Year 6 SATs Targeted Practice Workbook Sample - compressed

Year 6 Maths

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SATs Targeted Practice Workbook

with online quizzes

About this workbook Audio test 2 This book contains questions to target every topic in Year 6 Maths.

Questions split into three levels of increasing difficulty – Challenge 1, Challenge 2 and Challenge 3 – to aid progress.

Ratio

3 The ratios show yellow to white.

Draw lines to match each ratio to a diagram.

5:1

Challenge 1

1:2

1 Rana makes samosas.

For every 1 meat samosa, she makes 2 vegetable samosas.

1:5

a) On Monday Rana makes 20 meat samosas.

2:3

How many vegetable samosas does she make?

4 marks

b) On Tuesday Rana makes 28 vegetable samosas.

4 The ratio of red squares to yellow squares is 4 : 3

How many meat samosas does she make?

2 Hugo puts black and white counters in a row.

You can colour the squares to help you.

For every 1 black he puts 3 white counters.

How many squares of each colour are there?

Colour the counters to show the correct ratio.

Challenge 2

Challenge 3

1 Here are some yellow and purple cubes.

1 Here is a set of shapes.

The ratio of yellow to purple is 2 : 3

2 marks

a) Write the ratio of triangles to quadrilaterals.

:

b) Write the ratio of pentagons to triangles.

:

c) Write the ratio of shapes with vertices to shapes without vertices.

The ratio of yellow to purple is 3 : 2

:

d) Write the ratio of circles to quadrilaterals to triangles.

1 mark

2 a) Write the ratio of blue to grey for these cubes.

‘How am I doing?’ checks for self-evaluation.

yellow

red

1 mark

Tick (✓) the correct statement for these cubes.

:

:

The ratio of red to yellow sweets is 3 : 5

:

How many red sweets are there?

2 marks

1 mark

Total marks :

How am I doing?

54

1. Robbie buys a pencil.

130

180

230

Progress test charts to record results and identify which areas need further practice.

Progress test charts Use these charts to record your results in the four Progress tests. Colour in the questions that you got right to help you identify any areas that you might need to study and practise again. (These areas are indicated in the ‘See page…’ row in the charts.)

1. The numbers in this sequence increase by the same amount each time.

2 marks

Progress test 1:

Write the missing numbers.

He pays with a £2 coin and gets 45p change. £

1 mark

Number of laps

Jade

45

Terri

63

Nikhil

27

Q1

Q17

six million, four hundred and twenty-three thousand, five hundred and six

Q1

5

Q16

42

See page…

72

31

Q5

Q20

Q6

Q21

Q7

Q22

Q8

Q23

Q9

Q24

Q10 Q11 Q12 Q13 Q14 Q15 Q16

Q25

Q26

Q27

Q28

Q29

Q30

Q31

TOTAL /58

Q2

Q3

Q17

Q4

Q18

Q19

Q5

Q20

Q6

Q7

Q21

Q8

Q22

Q9

Q23

Q10

Q11

Q24

Q25

Q12

Q26

Q13

Q27

Q14

Q28

Q15

Q29

TOTAL /51

18-19 24-25 44-45 48-49 52-53 14-15 42-43 12-13 52-53 58-59 52-53 52-53 54-55 38-39

Progress test 3:

9

9 marks See page…

4. Write the number that is 100 less than 1010.

b) How many laps did the children run in total?

Q4

See page… 12-13 12-13 22-23 24-25 12-13 14-15 26-27 22-23 12-13 24-25 18-19 32-33 26-27 14-15 20-21

9

6

Q19

Progress test 2:

3. Complete this multiplication grid.

a) Who ran the most laps?

Q3

Q18

See page… 12-13 28-29 18-19 30-31 18-19 24-25 14-15 30-31 20-21 16-17 32-33 22-23 32-33 32-33 32-33

1 mark

×

Q2

See page… 12-13 12-13 22-23 24-25 12-13 14-15 26-27 22-23 12-13 24-25 18-19 32-33 26-27 14-15 20-21 22-23

2. Write this number in figures.

2. The table shows the number of laps some children ran.

55

QR codes link to online interactive quizzes for extra practice.

More practice

Four progress tests allow children to test how well they have remembered the information.

Progress test 1

Name

/ 17

Ratio and proportion

Starter test

Total marks boxes for each topic.

There are 15 yellow sweets on the cake.

:

How much does his pencil cost?

4 marks

2 Mario decorates a cake with coloured sweets.

b) Write the ratio of grey to blue for these cubes.

Starter test recaps skills covered in Years 3 to 5.

Mason

Handy tips included.

There are 28 squares in total.

2 marks

1 mark

See page…

5. Write these decimals in order, starting with the smallest.

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

Q11

64-65

82-83

66-67

66-67

86-87

66-67

82-83

74-75

56-57

66-67

68-69

Q12

Q13

Q14

Q15

Q16

Q17

Q18

Q19

Q20

Q21

Q22

42-43

68-69

78-79

76-77

72-73

84-85

72-73

50-51

76-77

84-85

54-55

Q7

Q8

Q9

TOTAL /52

Progress test 4: 0.23

0.02

0.3

0.032

0.203

0.003

Q1

Q2

Q3

Q4

Q5

Q6

Q10

Q11

Q12

Q13

Q14

Q15

TOTAL /29

See page… 90-91 90-91 92-93 106-107 104-105 94-95 78-79 90-91 96-97 100-101 98-99 54-55 102-103 106-107 40-41

c) How many more laps did Terri run than Nikhil? smallest

What am I doing well in?

largest 2 marks

3 marks

3. Write these numbers in order, starting with the smallest.

2.45

2.54

5.25

2.44

6. Write the missing numbers in these boxes on the number line.

0 1000

2.5 What do I need to improve?

3 marks

smallest

7. a) Write down all the factors of 36.

largest 2 marks

2 marks

b) Write all the common factors of 36 and 48.

2 marks

4

34

128

Answers are included at the back of the book.

Author: Katherine Pate About this workbook 27895_P001_003.indd 1

1 07/04/2025 14:56

Contents Starter test .................................................................................................................................................... 4 Number and place value Place value ..................................................................................................................................................... 12 Negative numbers ........................................................................................................................................ 14 Rounding ......................................................................................................................................................... 16 Prime, square and cube numbers ............................................................................................................. 18 Addition, subtraction, multiplication and division (calculations) Order of operations .................................................................................................................................... 20 Mental calculations ...................................................................................................................................... 22 Written addition and subtraction ............................................................................................................ 24 Common factors and multiples ................................................................................................................ 26 Written multiplication ................................................................................................................................. 28 Written division ............................................................................................................................................ 30 Mixed problems ............................................................................................................................................ 32 Progress test 1 .......................................................................................................................................... 34 Fractions, decimals and percentages Equivalent fractions ..................................................................................................................................... 38 Fractions of amounts .................................................................................................................................. 40 Adding and subtracting fractions ............................................................................................................. 42 Multiplying fractions .................................................................................................................................... 44 Dividing fractions ......................................................................................................................................... 46 Improper fractions and mixed numbers ................................................................................................. 48 Percentages ................................................................................................................................................... 50 Fraction, decimal and percentage problems ......................................................................................... 52 Ratio and proportion Ratio................................................................................................................................................................. 54 Scale factor..................................................................................................................................................... 56 Unequal sharing............................................................................................................................................. 58 Progress test 2 .......................................................................................................................................... 60 Algebra Equations ........................................................................................................................................................ 64 Formulae ........................................................................................................................................................ 66 Sequences........................................................................................................................................................ 68 Measurement Units of measurement ................................................................................................................................ 70 Imperial and metric units............................................................................................................................ 72

2 27895_P001_003.indd 2

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Contents Audio test 2 Perimeter and area....................................................................................................................................... 74 Area of triangles and parallelograms...................................................................................................... 76 Geometry – properties of shapes 2-D shapes – triangles, polygons and circles ....................................................................................... 78 2-D shapes – quadrilaterals ..................................................................................................................... 80 3-D shapes and nets .................................................................................................................................... 82 Volume ............................................................................................................................................................ 84 Progress test 3 .......................................................................................................................................... 86 Geometry – position and direction Missing angles ............................................................................................................................................... 90 Angle problems ............................................................................................................................................. 92 Coordinates ................................................................................................................................................... 94 Translations ................................................................................................................................................... 96 Reflections ...................................................................................................................................................... 98 Statistics Bar charts ...................................................................................................................................................... 100 Line graphs .................................................................................................................................................... 102 Pie charts ........................................................................................................................................................ 104 The mean ....................................................................................................................................................... 106 Progress test 4 .......................................................................................................................................... 108 Answers ........................................................................................................................................................ 112 Progress test charts ............................................................................................................................... 128

ACKNOWLEDGEMENTS The author and publisher are grateful to the copyright holders for permission to use quoted materials and images.

