. Calculate internal and external

angles in a regular polygon

2. Know how to sum the external angles of a polygon, considering only

a single external angle at each vertex

2. Complete the table of regular polygons, external and internal angles

2. Calculate angles in diagrams involving regular polygons

3. Understand that the sum of the

external angles of a pentagon is 360o

3. Demo: the angles of a triangle add

up to 180o

3. Calculate angles in diagrams


4. Understand that the sum of the

external angles of a polygon is 360o

4. Demonstration: the angles of a

quadrilateral add up to 360o



5. Calculate the external angle of a

regular polygon

5. Observe the pattern in splitting

polygons into triangles



6. Complete a table of external angles

and polygons

6. Calculate the total internal angles

by splitting a polygon into triangles

7. Answer mixed questions on Targets

3 and 4



Topic 10 - Perimeter

Target 1 Target 2

Calculate the perimeter of a simple

rectilinear shape

Calculate the circumference of a circle

and the perimeter of a complex shape with circular elements

1. Calculate the perimeter of a square and rectangle given all 4 sides

1. Know the formula for the circumference of a circle

2. Calculate the perimeter of a square

and rectangle given 2 sides

2. Calculate the circumference of a

circle

3. Calculate the perimeter of a

rectilinear shape given all the sides

3. Calculate the perimeter of a shape



rectilinear shape given some of the

sides


with circular elements; extension


rectilinear shape given some of the

sides



6. Calculate the perimeter of capital

letters drawn on a square background





Topic 11 - Area


Estimate the area of shapes by

counting squares and half-squares

Calculate the area of a square,

rectangle and complex shape

Convert between metric units of area

Calculate the area of a triangle and

complex shapes with triangular elements

Calculate the area of a circle and

complex shapes with circular elements

Calculate the area of a kite, rhombus,

trapezium, parallelogram and complex shape

1. Estimate area by counting squares 1. Calculate the area of a square and rectangle; whole number sides

1. Demo: Understand how the area of a triangle can be shown to be half the

area of a rectangle

1. Demo: Understand how the area of a circle can be shown to be r2

1. Demo: Understand how the area of a kite can be shown to be half the

area of the surrounding rectangle

2. Estimate area by counting squares 2. Calculate the area of a square and

rectangle; decimal side values

2. Demo: calculate the area of a

triangle

2. Calculate the area of a circle given

the radius or diameter

2. Calculate the area of a kite

3. Estimate area by counting squares 3. Demo: Understand how to calculate

the area of a complex shape

3. Calculate the area of a triangle 3. Calculate the area of a shapes with

circular elements

3. Demo: Understand how the area of

a parallelogram is the area of a

rectangle

4. Estimate area by counting squares 4. Calculate the area of a complex

shape

4. Calculate the area of a triangle 4. Calculate the area of a shapes with

circular elements; extension

4. Calculate the area of a

parallelogram

5. Calculate the area of a complex

shape


shape with triangular elements

5. Calculate the area of a shapes with



a rhombus can be calculated as a kite

or a parallelogram depending on the

information given

6. Demo: Understand how to calculate

the area of a shape with a cut-out


shape with triangular elements



6. Calculate the area of a rhombus

7. Calculate the area of a shape with a

cut-out




a trapezium can be calculated as a

rectangle

8. Convert between square units 8. Calculate the area of a trapezium

9. Solve problems on perimeter and

area


shape

10. Solve problems on perimeter and

area

10. Calculate the area under a graph;

extension



Topic 12 - Capacity & Volume


Understand and convert between units

of capacity and volume

Read a scale using interpolation to

find the amount of liquid in a container

Find the volume of a solid by counting

cubes and half-cubes

Calculate the volume of a cube and

cuboid

Calculate the capacity of a cuboid

container and the amount of liquid it contains

1. Know the difference between capacity and volume and the units of

each

1. Read a scale to find the amount of liquid in a container

1. Find the volume of a solid by counting cubes

1. Calculate the volume of a cube and cuboid: unit length markings

1. Calculate the capacity of a cuboid in millilitres

2. Know the equivalence of units of

capacity and volume, and the uses of

each

2. Read a scale using interpolation to

find the amount of liquid in a

container

2. Find the volume of a solid by

counting cubes

2. Calculate the volume of a cube and

cuboid: unit length markings

2. Calculate the capacity of a cuboid;

convert to litres

3. Know some uses of the units of

capacity and volume



container


counting cubes

3. Calculate the volume of a complex

solid: unit length markings

3. Calculate the quantity of liquid in a

container in millilitres

4. Convert between litres and

millilitres; litres to 1dp



container


counting cubes


container; convert to litres


millilitres; litres to 3dp


counting cubes


container; convert to litres where

necessary


centilitres; litres to 1dp


counting cubes and half cubes


container

7. Convert between centilitres and

millilitres; centilitres to 1dp




container

8. Convert between litres and cubic

centimetres; litres to 1dp




container

9. Convert between litres and cubic

centimetres; litres to 3dp




container

10. Solve problems in context involving capacity and volume

10. Find the volume of a solid by counting cubes and half cubes

10. Calculate the quantity of liquid in a complex container; extension

11. Solve problems in context involving capacity and volume

12. Speed response: identify two

equivalent amounts


equivalent amounts


equivalent amounts



Topic 13 - Volume


Calculate the volume of a cube,

cuboid and complex solid

Calculate the volume of a prism Calculate the volume of a cylinder and

complex solid with cylindrical elements

Calculate the volume of a pyramid,

cone, sphere and complex solid

1. Calculate the volume of a cube and cuboid

1. Calculate the volume of a prism given the cross-sectional area and the

length

1. Calculate the volume of a cylinder 1. Calculate the volume of a pyramid given the area of the base and the

height


cuboid

2. Calculate the volume of a prism;

cross-sectional area = complex

rectangular


cylindrical container; convert to litres

2. Calculate the volume of a pyramid


cuboid


cross-sectional area = complex

rectangular and triangular


cylindrical solid

3. Calculate the volume of a cone and

part cone


solid


cross-sectional area = trapezium,

parallelogram, rhombus, kite

4. Calculate the volume of a sphere

and part sphere


solid

5. Calculate the volume of complex

solids



Topic 14 - Surface Area


Calculate the surface area of a cube,

cuboid and complex solid

Calculate the surface area of a

cylinder and complex solids with cylindrical elements

Calculate the surface area of a cone Calculate the surface area of a sphere

and complex solids

1. Calculate the surface area of a cube 1. Calculate the curved surface area of a cylinder

1. Calculate the curved surface area of a cone

1. Calculate the surface area of a sphere

2. Calculate the surface area of a

cuboid

2. Calculate the total surface area of a

cylinder


cone

2. Calculate the curved surface area

of a sphere and part sphere


cuboid


of a part cylinder and complex

cylindrical solid


sphere and part sphere


complex solid


part cylinder and complex cylindrical

solid


of a complex solid


complex solid








wordsearch puzzles


crossword puzzles




Hangman




1 to 13


1 to 13


1 to 13


1 to 13


1 to 13


1 to 13


1 to 13









Topic 16 - Scale Drawings


Understand and measure angles of

elevation & depression

Use a scale to calculate real and map

distances

Read and measure a 3-figure bearing Locate a point and the relative

position of 2 points on a scale drawing given a bearing and a distance

Construct a triangle

Solve a scale drawing problem with bearings

1. Demo: Understand how an angle of elevation is measured

1. Simplify a map scale expressed as a ratio of quantities: unitary ratios

1. Demo: Understand how 3-figure bearings are written and calculated

1. Use a 360o angle measurer to locate a point on a given bearing

1. Construct a triangle given 1 side and 2 angles

2. Demo: Understand how an angle of

depression is measured

2. Simplify a map scale expressed as

a ratio of quantities

2. Use a 360o angle measurer to

measure a bearing

2. Locate a point on a given bearing 2. Construct a triangle given 1 side

and 2 angles: measure the sides

produced

3. Measure an angle of elevation with

a protractor

3. Convert between scales expressed

with units and scales expressed as

pure ratios

3. Read a 3-figure bearing given

clockwise angle

3. Locate the relative position of 2

points given a bearing measured from

either point

3. Construct a triangle given 2 sides

and the included angle

4. Measure an angle of depression

with a protractor

4. Calculate the real distance given

the scale and the map distance

4. Read a 3-figure bearing less than

100o given clockwise angle


points given a bearing and the

distance: scale 1cm:1km

4. Construct a triangle given 2 sides

and the included angle: measure 1

angle and the side produced

5. Calculate the map distance given

the scale and the real distance

5. Read a 3-figure bearing given

anticlockwise angle




5. Solve a bearing problem by

completing a scale drawing

6. Calculate the real or map distance

given the scale

6. Read the bearing of A from P or P

from A given a connecting angle




6. Solve a bearing problem by

completing a scale drawing

7. Use an ordinary 180o protractor to

measure a bearing of A from P or P from A


points given a bearing and the distance: variable scale in ratio form



Topic 17 - Loci


Construct the locus of a point with a

simple path


simple or complex path


simple or complex path

1. Draw the locus of a point which is

equidistant from 2 points: horizontal alignment


equidistant from a point

1. Draw the locus of the centre of a

ball as it moves around the inside of a container: with assistance


equidistant from 2 points: vertical

alignment


equidistant from a line segment

2. Draw the locus of the centre of a

ball as it moves around the inside of a

container


equidistant from 2 points: slant

alignment


equidistant from a square (outside)

3. Draw the locus of a dog which is

tethered to a square shed


equidistant from 2 parallel lines


equidistant from a rectangle (outside)

4. Draw the locus of a dog which is

tethered to a rectangular shed



Topic 18 - Speed, Distance & Time


Calculate distance, speed, time and

average speed

Read and interpret a distance-time

graph

Calculate speed


graph

Calculate speed and average speed

Construct a distance-time graph to

solve a problem

Construct a distance-time graph to

solve a problem

Calculate average speed

1. Calculate a journey time in hours and minutes: start and finish in the

same day: 24hr clock

1. Read and interpret a distance time graph: 3 sections

1. Read and interpret a distance-time graph

1. Construct a distance time graph: 3 sections

1. Construct a distance time graph: 5 sections

2. Calculate a journey time in hours

and minutes: some journeys across

midnight: 24hr clock

2. Read and interpret a distance time

graph: 3 sections

2. Read and interpret a distance-time

graph

2. Construct a distance time graph: 3

sections


sections

3. Complete missing entries in the

conversion between minutes, hours

and minutes, and tenths of hours


graph: 3 sections


graph


sections 3. Construct a distance time graph: 5

sections

4. Demo: Know formulas for steady

speed, distance and time: formula

triangle


graph: 5 sections


graph


sections


sections

5. Calculate steady speed, distance

and time


graph: 5 sections: calculate speed


graph


sections: return journey



6. Calculate steady speed, distance

and time


graph: 5 sections: calculate speed


graph


sections: return journey 6. Construct a distance time graph: 5


7. Demo: Know and use the formula

for average speed

7. Understand the meaning of the

gradient of a line and a horizontal line


graph




8. Calculate average speed given 2

journey parts


graph




9. Calculate average speed given 3

parts of a journey including a rest



10. Convert between m/s and km/h 10. Construct a distance time graph:

3 sections: return journey

11. Solve mixed problems with speed,

distance and time

12. Solve mixed problems with speed, distance and time



Topic 19 - Transformations 1


Identify the image of a reflection Perform a simple reflection by drawing

the image of an object reflected in a line

Perform and describe a translation:

non-vector instructions

Perform and describe a simple

rotation about a point: multiples of 15O

Perform and describe a simple

enlargement: no point of enlargement

1. Identify the correct position of the image of an object reflected in a

vertical line

1. Draw the image of a simple object reflected in a vertical line

1. Locate the image of a translated object

1. Locate the image of a rotated object rotated: shape attached to the

point of rotation: top centre start

1. Draw the image of an enlarged square: scale factor 2 or 3

2. Identify the correct position of the

image of an object reflected in a

vertical line

2. Draw the image of a simple object

reflected in a horizontal line

2. Locate the image of a translated

object

2. Locate the image of a rotated

object: shape attached to the point of

rotation

2. Draw the image of an enlarged

square



vertical line

3. Draw the image of a simple object

reflected in a slant line


object



rotation


rectangle



horizontal line

4. Draw the image of an object

reflected in a vertical line

4. Draw the image of a translated

object

4. Locate the image for an object

rotated around a point: top centre

start


right-angled triangle: scale factor 2 or

3



horizontal line


reflected in a horizontal line


object


rotated around a point


right-angled triangle



horizontal line


reflected in a slant line


object


rotated around a point

6. Draw the image of an enlarged non


7. Identify the correct position of the image of an object reflected in a line

at a 45o angle

7. Draw the image of a complex object reflected in a vertical line

7. Describe a translation given the object and image

7. Describe a rotation: shape attached to the point of rotation: top centre

start

7. Draw the image of an enlarged quadrilateral


image of an object reflected in a line

at a 45o angle

8. Draw the image of a complex

object reflected in a horizontal line

8. Describe a translation given the

object and image

8. Describe a rotation: shape attached

to the point of rotation


pentagon


image of an object reflected in a line

at a 45o angle


object reflected in a slant line


object and image


to the point of rotation


hexagon



10. Describe a rotation: top centre

start


octagon

11. Draw the image of a very complex


11. Describe a rotation 11. Identify the scale factor of

enlargement: quadrilaterals

12. Describe a rotation 12. Identify the scale factor of

enlargement: pentagons

13. Identify the scale factor of

enlargement: hexagons

14. Identify the scale factor of

enlargement: octagons



Topic 20 - Transformations 2


Perform and describe a reflection on a

coordinate grid

Perform and describe a translation on

a coordinate grid using vector notation

Perform and describe a rotation about

a point on a coordinate grid

Perform and describe an enlargement

on a coordinate grid with a centre of enlargement: whole positive scale

factor

Perform and describe an enlargement

on a coordinate grid with a centre of enlargement: fractional scale factor

(Tasks 1-6) and negative integer scale

factor (Tasks 7-12)


reflected in the y-axis


object


object rotated: shape attached to the point of rotation: top centre start

1. Demo: Understand how the centre

of enlargement, object and image are connected: triangle


of enlargement, object and image are connected: triangle


reflected in the x-axis


object



rotation


of enlargement, object and image are

connected: square



connected: square

3. Draw the image of an object reflected in the line y = x and y = -x

3. Locate the image of a translated object

3. Locate the image of a rotated object: shape attached to the point of

rotation

3. Identify the centre and scale factor of enlargement: triangles: 1st

quadrant

3. Identify the centre and scale factor of enlargement: triangles

4. Draw the image of an object reflected in a given vertical line:

equation given and line shown

4. Draw the image of a translated object

4. Locate the image for an object rotated around a point: top centre

start

4. Identify the centre and scale factor of enlargement: quadrilaterals: 1st

quadrant

4. Identify the centre and scale factor of enlargement: quadrilaterals

5. Draw the image of an object reflected in a given horizontal line:

equation given and line shown


5. Locate the image for an object rotated around a point


5. Draw the image of an enlarged triangle

6. Draw the image of an object reflected in a line with gradient 1 or -

1: equation given and line shown


6. Locate the image for an object rotated around a point



7. Identify the equation of the line of

reflection given object and image:

