How to be Good at Maths Workbook 1, Ages 7-9 (Key Stage 2) 9780241471418, 0241471419

Table of contents :
Contents
Numbers
Number symbols
Place value
Sequences and patterns
Positive and negative numbers
Comparing numbers
Ordering numbers
Estimating
Rounding
Fractions
Equivalent fractions
Finding a fraction of an amount
Comparing fractions with the same denominators
Comparing unit fractions
Calculating
Addition
Addition facts
Adding with a number line
Adding with a number grid
Partitioning for addition
Expanded column addition
Column addition
Shopkeeper’s addition
Subtraction
Subtraction facts
Subtracting with a number line
Partitioning for subtraction
Expanded column subtraction
Column subtraction
Multiplication
Counting in multiples
Multiplication tables
The multiplication grid
Multiplication patterns and strategies
Expanded short multiplication
Short multiplication
Division
Dividing with multiples
Division tables
The division grid
Partitioning for division
Expanded short division
Short division
Arithmetic laws
Measurement
Length
Perimeter
Area
Estimating area
Capacity
Volume
Mass
Calculating with mass
Telling the time
Calculating with time
Dates
Money
Using money
Geometry
What is a line?
Horizontal and vertical lines
Diagonal lines
Parallel lines
Perpendicular lines
2D shapes
Regular and irregular polygons
Triangles
Quadrilaterals
Naming polygons
3D shapes
Types of 3D shape
Prisms
Angles
Degrees
Right angles
Types of angle
Coordinates
Position and direction
Compass directions
Reflective symmetry
Statistics
Tally marks
Frequency tables
Data handling
Carroll diagrams
Venn diagrams
Pictograms
Block graphs
Bar charts
Answers

Citation preview

How to be

good at

maths

WORKBOOK 1 The simplest-ever visual workbook

Produced for DK by Dynamo Limited 1 Cathedral Court, Southernhay East, Exeter, EX1 1AF Authors Tim Handley, Linda Glithro Consultant Paul Broadbent Senior Editor Ankita Awasthi Tröger Senior Art Editor Amy Child Editors Lizzie Munsey, Catharine Robertson, Ben Ffrancon Davies Designer Anna Scully Managing Editor Christine Stroyan Managing Art Editor Anna Hall Senior Production Editor Andy Hilliard Production Editor George Nimmo Production Controller Sian Cheung Jacket Design Development Manager Sophia MTT Jacket Designer Tanya Mehrotra DTP Designer Rakesh Kumar Publisher Andrew Macintyre Associate Publishing Director Liz Wheeler Art Director Karen Self Publishing Director Jonathan Metcalf First published in Great Britain in 2021 by Dorling Kindersley Limited DK, One Embassy Gardens, 8 Viaduct Gardens, London, SW11 7BW The authorised representative in the EEA is Dorling Kindersley Verlag GmbH. Arnulfstr. 124, 80636 Munich, Germany Copyright © 2021 Dorling Kindersley Limited A Penguin Random House Company 10 9 8 7 6 5 4 3 2 1 001–322111–Oct/2021 All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior written permission of the copyright owner. A CIP catalogue record for this book is available from the British Library. ISBN 978-0-2414-7141-8 Printed and bound in China All images © Dorling Kindersley. For further information, visit www.dkimages.com. www.dk.com

This book was made with Forest Stewardship Council ™ certified paper – one small step in DK’s commitment to a sustainable future. For more information go to www.dk.com/our-green-pledge

Contents Numbers

Calculating

Number symbols...........................................6

Addition .......................................................28

Place value ....................................................8

Addition facts ..............................................30

Sequences and patterns ............................. 10

Adding with a number line .........................32

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

Adding with a number grid ........................34

Comparing numbers .................................. 14

Partitioning for addition ............................ 36

Ordering numbers ..................................... 16

Expanded column addition.........................38

Estimating .................................................... 18

Column addition .........................................40

Rounding ..................................................... 19

Shopkeeper’s addition ................................42

Fractions ......................................................20

Subtraction ..................................................44

Equivalent fractions .....................................22

Subtraction facts .........................................46

Finding a fraction of an amount .................24

Subtracting with a number line ..................48

Comparing fractions with the

Partitioning for subtraction .........................50

same denominators ................................26 Comparing unit fractions ............................27