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Published by Collins An imprint of HarperCollinsPublishers 1 London Bridge Street London SE1 9GF HarperCollinsPublishers Macken House, 39/40 Mayor Street Upper, Dublin 1, D01 C9W8, Ireland © HarperCollinsPublishers Limited 2025 ISBN 9780008727895 First published 2025 10 9 8 7 6 5 4 3 2 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Collins.

British Library Cataloguing in Publication Data.

A CIP record of this book is available from the British Library.

Publisher: Fiona McGlade Author: Katherine Pate Contributor: Frances Naismith Project manager and editorial: Chantal Addy Cover design: Sarah Duxbury Inside concept design: Ian Wrigley Text design and layout: Rose & Thorn Creative Services Ltd Artwork: Shutterstock and Collins Production: Bethany Brohm Printed in India

Contents 27895_P001_003.indd 3

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Starter test 1. Robbie buys a pencil.

He pays with a £2 coin and gets 45p change.

How much does his pencil cost?

£

1 mark

2. The table shows the number of laps some children ran.

Name

Number of laps

Jade

45

Terri

63

Nikhil

27

Mason

31

a) Who ran the most laps? b) How many laps did the children run in total?

c) How many more laps did Terri run than Nikhil?

3 marks

3. Write these numbers in order, starting with the smallest.

2.45

smallest

2.54

5.25

2.44

2.5

largest 2 marks

4 27895_P004_011.indd 4

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4. Write this number in words.

126 397 1 mark

5. These numbers are written in Roman numerals.

Write them as ordinary numbers. a) XLVIII b) MMXIV

2 marks

6. Brodie catches a bus at 7.45 am.

He gets off the bus 25 minutes later.

What time does Brodie get off the bus?

1 mark

7. Kevin has 250 ml of water in a jug.

How much more water does he need to make 1 litre?

ml

1 mark

shelves

1 mark

8. Elias has 135 books.

He can put 9 books on each shelf.

How many shelves does he need for all his books?

Starter test 27895_P004_011.indd 5

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9. Write 358 as an improper fraction.

1 mark

10. Work out: 27 345 – 15 174 =

1 mark

11. How many sides does a hexagon have? sides

1 mark

12. Colour 15 of this shape.

1 mark

13. Write the missing numbers in the boxes.

0

500 2 marks

14. a) Tick (✓) the obtuse angles.

B

A

C

D

1 mark

b) Write the letters in order of angle size. smallest angle

largest angle

2 marks

15. Write this number in figures. three hundred and seven thousand and one

1 mark

6 27895_P004_011.indd 6

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16. Work out the volume of this cuboid.

1 cm 1 cm

cm3 17. Write 16 3 as a mixed number.

1 mark

1 mark

18. Write a multiple of 9 between 70 and 80.

1 mark

19. A tablet costs £230.

A school buys 15 of these tablets.

Work out the total cost.

£

1 mark

20. How many lines of symmetry does a regular pentagon have?

1 mark

21. 120 chairs are arranged in rows.

There are 8 chairs in each row.

How many rows of chairs are there?

1 mark

22. Work out 19 of 126 kg.

kg

Starter test 27895_P004_011.indd 7

1 mark

7 27/03/2025 10:17

23. Here is a rectangle.

7m

6m

a) Work out the area of this rectangle.

m2 b) Work out the perimeter of this rectangle.

m

2 marks

24. Write down all the factors of 32.

2 marks

25. What fraction of this shape is shaded?

Write your fraction in its simplest form.

1 mark

26. How many minutes are there in 512 hours? minutes

1 mark

ml

1 mark

27. Rosie pours water into a 2-litre bucket until it is 15 full.

How much water is in the bucket?

8 27895_P004_011.indd 8

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28. Write these fractions in order, starting with the smallest.

2 3

1 2

7 12

5 6

smallest

largest 2 marks

29. Write each fraction as a decimal. a)

74 100

b)

1 10

c)

57 1000 3 marks

30. Write in the missing number.

348 g +

g = 1 kg 1 mark

31. Colour 34 of this shape.

1 mark

32. Work out: a) 32 = b) 112 = c) 103 = 3 marks

33. Circle every prime number.

3

25

31

42

51

68

75

2 marks

34. Write the missing numbers in these calculations. a) 33 ÷ 10 = b) 130 ÷ c)

= 1.3 ÷ 100 = 0.33 3 marks

35. Work out: 9 1 7 16 + 16 + 16 =

Give your answer as a mixed number.

1 mark

Starter test 27895_P004_011.indd 9

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36. Complete these conversions. a) 36 cm =

mm

b)

1060 g =

kg

c) 3.5 km =

m

d)

1.45 m =

cm

–4 –3 –2 –1 0

1

2

3

4

4 marks

5 °C

37. The two thermometers show the temperature in Hull and the temperature in Cardiff.

–4 –3 –2 –1 0

1

2

3

4

5

–4 –3 –2 –1 0

1

°C

2

3

4

5 °C

Hull Cardiff –4 –3 –2 –1 0

1

2

3

4

5

a) Which city is warmer – Hull°C or Cardiff? b) How many degrees warmer?

°C

2 marks

38. Work out the size of each angle marked with a letter. a) x

76° x=

°

w=

°

b) 55°

w

2 marks

39. Here are some points on a coordinate grid. y 5 A 4 3 B 2 C 1 D 0 0 1 2 3 4 5

x

Write the coordinates of each point.

A (

,

)

B

(

,

)

C (

,

)

D

(

,

)

4 marks

10 27895_P004_011.indd 10

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40. The pictogram shows the numbers of people who went swimming on different days.

Monday Tuesday

Key

Wednesday

represents 20 people

Thursday Friday a) How many people went swimming on Monday? b) How many more people went swimming on Friday than on Wednesday?

c) Which was the most popular day for swimming?

3 marks

41. Draw the reflection of the shape in the mirror line.

Mirror line

1 mark

42. Round 5176: a) to the nearest 10 b) to the nearest 100 c) to the nearest 1000

How am I doing?

3 marks

Total marks :

Starter test 27895_P004_011.indd 11

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Place value Challenge 1 1 a) Write this number in words.

794 302

1 mark

b) Write this number in figures. two million

1 mark

c) Write this number in figures. thirty-four point zero six

1 mark

2 The numbers in this sequence increase by the same amount each time.

Write the missing numbers.

28 517

30 517

33 517 3 marks

3 Write these decimals in order, starting with the smallest.

0.14

0.07

0.6

0.002

0.125

smallest

0.03 largest

2 marks

Challenge 2 1 a) Write this number in words.

9 900 099

b) Write this number in figures. eight million, four hundred and fifty-two thousand

2 marks

12 27895_P012_037.indd 12

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2 In this number: 5 247 360.189 a) What is the value of the digit 4? b) What is the value of the digit 6? c) What is the value of the digit 9?

3 marks

3 Write the missing numbers in this table.

10 thousand less

Number

57 450

67 450

1 million more

482 000

1 482 000 2 500 030

1 995 000

6 marks

Challenge 3 1 Circle the values that are equivalent to thirty-two thousand.

One has been done for you.

320 tens

32 000 ones

3200 tens

320 hundreds

32 thousandths

2 marks

2 Write the missing numbers in the boxes.

2 500 000

5 000 000 2 marks

3 a) Write the number that is 1 hundredth greater than 2.67 b) Write the number that is 1 tenth less than 2.67 c) Write the number that is 1 thousandth less than 2.67

3 marks

4 Work out: a) 2 375 190 ÷ 10 =

b)

2 375 190 ÷ 1000 =

c) 24 000 × 100 =

d)

856.025 × 1000 =

How am I doing?

4 marks

Total marks :

Number and place value 27895_P012_037.indd 13

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Negative numbers Challenge 1 1 Write these temperatures in order, starting with the coldest. −6°C

7°C

3°C

−8°C

coldest

−2°C warmest

2 marks

2 The temperature is −5°C and it falls by 4°C. What is the new temperature?

°C

1 mark

3 The temperature is −6°C and it rises by 5°C. What is the new temperature?

°C

1 mark

Challenge 2 1 What is the difference between −5°C and 10°C? °

1 mark

°C

1 mark

°

1 mark

°C

1 mark

2 The temperature is 3°C and it falls by 11°C. What is the new temperature?

3 9°C is warmer than −7°C. How many degrees warmer?

4 The temperature is −6°C and it rises by 15°C. What is the new temperature?

5 −21°C is colder than 5°C. How many degrees colder? ° 6 One morning the temperature is −4°C.