vertical line


object and image


to the point of rotation: top centre

start

7. Identify the centre and scale factor

of enlargement: pentagons



connected: triangle

8. Identify the equation of the line of reflection given object and image:

horizontal line


8. Describe a rotation: shape attached to the point of rotation


8. Demo: Understand how the centre of enlargement, object and image are

connected: square

9. Identify the equation of the line of reflection given object and image:

gradient 1 or -1


9. Describe a rotation: shape attached to the point of rotation



10. Identify the equation of the line of reflection given object and image: any

of the above

10. Describe a rotation: top centre start

10. Draw the image of an enlarged pentagon


11. Draw the image of an object reflected in vertical line: only equation

given

11. Describe a rotation 11. Draw the image of an enlarged hexagon



reflected in a horizontal line: only equation given

12. Describe a rotation 12. Draw the image of an enlarged

octagon


quadrilateral


reflected in a line with gradient 1 or -

1: only equation given

14. Draw the image of an object reflected in a line: only equation given



Topic 21 - Similarity


Understand similarity and congruence

Identify corresponding sides and angles

Prove similarity for two triangles

Calculate lengths on similar shapes

using ratio of corresponding sides

Calculate length and area using the

linear scale factor and area scale factor

Calculate length, area, surface area,

volume and capacity using the linear, area and volume scale factors

Calculate length, area, surface area,

volume and capacity using the linear, area and volume scale factors

Solve problems with similar shapes

and solids

1. Demo: Know basic idea of similarity

and congruence and the connection

with enlargement

1. Demo: Calculate a length on a

similar shape using the ratio of

corresponding sides

1. Demo: Identify the linear scale

factor (l.s.f.) for an enlargement

1. Investigation: Derive the volume

scale factor (v.s.f.) from the linear

scale factor (l.s.f.)

1. Calculate a volume on a similar

solid given the l.s.f. as a fraction

2. Speed response: Identify congruent

shapes

2. Calculate lengths on similar

triangles: enlargement: whole

answers

2. Calculate the l.s.f. for an

enlargement

2. Demo: Derive the v.s.f. from the

l.s.f and calculate a volume

2. Calculate a length on a similar solid

given the v.s.f.

3. Speed response: Identify similar

shapes


triangles: reduction: whole answers

3. Calculate the l.s.f. for a reduction 3. Derive the v.s.f. from the l.s.f. and

calculate a volume

3. Calculate a length on a similar solid

given both volumes

4. Speed response: Identify which

pairs shapes must be similar and

which are not necessarily similar


shapes: whole answers

4. Demo: Calculate a length on a

similar shape using the l.s.f.

4. Derive the v.s.f. from the l.s.f. and

calculate a capacity in ml

4. Solve mixed problems involving

similarity including surface area

5. Demo: Know conditions for

similarity

5. Calculate lengths on similar shapes 5. Calculate a length on a similar

shape using the l.s.f.

5. Derive the v.s.f. from the l.s.f. and

calculate a capacity in litres




corresponding sides in two similar

shapes


shapes: obscure diagrams

6. Calculate a length on a similar

shape using the l.s.f. in reverse

6. Derive the v.s.f. and from the l.s.f.

and vice versa, and calculate a length:

table form



7. Speed response: Identify the corresponding angles in two similar

shapes

7. Calculate lengths on similar shapes: obscure diagrams

7. Calculate a length on a similar shape using the l.s.f. as a fraction

7. Derive the v.s.f. and a.s.f. from the l.s.f. and vice versa, and calculate a

length, area or volume: table form

7. Solve mixed problems involving similarity including surface area

8. Demo: Prove similarity for 2

triangles by comparing angles


shapes: obscure diagrams (algebra)

8. Investigation: Derive the area scale

factor (a.s.f.) from the l.s.f.

9. Demo: Prove similarity for 2

triangles by comparing sides


shapes: obscure diagrams

9. Demo: Derive the a.s.f. from the

l.s.f. and calculate an area

10. Derive the a.s.f. from the l.s.f.

and calculate an area


and vice versa, and calculate a length:

table form


and vice versa, and calculate a length

or area: table form

13. Solve mixed problems on similar

shapes

14. Solve mixed problems on similar

shapes



Topic 22 - Pythagoras


Investigate, know and prove

Pythagoras

Calculate the hypotenuse in a right

angled triangle

Calculate a shorter side in a right

angled triangle

Solve mixed problems using

Pythagoras

Apply Pythagoras in 3D

1. Distinguish between triangles with

a right angle and triangles without

1. Demo: Calculate the hypotenuse in

a right-angled triangle

1. Demo: Calculate a shorter side in a


1. Use Pythagoras in a right-angled

triangle; horizontal base; whole number starting values

1. Demo: Apply Pythagoras in 3D

2. Investigate Pythagoras by

collecting data of side lengths, then

squaring them

2. Demo: Calculate the hypotenuse in

a right-angled triangle

2. Demo: Calculate a shorter side in a


2. Use Pythagoras in a right-angled

triangle; slant angle; decimal number

starting values

2. Demo: Apply Pythagoras in 3D

3. Demo: Know Pythagoras’ Theorem 3. Calculate the hypotenuse in a right-

angled triangle; Pythagorean triples

3. Calculate a shorter side in a right-

angled triangle; Pythagorean triples

3. Solve a problem in context using

Pythagoras; diagram given

3. Apply Pythagoras in 3D in a cube;

with diagrams

4. Demo: Prove Pythagoras’ Theorem 4. Calculate the hypotenuse in a right-

angled triangle; horizontal base;

whole number sides



whole number sides

4. Solve a problem in context using

Pythagoras; diagram given

4. Apply Pythagoras in 3D in a cube;

with diagrams

5. Engage with Pythagoras by creating

a physical square on the 3 sides of a

right angled triangle

5. Calculate the hypotenuse in a right-

angled triangle; slant angle; whole

number sides


angled triangle; slant angle; whole

number sides

5. Use Pythagoras in a complex

diagram

5. Apply Pythagoras in 3D in a cuboid;

with diagrams


a physical square on the hypotenuse

from squares on the other two sides;

with guidance



decimal sides



decimal sides

6. Use Pythagoras in a complex

diagram

6. Apply Pythagoras in 3D in a cuboid;

with diagrams


a physical square on the hypotenuse from squares on the other two sides;

no guidance


angled triangle; slant angle; decimal sides


angled triangle; slant angle; decimal sides

7. Use Pythagoras twice in a complex

diagram

7. Apply Pythagoras in 2D and 3D in a

cuboid; with diagram


a physical square on the hypotenuse

from squares on the other two sides;

no guidance; rotated

8. Solve problems with Pythagoras;

no diagrams

8. Apply Pythagoras in 2D and 3D in a

cuboid; with diagram


no diagrams

9. Solve problems in 3D without

diagrams


find the area of an Isosceles triangle


find the area of a shape



Topic 23 - Trigonometry 1


Engage with trigonometric

nomenclature and SOHCAHTOA

Calculate an angle using sin, cos and

tan

Calculate a side using sin, cos and

tan; required side is the numerator

Calculate a side using sin, cos and

tan; required side is the denominator

Know the formula triangles from

SOHCAHTOA

Calculate any side and any angle

1. Know the names ‘Hypotenuse’, ‘Opposite’ and ‘Adjacent’

1. Demo: Calculate an angle using sin 1. Demo: Calculate a side using sin 1. Demo: Calculate a side using sin 1. Demo: Extract 3 formula triangles from SOHCAHTOA


hypotenuse in a right angle triangle

2. Calculate an angle using sin;

horizontal/vertical orientation

2. Calculate a side using sin;


2. Calculate a side using sin;


2. Select which ratio to use to

calculate any side length


opposite in a right angle triangle

3. Calculate an angle using sin 3. Calculate a side using sin 3. Calculate a side using sin 3. Calculate a side using sin, cos or

tan: horizontal/vertical orientation


adjacent in a right angle triangle

4. Demo: Calculate an angle using cos 4. Demo: Calculate a side using cos 4. Demo: Calculate a side using cos 4. Calculate a side using sin, cos or

tan

5. Know SOHCAHTOA and use a

mnemonic, such as ‘Silly Old Hens’

5. Calculate an angle using cos;


5. Calculate a side using cos;


5. Calculate a side using cos;


5. Calculate an angle using sin, cos or


6. Know and write out the 3

trigonometric ratios

6. Calculate an angle using cos 6. Calculate a side using cos 6. Calculate a side using cos 6. Calculate an angle using sin, cos or

tan

7. Demo: Calculate an angle using tan 7. Demo: Calculate a side using tan 7. Demo: Calculate a side using tan

8. Calculate an angle using tan;


8. Calculate a side using tan;


8. Calculate a side using tan;


9. Calculate an angle using tan 9. Calculate a side using tan 9. Calculate a side using tan


calculate an angle


calculate a side length


calculate a side length in the

denominator

11. Calculate an angle using sin, cos

or tan


or tan


or tan


or tan


or tan


or tan



Topic 24 - Trigonometry 2


Calculate any side and any angle

using trigonometry

Solve problems using trigonometry

and Pythagoras

Use the formula: area of a triangle =

½ absinC

Calculate sides and angles with the

sine rule

Calculate sides and angles with the

cosine rule

Solve mixed trigonometry problems

1. Calculate a side using sin, cos or


1. Demo: know the labelling

convention used in triangles

1. Demo: Know both expressions of

the sine rule

1. Demo: Know both expressions of

the cosine rule

1. Solve trigonometry problems:

geometry


tan

2. Demo: Derive the formula: area of

a triangle = ½ absinC

2. Demo: Calculate a side using the

sine rule

2. Demo: Calculate a side using the

cosine rule


geometry & bearings


tan; complex diagram

3. Demo: Calculate the area of a

triangle using ½ absinC

3. Calculate a side using the sine rule 3. Calculate a side using the cosine

rule


geometry



4. Calculate the area of a triangle

using ½ absinC: simple data

4. Calculate a side using the sine rule:

no diagrams: some obscure data

4. Calculate a side using the cosine

rule: no diagrams: some obscure data


bearings


tan


using ½ absinC: obscure data

5. Demo: Calculate an angle using the

sine rule

5. Demo: Calculate an angle using the

cosine rule


bearings


tan; complex diagram


using ½ absinC: no diagrams: simple

data

6. Calculate an angle using the sine

rule

6. Calculate an angle using the cosine

rule


angles of depression

7. Solve problems using trigonometry:

calculate the area of a regular polygon

7. Solve problems using area of a

triangle using ½ absinC: complex

diagrams

7. Calculate an angle using the sine

rule: no diagrams

7. Calculate an angle using the cosine

rule: no diagrams


angles of elevation

8. Solve problems using trigonometry;

no diagrams

8. Solve problems using area of a

triangle using ½ absinC: no diagrams:

obscure data

8. Solve a bearing problem requiring

the use of the sine rule: diagrams


the use of the cosine rule: diagrams


geometry

9. Solve problems using trigonometry

in 3D; angles in cuboids


the use of the sine rule: no diagrams


the use of the cosine rule: no

diagrams


geometry

10. Solve problems using trigonometry in 3D; angles in cuboids

10. Solve trigonometry problems: geometry



Topic 25 - Circle Geometry


Calculate the circumference of a circle

and the perimeter of a complex shape

Calculate the area of a circle and a

complex shape

Calculate the length of an arc, the

area of a sector and the area of a segment

Know and use circle theorems not

involving tangents

Know and use circle theorems

involving tangents

1. Know the formula for the circumference of a circle


a circle can be shown to be r2

1. Demo: Calculate the length of an arc

1. Demo: Know that the angle in a semi-circle is a right angle

1. Demo: Know that the angle between a tangent and a radius is a

right angle

2. Calculate the circumference of a

circle

2. Calculate the area of a circle given

the radius or diameter

2. Calculate the length of an arc 2. Calculate missing values in

diagrams using ‘angle in a semi-circle’

2. Calculate missing values using

‘angle between a tangent and radius

is a right angle’




circular elements

3. Calculate the angle at the centre or

the radius given the arc length

3. Demo: Know that angles in the

same segment are equal

3. Demo: Know that from any point

outside a circle there are exactly two

tangents and they have equal length






sector

4. Calculate missing values in

diagrams using ‘angles in the same

segment are equal’

4. Calculate missing values using

‘from any point outside a circle there

are exactly two tangents and they

have equal length’





5. Calculate the area of a sector 5. Demo: Know that the angle at the

centre is twice the angle at the

circumference

5. Demo: Know that the angle

between a tangent and a chord is

equal to the angle in the alternate segment

6. Calculate the perimeter of a shape with circular elements; extension

6. Calculate the area of a shapes with circular elements; extension

6. Calculate the angle at the centre or the radius given the area of the sector

6. Calculate missing values in diagrams using ‘the angle at the

centre is twice the angle at the

circumference’

6. Calculate missing values using ‘the angle between a tangent and a chord

is equal to the angle in the alternate

segment’



7. Calculate length of an arc and the

area of a sector: table form

7. Demo: Know that opposite angles

in a cyclic quadrilateral add up to 180o

7. Summary Demo: All 3 circle

theorems involving tangents

8. Calculate angle at centre, radius,

length of an arc or the area of a

sector: table form

8. Calculate missing values in

diagrams using ‘opposite angles in a

cyclic quadrilateral add up to 180 o’

