How to use this book ......................5

Revision tracker .................................7

Numbers up to 1,000,000 .............................8

Counting in steps up to 1,000,000 ..............10

Positive and negative numbers ....................12

Rounding numbers ......................................14

Roman numerals .........................................16

Number and place value

Mental methods for adding and subtracting ..17

Adding large numbers ..................................18

Subtracting large numbers ...........................20

Multiples and factors ....................................22

Prime numbers .............................................24

Multiplying large numbers .............................26

Dividing large numbers .................................28

Mental methods for multiplying and dividing ...30

Square numbers and cube numbers .............31

Multiplying and dividing by 10, 100 and 1000 ..32

Scaling and rates ..........................................34

Using all four operations ...............................36

Calculations

Comparing and ordering fractions .................38

Tricky fractions ..............................................40

Adding and subtracting fractions ..................42

Multiplying fractions and whole numbers ......44

Converting simple decimals and fractions .....46

Decimal fractions ..........................................48

Numbers with three decimal places ..............50

Rounding decimals .......................................52

Simple percentages ......................................54

Fractions, decimals and percentages

3

Contents

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Answers .................................................82

Glossary ................................................86

Multiplication table .........................88

Angle facts ...................................................68

Rotating angles ............................................70

2D shapes ....................................................72

3D shapes ....................................................74

Reflecting and translating shapes .................76

Geometry

Length and distance .....................................56

Perimeter ......................................................58

Area .............................................................60

Mass, capacity and volume ..........................62

Time .............................................................64

Money ..........................................................66

Measurement

Line graphs ..................................................78

Tables and timetables ...................................80

Statistics

4

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16

Nu

mb

er an

d

pla

ce va

lue

Roman numerals

RecapLook at the clock and check that you know the Roman numerals for numbers 1–12.

Number 1 2 3 4 5 6 7 8 9 10

Roman numeral I II III IV V VI VII VIII IX X

Number 11 12 13 14 15 16 17 18 19 20

Roman numeral XI XII XIII XIV XV XVI XVII XVIII IXX XX

Number 30 40 50 60 70 80 90 100 500 1000

Roman numeral XXX XL L LX LXX LXXX XC C D M

XII

VI

IV

IIIIX

II

VIII

XI

V

XI

VII

check1. Write these Roman numerals in numbers.

a. VIII b. XXIII c. CCC d. XCV

e. CIV f. CXL g. DCX h. CM

2. Write these numbers in their Roman numeral equivalent.

a. 22 b. 1 c. 55 d. 93

e. 112 f. 160 g. 212 h. 965

Brain-buster The Romans left Britain in the year ad410, 465 years after they first arrived. Use Roman numerals to write the date they left, and the number of years they spent in Britain.

Date: Years in Britain:

What are the rules for making 4 and 9 with Roman

numerals?

With a bit of brain power, you can use this

chart to find out any Roman numeral up to 1000!

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17

Ca

lcula

tion

sMental methods for adding and subtracting

RecapYou will probably know several ways of doing mental calculations.

You must know your number bonds: 7 + 8 = 15 15 − 8 = 7 15 − 7 = 8

Partitioning numbers is important too: 25 + 12 = 37

25 26

+10 +2

27 2928 30 31 34 353332 36 37

Mental methods can work just as well for larger numbers, but you need to be confident and know your limits!

45,356 + 12,103 ✓ There is no carrying necessary; just add each column.

123,729 + 943,509 ✗ Too much carrying!

34,302 − 8753 ✗ Too much carrying!

16,583 − 8000 ✓ The 100s, 10s and 1s stay exactly the same!

check1. Add these numbers using mental methods.

a. 46 + 50 = b. 127 + 99 =

c. 3274 + 2002 = d. 2500 + 7454 =

e. 120,000 + 10,320 =

2. Subtract these numbers using mental methods.

a. 80 − 46 = b. 160 − 65 =

c. 345 − 99 = d. 4000 − 2500 =

e. 275,675 − 10,000 =

Brain-teaser Jason has read 123 pages of his book. If he reads another 150 pages he will finish it. How many pages does the book have altogether?

Brain-buster Armchairs cost £299 and sofas cost £499. How much would two armchairs and one sofa cost altogether?

Remember, adding 99 is easy: add 100 and take

away 1!

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