1 mark

During the day the temperature rises by 6°C and then falls by 12°C. What is the new temperature?

°C

1 mark

14 27895_P012_037.indd 14

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7 Work out the calculations below.

You can use this number line to help you.

–6

–5 –4

–3 –2

–1

0

1

2

3

4

5

6

a) 4 – 5 = b)

–3 + 3 =

c) –3 – 2 = d) –4 + 6 = e) 5 – 8 = f) –1 + 6 =

6 marks

Challenge 3 1 The temperatures in this sequence decrease by the same amount each time.

Write the missing numbers in the sequence. −4°C

7°C

3 marks

2 Write the temperature at A and the temperature at B. + 35°C

0 A

B

°C

°C

2 marks

3 The top of a cliff is 45 metres above sea level.

The seabed at the bottom of the cliff is 6 metres below sea level.

What is the distance from the top of the cliff to the seabed?

1 mark

4 Work out: a) –2 – 3 =

b)

–2 + 3 =

c) –5 + 8 =

d)

4 – 10 =

e) –6 – 8 =

f)

–17 + 10 =

How am I doing?

6 marks

Total marks :

Number and place value 27895_P012_037.indd 15

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Rounding Challenge 1 1 R ound each number to the nearest 1000.

The first one has been done for you.

Number

Rounded to nearest 1000

23 419

23 000

5500 148 600 1 218 450 3 marks

2 C ircle every number that rounds to 5.8, to 1 decimal place.

5.65

5.82

5.76

5.74

5.85

5.67 2 marks

3 R ound 526.37: a) to one decimal place. b) to the nearest whole number. c) to the nearest ten.

3 marks

Challenge 2 1 Round these numbers to the nearest hundred.

580

320

Use your rounded numbers to calculate an estimate for 580 × 320 Estimate =

2 marks

2 Round these numbers to the nearest whole number.

29.742

12.04

Use your rounded numbers to calculate an estimate for 29.742 × 12.04

Estimate =

2 marks

16 27895_P012_037.indd 16

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3 Round 5 555 555: a) to the nearest thousand. b) to the nearest ten thousand. c) to the nearest million.

3 marks

4 1 pen costs £1.80 Jack says that 33 of these pens cost £594 Work out this estimate for the cost.

30 × 2 = Use the estimate to explain why Jack is wrong.

1 mark

Challenge 3 1 Maisie and Liam are playing a game.

Maisie’s score rounds to 300 000, to the nearest hundred thousand. a) What is the lowest number her score could be?

Liam’s score rounds to 320 000, to the nearest ten thousand. b) What is the highest number Liam’s score could be?

2 marks

2 The table shows the number of bus passengers each day, for a week. a) Round each number to the nearest thousand.

Day

Number of passengers

Monday

23 407

Tuesday

19 780

Wednesday

16 214

Thursday

20 697

Friday

24 306

Saturday

15 450

Sunday

9875

b) Use your rounded values to calculate an estimate for the total number of passengers that week.

c) Round your estimate to the nearest ten thousand.

How am I doing?

4 marks

Total marks :

Number and place value 27895_P012_037.indd 17

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Prime, square and cube numbers Challenge 1 1 Work out: a) 72 =

b)

12 =

c)

62 =

b)

13 =

c)

32 =

3 marks

2 Work out: a) 33 =

3 marks

3 Circle all the prime numbers in this list.

1

2

4

9

15

19 2 marks

Challenge 2 1 Write <, > or = in each box to make the statement correct. a) 52

23

b)

12

13

c) 32

23

d)

52

33

e) 53

102

f)

72

43 6 marks

2 Circle the square numbers in this list.

27

36

49

65

82

100

121

2 marks

3 Write the missing number in each box. a)

2

= 64

b)

2

= 81

c)

3

= 27

d)

2

= 144

e)

2

= 100

f)

3

=8

6 marks

18 27895_P012_037.indd 18

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4 Circle the cube numbers from the list.

1

4

9

27

49

64

100

125

5 Write the smallest three-digit prime number.

2 marks

1 mark

Challenge 3 1 Luis arranges 9 counters into a square shape.

Rani has 40 counters.

She arranges the counters into the biggest square shape possible.

Rani has some counters left over.

How many counters does she have left over?

1 mark

2 Work out: a) 52 + 22 =

b)

43 + 32 =

c) 103 − 102 =

d)

4 3 − 82 =

f)

92 – 33 =

e) 12 + 22 + 32 =

6 marks

3 Write a number less than 30 in each box, to make the statement correct. prime number

square number

+

square number

= 1 mark

4 Write a number less than 30 in each box, to make the statement correct. square number

square number

+

square number

=

5 Write all the numbers from 1 to 20 in the correct places in this diagram. prime number

1 mark

multiples of 3

4 marks

How am I doing?

Total marks :

Number and place value 27895_P012_037.indd 19

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Order of operations Challenge 1 1 Work out: a) 3 + 5 – 2 =

b)

11 – 5 + 4 =

c) 15 – 7 + 3 =

d)

10 – 3 – 2 =

a) 3 × 4 × 2 =

b)

15 ÷ 5 × 2 =

c) 4 × 6 ÷ 8 =

d)

40 ÷ 2 ÷ 5 =

4 marks

2 Work out:

4 marks

Challenge 2 1 Work out: a) 2 + 5 × 6 =

2×5+6=

c) 17 – 3 × 2 =

b)

d)

6×3–5=

4 marks

2 Draw lines to match each calculation to the correct answer. a)

10 + 8 ÷ 2

b)

(10 + 8) ÷ 2

10

c)

20 – 5 × 2

30

d)

(20 – 5) × 2

14

9

4 marks

3 Work out: a) 2 + 5 × 3 + 4 =

c) 4 × 2 + 3 × 7 =

b)

8÷2+6÷3=

d)

5 + 12 ÷ 4 − 6 =

4 marks

20 27895_P012_037.indd 20

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4 Write these four digits in the calculation below, to give the highest possible answer.

2 (

4

5

+

)×

7 –

=

2 marks

5 Work out: a) 6 × 12 – (25 – 9) ÷ 4 = b) (3 + 5) × (9 – 2) ÷ 2 =

2 marks

Challenge 3 1 Work out: a) 32 + 4 = b) (3 + 4)2 = c) 3 + 42 = d) 32 + 42 =

4 marks

2 Work out: a) 4 + 32 – 5 = b) (7 – 3) + 4 × 2³ = c) (3 + 5) × 8 – 8² = d) 6² – 3 + 2 =

4 marks

3 Lou and Jay write these calculations using the same numbers.

Tick (✓) the calculation that has the greatest answer.

Lou

26 – (3 + 2) × 4 + 3

Jay

26 – 3 + 2 × (4 + 3)

1 mark

4 Write brackets in this calculation, so that the answer is 20.

2² + 4 × 5 + 7 ÷ 3

How am I doing?

1 mark

Total marks :

Addition, subtraction, multiplication and division (calculations) 27895_P012_037.indd 21

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21 27/03/2025 11:07

Mental calculations Challenge 1 1 Work out: a) 4600 + 750 = b) 3500 − 50 + 200 = c) 140 000 + 20 500 − 3000 = d) 1 000 000 – 200 + 5000 =

4 marks

2 Jo buys these three items.

£1.99 65p £2.05

a) How much does Jo spend in total?

£

b) How much change does Jo get from £10?

£

2 marks

3 Marcus had his 19th birthday on 1st January 2014.

In which year was Marcus born?

1 mark

Challenge 2 1 Work out: b)

a) 3000 × 5 =

c) 80 000 ÷ 4 =

d)

400 ÷ 20 =

f)

2500 ÷ 50 =

b)

3490 ÷ 100 =

d)

17.14 × 10 =

f)

980 ÷ 1000 =

e) 120 × 30 =

500 000 × 8 =

6 marks

2 Work out: a) 227 ÷ 10 = c) 4.08 × 1000 = e) 500 000 ÷ 100 =

6 marks

3 Mr Smith has 40 boxes of pens.

Each box contains 10 packs of pens.

Each pack contains 12 pens.

How many pens does Mr Smith have in total?

1 mark

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4 In this multiplication wall, each number is found by multiplying the two numbers below.

280 4 0.04

3 marks

Write the missing numbers in the wall.