8. Mixed calculations from tasks 1 to 7


segment


theorems not involving tangents

9. Mixed calculations from tasks 1 to 7

10. Calculate the area of a segment 10. Mixed calculations from Tasks 1 to

9


theorems

11. Mixed calculations from Tasks 1 to

9

11. Mixed calculations from targets 3

and 4

12. Mixed calculations from Tasks 1 to 12. Mixed calculations from targets 3

and 4








wordsearch puzzles


crossword puzzles




Hangman




14 to 24


14 to 24


14 to 24


14 to 24


14 to 24


14 to 24


14 to 24






Maths Workout - Statistics & Probability


Statistics & Probability Topics


1 Tables & Diagrams 1 Read, interpret and

construct a two-way table

Read, interpret and

construct a distance table and diagrams

Read and interpret a Venn

diagram

Construct a Venn diagram Read, interpret and

construct a cinema schedule in am/pm time

2 Tables & Diagrams 2 Read, interpret and construct a cinema

schedule in 24h clock time

Read, interpret and construct a train timetable

in am/pm time

Read, interpret and construct a train timetable

in 24h clock time

Read, interpret and construct a calendar

Read and interpret a table of dates, times and other

information

3 Mean, Median, Mode & Range

Introduction to Averages

Identify the mode of a set

of raw data

Work out the median of a

set of raw data

Calculate the mean of a set

of raw data

Solve problems with the

mean

Calculate the range of a set

of raw data

Summary of the uses of

mean, median and mode

Solve problems on mean,

median, mode and range

Compare sets of data

4 Pictograms


pictogram


pictogram

Construct a pictogram from

a frequency table

Construct a pictogram from

given information

5 Bar Charts Read and interpret a bar

chart

Construct a bar chart from

a frequency table

Construct a bar chart from

given information

Work with multiple column

and segmented bar charts

Read and interpret a back-

to-back bar chart

6 Line Graphs


distance-time graph

Read and interpret a real-

life line graph

Identify a trend or

description of a graph

Match a graph to its corresponding process

Use a conversion graph

Read and interpret a time

series graph

Calculate a moving average

7 Scatter Graphs

Understand and distinguish between positive and

negative correlation

Plot and interpret a scatter graph

Draw and use a line of best fit

8 Pie Charts Revise the calculations

required to construct and

read a pie chart

Read and interpret a pie

chart

Read and interpret a pie

chart: extension

Construct a pie chart from a

frequency table

Construct a pie chart from

given information

9 Stem & Leaf Diagrams

Read, interpret and

construct a stem and leaf

diagram

Find the range and median

from a stem and leaf

diagram

Interpret and construct a

back-to-back stem and leaf

diagram

10 Introduction to Probability

Know the probability scale

Use probability words to

describe outcomes

Simplify and compare

probabilities in chance form

Calculate simple probability

Express a probability in the

equivalent forms of chance,

fraction, decimal and percentage


in the forms of chance,

fraction, decimal and percentage

Solve problems with simple

probability

Calculate probabilities using

a possibility space diagram

11 Probability Lab

Use probability theory to

predict the most likely

outcome on a spinner

Use probability theory in

games of chance: ‘Higher,

Lower or Equal’ dice game

Use probability theory in

games of chance: ‘Higher

or Lower’ card game

Engage with experimental

probability

Calculate expectation; work

with mutually exclusive

events; list possible

outcomes



Statistics & Probability Topics


12 Language Tasks & Quizzes 1 Engage with Maths

language by matching terms to their descriptions

Engage with Maths

language through wordsearch puzzles

Engage with Maths

language through crossword puzzles

Engage with Maths

language by completing sentences

Quizzes: Questions from

the whole unit differentiated from 1 to 7

13 Data Handling Theory

Understand types of data, the use of a frequency table

and grouped frequency

table

Understand the data handling cycle

Understand how to create a questionnaire and avoid

bias

Understand key points of 4 sampling methods

Understand: 3 averages; bar chart, frequency chart,

and histogram; frequency

polygon and frequency

chart

14 Frequency Tables

Sort categorical and

numerical data into a

frequency table using tallies


frequency table

Find the median from a

frequency table

Find the mean from a

frequency table

Find the range, median and

mode from a frequency

table

Sort numerical data into a

grouped frequency table

Identify the modal class

and the class that contains

the median

Estimate the mean from a


15 Frequency Charts & Polygons

Construct a frequency chart Read and interpret a

frequency chart


frequency chart

Estimate the mean from a frequency chart

Construct a frequency

polygon


frequency polygon

Estimate the mean from a frequency polygon

16 Histograms

Understand and calculate frequency density

Construct a histogram Read and interpret a histogram

Read and interpret a histogram

Estimate the mean from a

histogram

Construct, read and interpret histograms

displaying age and rounded

continuous data

17 Measures of Spread 1

Calculate the range of a set

of raw data

Revision: Calculate the

median from a set of raw

data

Calculate the interquartile

range of a small set of raw

data and a larger set of

data in a frequency table

Construct a box plot from

raw data

Read and interpret a box

plot

18 Measures of Spread 2

Calculate cumulative

frequency

Plot a cumulative frequency

curve

Estimate the median and

interquartile range from a

cumulative frequency curve

Interpret a cumulative

frequency curve

Construct a box plot from

grouped data

Compare box plots

19 Probability 1

Revision of simple

probability

Understand mutual

exclusivity

Calculate probabilities of ‘A’ and ‘not A’

Calculate with the sum of

the probabilities of all

mutually exclusive events.

Calculate probabilities for

mutually exclusive events

using the addition rule or otherwise

Calculate probabilities for

mutually exclusive events

using the addition rule or otherwise: extension

20 Probability 2

Understand independence

Know and use the

multiplication rule

Understand and complete a

tree diagram: independent

and dependent events

Use a tree diagram to

calculate probabilities of

independent events

Use a tree diagram to

calculate probabilities of

dependent events

Calculate ‘At Least’

probability

Identify and calculate

conditional probability

21 Language Tasks & Quizzes 2 Engage with Maths



Engage with Maths

language through

wordsearch puzzles

Engage with Maths

language through

crossword puzzles

Engage with Maths


sentences

Quizzes: Questions from

the whole unit

differentiated from 1 to 7



Topic 1 - Tables & Diagrams 1


Read, interpret and construct a two-

way table

Read, interpret and construct a

distance table and diagrams

Read and interpret a Venn diagram Construct a Venn diagram Read, interpret and construct a

cinema schedule in am/pm time

1. Read and interpret a two-way table 1. Read and interpret a distance table

(3 Places)

1. Read and interpret a Venn

diagram: 2 categories

1. Construct a Venn diagram: 2

categories

1. Read and interpret a cinema

schedule

2. Read and interpret a two-way table 2. Read and interpret a distance table (4 Places)

2. Read and interpret a Venn diagram: 2 categories

2. Construct a Venn diagram: 2 categories

2. Read and interpret a cinema schedule

3. Read and interpret a two-way table 3. Read and interpret a distance table (5 Places)

3. Read and interpret a Venn diagram: 2 categories

3. Construct a Venn diagram: 2 categories



(5 Places)




categories


schedule


(6 Places)




categories


schedule

6. Enter missing elements in a two-

way table and interpret the table

6. Read and interpret a distance table

(6 Places)




categories

6. Enter missing elements in a cinema

schedule



7. Construct a distance table from

map (3 Nodes: 3 Arcs)




categories


schedule








categories


schedule

9. Enter raw data into a two-way table 9. Construct a distance table from





categories


schedule

10. Enter raw data into a two-way

table




categories

10. Enter missing elements in a

cinema schedule


table

11. Read and interpret a map with an

approximate radial distance indicator


categories


cinema schedule


table

12. Read and interpret a map with an

approximate radial distance indicator


categories



Topic 2 - Tables & Diagrams 2



cinema schedule in 24h clock time

Read, interpret and construct a train

timetable in am/pm time

Read, interpret and construct a train

timetable in 24h clock time


calendar

Read and interpret a table of dates,

times and other information


schedule

1. Read and interpret a train timetable 1. Read and interpret a train timetable 1. Operate and read a basic electronic

diary

1. Read and interpret a table of

campsite charges


2. Read and interpret a train timetable 2. Read and interpret a train timetable 2. Complete the dates in a month given one starting point

2. Read and interpret a table of campsite charges


3. Read and interpret a train timetable 3. Read and interpret a train timetable 3. Operate and read a basic electronic diary

3. Read and interpret a table of campsite charges: calculator provided


schedule

4. Read and interpret a train timetable 4. Read and interpret a train timetable 4. Work out an interval given the start

and end date, including both end

points: Electronic calendar provided


holiday prices: calculator provided


schedule

5. Read and interpret a train timetable 5. Read and interpret a train timetable 5. Work out an interval given the start

and end date, including both end

points: Electronic calendar provided


holiday prices: calculator provided


schedule

6. Read and interpret a train timetable 6. Read and interpret a train timetable 6. Operate, read and interpret a basic

electronic diary

6. Read and interpret a swimming

pool schedule


schedule

7. Read and interpret a train timetable 7. Read and interpret a train timetable 7. Complete a section of a monthly

view calendar


pool schedule: calculator provided


schedule

8. Read and interpret a train timetable 8. Read and interpret a train timetable 8. Operate, read and interpret a basic

electronic diary


pool schedule: calculator provided


schedule

9. Read and interpret a train timetable 9. Read and interpret a train timetable 9. Work out the finish date, given the

start date and duration, including both

end points: Electronic calendar

provided


weather information


cinema schedule

10. Enter missing elements in a train

timetable


timetable


weather information


cinema schedule


timetable


timetable


cinema schedule


timetable


timetable


cinema schedule



Topic 3 - Mean, Median, Mode & Range


Introduction to Averages

Identify the mode of a set of raw data

Work out the median of a set of raw

data

Calculate the mean of a set of raw

data

Solve problems with the mean

Calculate the range of a set of raw

data

Summary of the uses of mean,

median and mode

Solve problems on mean, median,

mode and range

Compare sets of data

1. Know the 3 types of average 1. Identify the median of an ordered

data set: odd number of data items

1. Demo: Know how to calculate the

mean of a raw data set

1. Calculate the range of a set of

ordered raw data

1. Demo: Summary of the uses of

mean, median and mode

2. Identify the mode of a set of raw

data set by inspection

2. Identify the median of a data set by

ordering: odd number of data items

2. Calculate the mean of a raw data

set: whole answers

2. Calculate the range of a set of raw

data

2. Sort a raw data set, then calculate

the mean, median, mode and range


data set by sorting

3. Demo: Identify the median of a raw

data set: even number of values


set: exact decimal answers


data by sorting

3. Calculate the mean, median, mode

and range of a data set in context


data set by sorting


ordering: even number of data items


set


data by sorting

4. Calculate the mean, median, mode

and range of a data set in context


data set by sorting


ordering


set


data by sorting

5. Solve a problem involving mean,

median and range


data set by inspection

6. Speed Response: Identify a

matching median and data set

6. Calculate the mean of data in a bar

chart

6. Calculate the range from data in a

bar chart


median and range

7. Identify the mode from data in a

bar chart.

7. Solve a problem involving mean 7. Speed Response: Identify a

matching range and data set


median and range

8. Solve a problem involving mean 8. Speed Response: Identify a


8. Compare two data sets by

considering their mean, median and

range

9. Solve a problem involving mean 9. Compare two data sets by


range

10. Solve a problem involving mean 10. Compare two data sets by

considering their mean, median and range

11. Compare two data sets by considering their mean, median and

range

12. Compare two data sets by


range



Topic 4 - Pictograms


Read and interpret a pictogram

Read and interpret a pictogram

Construct a pictogram from a

frequency table

Construct a pictogram from given

information

1. Read and interpret a pictogram 1. Read and interpret a pictogram 1. Construct a pictogram from a

frequency table

1. Solve a logic problem then

construct a pictogram

2. Read and interpret a pictogram 2. Read and interpret a pictogram 2. Construct a pictogram from a frequency table

2. Solve a logic problem then construct a pictogram

3. Read and interpret a pictogram 3. Read and interpret a pictogram 3. Construct a pictogram from a frequency table

3. Solve a logic problem then construct a pictogram


frequency table




frequency table









Topic 5 - Bar Charts


Read and interpret a bar chart Construct a bar chart from a

frequency table

Construct a bar chart from given

information

Work with multiple column and

segmented bar charts

Read and interpret a back-to-back bar

chart

1. Read and interpret a bar chart 1. Construct a bar chart from a

frequency table


construct a bar chart

1. Read and interpret a multiple

column bar chart

1. Read and interpret a back-to-back

bar chart

2. Read and interpret a bar chart 2. Construct a bar chart from a frequency table

2. Solve a logic problem then construct a bar chart

2. Read and interpret a multiple column bar chart

2. Read and interpret a back-to-back bar chart

3. Read and interpret a bar chart 3. Construct a bar chart from a frequency table

3. Solve a logic problem then construct a bar chart

3. Read and interpret a multiple column bar chart

3. Read and interpret a back-to-back bar chart


frequency table



4. Construct a multiple column bar

chart from a frequency table


bar chart


frequency table



5. Construct a multiple column bar

chart from a frequency table


bar chart

6. Read and interpret a bar chart 6. Solve a logic problem then


6. Read and interpret a segmented

bar chart

7. Read and interpret a bar chart 7. Solve a logic problem then


7. Read and interpret a segmented

bar chart

8. Complete the frequency scale from

given information, then read and

interpret a bar chart

9. Complete the frequency scale from

given information, then read and


10. Complete the frequency scale

from given information, then read and




Topic 6 - Line Graphs



graph

Read and interpret a real-life line

graph

Identify a trend or description of a

graph

Match a graph to its corresponding

process

Use a conversion graph

Read and interpret a time series graph

Calculate a moving average


graph


real life

1. Identify a trend or description of a

graph

1. Use a conversion graph 1. Read and interpret a time series

graph


graph


real life


graph


graph


graph


real life

3. Match the language of trends to an

equivalent term


graph


graph


real life


graph in context


graph


graph


real life


graph in context

5. Demo: Calculate a moving average


graph


real life


graph in context

6. Calculate a moving average


graph


real life

7. Match a physical process involving

rate to its corresponding graph



graph


real life





real life




real life





Topic 7 - Scatter Graphs


Understand and distinguish between

positive and negative correlation

Plot and interpret a scatter graph

Draw and use a line of best fit

1. Demo: Understand a scatter graph

and the 3 main types of correlation

1. Plot a scatter graph and interpret

the correlation

1. Practise drawing a line of best fit

2. Distinguish between examples of positive and negative correlation

2. Plot a scatter graph and interpret the correlation

2. Draw and use a line of best fit to predict results

3. Distinguish between examples of positive and negative correlation

3. Plot a scatter graph and interpret the correlation



Topic 8 - Pie Charts


Revise the calculations required to

construct and read a pie chart

Read and interpret a pie chart Read and interpret a pie chart:

extension

Construct a pie chart from a

frequency table

Construct a pie chart from given

information

1. Revision: Simplify a fraction 1. Demo: Read a pie chart: 2 methods 1. Read and interpret a pie chart

given the population: 5 sectors

1. Demo: Construct a pie chart from a

frequency table


construct a pie chart

2. Revision: Simplify a fraction 2. Read and interpret a pie chart given the population: 3 sectors

2. Read and interpret a pie chart given the population: 5 sectors

2. Construct a pie chart from a frequency table

2. Solve a logic problem then construct a pie chart

3. Demo: Complete a fraction calculation as required for pie charts



3. Construct a pie chart from a frequency table

3. Solve a logic problem then construct a pie chart

4. Complete a fraction calculation as

required for pie charts

4. Read and interpret a pie chart




4. Construct a pie chart from a

frequency table





5. Calculate the population then read

and interpret a pie chart


frequency table








frequency table








frequency table






frequency table




frequency table




frequency table



Topic 9 - Stem & Leaf Diagrams

Target 1 Target 2

Read, interpret and construct a stem

and leaf diagram

Find the range and median from a

stem and leaf diagram

Interpret and construct a back-to-

back stem and leaf diagram

1. Demo: Understand a stem and leaf

diagram

1. Find the range and median from a

stem and leaf diagram

2. Demo: Understand a stem and leaf

diagram

2. Interpret a back-to-back stem and

leaf diagram

3. Construct a stem and leaf diagram

from raw data

3. Construct a back-to-back stem and

leaf diagram


from raw data


from raw data


from raw data


from raw data



Topic 10 - Introduction to Probability


Know the probability scale

Use probability words to describe outcomes


Simplify and compare probabilities in chance form

Express a probability in the equivalent

forms of chance, fraction, decimal and percentage

Calculate simple probability in the

forms of chance, fraction, decimal and percentage

Solve problems with simple probability

Calculate probabilities using a

possibility space diagram

1. Demo: Know basic probability

concepts

1. Demo: Know how to calculate

simple probability

1. Express a probability in the

equivalent forms of chance, fraction,


1. Calculate simple probability on a

spinner in chance form

1. Demo: Calculate a probability using

a possibility space diagram

2. Engage with the language of

probability by matching probability

words with a value on the probability

scale

2. Simplify a probability in chance

form





spinner in chance form

2. Enter the possible total scores for 2

dice on a possibility space diagram

3. Engage with the language of

probability by matching a probability

value with a probability word


form





spinner as a fraction

3. Calculate probabilities using a


4. Describe the probability of an

outcome


form





spinner as a decimal




outcome


form


equivalent forms of chance, fraction, decimal and percentage


spinner as a percentage



6. Describe the probability of an outcome

6. Speed Response: Identify probabilities that are equivalent to 1

in 2

6. Identify 2 equivalent probabilities in the form of chance, fraction or

percentage

6. Calculate simple probability on a spinner in the form of chance,

fraction, decimal or percentage

6. Calculate probabilities using a possibility space diagram


outcome

7. Speed Response: Identify

probabilities that are more likely than

1 in 2

7. Identify 2 equivalent probabilities in

the form of chance, fraction, decimal

or percentage

7. Solve problems with simple

probability



8. Speed Response: Identify

probabilities that are less likely than 1

in 2


probability

9. Calculate simple probability on an

ordinary die


probability

10. Calculate simple probability on an

ordinary die


probability

11. Calculate simple probability with

beads in a bag


probability

12. Calculate simple probability with

playing cards



Topic 11 - Probability Lab


Use probability theory to predict the

most likely outcome on a spinner

Use probability theory in games of

chance: ‘Higher, Lower or Equal’ dice game

Use probability theory in games of

chance: ‘Higher or Lower’ card game

Engage with experimental probability Calculate expectation; work with

mutually exclusive events; list possible outcomes

1. Use probability theory to predict the most likely outcome on a spinner

1. Use probability theory to predict if the next outcome will be higher or

lower than the previous outcome: 1

die

1. Use probability theory to predict if the next outcome will be higher or

lower than the previous outcome:

cards

1. Simulation of throwing a drawing pin: record scores in tally chart,

calculate relative frequency

1. Demo: = Probability x Number of Trials = Expected Number of

Successes

2. Use probability theory to predict if

the next outcome will be higher or

lower than the previous outcome: 2

dice

2. Demo: Experimental probability

basics

2. Calculate the expected number of

successes

3. Estimate the probability of getting a

six on a biased die: simulation of

rolling a biased die 50 times

3. Calculate with the expected number

of successes with one die

4. Estimate the probability of getting a

six on a biased die: simulation of

rolling a biased die 50 times

4. Calculate with the expected number

of successes with two dice

5. Enrichment: Generate from

experimental probability

5. Demo: Mutually exclusive events

6. Calculate the probability of one

event given the probability of a

mutually exclusive event

7. Calculate the probability of one

event given the probability of a

mutually exclusive event

8. List possible outcomes using a

system


system


system


system


system








wordsearch puzzles


crossword puzzles






1 to 11

2. Match terms to their definitions 2. Complete a wordsearch 2. Complete a crossword 2. Enter missing words in sentences 2. Quiz: Mixed questions from Topics 1 to 11


4. Match terms to their definitions 4. Complete a wordsearch 4. Complete a crossword 4. Enter missing words in sentences 4. Quiz: Mixed questions from Topics

1 to 11


1 to 11


1 to 11

7. Match terms to their definitions 7. Enter missing words in sentences 7. Quiz: Mixed questions from Topics

1 to 11

8. Match terms to their definitions 8. Enter missing words in sentences


10. Match terms to their definitions






Topic 13 - Data Handling Theory


Understand types of data, the use of a

frequency table and grouped frequency table

Understand the data handling cycle Understand how to create a

questionnaire and avoid bias

Understand key points of 4 sampling

methods

Key points: 3 averages; bar chart,

frequency chart, and histogram; frequency polygon and frequency

chart

1. Presentation: Know the difference

between categorical and numerical

data

1. Presentation: Introduction to the 4

stages of the data handling cycle

1. Presentation: Some basic principles

of writing a questionnaire

1. Presentation: Understand the terms

sample, population, survey and

census

1. Presentation: The 3 averages:

Interactive diagram

2. Speed response: Distinguish

between categorical and numerical

data

2. Presentation: Stage 1: Identify the

problem



2. Presentation: Introduction to 4 of

the main types of sampling


between a bar chart, a frequency

chart and a histogram: Interactive

diagram


between discrete and continuous data

3. Presentation: Stage 1: Plan the

Process



3. Presentation: Random sampling:

uses, advantages & disadvantages

3. Presentation: Understand how a

frequency chart and frequency

polygon are related


between discrete and continuous data

4. Presentation: Stage 2: Collect the

data

4. Presentation: Biased questions 4. Presentation: Stratified sampling,:



between categorical, numerical

discrete and numerical continuous data

5. Presentation: Stage 3: Process &

present the data

5. Presentation: Biased questions 5. Calculate the correct values for a

stratified sample

6. Speed response: Distinguish between categorical, numerical

discrete and numerical continuous

data

6. Presentation: Stage 4: Interpret and summarise the results

6. Speed Response: Distinguish between a biased question and a fair

question

6. Calculate the correct values for a stratified sample: extension

7. Presentation: Know the terms raw

data and frequency table

7. Presentation: Stage 4: Evaluate the

results and the whole process

7. Speed Response: Distinguish

between a biased question and a fair

question

7. Calculate the correct values for a

stratified sample: extension

8. Presentation: Understand a


8. Presentation: All 4 Stages of DHC:

interactive diagram

8. Presentation: Quota sampling:


9. Presentation: Systematic sampling:


10. Presentation: All 4 sampling

methods: Interactive diagram



Topic 14 - Frequency Tables


Sort categorical and numerical data

into a frequency table using tallies

Read and interpret a frequency table

Find the median from a frequency

table

Find the mean from a frequency table

Find the range, median and mode from a frequency table

Sort numerical data into a grouped

frequency table

Identify the modal class and the class

that contains the median

Estimate the mean from a grouped

frequency table

1. Sort categorical data into a

frequency table using tallies and

complete the totals

1. Demo: Find the median of data in a

frequency table; odd set size

1. Find the mean of data in a

frequency table: assisted

1. Sort numerical data into a grouped

frequency table

1. Estimate the mean of discrete data

in a grouped frequency table: assisted

2. Sort categorical data into a


complete the totals


frequency table; even set size




frequency table



3. Sort numerical data into a


complete the total

Read and interpret the tally chart


frequency table; even set size, middle

terms from different groups




frequency table



4. Sort numerical data into a


complete the total

Read and interpret the tally chart

4. Find the median of data in a

frequency table



4. Identify the modal class and the

class that contains the median in a




5. Read and interpret a frequency table of categorical data

5. Find the median of data in a frequency table: extension

5. Find the mean of data in a frequency table

5. Identify the modal class and the class that contains the median in a


5. Estimate the mean of discrete data in a grouped frequency table

6. Read and interpret a frequency

table of categorical data

6. Find the range, mean, median and

mode of data in a frequency table

6. Estimate the mean of continuous

data in a grouped frequency table:

assisted


table of numerical data

7. Find the range, mean, median and

mode of data in a frequency table



assisted



8. Solve a problem involving the mean

from a frequency table



assisted





assisted




data in a grouped frequency table



Topic 15 - Frequency Charts & Polygons


Construct a frequency chart Read and interpret a frequency chart Read and interpret a frequency chart

Estimate the mean from a frequency chart

Construct a frequency polygon Read and interpret a frequency

polygon

Estimate the mean from a frequency

polygon

1. Construct a frequency chart from a



chart


chart

1. Construct a frequency polygon from

continuous data in a grouped

frequency table: with assistance


polygon




chart


chart





polygon




chart


chart





polygon


chart


data in a frequency chart



frequency table


data in a frequency polygon


chart





frequency table




chart




continuous data in a grouped frequency table





Topic 16 - Histograms


Understand and calculate frequency

density

Construct a histogram Read and interpret a histogram Read and interpret a histogram

Estimate the mean from a histogram

Construct, read and interpret

histograms displaying age and rounded continuous data

1. Calculate frequency density from a grouped frequency table

1. Construct a histogram 1. Demo: Read a histogram: equal width columns

1. Demo: Read a histogram: multiple column query

1. Demo: Understand class intervals when displaying age

2. Calculate frequency density from a


2. Construct a histogram 2. Read a histogram: equal width

columns: single column query

2. Read a histogram: multiple column

query

2. Calculate frequency density from

age data

3. Calculate with frequency, frequency

density and interval width

3. Construct a histogram 3. Read a histogram: equal width


3. Read a histogram: multiple column

query

3. Construct a histogram displaying

age



4. Construct a histogram 4. Complete a frequency table from a

histogram: equal width columns

4. Read a histogram: calculate the

total frequency


age



5. Construct a histogram 5. Demo: Read a histogram: unequal

width columns

5. Read a histogram: calculate the

total frequency


age

6. Construct a histogram 6. Read a histogram: unequal width


6. Read a histogram: estimate the

mean

6. Read a histogram displaying age:

single column query

7. Construct a histogram 7. Read a histogram: unequal width


7. Read a histogram: estimate the

mean

7. Read a histogram displaying age:

multiple column query

8. Construct a histogram 8. Complete a frequency table from a

histogram: unequal width columns

8. Demo: Estimate frequency in a

histogram: partial column query

8. Demo: Understand class intervals

when displaying rounded continuous

data

9. Construct a histogram 9. Estimate frequency in a histogram:

partial column query

9. Calculate frequency density from

rounded continuous data

10. Construct a histogram 10. Estimate frequency in a

histogram: multiple and partial

column query


rounded continuous data

11. Construct a histogram 11. Read a histogram displaying

rounded continuous data: single

column query

12. Construct a histogram 12. Read a histogram displaying

rounded continuous data: multiple column query



Topic 17 - Measures of Spread 1


Calculate the range of a set of raw

data

Revision: Calculate the median from a

set of raw data

Calculate the interquartile range of a

small set of raw data and a larger set of data in a frequency table

Construct a box plot from raw data Read and interpret a box plot

1. Calculate the range of a set of ordered raw data

1. Identify the median of an ordered data set: odd number of data items

1. Demo: Calculate the interquartile range of a set of raw data: data size

even

1. Demo: Construct a box plot 1. Demo: Read and interpret a box plot


data


ordering: odd number of data items

2. Demo: Calculate the interquartile

range of a set of raw data: data size

odd

2. Construct a vertical box plot given

min, Q1, Q2, Q3 and max values

2. Read and interpret a vertical box

plot


data by sorting

3. Demo: Identify the median of a raw

data set: even number of values

3. Calculate the interquartile range of

a set of raw data

3. Construct two vertical box plots

given min, Q1, Q2, Q3 and max

values

3. Read and interpret two vertical box

plots


data by sorting


ordering: even number of data items


a set of raw data

4. Construct a horizontal box plot


values

4. Read and interpret a vertical box

plot


data by sorting


ordering


a set of raw data

5. Construct two horizontal box plots


values

5. Read and interpret two vertical box

plots

6. Calculate the range from data in a

bar chart

6. Speed Response: Identify a median

and its matching data set


a set of raw data

6. Construct a box plot from raw data 6. Read and interpret a horizontal box

plot

7. Speed Response: Identify a


7. Demo: Calculate the interquartile

range from a frequency table using Q1 = (n+1)/4, Q3 = 3(n+1)/4

7. Construct two box plots from raw

data

7. Read and interpret two horizontal

boxplots

8. Speed Response: Identify a matching range and data set

8. Calculate the interquartile range from a frequency table

8. Construct a box plot from a frequency table

8. Read and interpret two horizontal boxplots

9. Calculate the interquartile range from a frequency table

9. Construct a box plot from a frequency table

9. Read and interpret two horizontal boxplots

10. Calculate the interquartile range

from a frequency table

10. Construct a box plot from a

frequency table

10. Read and interpret two horizontal

boxplots



Topic 18 - Measures of Spread 2


Calculate cumulative frequency

Plot a cumulative frequency curve

Estimate the median and interquartile

range from a cumulative frequency curve

Interpret a cumulative frequency

curve

Construct a box plot from grouped

data

Compare box plots

1. Demo: Calculate cumulative frequency

1. Demo: Estimate the median and interquartile range from a cumulative

frequency curve

1. Interpret a cumulative frequency curve, reading from the vertical axis

to the horizontal axis

1. Demo: Construct a box plot from grouped data

1. Compare horizontal box plots: identify a correct statement

2. Speed response: Calculate

cumulative frequency

2. Estimate the median and

interquartile range from a cumulative

frequency curve

2. Interpret a cumulative frequency

curve, reading from the vertical axis

to the horizontal axis

2. Construct a box plot from grouped

data

2. Compare horizontal box plots:

identify a correct statement

3. Enrichment: Calculate frequency

from cumulative frequency



frequency curve


curve, reading from 2 points on the

vertical axis to the horizontal axis


data


identify a correct statement

4. Demo: Understand the meaning of

cumulative frequency



frequency curve


curve, reading from 2 points on the

vertical axis to the horizontal axis


data


identify two correct statements

5. Plot the points for a cumulative

frequency curve



frequency curve


curve, reading from the horizontal

axis to the vertical axis


data

5. Compare vertical box plots: identify

a correct statement


frequency curve



frequency curve


curve, reading from the horizontal



data


a correct statement

7. Plot the points for a cumulative frequency curve

7. Estimate the median and interquartile range from a cumulative

frequency curve

7. Interpret a cumulative frequency curve, reading from the horizontal


7. Construct a box plot from grouped data with the cumulative frequency

chart on the same scale

7. Compare vertical box plots: identify a correct statement


frequency curve



frequency curve


curve, reading from the either axis

using percentages


data with the cumulative frequency



two correct statements


frequency curve



frequency curve


data with the cumulative frequency



frequency curve



frequency curve

10. Demo: Understand how a steep

ogive leads to a narrow box plot


frequency curve


frequency curve



Topic 19 - Probability 1


Revision of simple probability Understand mutual exclusivity

Calculate probabilities of ‘A’ and ‘not A’

Calculate with the sum of the

probabilities of all mutually exclusive events.