Expanded column subtraction ....................52 Column subtraction.....................................54 Multiplication ...............................................56 Counting in multiples ..................................58 Multiplication tables ....................................60

The multiplication grid ................................62

Capacity ......................................................94

Multiplication patterns and strategies........64

Volume ........................................................95

Expanded short multiplication ...................66

Mass ............................................................96

Short multiplication .....................................68

Calculating with mass ................................98

Division ........................................................70

Telling the time .......................................... 100

Dividing with multiples ................................72

Calculating with time ................................ 102

Division tables .............................................74

Dates ......................................................... 104

The division grid ..........................................76

Money ....................................................... 106

Partitioning for division ...............................78

Using money ............................................. 108

Expanded short division..............................80 Short division ...............................................82 Arithmetic laws ..........................................84

Measurement

Geometry What is a line? ............................................ 110 Horizontal and vertical lines .......................111 Diagonal lines ............................................ 112

Length..........................................................86

Parallel lines ............................................... 114

Perimeter .....................................................88

Perpendicular lines .................................... 115

Area .............................................................90

2D shapes .................................................. 116

Estimating area ...........................................92

Regular and irregular polygons................. 118

Triangles .................................................... 120

Data handling ........................................... 150

Quadrilaterals ........................................... 122

Carroll diagrams ....................................... 152

Naming polygons ..................................... 124

Venn diagrams ......................................... 154

3D shapes ................................................. 126

Pictograms ................................................ 156

Types of 3D shape .................................... 128

Block graphs ............................................ 158

Prisms ........................................................ 130

Bar charts .................................................. 160

Angles ....................................................... 132

Answers .................................................... 162

Degrees ..................................................... 133 Right angles ............................................. 134 Types of angle ........................................... 136 Coordinates ............................................... 138 Position and direction ............................... 140 Compass directions .................................. 142 Reflective symmetry .................................. 144

Statistics

Carol Vorderman, one of Britain’s best known and loved TV personalities, feels passionately about the value of education. She joined forces with DK in 1999 to become DK’s Education Champion and has helped us to build the bestselling Made Easy and How to be Good at series, which include topics in English, maths, and science and technology. Carol has a degree in engineering from the University of Cambridge, and was awarded an MBE in 2000 for services to broadcasting.

Tally marks ................................................ 146 Frequency tables ....................................... 148

Pages 000–000

The page numbers next to this icon refer to pages in DK’s How to be Good at Maths.

6

NUMBERS • NUMBER SYMBOLS

DID YOU KNOW? Roman, and The Babylonian, Ancient er systems did Ancient Egyptian numb ro. not have a symbol for ze

Number symbols People have used numbers in their daily lives since the earliest times. We use numbers to count, measure, tell time, and buy or sell things.

0

Hindu-Arabic Ancient Roman

1

2

3

4

5

6

7

8

9

I

II

III

IV

V

VI

VII

VIII

IX

Babylonian Ancient Egyptian

Warm-up

Colour the Hindu-Arabic symbols in red, the Egyptian symbols in green, the Roman symbols in blue, and the Babylonian symbols in yellow.

7

5

V

3

6

IX

VII

III VI

1

9

Use the chart at the top of the page to help you fill in the numbers for each of these symbols.

a

IV =

e

=

4

b

=

c

f

=

g

VIII

=

d

=

h

= IX

=

7

NUMBERS • NUMBER SYMBOLS

2

The seven letters I, V, X, L, C, D, and M are put together to make up all of the numbers in the Roman number system:

Ones

I

II

III

IV

Tens

X

XX

XXX

XL

C

CC

CCC

CD

M

MM

MMM

1

10

Hundreds Thousands

100

1000

2

20

200

2000

3

4

30

40

300

3000

400

IV

4000

Draw lines to match each Hindu-Arabic number with the correct Roman numeral. Use the chart above to help you. a

2000

XXXVIII

b

7

MM

c

99

XIX

d

38

VII

e

550

LIV

f

19

V

VI

VII

VIII

IX

L

LX

LXX

LXXX

XC

D

DC

DCC DCCC

CM

5

50

500

V

5000

6

7

60

600

VI

6000

70

8

80

700

800

VII

VIII

7000

9

90

900

IX

8000

9000

MATHS IN CONTEXT

What year was that? TV programmes and films often have the year they were made in Roman numerals at the end of the credits. Work out the dates that these imaginary films were made.

Ghoul the Classroom Ghost!