5 Work out: a) 0.7 × 5 =

b)

0.03 × 8 =

c) 0.9 × 40 =

d)

300 × 0.6 =

f)

7000 × 0.2 =

e) 200 × 0.03 =

6 marks

Challenge 3 1 Work out these calculations. Write your answers in ordinary numbers. a) MCMIV + DCC = b) MMLX – MCCCXX =

2 marks

2 Write a number in each box to make the statement correct. a) 0.1 is

times greater than 0.001

b) 0.01 is

times smaller than 0.1

2 marks

3 Work out: a) 24 × 10 + 6 =

b)

c) 3.5 × 100 + 20 =

e) 0.042 × 100 – 1.5 =

3750 ÷ 100 + 2.5 =

d)

1.25 × 100 + 15 × 10 =

f)

536 ÷ 100 – 0.2 × 10 =

6 marks

4 Complete these conversions. a) 20 m =

cm

b)

c) 56 km =

cm

d)

2400 mm =

e) 4850 ml =

litres

f)

840 g =

How am I doing?

ml = 5 litres m kg

Total marks :

Addition, subtraction, multiplication and division (calculations) 27895_P012_037.indd 23

6 marks

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23 27/03/2025 11:07

Written addition and subtraction Challenge 1 1 W ork out: a)

4531

20 500

b)

+ 457

752 410

c)

– 359

d)

+ 25 337

900 000 – 39 702 4 marks

2 T hese are the prices for hiring boats.

Speedboat Canoe Sailing boat Rowing boat

£145.99 £24.50 £224.50 £44.25 Neil’s family hire the speedboat and the canoe.

Ellie’s family hire the sailing boat and the rowing boat.

How much more does Ellie’s family spend than Neil’s family?

£

1 mark

3 W ork out: a)

12.457 b) + 0.026

15.00 – 1.09 2 marks

Challenge 2 1 In this addition pyramid, add two numbers to get the number in the space above.

Complete the pyramid.

1187 745

26 300

3 marks

24 27895_P012_037.indd 24

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2 Here are the weights of four people in a lift.

63 kg

85 kg

72 kg

59 kg

The maximum weight for the lift is 400 kg.

Another person weighs 78 kg.

Can all five people go in the lift at the same time?

Show working to explain your answer.

1 mark

3 Circle two numbers that add together to make 2.

1.04

0.096

1.034

0.996

0.966 1 mark

4 Work out: b) 14.59 + 3.025 – 11.3 =

a) 20 – 3.75 =

2 marks

Challenge 3 1 A stack of 20 boxes is 3 metres tall.

Lola takes 4 boxes off the top of the stack.

How tall is the stack now? m

3m

2 Jess is making fruit salad for a party.

Strawberries cost £4.50 per kg.

1 mark

Bananas cost £2.40 per kg.

Grapes cost £1.90 per kg.

10 paper bowls cost £1.60 She uses 2 kg of strawberries, 1 kg of bananas and 0.5 kg of grapes to make 30 bowls of fruit salad.

Calculate the total cost to make 30 bowls of fruit salad.

£ How am I doing?

1 mark

Total marks :

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Common factors and multiples Challenge 1 1 W rite the first 5 multiples of 8.

1 mark

2 a) Write all the factors of 28.

b) Write all the factors of 40.

c) Write all the common factors of 28 and 40.

3 marks

3 Circle all the multiples of 3 in this grid.

101

102

103

104

105

106

107

108

109

110

2 marks

Challenge 2 1 Write all the common factors of 24 and 32.

1 mark

2 a) Write the first ten multiples of 5.

b) Write the first ten multiples of 4.

c) Write two common multiples of 4 and 5.

3 marks

3 a) Write all the common factors of 8 and 6.

b) Write the first three common multiples of 8 and 6.

2 marks

26 27895_P012_037.indd 26

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4 Circle the numbers that are divisible by 9 and also by 4.

8

18

36

49

54

94

108 2 marks

5 I think of a prime number greater than 5.

The number is a factor of 39 and of 52.

What is my number?

1 mark

Challenge 3 1 Write two common multiples of 2, 3 and 5. and

1 mark

2 Write all the common factors of 8, 16 and 20.

1 mark

3 I think of a number between 100 and 200.

My number is a factor of 600 and a multiple of 20.

What is my number?

1 mark

4 In a perfect number, the sum of the factors (excluding the number itself) equals the number itself.

For example, the factors of 6 are 1, 2 and 3.

The sum of factors = 1 + 2 + 3 = 6 So, 6 is a perfect number.

Which of these is a perfect number?

14

28

32

1 mark

5 Tisha writes a list of common multiples of 3, 6 and 8.

What is the smallest number in Tisha’s list?

1 mark

How am I doing?

Total marks :

Addition, subtraction, multiplication and division (calculations) 27895_P012_037.indd 27

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Written multiplication Challenge 1 1 W ork out: 48

a)

943

b)

× 7

c)

× 6

4026 × 32 3 marks

2 W rite the missing numbers in this long multiplication.

4 5 ×

2 3 1

5 0

1 mark

3 H ow many hours are there in 3 weeks?

hours

1 mark

Indian rupees

1 mark

Challenge 2 1 £1 = 108 Indian rupees.

Baldeep has £65.

How many Indian rupees are equal to £65?

2 Work out the number of seconds in 24 hours.

1 mark

28 27895_P012_037.indd 28

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3 Work out: 8.2

a) ×

9.8

b) ×

4

3 2 marks

4 An egg tray holds 144 eggs.

An egg box holds 12 eggs.

A farmer sells 23 trays of eggs and 65 boxes of eggs.

How many eggs does the farmer sell in total?

1 mark

Challenge 3 1 Work out:

452

1 mark

2 Work out:

133

1 mark

3 Work out the area of this rectangle.

1425 m 78 m

m2

1 mark

4 Write <, > or = to make this statement correct.

79 × 532

81 × 519

1 mark

How am I doing?

Total marks :

Addition, subtraction, multiplication and division (calculations) 27895_P012_037.indd 29

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Written division Challenge 1 1 Work out: a) 7 371 b)

8 592

c) 6 1962 d)

9 3105

4 marks

7000 is divided by 3

2 marks

2 Work out the remainder when: a) 500 is divided by 6

b)

3 A box holds 8 batteries.

1 mark

How many boxes can be filled with 300 batteries?

Challenge 2 1 Write the missing numbers in these long divisions. a)

b)

4 15 6 6

4 0

5 5

4

5 0

3 21 7

5

6

1

2

6

1

2

6 0

2 marks

2 Use long division to work out: a) 16 192

b) 24 432

c) 13 2795

3 marks

30 27895_P012_037.indd 30

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3 There are 330 children in Key Stage 2.

The children are put into teams of 15 for sports day.

How many teams are there?

1 mark

4 Shappi uses 34 cm of wire to make a star shape.

She has 5 metres of wire. a) How many 34 cm lengths can she cut from 5 metres of wire?

b) How much wire is left over?

cm

2 marks

5 Work out these divisions. Give the remainders as fractions. a) 6 393 b)

11 2351

2 marks

Challenge 3 1 Four flying lessons cost £395.

How much does one flying lesson cost?

£

1 mark

2 Work out: 8 5.0 Give your answer as a decimal.

1 mark

3 Write the missing numbers in the boxes to make each calculation correct. a) 17 ×

= 884

b)

32 ×

= 7136

2 marks

4 A factory makes crackers.

There are 12 crackers in one box.

The factory makes 10 000 crackers a day.

How many full boxes of crackers is this?

1 mark

How am I doing?

Total marks :

Addition, subtraction, multiplication and division (calculations) 27895_P012_037.indd 31

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Mixed problems Challenge 1 1 W ork out: a) 12 tens less than 12 thousand. b) 15 tens more than 15 hundreds.

2 marks

2 A full bucket of water holds 5 litres.

Ben pours 2465 ml of water out of the bucket.

Then Carys pours 1130 ml of water into the bucket.

How much water is in the bucket now?

1 mark

3 283 children go on a school trip.

The children are in groups of 12, and one smaller group.

There is one adult with each group of children.

How many adults are there?

1 mark

4 A time capsule was buried in MCMXIV. It was dug up 108 years later.

In which year was it dug up?

Write your answer in ordinary numbers.

1 mark

Challenge 2 1 Mrs Jones buys 7 packs of stickers.

Each pack contains 48 stickers.

Mrs Jones shares all the stickers fairly between the 28 children in her class.

How many stickers does each child get?

1 mark

2 Cherry has a box of beads.

She gives 5 of her friends 75 beads each.

She has 220 beads left.

How many beads were in the box to start with?

1 mark

32 27895_P012_037.indd 32

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3 There are 75 g of pasta in one portion. a) How many portions are there in a 2 kg bag of pasta? b) How much pasta is left over?

g

2 marks

4 Miles is planning a tea party for 47 people.

Each person needs two scones.

Scones come in packs of 5.

How many packs of scones does Miles need?