Calculate probabilities for mutually

exclusive events using the addition rule or otherwise

Calculate probabilities for mutually

exclusive events using the addition rule or otherwise: extension

1. Demo: Revision of simple probability

1. Demo: Understand mutually exclusive events

1. Demo: Understand that the sum of the probabilities of all mutually

exclusive events is 1

1. Demo: Calculate probabilities for mutually exclusive events using the

addition rule or otherwise

1. Calculate probabilities for mutually exclusive events

2. Calculate simple probability 2. Demo: Understand mutually

exclusive events using Venn diagrams

2. Calculate probabilities based on the

fact that the sum of the probabilities

of all mutually exclusive events is 1

2. Calculate probabilities for mutually

exclusive events


exclusive events

3. Calculate simple probability 3. Distinguish between mutually

exclusive events and non-mutually

exclusive events

3. Solve problems with mutually

exclusive events


exclusive events


exclusive events



exclusive events

4. Solve problems with mutually

exclusive events


exclusive events


exclusive events



exclusive events

5. Demo: Understand that the sum of

the probabilities of all mutually

exclusive events is 1: more than 2

events


exclusive events


exclusive events

6. Calculate simple probability 6. Calculate probabilities of ‘A’ and

‘not A’


fact that the sum of the probabilities of all mutually exclusive events is 1


exclusive events

6. Calculate simple probabilities:

Revision for Task 7

7. Calculate simple probability 7. Calculate probabilities of ‘A’ and

‘not A’


fact that the sum of the probabilities

of all mutually exclusive events is 1


exclusive events

8. Calculate simple probability 8. Solve problems with mutually

exclusive events


exclusive events


exclusive events



Topic 20 - Probability 2


Understand independence

Know and use the multiplication rule

Understand and complete a tree

diagram: independent and dependent events

Use a tree diagram to calculate

probabilities of independent events

Use a tree diagram to calculate

probabilities of dependent events

Calculate ‘At Least’ probability

Identify and calculate conditional probability

1. Demo: Understand independence and the multiplication rule

1. Demo: Understand and complete a tree diagram: independent events

1. Demo: Use a tree diagram to calculate probabilities: independent

events

1. Demo: Use a tree diagram to calculate probabilities: dependent

events

1. Demo: Calculate ‘At Least’ probabilities

2. Calculate probabilities of

independent events using the

multiplication rule

2. Complete a tree diagram 2. Calculate probabilities of

independent events using a tree

diagram

2. Calculate probabilities of dependent

events using a tree diagram

2. Demo: Calculate ‘At Least’

probabilities: alternative approach



multiplication rule



diagram



3. Calculate ‘At Least’ probabilities



multiplication rule

4. Complete a tree diagram 4. Demo: Use a tree diagram to

calculate probabilities: independent

events






multiplication rule



diagram






multiplication rule



diagram




7. Calculate probabilities of independent events using the

multiplication rule

7. Demo: Understand and complete a tree diagram: dependent events

7. Calculate probabilities of independent events

7. Calculate probabilities of dependent events

7. Demo: Identify conditional probabilities in a tree diagram



multiplication rule

8. Complete a tree diagram 8. Identify conditional probabilities in

a tree diagram



multiplication rule

9. Complete a tree diagram 9. Identify conditional probabilities in

a tree diagram

10: Demo: Summary of addition rule

and multiplication rule

10. Complete a tree diagram 10. Calculate with conditional

probabilities


probabilities


probabilities








wordsearch puzzles


crossword puzzles






13 to 20




13 to 20


13 to 20


13 to 20


13 to 20





Maths Workout - Algebra & Problem Solving


Algebra & Problem Solving Topics


1 Writing Algebra 1

Multiply a constant by a variable and a variable by a

variable, e.g. 4xb=4b,

3x4b=12b

Multiply 2 terms, e.g.

3ax4b=12ba, c x c=c2

Express an addition or

subtraction phrase with a single variable as an

expression

Express a multiplication or

division phrase with a single variable as an

expression

Express a single stage

phrase with up to 2 variables as an expression

2 Writing Algebra 2

Express a 2-stage phrase

with a single variable as an

expression: multiply, add

and subtract


with a single variable as an

expression: divide, add and

subtract


with 2 variables as an

expression


with up to 2 variables as an

expression (using brackets)


with up to 2 variables as an

expression (using algebraic

brackets and fractions)

3 Like Terms

Simplify an expression of

up to 3 single variable

terms by collecting like terms (positive answers)

Add and subtract integers:

Revision prior to adding and

subtracting terms


up to 3 single variable

terms by collecting like terms (pos and neg

answers)


up to 4 double variable

terms by collecting like terms


up to 6 double variable

terms by collecting like terms

4 Expanding Brackets

Expand brackets of the

form 2(a+3), 3(2t-3):

single variable


form 4a(2b-2), a(3a+2): up

to 2 variables


form -(y–4),-4a(3b+2): up

to 2 variables


form 4a(b-c), -3b(a+b-c):

up to 4 variables

Expand brackets and

simplify an expression of

the form 3(7x+2)+3x,

-3a(7a+2)-3a(a+2)

5 Factorising

Identify the HCF of 2 or 3

numbers

Identify the HCF of up to 3

algebraic terms

Factorise an expression of

the form 3t+6, 9ab-3b


the form ab2+6b, 3cd2–12d


the form 15a2-3ac+9ab

Simplify an algebraic

fraction by factorisation

6 Solving Equations 1

Solve a simple equation by inspection: x+4=12, 2x=4,

x/2=5

Complete the solution to a simple equation:

2x+3x=10, 2x+1=7,

x/2+3=5


3(x+4)=15, 3(x+1)=x-8,

3(x+1)=3(x-8)

Solve a simple equation of the form 2x+3x=10,

2x+1=7

Solve a simple equation of the form x/2+3=5,

3(x+4)=15, 3(x+1)=x-8,

3(x+1)=-3(x-8)

7 Algebraic Modelling

Use algebraic modelling to solve a single-stage

problem

Use algebraic modelling to solve a 2-stage problem



including the use of

brackets


including the use of

brackets

8 Substitution

Revise the order of

operations

Find the value of an

expression by substitution;

non-negative values

Find the value of an expression by substitution;

non-negative values


some negative values


extension

9 Formulae

Substitute into formulae;

convert between Fahrenheit

and Celsius; recognise

common formulae

Use a formula in reverse

given the subject

Use a formula in reverse

given the subject

Solve a problem using a

formula

Solve a problem using a

formula

Construct a formula from

given information

10 Problem Solving Theory Identify the features of a problem versus a

straightforward question

Identify the abilities and qualities required to solve a

problem

Understand the 4-stage

problem solving process

Be aware of some useful

problem solving strategies





11 Spotting Patterns

Copy a shape pattern Complete missing elements

in a pattern or sequence of objects

Extend a sequence of

shapes and extract information to form a

simple number sequence

Extend a sequence of

shapes or a line pattern Extend a sequence of

shapes

12 Problems & Puzzles 1

Solve a space-filling

problem: Pentominoes

Solve a matchstick puzzle Play Solitaire

Play Lights Out

Solve an anagram-style

number puzzle

Play Noughts & Crosses

Solve the frog puzzle

Solve the Queens problem

Play 4-in-a-Row

Solve a logic problem:

Guess the Pegs


Engage with Maths



Engage with Maths

language through

wordsearch puzzles

Engage with Maths

language through

crossword puzzles

Engage with Maths


sentences and through Hangman game

Quizzes: Puzzles and

problems differentiated

from 1 to 7

14 Sequences 1

Enter missing terms in a sequence with a common

difference

Enter missing terms in a sequence with a common

difference

Enter missing terms in a sequence with next term

rule of the form: Un+1=

3Un+1, 3(Un+1), Un/3+1,

(Un+1)/3

Enter missing terms in a sequence with a

miscellaneous next term

rule, including a Fibonacci

sequence

Enter missing terms in a sequence with a

miscellaneous next term

rule, including a Fibonacci

sequence

15 Sequences 2 Use the nth term rule to

generate a sequence

Identify the nth term rule of a sequence with a common

difference

Use the nth term rule to

generate a sequence

Identify the nth term rule of a quadratic sequence

using differences

Identify the nth term rule of a quadratic sequence using

differences

16 Solving Equations 2 Solve an equation with up

to 1 bracket on each side

Solve an equation with up

to 3 brackets on each side

Solve an equation with

fractions

Solve a problem using

algebraic modelling

Solve an equation by trial

and improvement

17 Straight Lines 1

Read and plot coordinates

in all 4 quadrants

Read and plot coordinates

in all 4 quadrants

Draw a straight line by

calculating and plotting points

Calculate the gradient of a

straight line between two points

Calculate the equation of a

straight line by calculating the gradient and identifying

the y-intercept

Know y=mx+c

18 Straight Lines 2

Calculate the equation of a

straight line

Rearrange an equation to

the form y=mx+c to find

the gradient and intercept

Find the midpoint between

2 points the length of a line

segment

Calculate the length of a

line segment

Solve problems with

parallel and perpendicular

lines

19 Simultaneous Equations

Solve a pair of

simultaneous equations

graphically

Solve a pair of

simultaneous equations by

elimination: adding or subtracting leads directly to

solution

Solve a pair of


elimination: multiply one equation

Solve a pair of


elimination: multiply both equations

Solve a pair of


substitution

Solve a pair of

simultaneous equations: 1

linear; 1 quadratic

20 Change the subject of a Formula

Change the subject of a formula: 1 or more

operations required


operations required


operations required

Change the subject of a formula involving squares

and square roots


operations required

including factorisation

21 Quadratics 1 Draw a quadratic by

calculating and plotting

points

Draw a quadratic by

calculating and plotting

points

Identify the intersection

points of a quadratic and a

straight line

Identify the intersection

points of a quadratic and a

straight line

Multiply out a factorised

quadratic expression





22 Quadratics 2

Factorise a quadratic

expression

Solve a quadratic equation

Multiply out and factorise using the difference of 2

squares


by rearranging and factorising

Solve problems involving

quadratics


with non-unit x2 coefficient


by completing the square


using the quadratic formula

Solve further problems

23 Indices 2

Know and apply the rules of

indices to numerical

expressions


indices to algebraic

expressions


indices to numerical and

algebraic expressions

Convert between fractional

indices and surds, and

evaluate expressions

Solve equations involving

indices

Evaluate and simplify

expressions in index form

Solve equations involving

indices

24 Algebraic Fractions Simplify an algebraic fraction Simplify an algebraic

fraction

Multiply and divide, add

and subtract algebraic

fractions

Add and subtract algebraic

fractions

25 Inequalities

Write and interpret an inequality and represent it

on a number line

Write and interpret a combined inequality and

represent it on a number

line

Solve an inequality algebraically

Solve an inequality with fractions algebraically

26 Proportion 2 Solve a direct proportion

question using a constant

of proportionality

Solve a direct proportion


of proportionality

Solve an inverse proportion


of proportionality

Solve an inverse proportion


of proportionality

27 Problems & Puzzles 2

Solve a spatial puzzle:

Gridlock

Solve Tile Slide, Towers of

Hanoi

Play a sequence memory

game

Solve a nonogram puzzle Solve a logic problem based

on sequencing

Solve a logic problem based

on information handling

28 Problems & Puzzles 3 – Coming 2015

29 Language Tasks & Quizzes 2 Engage with Maths language by matching



wordsearch puzzles


crossword puzzles

Engage with Maths language by completing

sentences

Quizzes: Puzzle & problems; Differentiated

from 1 to 7



Topic 1 - Writing Algebra 1


Multiply a constant by a variable and a variable by a variable, e.g. 4xb=4b,

3x4b=12b

Multiply 2 terms, e.g. 3ax4b=12ba, c

x c=c2

Express an addition or subtraction

phrase with a single variable as an expression

Express a multiplication or division

phrase with a single variable as an expression

Express a single stage phrase with up

to 2 variables as an expression

1. Demo: Basic algebraic terms 1. Multiply 2 variables together, e.g. c

x d=cd, c x c=c2

1. Convert an addition phrase to an

expression, e.g. a plus 4 a+4

1. Convert a phrase into an

expression

1. Convert an addition or subtraction

phrase to an expression, e.g. a plus b

a+b

2. Multiply a variable by a constant and write in proper notation, e.g. 4 x

a=4a, 1xb=b

2. Calculate the area of a square, rectangle or triangle with algebraic

edge lengths

2. Calculate the total length of a shape with part lengths as algebraic

terms

2. Convert a phrase into an expression: includes addition and

subtraction

2. Calculate the total length of a shape with part lengths as algebraic

terms

3. Calculate the area of a rectangle

with algebraic edge lengths

3. Multiply 2 terms and write in proper

notation, e.g. 3c x d=3cd, 4e x

2e=8e2

3. Convert a subtraction phrase to an

expression, e.g. h take away 4 h–4

3. Convert a multiplication phrase to

an expression, then simplify to a

single term, e.g. 4 times h 4xh=4h

3. Convert a addition or subtraction

phrase in graphical form to an

expression

4. Multiply a variable by a constant

and write in proper notation, e.g.

4x2a=8a, 1x4b=4b

4. Calculate the area of a square,

rectangle or triangle with edge lengths

as algebraic terms

4. Convert a subtraction phrase in

graphical form to an expression

4. Convert a multiplication phrase to

an algebraic term, e.g. 4 times h

4h

4. Convert a phrase to an expression

(single variable) e.g. What number is

5 more than b?

5. Calculate the area of a rectangle

with algebraic edge lengths

5. Speed response: Identify a

multiplication and the correct answer,

e.g. c x d=cd, c x c=c2

5. Convert a phrase into an

expression: Summary task

5. Solve simple proportion problems

with algebraic values


(single variable) e.g. What number is

b less than 4?



e.g. 3xd=3d, 1xe=e



e.g. 5c x 3d=15cd, 2c x 3c=6c2

6. Convert a division phrase to an

expression, then simplify to a single

term


(2 variables) e.g. What number is c

more than b?



e.g. 3x4d=12d

7. Solve simple proportion problems

with algebraic values

7. Solve an algebra problem in

context, e.g. Priya is n years old. How

old will she be in 4 years’ time?


context, e.g. Priya is n years old. How

old will she be in m years’ time?


context (Extension)


context (Extension)



Topic 2 - Writing Algebra 2


Express a 2-stage phrase with a single

variable as an expression: multiply, add and subtract

Express a 2-stage phrase with a single

variable as an expression: divide, add and subtract

Express a 2-stage phrase with 2

variables as an expression

Express a 2-stage phrase with up to 2

variables as an expression (using brackets)

Express a 2-stage phrase with up to 2

variables as an expression (using algebraic brackets and fractions)

1. Convert a phrase to an expression, e.g. What number is 5 more than 2

times b?