MMXVI

Dave and Dottie

MMXX

1. MMXVI

= 2016

2. MMXX

=

CDLIX

g

333

DL

h

170

XCIX

i

54

CLXX

j

459

CCCXXXIII

Super Dooper Paratrooper

MMIX

Warrior Queens

MMXVII

3. MMIX

=

4. MMXVII

=

Pages 10–11

8

NUMBERS • PLACE VALUE

Place value In our number system, the amount a digit is worth depends on where it’s placed in a number. This is called its place value. For example, the digit 1 is worth 10 in 5610, but 1000 in 1584.

Warm-up 1

6

5

1

Th

H

T

O

5

6

1

0

1

5

8

4

We can work out the value of a digit by using a place value grid.

Circle the digit that shows the tens in each number below.

4

3

7

2

2

8

9

6

5

3

2

1

3

6

4

1

7

8

7

5

9

4

2

3

8

2

5 hundreds

98

thousands

hundreds

tens

ones

c

2425

thousands

hundreds

tens

ones

d

897

thousands

hundreds

tens

ones

e

3774

thousands

hundreds

tens

ones

f

798

thousands

hundreds

tens

ones

b

4

6

thousands

4567

a

7

6

9

7

Fill in how many thousands, hundreds, tens, and ones each of these numbers has.

a

2

5

tens

7

ones

These numbers all contain the digit 5, but it has a different value in each of them. Draw lines to match each digit 5 with its correct place value. 5

6

50

8 13

b

4

8

5

5000

2

c

9

3

2

500

5

d

2

5

4

5

8

9

NUMBERS • PLACE VALUE

3

Fill in the number that is being described in each of these sentences.

a

This number has 7 tens, 8 ones, 3 thousands, and 2 hundreds.

This number is:

b

This number has 4 thousands, 9 tens, 8 ones, and 3 hundreds.

This number is:

c

This number has 5 ones, 6 thousands, 8 tens, and 4 hundreds.

This number is:

d

This number has 6 tens, 4 ones, 9 thousands, and 3 hundreds.

This number is:

e

This number has 6 hundreds, 1 ten, 2 ones, and 3 thousands.

This number is:

f

This number has 4 tens, 7 thousands, 0 ones, and 8 hundreds.

This number is:

g

This number has 3 tens, 4 ones, 5 thousands, and 7 hundreds.

This number is:

h

This number has 5 hundreds, 9 ones, 2 tens, and 2 thousands.

This number is:

4

Use the number box to help you find five different numbers that have the digit 3 in the tens column.

380 a

3278

4237

4237

9370 b

1439

9803

37

3970 c

5322

31

3128

830

340

2380

d

e

i

j

5493

Now use the number box to find five different numbers that have the digit 3 in the hundreds column. f

380

g

h

Pages 12–13

10

NUMBERS • SEQUENCES AND PATTERNS

Sequences and patterns

+3

A sequence is a set of numbers that follows a pattern or rule. Using the rule lets us work out other numbers in the sequence.

5

+3

8

+3

11

+3

14

17

This sequence increases by 3 each time.

Warm-up +2

1

11

+2

13 +6

3

11

1

Fill in the next two numbers in each of these sequences. +2

15 +6

17

+2

17 +6

+1

2

+1

11

19 +6

+7

4

23

12

11

–3

18

–3

15

–3

12

c

–3

9

+7

18

25

b

6

24

20

16

86

81

76

25

23

21

d

20

19

18

e

f

99

93

87

+1

+7

+7

13

The numbers below follow sequences with subtraction rules. Work out the patterns, then fill in the numbers to complete the sequences.

a

+1

11

NUMBERS • SEQUENCES AND PATTERNS

2

Fill in the next two numbers for each sequence. Then complete the sentences to describe each pattern.

8, 12, 16, 20, 24,

28 ,

b

4, 14, 24, 34, 44,

,

The pattern is

each time.

c

7, 14, 21, 28, 35,

,

The pattern is

each time.

d

4, 7, 10, 13, 16,

The pattern is

each time.

3

32

+4

a

The pattern is

,

each time.

Write four different sequences of your own. The start number is given to you. Write the rule for each.

a

24,

21 ,

18 ,

15 ,

12 ,

b

30,

,

,

,

,

The rule is

.

c

18,

,

,

,

,

The rule is

.

d

45,

,

,

,

,

The rule is

.