1 mark

5 Work out the total cost of: 25 drinks at £2.40 each and 22 cakes at £3.25 each

1 mark

Challenge 3 1 Tristan thinks of a number.

He squares his number.

Then he adds 12.

The answer is 93.

What is Tristan’s number?

1 mark

2 One horse eats 8 kg of hay each day.

Work out the amount of hay needed for 6 horses for 4 weeks.

1 mark

3 Is 14 a factor of 903?

Explain how you know.

1 mark

4 An ice cream shop sells: • 8 flavours of ice cream: vanilla, strawberry, chocolate, toffee, raspberry, banana, mint, lemon • 4 sizes of cone: small, medium, large, giant One possible combination is: vanilla with small cone.

How many possible combinations are there?

How am I doing?

1 mark

Total marks :

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33 27/03/2025 11:07

More practice

Progress test 1 1. The numbers in this sequence increase by the same amount each time.

130

180

230

2 marks

Write the missing numbers.

2. Write this number in figures. six million, four hundred and twenty-three thousand, five hundred and six

1 mark

3. Complete this multiplication grid.

×

5

6

9 42 72

9

9 marks

4. Write the number that is 100 less than 1010.

1 mark

5. Write these decimals in order, starting with the smallest.

0.23

0.02

0.3

0.032

0.203

smallest

0.003

largest 2 marks

6. Write the missing numbers in these boxes on the number line.

0 1000

3 marks

7. a) Write down all the factors of 36.

2 marks

b) Write all the common factors of 36 and 48.

2 marks

34 27895_P012_037.indd 34

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8. Work out: 1999 + 300 =

1 mark

9. Write the value of the digit 2 in each number. a) 32 456 b) 3765.2 c) 245 763

3 marks

10. In this number pyramid, each number is the difference between the two numbers above.

1426

875

Difference between 1426 and 875

301 3 marks

Complete the pyramid.

11. Circle every prime number in this list.

32

37

39

43

51

67

85

97

2 marks

12. Meghan puts eggs into boxes.

She has 340 eggs.

Each box holds 12 eggs. a) How many boxes can Meghan fill with eggs?

boxes

b) How many eggs are left over?

eggs

2 marks

13. Write three common multiples of 6 and 10.

3 marks

14. At 2 pm the temperature is 8°C. At 9 pm the temperature is −5°C. Work out the difference between these two temperatures.

°C

Progress test 1 27895_P012_037.indd 35

1 mark

35 27/03/2025 11:07

15. Work out: 6+4×3–2=

1 mark

16. Work out: 12 200 – 1250 =

1 mark

17. Write the number 37 609 in words.

1 mark

18. Work out: 275 × 34 =

1 mark

19. Work out: 53 – 42 =

1 mark

20. Work out: 7 2702

1 mark

21. Circle every square number: 12

16

55

81

32

25

64

2 marks

22. Work out: 18.36 – 4.5 = 1 mark

23. Write the temperature that is 15 degrees lower than 6°C.

24. Divide 132 by 5.

°C

1 mark

Write the remainder as a fraction.

1 mark

25. Work out: (3 × 7 + (11 – 8)) ÷ 4 =

1 mark

36 27895_P012_037.indd 36

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26. Round 46 237.95: a) to the nearest whole number. b) to the nearest ten. c) to the nearest thousand. d) to the nearest ten thousand.

4 marks

27. There are 792 children in a school.

The children are put into classes of 24.

How many classes are there?

1 mark

28. 1 notepad costs £2.30 Write a calculation to estimate the cost of 82 of these notepads.

1 mark

2m

29. Tom wants to put LED lights all along the top of his bedroom walls.

Here is a plan of his bedroom.

1.75 m 3.2 m

Calculate an estimate of the length of LED lights Tom needs.

4.15 m

Give your answer to the nearest metre.

m

1 mark

30. A packet of stickers costs 89p.

Work out the cost of 75 packets of stickers.

£

1 mark

31. Mike cuts 3 metres of wood into 11 equal pieces.

Work out the length of one piece in centimetres, accurate to one decimal place.

How am I doing?

cm

Total marks :

Progress test 1 27895_P012_037.indd 37

1 mark

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37 27/03/2025 11:07

Equivalent fractions Challenge 1 1 S hade 14 of each shape. a) b)

2 marks

2 For each shape, write the fraction shaded in its simplest form. a)

b)

2 marks

3 Write <, > or = between each pair of fractions to make the statements correct. a)

3 4

6 8 b)

2 3

5 9

c)

5 12

3 6

d)

2 3

3 6

e)

3 4

16 20

f)

4 15

1 5

6 marks

Challenge 2 1 Write each fraction in its simplest form. a)

3 12 =

b)

2 10 =

c)

6 18 =

d)

5 30 =

4 marks

2 Write the missing numbers in these equivalent fractions.

6

9 1 3

21 15

33 12

6 marks

38 27895_P038_063.indd 38

28/03/2025 15:29

12 3 Write three equivalent fractions for 18

3 marks

4 a) Write a number less than 15 which is a common multiple of 2, 3 and 4.

1 mark

b) Write all these fractions with your answer to part a) as the denominator (bottom number).

23

1 4

3 4

1 2

1 3

5 marks

c) Write the fractions from part b) in order, starting with the smallest. smallest

largest 2 marks

Challenge 3 1 Write these fractions in order, starting with the smallest.

8 12

12 20

12 16

20 60

smallest

largest

2 marks

2 In each set, circle the fraction that is not equivalent to the others. a)

8 32

1 4

7 28

3 8

6 24

b)

2 10

3 15

4 20

6 30

8 50

c)

6 14

30 70

18 42

9 27

15 35

3 marks

3 Jayesh has 24 counters.

15 of these counters are yellow.

What fraction of the counters are yellow?

Write your answer in its simplest form.

How am I doing?

1 mark

Total marks :

Fractions, decimals and percentages 27895_P038_063.indd 39

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Fractions of amounts Challenge 1 1 D raw lines to match each box to the correct number.

20

One has been done for you.

25

1 of 120 3

1 of 150 5

30 35

1

4 of 100 40 1

8 of 160 45 2 Work out:

3 marks

a)

1 8 of £40 =

b)

c)

1 12 of 72 m =

d)

1 9 of 36 kg = 1 7 of 63 litres =

3 Work out: a)

1 4 × 20 =

b)

1 5 × 45 =

c)

3 8 × 24 =

d)

2 9 × 36 =

4 marks

4 marks

Challenge 2 1 Isabella had 75 beads.

She gave 25 of these beads to Rora.

How many beads did she give to Rora?

1 mark

2 Write the answers as improper fractions and as mixed numbers.

The first one is done for you. a) 3 × 34 = 94 = 214 b)

7 × 38 =

c) 13 × 14 =

d)

3 × 57 =

e) 5 × 56 =

f)

5 10 × 11 =

5 marks

40 27895_P038_063.indd 40

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3 Work out: a)

3 4 of 2000 kg =

c)

5 6 of £288 =

b)

2 7 of 840 km =

d)

2 3 of £15.99 =

4 marks

4 A book has 225 pages.

Ivy has read 35 of the book.

How many more pages are left for Ivy to read?

1 mark

5 I am thinking of a number.

2 5 of my number is 24.

What is my number?

1 mark

6 Three-sevenths of a number is 15.

What is the number?

1 mark

Challenge 3 1 Work out: a) 112 × 30 =

b)

214 × 8 =

c) 11 × 112

d)

12 × 123 =

4 marks

2 What is half of one-third of 114?

1 mark

3 Leo has green marbles and blue marbles.

1 5 of the marbles are green.

Leo has 24 blue marbles. a) What fraction of the marbles are blue? b) How many marbles does Leo have in total?

2 marks

4 The length of a day on Earth is 24 hours.

The length of a day on Pluto is 625 times the length of a day on Earth.

What is the length of a day on Pluto?

How am I doing?

hours Total marks :

Fractions, decimals and percentages 27895_P038_063.indd 41

1 mark

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41 28/03/2025 15:29

Adding and subtracting fractions Challenge 1 1 Work out: a)

1 1 3 + 6 =

b)

1 1 8 + 4 =

c)

7 1 8 − 4 =

d)

7 3 10 − 5 =

e)

1 1 2 + 12 =

f)

47 3 100 − 10 =

6 marks

2 Write the answer to each calculation as an improper fraction and a mixed number.

1

b)

15 5 − 12 = 6

d)

a) 2 + 5 = =1 8 8 8 c)

4 7 + = 5 10 7 1 − = 3 6

4 marks

3 Rick painted 25 of a wall.

3 of the same wall.

Mo painted 10

What fraction of the wall was not painted?