1. Convert a phrase to an expression, e.g. Divide x by 2 then add 3

1. Convert a phrase to an expression, e.g. What number is 5 more than 2

times b?

1. Demo: Use of brackets 1. Demo: Use of algebraic fractions with and without brackets

2. Calculate missing lengths of a

shape with part lengths as algebraic

terms



terms



terms

2. Convert a phrase to an expression,

e.g. add 2 to b, then multiply the

result by 2


e.g. add 2 to b, then divide/multiply

the result by 2



terms


e.g. What number is 2 less then a half

of b?



terms



terms


e.g. What number is half the sum of a

and b?


e.g. What number is 5 more than 3

times d?


e.g. I start with d, divide by 2 then

add 6. What am I left with?


e.g. What number is 5 more than 3

times d?


e.g. What number is twice the sum of

a and b?


e.g. I start with d, add 2 then

divide/multiply by 6. What am I left

with?


e.g. I start with d, multiply by 2 then


4. Complete a number machine 5. Convert a phrase to an expression,

e.g. I start with d, multiply by 2 then



e.g. I start with d, add 2 then multiply

by 6. What am I left with?

5. Complete a number machine

6. Complete a number machine 6. Complete a number machine 6. Complete a number machine 6. Complete a number machine 6. Complete a number machine

7. Complete a number machine 7. Speed Response: Assemble a

number machine

7. Complete a number machine 7. Complete a number machine 7. Speed Response: Assemble a

number machine

8. Complete a number machine 8. Speed Response : Fun: Assemble a

number machine with inverted elements

8. Speed Response: Assemble a

number machine

8. Complete a number machine 8. Speed Response: Fun: Assemble a

number machine with inverted elements

9. Speed Response: Assemble a number machine

9. Speed Response: Fun: Assemble a number machine with inverted

elements

9. Speed Response: Assemble a number machine

10. Speed Response: Fun: Assemble a

number machine with inverted

elements

10. Speed Response: Fun: Assemble a

number machine with inverted

elements



Topic 3 - Like Terms


Simplify an expression of up to 3

single variable terms by collecting like terms (positive answers)

Add and subtract integers: Revision

prior to adding and subtracting terms


single variable terms by collecting like terms (pos and neg answers)


double variable terms by collecting like terms


double variable terms by collecting like terms

1. Demo: Know ‘like terms’ and to simplify an expression consisting of 2

like terms, e.g. 2x+3x=5x, 3t-2=2t

1. Subtract a positive 1-digit or 2-digit integer from a positive 1-digit integer

1. Demo: Simplify an expression consisting of 2 like terms, e.g. 2x-

3x=-x; Compare with integers

1. Speed Response: Identify double variable like terms

1. Simplify an expression consisting of 4 single variable terms,

e.g. 2x+3b-3x+b=5x+2b

2. Speed Response: Identify like

terms


positive 1-digit or 2-digit integer

2. Simplify an expression consisting of

2 like terms, e.g. 2x-3x=-x


2 like double variable terms,

e.g. ab+3ba=4ab, 2x2-3x2=-x2


4 double variable terms,

e.g. 2xy+3ab+3xy+ab=5xy+ab


2 like terms, e.g. 2x+3x=5x

3. Subtract a 1-digit or 2-digit positive

integer from a 1-digit integer


2 like terms with 2 adjacent signs,

e.g. 2x--3x=2x+3x=5x Showing

intermediate working


2 like terms with or without 2

adjacent signs


5 single variable terms,

e.g. 2x+3b-3x+b–4x=x+2b



terms


1-digit or 2-digit negative integer


2 like terms with 2 adjacent signs,

e.g. 2x--3x=5x


3 like terms, e.g. 2xy+3xy-xy=4xy


5 double variable terms,

e.g. 2xy+3ab+3xy+ab–xy=4xy+ab



terms

5. Add a negative single digit integer

to a negative single or 2-digit integer


2 like terms with or without 2

adjacent signs


2 like terms and a constant or other

variable, e.g. 2xy+6-xy=xy+6


6 single variable terms,

e.g. 2x+3b-3x+b+5x–3b=10x+b


3 like terms, two of them like, e.g. 2x+3b+3x=5x+3b


digit integer from a positive 1-digit integer


3 like terms, e.g. 2x+3x-x=4x

6. Demo: Rearrange an expression to

enable easy simplification


6 double variable terms, e.g. 2xy+3ab–3yx+ba+5xy–

3ab=10xy+ab


rectangle with edge lengths as

algebraic terms and constants


digit integer from a negative 1-digit

integer


2 like terms and a constant or other

variable, e.g. 2x+6-x=x+6


4 single variable terms, e.g. 2x+3b-

3x+b=5x+2b

7. Solve an algebra wall puzzle with

single variables: 3 along base: all

positive


rectilinear shape with edge lengths as

algebraic terms and constants

8. Mixed additions and subtractions of

integers

8. Speed Response: Identify an

expression and its correct

simplification, e.g. 3d-4d=-d


4 double variable terms, e.g.

2xy+3ab+3xy+ab=5xy+ab


single variables: 3 along base


expression and the correct

simplification, e.g. 3d-4d=-d

9. Solve a magic square puzzle with

integers 3x3


expression and its correct

simplification, e.g. 3d-4d+7=-d+7


single variables: 3 along base: cryptic

10. Solve a magic square puzzle with

integers 4x4


single variables: 4 along base: all

positive

11. Solve a number triangle puzzle

with integers; 3 along base


single variables: 4 along base

12. Solve a number triangle puzzle

with integers; 4 along base


single variables: 4 along base: cryptic



Topic 4 - Expanding Brackets


Expand brackets of the form

2(a+3), 3(2t-3): single variable


4a(2b-2), a(3a+2): up to 2 variables


-(y–4),-4a(3b+2): up to 2 variables

Expand brackets of the form 4a(b-c),

-3b(a+b-c): up to 4 variables

Expand brackets and simplify an expression of the form 3(7x+2)+3x,

-3a(7a+2)-3a(a+2)

1. Demo: Expand brackets of the form

2(x+3)

1. Expand brackets of the form

a(b+3)


-2(x+3)


-2a(3b+3), -c(4-2c)

1. Expand brackets and simplify an

expression of the form -2(x+3)+3 and


2(x+3), 3(2+t)

2. Find the area of a rectangle with

algebraic edge lengths


-2(x-3)


5(a+c), -2a(b-c)


expression of the form 3-2(x+3)


algebraic edge lengths with assistance

3. Expand brackets of the form a(b –

3), c(1-d)


-(x+3)


-2(a+b-c)


expression of the form -2(x+3)+3x






-(x–2)


-2a(a+b-c)


expression of the form 3x-2(x+3)


expression and its expanded form.


a(a+3), c(1-c)


-2a(b+3), -c(c+4)


-2a(a2+a-1)


expression of the form -2x(x+3)+3x


2(x–3), 3(4-r)


a(2a+3), 3c(1-c)


-2a(b-3), -c(5-c)


-2(3a+2b-c+4)


expression of the form 3x-2x(x+3)


2(2x+3)


3a(2a+3), 3c(1-4c)


-2a(3b+3), -c(4-2c)


-2b(3a2+2b–c+4)


expression of the form 3(x-3)+2(x-5):

1 variable


2(2x-3)

8. Mixed examples from tasks 1 to 7 8. Mixed examples of tasks 1 to 8 8. Expand brackets and simplify an

expression of the form 3(x-y)-2(x+y):

2 variables

9. Mixed examples from tasks 1 to 10 9. Memory Game: Identify an expression and its expanded form

9. Mixed examples of tasks 1 to 8 including positive bracket multipliers

9. Expand brackets and simplify an expression of the form 3x(x-1)-2x(x-

2): 1 variable


expression and its expanded form.

10. Memory Game: Identify an

expression and its expanded form:

expanded form in reverse order

10. Speed Response: Match an

expression in brackets and its

expanded form


expression of the form 3x(x-y)-2x(y-

x): 2 variables



Topic 5 - Factorising


Identify the HCF of 2 or 3 numbers

Identify the HCF of up to 3 algebraic

terms

Factorise an expression of the form

3t+6, 9ab-3b


ab2+6b, 3cd2–12d


15a2-3ac+9ab

Simplify an algebraic fraction by

factorisation



lists of factors

1. Demo: Identify the HCF of 2

algebraic terms 1. Demo: Factorise an expression of

the form 2t+6, 2t-6, 6+2t, 6-2t

1. Factorise an expression of the form

b2-6b, 6b-b2


(3x+6)/3

2. Find the HCF of two numbers by identifying the greatest factor in both

lists of factors

2. Identify the HCF of 2 algebraic

terms


2t+6 and 6+2t


10b2-6b, 6b-4b2


(6x+12)/2



lists of factors


terms: more complex terms


4-2t and 2t-4


ab2+6b, 3cd2–12d


(4x+8)/(x+2)






expression and its factorised form. 4. Factorise an expression of the form

15a+3b+9, 10d+15e+5f


(4x+8)/(3x+6)






8b+14, 20c-12


15a2-3a+9ab


(12x2-6x)/3




terms: extension


expression and its factorised form. 6. Factorise an expression of the form

15a2b-3abc+9ab2


(6x2+2x)/(3x+1)

7. Complete a Venn diagram of factors and thereby find the HCF of 30, 32

and 48

7. Divide two terms of the type: 3x/2

in preparation for factorising

7. Mixed examples from Tasks 2,3 and

5


(12x–4y+2)/2


and thereby find the HCF of 48, 64

and 72

8. Divide two terms of the type:

6x2/2x


ab+6b, 3b-bc


(12x–4y+8z)/2

9. Find the HCF of two numbers < 100 9. Divide two terms of the type: 3pq/p 9. Factorise an expression of the form

16ab+6b, 3cd-12c

10. Find the HCF of two numbers <

200

10. Mixed exercise from Tasks 7 to 9 10. Mixed examples from Tasks 8 and

9



Topic 6 - Solving Equations 1


Solve a simple equation by inspection: x+4=12, 2x=4, x/2=5


2x+3x=10, 2x+1=7, x/2+3=5


3(x+4)=15, 3(x+1)=x-8,

3(x+1)=3(x-8)

Solve a simple equation of the form 2x+3x=10, 2x+1=7

Solve a simple equation of the form x/2+3=5, 3(x+4)=15, 3(x+1)=x-8,

3(x+1)=-3(x-8)

1. Demo: Solve an equation by inspection

1. Demo: Solve a simple equation of the form 2x+3=10, 6(x-3)=12 using

formal methods

1. Complete the solution to a simple equation of the form 2(x+1)=8

1. Solve a simple equation of the form 2x+3x=10, 6x-3x=9

1. Solve a simple equation of the form x/2+3=10, x/2-3=9

2. Solve a simple equation of the form x+2=5 by inspection

2. Complete the solution to a simple equation of the form 2x+3x=10, 6x-

3x=9

2. Complete the solution to a simple equation of the form 2(x-1)=8

2. Solve a simple equation of the form 3x=-2t+10

2. Solve a simple equation of the form 2(x+1)=8, 2(x-1)=-5

3. Solve a simple equation of the form

x+2=5 by inspection, some negative

answers

3. Complete the solution to a simple

equation of the form 5x=2x+9


equation of the form 4x+1=2x+9


3x+1=10


-2(x+1)=8, -(x-1)=5


x-2=5 by inspection


equation of the form 2x+1=7


equation of the form 4(x+1)=2(x+3)

4. Mixed examples from Tasks 1 to 3 4. Solve a simple equation of the form

4x+1=-2x-9

5. Solve a simple equation of the form x-2=5 by inspection, some negative

answers

5. Complete the solution to a simple equation of the form 2x-1=7

5. Complete the solution to a simple equation of the form 4(x-1)=2(x+3)

5. Solve a simple equation of the form 2(x+1)=8x+1, 2(x-1)=-8x+1

6. Solve a simple equation of the form 2x=6 by inspection

6. Complete the solution to a simple equation of the form x/2+1=7

6. Complete the solution to a simple equation of the form -4(x-1)=2(x-3)

6. Solve a simple equation of the form -2(x+1)=8x+1, -(x-1)=-8x+1


2x=6 by inspection, including some negative answers


equation of the form x/2-1=7


4(x-1)=2(x+2)


x/2=3 by inspection


-4(x-1)=-2(x+2)

9. Solve a simple equation of the form x/2=3 by inspection, including some

negative answers

10. Mixed examples from Tasks 1 to 8, all positive answers

11. Mixed examples from Tasks 1 to

8, some negative answers



Topic 7 - Algebraic Modelling


Use algebraic modelling to solve a single-stage problem



Use algebraic modelling to solve a 3-stage problem including the use of

brackets

Use algebraic modelling to solve a 3-stage problem including the use of

brackets

1. Demo: Use algebraic modelling to solve a single-stage ‘I think of a

number problem’

1. Demo: Using algebraic modelling to solve a 2-stage problem

1. Demo: Use algebraic modelling to solve a 2-stage ‘I think of a number

problem’


problem’


problem’

2. Use algebraic modelling to solve a

single-stage ‘I think of a number problem’: adding and subtracting


2-stage problem: money in 5p steps


2-stage ‘I think of a number problem’


3-stage ‘I think of a number problem’: mostly positive coefficients


3-stage ‘I think of a number problem’: mostly positive coefficients


single-stage ‘I think of a number

problem’: multiplying and dividing


2-stage problem: money in 1p steps


2-stage ‘I think of a number problem’:

more negatives involved



some negative coefficients



some negative coefficients


single-stage ‘I think of a number

problem’


2-stage age problem


consecutive number problem

4. Use algebraic modelling to solve

mixed ‘I think of a number problem’

problems

5. Use algebraic modelling to solve a single-stage ‘I think of a number

problem’

5. Solve mixed problems through algebraic modelling

5. Use algebraic modelling to solve a consecutive number problem

6. Use algebraic modelling to solve miscellaneous angle problems

7. Use algebraic modelling to solve

miscellaneous age problems



Topic 8 - Substitution


Revise the order of operations

Find the value of an expression by

substitution; non-negative values


substitution; non-negative values


substitution; some negative values


substitution; extension

1. Complete calculations using the correct order of operations: revision

1. Demo: find the value of an expression by substitution: brackets

and ‘of’