4 a

The rule is

–3

.

Sometimes, a rule can have more than one part. Complete these sequences with two-part patterns. Pattern: add 3, then take away 1.

+3

8 c

9

+3

–1

11

10

Pattern: add 8, then take away 3.

–1

13

Pattern: add 5, then take away 2.

4

b

12

5 d Pattern: take away 5, then add 4.

20 Pages 14–15

12

NUMBERS • POSITIVE AND NEGATIVE NUMBERS

Positive and negative numbers Positive numbers are all of the numbers that are greater than zero. Negative numbers are less than zero, and they always have a negative sign (−) in front of them, like this: −4. Negative numbers are numbers less than zero.

−10 −9

−8 −7

Warm-up

−6

Zero is not positive or negative.

−5

−4 −3 −2

A number without a sign is always a positive number.

−1

1

3

4

5

6

7

8

9

10

Fill in the missing numbers on the number lines below.

1

2

–4

–3

–2

–1

1

0

2

–9

3

–7

–3

–4

0

4

–1

1

2

5

1

Count back five steps from the number circled on each of the number lines below. Then fill in the number that you land on.

a

−5

−4

−3

−2

−1

0

1

2

3

4

−4

−3

−2

−1

0

1

2

3

4

−4

−3

−2

−1

0

1

2

3

4

−4

−3

−2

−1

0

1

2

3

4

.

I landed on

.

I landed on

.

5

d

−5

I landed on 5

c

−5

.

5

b

−5

I landed on –2

5

13

NUMBERS • POSITIVE AND NEGATIVE NUMBERS

2

Count backwards five times from each number shown.

a

5, 4 ,

c

3,

e

12 ,

3

,

3 ,

2 ,

,

,

,

,

1

0

, ,

,

,

b

9,

,

,

,

,

d

1,

,

,

,

,

f

7,

,

,

,

,

b

4,

,

,

,

,

Count backwards five times in 2s.

8 ,

6 ,

4 ,

2 ,

0

a

10 ,

c

3,

,

,

,

,

d

1,

,

,

,

,

e

7,

,

,

,

,

f

9,

,

,

,

,

4 a

−4

Work out the difference between each pair of numbers, using the number lines to help you.

5 .

The difference between −3 and 2 is

−3

−2

−1

0

1

MATHS IN CONTEXT

2

3

Getting warmer?

5

Use the thermometer to find the answers to these word puzzles.

4

1. The temperature outside at 4am was –4°C. At 10 am, it was 5°C. How much warmer was it at 10am than at 4 am?

3

It was

b

3

The difference between 4 and 10 is

4

c

5

6

7

8

2. The temperature outside at noon was 5°C. At 8 pm it was –3°C. How much cooler was it at 8 pm than midday?

.

9

The difference between –5 and –1 is

10

It was

−5

−4

−3

–2

–1

.

0

°C cooler.

3. The temperature in Greenland was –5°C. In Norway it was 2°C. How much warmer was it in Norway than in Greenland? It was

−6

°C warmer.

°C warmer.

2 1 0 −1 −2 −3 −4 −5

1 Pages 18–19

14

NUMBERS • COMPARING NUMBERS

Comparing numbers We can compare numbers to find out if a number is the same as, smaller than, or larger than another number. We sometimes use symbols to help us compare numbers.

Warm-up

1 a

b

e

Less than

Circle the greater number in each of the pairs below.

305

350

2

989

99

3

288

828

4

123

1127

5

46

408

6

674

2674

7

531

513

8

822

82

Compare these pairs of numbers by writing less than (), or equal to (=). H

T

O

H

T

O

6

8

9

6

7

3

H

T

O

H

T

O

1

3

7

3

1

7

H

T

O

H

T

O

3

3

2

7

H

T

O

H

T

O

4

8

5

4

8

4

H

T

O

H

T

O

9

3

5

9

3

5

H

T

O

H

T

O

4

9

9

4

H

T

O

H

T

O

2

2

6

2

6

2

f

g

Greater than

1

c

d

Equal to

15

NUMBERS • COMPARING NUMBERS

2

Count how many items there are in each set. Then compare the sets by writing less than (), or equal to (=).

10

a

8

b

c

d

e

f

3

Fill in the missing numbers to make these comparisons true.

a

6

5

3

b

3

2

6

c

4

9

7

8

1

=

6

5

3

8

>

3

2

6

8