1 mark

Challenge 2 1 Work out: a)

1 1 4 + 6 =

b)

1 1 9 + 5 =

c)

7 1 8 − 3 =

d)

9 3 10 − 4 =

e)

1 2 3 + 5 =

f)

11 3 12 − 5 =

6 marks

2 In this circle, 14 and 25 are coloured.

What fraction is not coloured?

1 mark

42 27895_P038_063.indd 42

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3 Write the answer to each calculation as an improper fraction and a mixed number.

3

2

a) 4 + 5 = 20 = 1 20 c)

12 1 5 − 6 =

b)

4 2 5 + 3 =

d)

11 2 4 − 3 =

4 marks

4 Work out: 1 1 1 2 + 3 + 4 =

1 mark

Challenge 3 1 In these addition walls, the number in each box is the sum of the numbers below it.

Fill in the missing numbers.

a)

b) 17 24

2 7

1 5

4 9

1 3

1 6

6 marks

2 Work out: 1 − 15 + 16 =

1 mark

3 Ali, Ben and Cat share some sweets.

Ali has twice as many sweets as Cat. Ben has 23 of the sweets.

What fraction of the sweets does Cat have?

1 mark

4 This sequence grows by adding the same fraction each time.

1 5

13 40

9 20 2 marks

Work out the next two terms in the sequence.

How am I doing?

Total marks :

Fractions, decimals and percentages 27895_P038_063.indd 43

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Multiplying fractions Challenge 1 1 Work out: a)

1 1 3 × 2 =

b)

1 1 4 × 3 =

c)

1 1 8 × 5 =

d)

1 1 9 × 6 =

4 marks

1 2 a) Tick (✓) two fractions that multiply to make 28 1 8

1 9

1 4

1 7

1 20

15 b) Circle two fractions that add to make 56

2 marks

3 For each rectangle, complete the calculation and write the fraction shaded in its simplest form. a)

b)

1

1

1

2 × 6 = 4 × c)

1

=

×

1

d) 1

×

1

=

=

4 marks

Challenge 2 1 Work out: a)

1 4 7 × 5 =

b)

1 5 4 × 9 =

c)

3 5 8 × 11 =

d)

2 4 3 × 7 =

e)

7 3 20 × 8 =

f)

3 11 4 × 25 =

6 marks

2 Write in the missing fractions. a)

1 4 ×

1 = 24

b)

1 4 ×

1 = 28

c)

1 5 ×

1 = 20

d)

1 3 ×

1 = 45

4 marks

44 27895_P038_063.indd 44

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3 Work out these multiplications.

Write your answers in their simplest form. a)

1 4 2 × 5 =

b)

1 8 4 × 9 =

c)

3 5 10 × 6 =

d)

2 9 3 × 10 =

e)

5 3 7 × 5 =

f)

5 18 9 × 25 =

6 marks

4 In this multiplication wall, you multiply two fractions to get the fraction in the box above.

2 5

Fill in the missing fractions.

1 3

5 6

3 marks

Challenge 3 1

(12)2 = 12 × 12 = 14 Work out:

(13)2 = 2 c) (25) = 3 e) (12) =

b)

a)

d) f)

(16)2 = (34)2 = (34)3 =

6 marks

2 Work out the area of this rectangle.

5 8 metre 7 10 metre

m2 3

1 mark

4 5 of the children in a class like milkshakes.

1 3 of the children who like milkshakes like banana milkshakes.

What fraction of the children in the class like banana milkshakes?

1 mark

3 Work out: a)

1 2 1 2 × 6 + 3 × 5 =

b)

1 2 ×

(23 + 14) =

How am I doing?

Use the order of operations.

2 marks

Total marks :

Fractions, decimals and percentages 27895_P038_063.indd 45

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Dividing fractions Challenge 1 1 12 of this shape is shaded:

Work out 12 ÷ 2 =

1 mark

2 Use these shapes to help you work out: a) 12 ÷ 3 =

12 ÷ 5 =

b)

2 marks

3 Use these shapes to help you work out: a) 14 ÷ 2 =

b)

13 ÷ 4 =

2 marks

Challenge 2 1 Work out: a) 12 ÷ 4 =

b)

14 ÷ 4 =

1 c) 10 ÷3=

d)

17 ÷ 5 =

e) 18 ÷ 2 =

f)

1 10 ÷ 10 =

2 Draw lines to match the calculations with the same answer.

One is done for you.

1 3÷5

8 ÷ 4

1 4÷8

5 ÷ 4

1 6÷3

5 ÷ 3

1 10 ÷ 2

2 ÷ 9

6 marks

1 1 1 1

3 marks

46 27895_P038_063.indd 46

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3 Work out: a)

3 5 ÷ 4 =

b)

5 7 ÷ 2 =

c)

7 10 ÷ 4 =

d)

4 9 ÷ 3 =

e)

3 8 ÷ 5 =

f)

5 6 ÷ 9 =

6 marks

Challenge 3 1 Work out these calculations.

Give each answer in its simplest form. a)

3 4 ÷ 3 =

b)

5 8 ÷ 5 =

c)

2 7 ÷ 4 =

d)

5 6 ÷ 10 =

e)

2 3 ÷ 8 =

f)

9 10 ÷ 6 =

6 marks

2 The area of this rectangle is 35 m2 2 m2 ?

3 2 5m

Work out the width of this rectangle.

m

1 mark

m2

1 mark

3 The perimeter of this square is 23 metres.

Work out the area of this square.

4 Work out: a)

1 2 6 2 ÷ 5 + 3 × 7 =

b)

5 2 8 + 3 ÷ 6 =

How am I doing?

Use the order of operations.

2 marks

Total marks :

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Improper fractions and mixed numbers Challenge 1 1 W rite each number as an improper fraction and a mixed number.

The first one is started for you. a)

b)

=1 1

4

c)

d)

4 marks

2 W rite each mixed number as an improper fraction. a) 1 15 =

b)

1 37 =

c) 2 38 =

d)

6 23 =

4 marks

3 W rite each improper fraction as a mixed number. a) 25 8 =

b)

11 4 =

c) 40 9 =

d)

51 6 =

4 marks

Challenge 2 1 1 23 of these shapes are shaded.

Use these shapes to help you work out: 1 23 × 2 = Write your answer in its simplest form.

1 mark

2 Work out: a) 1 14 × 3 = b) 1 14 × 4 =

Use the shapes to help you.

48 27895_P038_063.indd 48

27/03/2025 11:12

c) 213 × 2 = d) 223 × 5 =

4 marks

3 Write: 112

8 6

3 8

in the correct places on this number line.

0

2 2 marks

4 Work out: a) 114 + 312 =

b)

1 225 + 310 =

c) 4 − 116 =

d)

523 − 249 =

4 marks

5 Write < or > to make each statement true. a) 134

5 3 b)

347

359

c) 278

35 12 d)

513

49 9

4 marks

Challenge 3 1 Write these in order, from smallest to largest.

258

29 10

279

53 18

smallest

32 11

largest

2 marks

2 Work out: a) 235 × 4 =

b)

314 × 6 =

c) 7 × 434 =

d)

10 × 147 =

How am I doing?

4 marks

Total marks :

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Percentages Challenge 1 1 W rite the missing fractions and percentages in this table.

Fraction

Percentage

41 100 1 2

25% 3 4

10% 1 5

60% 4 5

8 marks

2 Work out: a) 50% of £48

£

b) 25% of 72 cm

cm

c) 75% of 56 miles

miles

d) 20% of 45 kg

kg

4 marks

Challenge 2 1 Draw lines to match each percentage to its equivalent fraction.

35%

48%

90%

52%

9%

26 50

9 100

7 20

12 25

9 10

5 marks

2 Work out: 10% of £80

5% of £80

15% of £80 3 marks

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3 Work out: 10% of £45

20% of £45

40% of £45 3 marks

4 A clothes shop is having a sale.

All the prices have been reduced by 30%.

How much money do you save on each item?

£51 £24

Save

£27.50

£

£

£

17 5 Here are Peter’s test marks: English 20

3 marks

21 Maths 25

a) Convert these test marks to percentages.

17

20 = 100 =

%

21 = = 25 100

%

2 marks

b) Which subject did Peter get the best mark for?

1 mark

Challenge 3 1 Kiera is buying this house.

It costs £270 000.

She needs to pay 20% of the price as a deposit.

How much is the deposit?

£ 2 There are 25 children in tennis team A.

1 mark

7 of the children in tennis team A are left-handed.

There are 40 children in tennis team B. 12 of the children in tennis team B are left-handed.

Which team has the highest percentage of left-handed children?

Team How am I doing?