1. Demo: find the value of an expression by substitution with some

negative values

1. Find the value of an expression by substitution: 1 or 2 negative values

out of 4: extension

2. Complete calculations using the

correct order of operations: revision

2. Find the value of an expression by

substitution: positive values: brackets

and ‘of’


substitution: 1 negative value: simple

positive operations


substitution: 2 or 3 negative values

out of 4: extension

3. Demo: find the value of an

expression by substitution


substitution: non-negative values


substitution: 2 negative values: more

complex operations



out of 4: extension


substitution: positive values: simple

positive operations


substitution: non-negative values:

extension


substitution: 1 or 2 negative values:

brackets and ‘of’


substitution: positive values: more

complex positive and negative

operations





Topic 9 - Formulae


Substitute into formulae; convert between Fahrenheit and Celsius;

recognise common formulae

Use a formula in reverse given the

subject

Use a formula in reverse given the

subject

Solve a problem using a formula Solve a problem using a formula

Construct a formula from given

information

1. Demo: Substitute into a formula 1. Demo: Use a formula in reverse given the value of the subject

1. Substitute into a formula and use a formula in reverse

1. Solve a problem using a formula 1. Solve a problem using a complex formula

2. Substitute into a formula 2. Substitute into a formula and use a

formula in reverse: whole positive

values

2. Substitute into a formula and use a

formula in reverse: integer values

2. Solve a problem using a formula 2. Solve a problem using a complex

formula

3. Substitute into a formula 3. Substitute into a formula and use a

formula in reverse


formula in reverse


formula

4. Convert from Fahrenheit to Celsius 4. Convert between Fahrenheit and

Celsius


formula in reverse


formula

5. Convert from Celsius to Fahrenheit 5. Convert between Celsius and

Fahrenheit


formula in reverse: extension


formula

6. Recognise common formulae 6. Construct a formula from given

information; 1 variable in formula

7. Recognise common formulae 7. Construct a formula from given

information; formula consists of just

variables



Topic 10 - Problem Solving Theory


Identify the features of a problem

versus a straightforward question

Identify the abilities and qualities

required to solve a problem

Understand the 4-stage problem

solving process

Be aware of some useful problem

solving strategies



Topic 11 - Spotting Patterns


Copy a shape pattern Complete missing elements in a

pattern or sequence of objects

Extend a sequence of shapes and

extract information to form a simple number sequence

Extend a sequence of shapes or a line

pattern Extend a sequence of shapes

1. Copy a pattern of triangles 1. Complete missing squares on a

pattern of squares

1. Extend a sequence of shapes and

form a number sequence

1. Extend a set of three identical

shapes

1. Extend a sequence of shapes

2. Copy a pattern of triangles 2. Complete missing elements in a

pattern of triangles



2. Extend a line pattern by selecting

line segments


3. Copy a pattern on a triangular grid 3. Complete missing elements of a circular pattern with 2 distinct

elements




line segments



elements




line segments



elements




line segments


6. Copy a pattern on a triangular grid 6. Complete missing elements of a

circular pattern with 2 distinct

elements





elements




8. Complete missing elements of a


elements




9. Complete missing elements of a circular pattern with 3 distinct

elements




10. Complete missing elements of a


elements












Topic 12 - Problems & Puzzles 1


Solve a space-filling problem:

Pentominoes

Solve a matchstick puzzle Play Solitaire Play Lights Out

Solve an anagram-style number

puzzle

Play Noughts & Crosses Solve the frog puzzle

Solve the Queens problem

Play 4-in-a-Row

Solve a logic problem: Guess the Pegs

1. Solve a pentomino problem on a 3

x 10 board

1. Solve a matchstick puzzle 1. Solve the Solitaire puzzle 1. Play Noughts & Crosses with a

partner or against the computer

1. Solve a peg colour problem: 3 pegs

& 6 colours


x 10 board

2. Solve a matchstick puzzle 2. Play lights out 3x3 2. Solve the frog puzzle with 3 frogs

each side


& 8 colours

3. Solve the pentomino problem on a

3 x 10 board


each side


& 6 colours


3 x 10 board


each side


& 8 colours


3 x 10 board

5. Solve a matchstick puzzle 5. Play lights out 6x6 5. Solve the frog puzzle with from 1 to

5 frogs each side


& 4 colours


x 10 board

6. Solve a matchstick puzzle 6. Play lights out 7x7 6. Solve the ‘Queens’ chess puzzle

4x4


& 6 colours


3 x 10 board

7. Solve a matchstick puzzle 7. Speed Response: Solve an anagram-style number puzzle: 4

Letters

7. Solve the ‘Queens’ chess puzzle

5x5


& 8 colours


3 x 10 board

8. Solve a matchstick puzzle 8. Speed Response: Solve an

anagram-style number puzzle: 5

Letters


6x6


& 4 colours


3 x 10 board

9. Solve a matchstick puzzle 9. Speed Response: Solve an anagram-style number puzzle: 6

Letters


7x7


3 x 10 board

10. Solve a matchstick puzzle 10. Solve the ‘Queens’ chess puzzle

8x8

11. Play 4-in-a-Row with a partner.

One go each

12. Play 4-in-a-Row with a partner. First person has one go, then 2 goes

each








wordsearch puzzles


crossword puzzles



Engage with basic problem solving

theory


Hangman




1 to 12


1 to 12


1 to 12


1 to 12


1 to 12


1 to 12


1 to 12






Topic 14 - Sequences 1


Enter missing terms in a sequence

with a common difference

Enter missing terms in a sequence


Enter missing terms in a sequence with next term rule of the form: Un+1=

3Un+1, 3(Un+1), Un/3+1, (Un+1)/3

Enter missing terms in a sequence with a miscellaneous next term rule,

including a Fibonacci sequence

Enter missing terms in a sequence with a miscellaneous next term rule,

including a Fibonacci sequence

1. Add the next two terms to an

increasing sequence of non-negative

integers with a common difference

1. Add the next two terms to an

decreasing sequence of integers with

a common difference

1. Complete a sequence given the

next term rule of the form Un+1=

3Un+1, 3(Un+1), Un/3+1, (Un+1)/3

1. Complete a sequence given a term

and next term rule: miscellaneous

1. Add a missing term to a sequence

of integers

2. Add missing terms to an increasing

sequence of non-negative integers


2. Add missing terms to a decreasing

sequence of integers with a common

difference

2. Complete a sequence given the

next term rule of the form Un+1= 3Un-

1, 3(Un-1), Un/3-1, (Un-1)/3

2. Complete a sequence given the first

1 or 2 terms and next term rule:

miscellaneous


of integers

3. Add the next two terms to an increasing sequence of integers with a

common difference

3. Add the next two terms to an increasing or decreasing sequence of

integers with a common difference

3. Complete a sequence given the next term rule of the form Un+1=

3Un+1, 3(Un+1), Un/3+1, (Un+1)/3

3. Complete a sequence given 1 or 2 terms and next term rule:

miscellaneous

3. Add a missing term to a Fibonacci

style sequence of integers

4. Add missing terms to an increasing sequence of integers with a common

difference

4. Add missing terms to an increasing or decreasing sequence of integers


4. Summary task of tasks 1 and 2

with given term in any position

4. Complete a sequence given 1 or 2 terms and next term rule:

miscellaneous Fibonacci sequences


5. Add missing terms to an increasing or decreasing sequence of decimal

numbers with a common difference

5. Add the next term to a sequence of

integers: positive multiplier/divisor

5. Complete a sequence given 1 or 2

terms and a description


of Roman Numerals

6. Solve a problem involving a

sequence with a common difference


of integers: positive multiplier/divisor

6. Complete a sequence given 1 or 2

terms and a description: the alphabet


of Roman Numerals

7. Add the next term to a sequence of

integers: negative multiplier/divisor


of integers: negative multiplier/divisor

9. Summary task of Tasks 6 and 8

10. Solve a problem involving a

sequence given the next term rule



Topic 15 - Sequences 2


Use the nth term rule to generate a

sequence

Identify the nth term rule of a


Use the nth term rule to generate a

sequence


quadratic sequence using differences


quadratic sequence using differences

1. Demo: Use the nth term rule to

generate a sequence with a common

difference

1. Demo: Identify the nth term in a

simple sequence with a common

difference

1. Use the nth term rule to generate a

quadratic sequence


quadratic sequence of the form Un+1=

Un=3n2+2 using differences


quadratic sequence of the form

Un=3n2+2n+2 using differences



2. Identify the nth term in a simple



quadratic sequence

2. Identify the nth term in a quadratic

sequence of the form Un=3n2+2


sequence of the form Un=3n2+2n+2


simple sequence




quadratic sequence


sequence of the form Un=3n2+2 and

use it to calculate a specific term


sequence of the form Un=3n2+2n+2


simple sequence




quadratic or cubic sequence

4. Identify the nth in a quadratic sequence of the form Un=3n2+2n+2

and use it to calculate a specific term

5. Use the nth term rule to calculate a

single term in a sequence




quadratic or cubic sequence

5. Identify the nth in a quadratic sequence of the form Un=3n2+2n+2

and use it to calculate a specific term

6. Use the nth term rule to calculate a

single term in a sequence

6. Identify the nth term and use it to

calculate a specific term

7. Identify the nth term and use it to

calculate a specific term



Topic 16 - Solving Equations 2


Solve an equation with up to 1

bracket on each side

Solve an equation with up to 3

brackets on each side

Solve an equation with fractions Solve a problem using algebraic

modelling

Find an approximate solution to an

equation by trial and improvement

1. Complete the solution to an

equation of the form 4x+1=2x+9

1. Solve an equation of the form

4(x-1)+3=2(x+2)

1. Demo: Solve an equation with a

fraction by multiplying both sides by

the denominator

1. Solve a problem using an equation 1. Demo: Find an approximate

solution to an equation by trial and

improvement (1.d.p.)


4x+1=-2x-9


3-4(x-1)=2(x+2)


equation of the form x/2+1=7

2. Solve a problem using an equation 2. Find an approximate solution to an


(1.d.p.)

3. Using an equation to solve a problem.

3. Solve an equation of the form 3-4(2x-1)=2(5x+2)

3. Complete the solution to an equation of the form x/2-1=7

3. Solve a problem using an equation 3. Demo: Find an approximate solution to a more complex equation

by trial and improvement (1.d.p.)

4. Solve a simple equation of the form 2(x+1)=8, 2(x-1)=-5

4. Solve an equation of the form 4(x-1)+3x=2(x+2)

4. Solve an equation of the form x/2+3=10, x/2-3=9

4. Solve a problem using an equation 4. Find an approximate solution to an equation by trial and improvement

(1.d.p.)


-2(x+1)=8, -(x-1)=5


4(x-1)+3x=2(x+2)+3

5. Complete the solution to a equation

of the form (x+-1)/2=7, ½(x+-2)=8 5. Solve a problem using an equation 5. Demo: Find an approximate

solution to an equation by trial and improvement (2.d.p.)


equation of the form 4(x+1)=2(x+3)


2(x-2)+3x-3(x-2)=3(x+1)-4(x-1)+4

6. Demo: Solve an equation with a

fraction by multiplying throughout by

the denominator

6. Solve a problem using an equation 6. Find an approximate solution to an


(2.d.p.)


equation of the form 4(x-1)=2(x+3)


2(x-2)+3(4-x)+3(x-2)=3(x+1)+4(x-

1)+4


(x+-1)/2+1=7, ½(x+-2)+x=8 7. Solve a problem using an equation 7. Solve a problem by trial and

improvement

8. Complete the solution to an equation of the form -4(x-1)=2(x-3)

8. Speed Response: Solve equations of the form 2(x-2)+3(4-x)+3(x-

2)=3(x+1)+4(x-1)+4

8. Solve an equation of the form (x+-1)/x+1=x+1 ½(x+2)+x=2-3

8. Solve a problem using an equation 8. Solve a problem by trial and improvement

9. Solve an equation of the form 4(x-1)=2(x-2)

9. Demo: Solve an equation with fractions by multiplying throughout by

the LCM of the denominators

9. Solve a problem using an equation

10. Solve an equation of the form -4(x-1)=-2(x+2)

10. Solve an equation with up to 2 different denominators


11. Solve an equation with up to 3

different denominators 11. Solve a problem using an equation




Topic 17 - Straight Lines 1


Read and plot coordinates in all 4

quadrants

Plot coordinates in all 4 quadrants Draw a straight line by calculating and

plotting points

Calculate the gradient of a straight

line between two points

Calculate the equation of a straight

line by calculating the gradient and identifying the y-intercept

Know y=mx+c

1. Read coordinates in all 4 quadrants 1. Coordinates Puzzle: Plot the points

and guess the shape

1. Draw a vertical or horizontal

straight line given the equation

1. Demo: Calculate the gradient of a

straight line between 2 points

1. Identify the equation of a vertical

or horizontal straight line

2. Speed Response: Read coordinates

in all 4 quadrants

2. Coordinates Puzzle: Plot the points

and guess the shape

2. Demo: Draw a straight line by

calculating 3 points

2. Calculate the gradient of a straight

line between 2 given points

2. Demo: Calculate the equation of a

straight line in the form y = mx+c

3. Plot coordinates in all 4 quadrants 3. Coordinates Puzzle: Plot the points

and guess the shape

3. Draw a straight line by calculating

and plotting points, e.g. y = 2x-2

3. Calculate the gradient of a straight

line between 2 points on a grid

3. Identify the equation of a straight

line given the gradient and y-intercept

4. Speed Response: Plot coordinates

in all 4 quadrants


and guess the shape


and plotting points, e.g. y+3x = 2

4. Demo: Summary of positive,

negative, zero and undefined gradient

4. Calculate the equation of a straight

line of the form y = 3x, y= 2/3x


and guess the shape


and guess the shape


and plotting points, e.g. 2y-3x = 12

5. Solve a problem involving gradients 5. Calculate the equation of a straight

line of the form y = 3x, y= 2/3x


and guess the shape


and guess the shape

6. Solve a problem involving gradients 6. Calculate the equation of a straight

line of the form y = 3x+1


and guess the shape


and guess the shape


line of the form y = 3x/2+1

8. Match a sketch of a graph with its

equation


equation


equation


equation



Topic 18 - Straight Lines 2


Calculate the equation of a straight

line

Rearrange an equation to the form

y=mx+c to find the gradient and intercept

Find the midpoint between 2 points

the length of a line segment

Calculate the length of a line segment Solve problems with parallel and

perpendicular lines

1. Demo: Calculate the equation of a straight line given 1 point and the

gradient

1. Demo: Rearrange an equation to the form y=mx+c to find the gradient

and y-intercept

1. Demo: Find the midpoint between 2 points

1. Demo: Find the length of a line segment

1. Demo: Find the equation of a line which is parallel to another


line given 1 point and the gradient

(integer gradient)

2. Rearrange an equation to the form

y=mx+c to find the gradient and y-

intercept (y positive)

2. Find the midpoint between 2

points.