1 mark

Total marks :

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Fraction, decimal and percentage problems Challenge 1 1 4 00 children were asked which animal they like best.

The table shows the results. dogs

cats

rabbits

hamsters

10%

25%

60%

5%

a) How many children chose each animal? dogs

children

rabbits

children

cats hamsters

b) How many more children chose cats than chose dogs?

children children children

4 marks

1 mark

2 W rite each decimal as a fraction in its simplest form: a) 0.3 =

b)

0.53 =

c) 0.217 =

d)

0.6 =

e) 0.42 =

f)

0.408 =

g) 0.08 =

h)

0.072 =

8 marks

3 T o write 38 as a decimal, work out: 8 3.000 4

1 mark

7 To write 20 as a decimal, work out:

20 7.00

1 mark

Challenge 2 1 Milo’s sticker album holds 832 stickers.

Milo’s album is 75% full.

How many more stickers does Milo need to fill his album?

1 mark

2 Muhammad thinks of a number.

30% of his number is 18.

What is Mohammad’s number?

1 mark

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3 Write these fractions as decimals. a)

1 8

7 8

b)

2 marks

4 A farmer has 140 sheep.

60% of these sheep are brown. a) How many of the sheep are brown?

1 mark

b) Half of the remaining sheep are white.

What fraction of the 140 sheep are white?

Write your answer in its simplest form.

1 mark

5 Write < or > between each pair of values, to make the statement correct. a)

9 20

0.42

b)

5 8

0.65

c)

8 11

70% d)

2 3

60%

4 marks

Challenge 3 1 Two shops are selling the same model of TV.

TVs R Us TV price £1984 with 30% off

TV Deals TV price £1900 with 25% off

a) At which shop is the TV the cheapest?

2 marks

b) How much cheaper is the TV at that shop?

2 Write each set of values in order, starting with the smallest. a)

0.23

1 4

0.2

21%

smallest

b)

largest

1.9 smallest

How am I doing?

150%

9 5

1.95 largest

Total marks :

Fractions, decimals and percentages 27895_P038_063.indd 53

2 marks

2 marks

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Ratio Challenge 1 1 Rana makes samosas.

For every 1 meat samosa, she makes 2 vegetable samosas. a) On Monday Rana makes 20 meat samosas.

How many vegetable samosas does she make? b) On Tuesday Rana makes 28 vegetable samosas.

How many meat samosas does she make?

2 marks

2 Hugo puts black and white counters in a row.

For every 1 black he puts 3 white counters.

Colour the counters to show the correct ratio.

1 mark

Challenge 2 1 Here are some yellow and purple cubes.

Tick (✓) the correct statement for these cubes.

The ratio of yellow to purple is 2 : 3 The ratio of yellow to purple is 3 : 2

1 mark

2 a) Write the ratio of blue to grey for these cubes.

: b) Write the ratio of grey to blue for these cubes.

:

2 marks

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3 The ratios show yellow to white.

Draw lines to match each ratio to a diagram.

5:1 1:2 1:5 2:3 4 marks

4 The ratio of red squares to yellow squares is 4 : 3 There are 28 squares in total.

You can colour the squares to help you.

How many squares of each colour are there? red

yellow

2 marks

Challenge 3 1 Here is a set of shapes.

a) Write the ratio of triangles to quadrilaterals.

:

b) Write the ratio of pentagons to triangles.

:

c) Write the ratio of shapes with vertices to shapes without vertices.

:

d) Write the ratio of circles to quadrilaterals to triangles.

:

:

4 marks

2 Mario decorates a cake with coloured sweets.

The ratio of red to yellow sweets is 3 : 5 There are 15 yellow sweets on the cake.

How many red sweets are there?

How am I doing?

1 mark

Total marks :

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Scale factor Challenge 1 1 Here is a square.

Draw a square that has sides 3 times as long.

1 mark

2 Enid builds a tower 7 cm tall.

Ollie’s tower is 3 times taller than Enid’s.

How tall is Ollie’s tower?

3 Sam and Riki have model boats.

cm

1 mark

Sam’s model Riki’s model

45 cm

5 cm

Riki’s model is shorter than Sam’s model.

How many times shorter?

1 mark

Challenge 2 1 Rectangle B is an enlargement of rectangle A.

A

What is the scale factor of the enlargement?

B 1 mark

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2 Here is a triangle.

Enlarge this triangle by a scale factor of 2.

1 mark

Challenge 3 1 Here is a triangle.

Enlarge this triangle by a scale factor of 112.

1 mark

2 Sameera is building a model plane.

Her model is 80 times smaller than the real plane.

Here are the measurements of the real plane.

b) 8 m a) 24 m c) 3.2 m

Work out the measurements of Sameera’s model. a)

cm

b)

cm

c)

cm

How am I doing?

3 marks

Total marks :

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Unequal sharing Challenge 1 1 Look at this diagram and answer the questions below. a) What is the ratio of green to white triangles in this diagram?

:

b) What fraction of the triangles are white?

c) What fraction of the triangles are green?

3 marks

2 A necklace has 1 blue bead for every 3 yellow beads.

a) What fraction of the beads are yellow?

b) What fraction of the beads are blue?

2 marks

3 Max and Tilly share 24 grapes.

Max has 13 of the grapes.

Tilly has 23 of the grapes.

How many grapes do they each have?

Max

grapes

Tilly

grapes

2 marks

Challenge 2 1 There are 4 black pens for every 1 red pen. a) What fraction of the pens are red?

1 mark

There are 30 pens.

b) How many of each colour are there?

red pens

black pens

2 marks

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2 In a car park there are 3 silver cars for every 4 blue cars. a) What fraction of the cars are silver?

1 mark

There are 21 cars in the car park. b) How many of each colour are there? blue cars

silver cars

2 marks

c) How many more blue cars than silver cars are there?

1 mark

3 Here is a bowl of oranges and bananas.

The ratio of bananas to oranges is 2 : 3 a) What fraction of the fruit in the bowl is oranges?

There are 20 pieces of fruit in the bowl. b) How many oranges are there in the bowl?

2 marks

Challenge 3 1 The ratio of red balls to blue balls to yellow balls is 3 : 2 : 1

There are 12 more red balls than blue balls.

How many of each colour are there? red

R

R

B

B

R

Y

blue

yellow

3 marks

2 In a set of 28 building blocks, there are: Twice as many green bricks as blue bricks.

An equal number of blue and yellow bricks.

Five times as many red bricks as green bricks.

How many of each colour are there? green

blue

red

yellow

4 marks

3 James makes a tropical fruit drink by mixing mango juice, orange juice and sparkling water in the ratio 2 : 3 : 5 How many millilitres of each does he need to make 1500 ml of tropical fruit drink? mango juice

How am I doing?

orange juice

sparkling water

Total marks :

Ratio and proportion 27895_P038_063.indd 59

3 marks

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More practice

Progress test 2 1. Write each fraction in its simplest form. a)

4 20 =

b)

12 18 =

2 marks

2. Write each fraction as a decimal. a)

31 100 =

b)

7 10 =

c)

27 50 =

3 marks

3. Write 235 as an improper fraction.

1 mark

4. Write each decimal as a fraction in its simplest form: a) 0.3 =

b)

0.48 =

2 marks

5. Fabian has a box of football cards.

He gives 6 of his friends 12 cards each.

He has 34 cards left.

How many cards were in the box to start with?

cards

1 mark

6. Work out 10% of £47 7. The ratios show green to white.

1 mark

Draw lines to match each ratio to a diagram.

4 : 1 1 : 3 1 : 4 1 : 1

4 marks

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8. Round 42 714.2 to the nearest hundred.

1 mark

9. Triangle B is an enlargement of triangle A.

B A

What is the scale factor of the enlargement?

10.

1 mark

9210 × 61

1 mark

11. Write these three fractions with the same denominator.

2 3

5 6

4 9

3 marks

12. Find 80% of 150 kg.

kg

1 mark

13. A time capsule was buried in MDCCCXCIX. It was dug up 105 years later.

In which year was it dug up?

Write your answer in ordinary numbers.

1 mark

14. Work out: a)

1 8 of £56 =

b)

3 7 of 42 kg =

2 marks

15. Work out: 3 × 45 =

= improper fraction

2 marks

mixed number

Progress test 2 27895_P038_063.indd 61

61 27/03/2025 11:12

16. Write in the missing numbers. b)

23 =

= 27 d)

2

a) 72 = 3

c)

= 81

4 marks

17. Work out: 1120 ÷ 32 = 1 mark

18. Work out: 1 1 6 × 4 =

1 mark

19. Write 24 7 as a mixed number.

1 mark

20. In a box there are 3 red balls for every 2 blue balls. a) What fraction of the balls are blue?

There are 20 balls in the box.