2. Find the length of a line segment 2. Find the equation of a line which is

parallel to another


line given 1 point and the gradient

(fractional gradient)

3. Rearrange an equation to the form

y=mx+c to find the gradient and y-

intercept

3. Find the midpoint between 2

points.

3. Find the length of a line segment 3. Demo: Find the equation of a line

which is perpendicular to another

using m1m2 = -1

4. Demo: Calculate the equation of a

straight line given 2 points

4. Solve a problem with midpoint 4. Solve a problem with the length of

a line segment

4. Speed response: Identify a gradient

and its corresponding perpendicular

gradient


line given 2 points (integer gradient)

5. Find the equation of a line which is

perpendicular to another


line given 2 points (fractional

gradient)

7. Calculate the equation of any

straight line from a graph



Topic 19 - Simultaneous Equations


Solve a pair of simultaneous

equations graphically


equations by elimination: adding or subtracting leads directly to solution


equations by elimination: multiply one equation


equations by elimination: multiply both equations


equations by substitution


equations: 1 linear; 1 quadratic

1. Demo: Solve a pair of simultaneous



equations by elimination







2. Solve a pair of simultaneous
































5. Demo: Solve a problem with







equations by substitution: 1 linear; 1

quadratic



6. Solve a problem with simultaneous

equations


equations


equations



quadratic




equations


equations


equations



quadratic




equations


equations


equations



quadratic



9. Demo: Solve further problems with



equations by substitution: 1 linear; 1 quadratic



10. Solve a problem with


10. Find the points of intersection of a

straight line and a quadratic

11. Solve a problem with


11. Find the points of intersection of a

straight line and a quadratic



Topic 20 - Changing the Subject of a Formula


Change the subject of a formula: 1 or

more operations required





Change the subject of a formula

involving squares and square roots


more operations required including factorisation

1. Change the subject of a formula of the form a+b=c, new subject positive

in original formula

1. Mixed exercises on Target 1:

extension

1. Demo: Change the subject of a formula of the form a=3(b+c),

a=b/c(x+d)

1. Demo: Change the subject of a formula involving squares and square

roots

1. Demo: Change the subject of a formula of the form 3(y+2)=4(x-1),

y+b=x+ax

2. Change the subject of a formula of the form a+b=c, ab+c=d, new

subject positive in original formula

2. Mixed exercises on Target 1:

extension

2. Change the subject of a formula of

the form a=3(b+-c)

2. Change the subject of a formula



the form 3(y+2)=4(x-1), y+b=x+ax


the form a-b=c, ab+c=d

3. Demo: Change the subject of a

formula of the form c=ut+d, c=a/b+f


the form c=f/g(u+-v)




the form 3(y+2)=4(x-1), y+b=x+ax

4. Mixed exercises from Task 1 to 3

with coefficients


the form c=ut+d

4. Mixed exercises on tasks 2-3 4. Change the subject of a formula


4. Change the subject of a formula:

miscellaneous examples

5. Change the subject of a formula of the form A=bh, d=cde, new subject

positive in original formula


the form c=a/b+-f

5. Demo: Change the subject of a formula of the form c=a/b+f,

a=(2x+y2)/3



5. Change the subject of a formula:

miscellaneous examples


the form A=bh, d=-4cde

6. Mixed exercises from Tasks 4 and 5

with coefficients


the form c=a/b+f, a=(2x+y2)/3

7. Change the subject of a formula of the form R=V/I, new subject positive

in original formula

7. Mixed exercises from Tasks 4 and 5

with coefficients

7. Mixed examples of changing the

subject of a formula


the form R=V/I



Topic 21 - Quadratics 1


Draw a quadratic by calculating and

plotting points

Draw a quadratic by calculating and

plotting points

Identify the intersection points of a

quadratic and a straight line

Identify the intersection points of a

quadratic and a straight line

Multiply out a factorised quadratic

expression

1. Calculate points, plot the points and draw a quadratic


1. Draw a quadratic and identify the points of intersection with the x-axis

1. Draw a quadratic and a horizontal straight line and identify the points of

intersection

1. Multiply out a factorised quadratic expression: no constant term in the

expanded expression: with assistance



2. Draw a quadratic and identify the points of intersection with the x-axis

2. Draw a quadratic and a straight line and identify the points of intersection

2. Multiply out a factorised quadratic expression: 2 terms

3. Calculate points, plot the points

and draw a quadratic



3. Draw a quadratic and identify the

points of intersection with the x-axis

3. Draw a quadratic and a straight line

and identify the points of intersection

3. Multiply out a factorised quadratic

expression: 2 terms





4. Draw a quadratic and a horizontal

straight line and identify the points of

intersection

4. Draw a quadratic and a straight line

and identify the points of intersection

4. Demo: Multiply out and simplify a

factorised quadratic expression: 3

terms in the expanded form



5. Draw a quadratic and a horizontal straight line and identify the points of

intersection

5. Draw a quadratic and a straight line and identify the points of intersection

5. Multiply out a factorised quadratic expression: 3 terms: unit x2

coefficient



6. Multiply out a factorised quadratic expression: 3 terms: unit x2

coefficient



7. Multiply out a factorised quadratic expression: 3 terms: non-unit x2

coefficient



Topic 22 - Quadratics 2


Factorise a quadratic expression


Multiply out and factorise using the difference of 2 squares

Solve a quadratic equation by

rearranging and factorising

Solve problems involving quadratics

Solve a quadratic equation with non-

unit x2 coefficient

Solve a quadratic equation by

completing the square

Solve a quadratic equation using the

quadratic formula

Solve further problems

1. Factorise a quadratic expression: 2

terms: unit x2 coefficient

1. Demo: Solve a quadratic equation

by factorising: unit x2 coefficient


by rearranging and factorising

1. Demo: Complete the square for a

quadratic expression: even x

coefficient


by using the quadratic formula


terms: non-unit x2 coefficient

2. Solve a quadratic equation by

factorising: unit x2 coefficient


rearranging and factorising

2. Complete the square for a

quadratic expression: even x

coefficient

2. Solve a quadratic equation by using

the quadratic formula

3. Demo: Factorise a quadratic expression: 3 terms: unit x2

coefficient

3. Solve a quadratic equation by factorising: unit x2 coefficient

3. Solve a quadratic equation by rearranging and factorising

3. Demo: Complete the square for a quadratic expression: odd x coefficient

3. Solve mixed problems involving quadratic equations

4. Factorise a quadratic expression: 3 terms: unit x2 coefficient

4. Demo: Solve a quadratic equation with two parts by factorising

4. Solve mixed problems using quadratic equations

4. Complete the square for a quadratic expression: odd x coefficient

4. Solve mixed problems involving quadratic equations


terms: unit x2 coefficient

5. Solve a quadratic equation with two

parts by factorising

5. Solve mixed problems using

quadratic equations


by completing the square

6. Demo: Factorise a quadratic

expression with three terms: non-unit

x2 coefficient

6. Demo: Multiply out and factorise a

quadratic expression in the form of a

difference of two squares

6. Solve gradient problems involving

quadratics


completing the square

7. Factorise a quadratic expression: non-unit x2 coefficient

7. Multiply out a factorised quadratic expression in the form of a difference

of two squares

7. Demo: Solve a quadratic equation by factorisation: non-unit x2

coefficient

7. Demo: Solve a quadratic equation by completing the square: non-unit x2

coefficient

8. Factorise a quadratic expression in the form of a difference of two

squares

8. Solve a quadratic equation by factorisation: non-unit x2

8. Solve a quadratic equation by completing the square: non-unit x2

coefficient

9. Factorise a quadratic expression in

the form of a difference of two squares: extension



Topic 23 - Indices 2


Know and apply the rules of indices to

numerical expressions


algebraic expressions


numerical and algebraic expressions

Convert between fractional indices

and surds, and evaluate expressions

Solve equations involving indices

Evaluate and simplify expressions in

index form

Solve equations involving indices

1. Write a numerical or algebraic expression in index form 3x3x3x3=34;

txtxt=t3

1. Simplify an expression in index form: 3a2 x 6a3=18a5

1. Simplify an expression in index form and evaluate: 9a2x4b3xa4

1. Express surd form as positive fractional index form

1. Complete missing elements when evaluating expressions in index form

2. Evaluate an expression in index

form: 43=64


expression in index form and its

matching simplified form

2. Simplify an expression in index

form and evaluate: 92x93/94 = 9

2. Express positive fractional index

form as a surd

2. Evaluate a numerical expression

with fractional indices

3. Speed response: Identify a value

and its matching index form

3. Simplify an expression in index

form and evaluate: 32/33=3-1=1/3

3. Simplify an algebraic expression in

index form: 6k2 x 3k3/2k = 9k4

3. Express positive fractional index

form as a surd and evaluate

3. Evaluate a unitary fraction raised to

an index


greater of 2 numerical expressions in

index form: 23 > 32

4. Speed response: Identify a division


matching expanded form


index form with more than one

variable: 6j2k3 x 3k2/2k = 9 j2k4

4. Express surds in denominators as

negative fractional index form

4. Evaluate a fraction raised to an

index

5. Simplify an algebraic expression

using positive indices: 6k2/2k3 = 3/k

5. Simplify and evaluate an

expression of the form (42)3

5. Express negative fractional index

form as a surd and evaluate

5. Simplify an algebraic expression

containing fractional indices

6. Speed response: Simplify a division

expression: k2/k3 = k-1


index form: (x2)3 = x6,(2x2)4 = 16x8

6. Evaluate expressions in index form 6. Solve equations with whole indices

7. Speed response: (balls) Identify an


matching expanded form: (x2)3 = x6

7. Solve equations with fractional

indices

8. Speed Response: True or False:

(x2)3 = x6, (2x2)3 = 8x6



Topic 24 - Algebraic Fractions


Simplify an algebraic fraction Simplify an algebraic fraction Multiply and divide, add and subtract

algebraic fractions

Add and subtract algebraic fractions

1. Complete a set of equivalent

algebraic fractions

1. Demo: Simplify an algebraic

fraction by factorising

1. Demo: Multiply and divide algebraic

fractions

1. Demo: Add and subtract algebraic

fractions

2. Complete a set of equivalent algebraic fractions

2. Simplify an algebraic fraction by factorising: 3x+6/x+2

2. Multiply and divide algebraic fractions: a/5 x 10/a

2. Add and subtract algebraic fractions: a/5 + 10/a

3. Simplify an algebraic fraction: 10a/5

3. Simplify an algebraic fraction by factorising: including quadratics

3. Multiply and divide algebraic fractions: ab2/5 x 10bc/a

3. Add and subtract algebraic fractions: 2a/5 + a/4

4. Simplify an algebraic fraction:

10a2/5b

4. Simplify an algebraic fraction by

factorising: including quadratics

4. Multiply and divide algebraic

fractions: 30ab2/5 x 15bc/a2

4. Add and subtract 3 algebraic

fractions: 2a/5 + a/4 + a/2

5. Simplify an algebraic fraction:

24ba2/16bc2




fractions: (x-1)/5 x 15/(2x-4)

5. Add and subtract algebraic

fractions: (x-1)/5 + (x+3)/4




fractions: (x2+2x-1)/x+1 x 10/(x-1)


fractions: 2(x-1)/5 + (x+3)/x




fractions: 2/(x-1) + 3/(x+3)



Topic 25 - Inequalities


Write and interpret an inequality and

represent it on a number line

Write and interpret a combined

inequality and represent it on a number line

Solve an inequality algebraically Solve an inequality with fractions

algebraically

1. Demo: Know the 4 inequality signs, and the representation of an

inequality on a number line

1. Demo: Understand a combined

inequality

1. Demo: Solve an inequality by

reversing the inequality sign

1. Solve an inequality with fractions

2. Match an inequality phrase with its

algebraic form

2. Match a combined algebraic inequality with its representation on a

number line

2. Demo: Understand the reason behind reversing the inequality sign,

and how to avoid it

2. Solve an inequality with fractions

3. Speed Response: Select the correct inequality symbol for a numerical

comparison

3. Represent a combined inequality on

a number line

3. Solve an inequality

4. Speed Response: Select the correct inequality symbol for a comparison of

quantities

4. Express a combined inequality in

context in algebraic form


5. Match an algebraic inequality with

its representation on a number line

5. Identify the solution set of integers

defined by a combined inequality


6. Represent an inequality on a

number line


7. Identify a particular value defined

by an inequality

7. Speed response: Solve an

inequality

8. Express an inequality in context in

algebraic form



Topic 26 - Proportion 2


Solve a direct proportion question

using a constant of proportionality

Solve a direct proportion question


Solve an inverse proportion question


Solve an inverse proportion question


1. Demo: Use of a constant of

proportionality to solve a direct proportion question


proportionality to solve a direct proportion question: yx2, yx3


proportionality to solve an inverse proportion question


proportionality to solve an inverse proportion question: yx2, yx3

2. Solve a direct proportion question 2. Solve a direct proportion question:

yx2, yx3: whole answers

2. Solve an inverse proportion

question


question: yx2, yx3

3. Solve a direct proportion question 3. Solve a direct proportion question: yx2, yx3: fractional answers

3. Solve an inverse proportion question

3. Solve an inverse proportion question: yx

4. Solve a direct proportion question:

fractional solution

4. Solve a direct proportion question:

yx


question: fractional solution

4. Solve a problem involving inverse

proportion

5. Solve a problem involving direct proportion



Topic 27 - Problems & Puzzles 2


Solve a spatial puzzle: Gridlock Solve Tile Slide, Towers of Hanoi

Play a sequence memory game

Solve a nonogram puzzle Solve a logic problem based on

sequencing

Solve a logic problem based on

information handling

1. Solve a spatial puzzle: Gridlock 1. Solve a spatial puzzle: Tile Slide

3x3

1. Solve a nonogram puzzle 1. Solve a logic problem 1. Solve a logic problem


4x4



5x5


4. Solve a spatial puzzle: Gridlock 4. Solve the Tower of Hanoi problem:

3 discs



4 discs



5 discs



6 discs



7 discs


9. Solve a spatial puzzle: Gridlock 9. Play a sequence memory game 9. Solve a nonogram puzzle 9. Solve a logic problem

10. Solve a spatial puzzle: Gridlock 10. Play a sequence memory game

11. Play a sequence memory game



Topic 28 - Problems & Puzzles 3 - Coming 2014









wordsearch puzzles


crossword puzzles






14 to 27




14 to 27


14 to 27


14 to 27


14 to 27

8. Match terms to their definitions 8. Complete a crossword 8. Enter missing words in sentences









Documents

Maths Workout · 2016. 8. 11. · aimed at Maths lessons covering NQF Levels 1 and 2. Maths Workout is versatile and simple to use. Teachers can teach a skill using Maths Workout