1 mark

b) How many of each colour are there? red balls

blue balls

2 marks

c) How many more red balls than blue balls are there?

1 mark

21. Ben recorded the temperature in his garden one month.

The lowest temperature was −9°C The highest temperature was 11°C What is the difference between the highest and lowest temperatures?

°C

22. Work out: 13 3 20 – 5 =

1 mark

23. Write these numbers in order, from smallest to largest.

33.4

smallest

24. Write 38 as a decimal.

1 mark

32.43

33.43

34.04

33.34

largest 2 marks

1 mark

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25. Grace puts 3 blue marbles, then 5 green marbles, like this:

a) Grace uses 45 green marbles in her pattern.

How many blue marbles does she use?

b) Grace uses 40 marbles in total.

blue marbles

1 mark

How many of each colour does she use? green

blue

2 marks

26. I am thinking of a number.

3 5 of my number is 12.

1 of my number?

What is 10

27. Luca had 54 toy cars.

1 mark

He gave 49 of these cars to Archie.

How many cars did Luca have left?

28. A smoothie recipe uses:

cars

1 mark

mangoes : bananas in the ratio

2

:

3

a) Ava makes smoothies using 8 mangoes.

How many bananas does she need? bananas

b) Theo makes smoothies using 9 bananas.

How many mangoes does he need? mangoes

29. Draw lines to match the equivalent fractions.

One has been done for you.

How am I doing?

3 4

5 8

1 2

1 6

8 48

45 90

54 72

60 96

1 mark

2 marks

Total marks :

Progress test 2 27895_P038_063.indd 63

1 mark

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Equations Challenge 1 1 H ere is a function machine. input

16

output

÷2

Work out the output.

2 H ere is a function machine. input

3

1 mark

output 9

What could the function be?

3 H ere is a function machine. input

12

×

2 marks

or

2 marks

output 4

What could the function be?

4 Here is a function machine. input

output

4

8

5

10

6

12

or +

What is the function?

1 mark

5 19 − ✸ = 7 Work out the value of ✸.

✸=

1 mark

Challenge 2 1 Work out the value of the letter in each equation. a) x + 4 = 13

x=

c) p − 6 = 5

p=

b)

3 × y = 18

y=

d)

r ÷ 5 = 4

r=

4 marks

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2 Write the missing inputs and outputs in this function machine. input

output

6

10

–5

5

18

13

20

2 marks

3 a and b are positive whole numbers. Neither a or b is zero. a+b=9 One possible pair of values for a and b is a = 4, b = 5 a) List all the possible pairs of values for a and b.

2 marks

b) How many possible pairs of values are there?

1 mark

Challenge 3 1 Work out the missing output and input for this function machine. input

output

2

6

14 +5

×2 28

2 marks

2 a and b are positive whole numbers. a × b = 12 How many possible pairs of values are there for a and b?

1 mark

3 Solve each equation. a) 2x + 3 = 11

x=

b)

5y + 6 = 56

y=

c) 4p − 1 = 13

p=

d)

r 6 = 7

r=

How am I doing?

4 marks

Total marks :

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Formulae Challenge 1 1 A bike hire company uses this formula: Hire cost = £6 × number of hours a) Work out the hire cost for:

1 hour

£

3 hours

£

2 marks

b) Daisy pays £24 to hire a bike.

hours

How many hours does she hire it for?

1 mark

2 A n online shop uses this formula to work out the total price: Total price = price of item + £2.95 delivery charge a) Work out the total price for these trainers.

£99.99 £

1 mark

b) Balvinder buys this T-shirt.

The total price is £27.45

Work out the price of the T-shirt.

£

1 mark

Challenge 2 1 Here is a formula: y = 4x + 3 Work out the value of y when x = 5

1 mark

2 Here is a formula: t s=3−7 Work out the value of s when t = 24

1 mark

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3 Jacob sells hats online.

He uses this formula to work out the total price: Total price = £9 × number of hats + £3.50 delivery charge a) Work out the total price for: 2 hats

5 hats

£

£

2 marks

b) Seren pays £30.50 to buy hats online. hats

How many hats does she buy?

1 mark

4 Complete this table.

The first one has been done for you. n

3n – 5

2

1

5 10 100

3 marks

Challenge 3 1 Bella’s rule for making green paint is: use twice as much yellow (y) as blue (b) Tick (✓) the formula that represents this. y = 2b

b = 2y

b=y–2

y = 2b

1 mark

2 The formula for the area of a triangle with base b and height h is: A = b ×h 2 Use the formula to work out the area of this triangle.

4m

m2

1 mark

7m

How am I doing?

Total marks :

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Sequences Challenge 1 1 T he numbers in this sequence increase by equal amounts each time.

Write in the next three numbers.

43

51

59

3 marks

2 The numbers in this sequence decrease by equal amounts each time.

Write in the next three numbers.

104

97

76

3 marks

3 Here is a sequence of patterns made from matchsticks.

Pattern 1

Pattern 2

Pattern 3

a) Draw the next pattern in the sequence.

1 mark

b) The table shows the numbers of matchsticks in each pattern.

Pattern 1

Pattern 2

6

11

Pattern 3

Pattern 4 2 marks

Write in the missing numbers.

c) Joe wants to make Pattern 5.

How many matchsticks does he need?

1 mark

Challenge 2 1 Here is part of a number sequence.

180

200

220

240

260

The numbers increase by the same amount each time.

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The sequence continues.

Circle all the numbers below that would appear in the sequence.

350

475

580

700

830

2 marks

2 The first number in a sequence is 2000.

The rule to get from one term to the next is: subtract 150.

Write the next 4 terms in this sequence.

4 marks

3 Here is a sequence of patterns made from counters.

a) Complete this rule to get from one pattern to the next: counters.

Add

b) How many counters will there be in pattern 6 in this sequence?

2 marks

counters

Challenge 3 1 The numbers in this sequence increase by 20 each time.

4

24

44

The sequence continues in the same way.

Write two consecutive numbers from the sequence that add to make a total of 228. +

= 228

1 mark

3 Ruby makes a sequence of numbers.

She chooses a starting number and then subtracts equal amounts each time.

The 3rd number in her sequence is 26.

The 10th number is −16.

26

–16

What is the first number in the sequence?

How am I doing?

1 mark

Total marks :

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Units of measurement Challenge 1 1 C onvert these measures. a) 100 cm =

m

b)

5000 g =

kg

c) 3 cm =

mm

d)

2 litres =

ml

minutes

f)

40 km =

m

e) 180 seconds =

6 marks

2 T ess pours 350 ml of water into a jug.

How much more does she need to pour in to fill the jug to the 2 litre mark?

1 mark

3 H akan is 1.85 m tall.

Noah is 94 cm tall.

How much taller is Hakan than Noah?

1 mark

Challenge 2 1 Write these times in order, starting with the shortest.

240 000 seconds

36 days

72 hours

6 weeks

shortest

4800 minutes longest

2 marks

2 Convert these measures: a) 750 m =

km

b)

485 g =

kg

c) 1670 mm =

m

d)

3.6 litres =

ml

e) 2.3 m =

cm

f)

10 090 g =

kg

6 marks

3 8 identical parcels weigh 1 kg.

What is the weight of 1 parcel?

1 mark

4 A row of 28 tiles is 2.072 m long.

How long is a row of 17 of these tiles?

1 mark

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Challenge 3 1 Here is a train timetable.

Sopley Bridge

08:45

12:27

17:25

Dramford Lane

09:25

13:25

18:00

Calshott

10:02

14:06

18:24

Inkley Town

10:56

14:42

19:37

Travett Centre

11:29

15:16

19:58

Somersby

12:24

16:03

20:35

Sophie leaves home at 1 pm.

She walks for 10 minutes to Dramford Lane station and catches the next train to Somersby.

When she arrives in Somersby she walks for 15 minutes to her grandmother’s house.

What time does she arrive at her grandmother’s house?

1 mark

2 Lily has 8.4 kg of cat food.

Her cat eats 40 g of cat food each day. weeks

How many weeks will the bag of food last?

1 mark

3 The table shows international athletics results.

USA

Ethiopia

Spain

Japan

13.8 seconds 5.32 minutes

Great Britain 14.01 seconds 6.53 minutes

14.2 seconds 7.23 minutes

12.98 seconds 6.2 minutes

12.84 seconds 5.49 minutes

13.5 seconds 5.55 minutes

5.12 m

5.92 m

6.45 m

8.1 m

7.65 m

7.35 m

7.3 m

8.93 m

7.88 m

8.17 m

7.75 m

7.9 m

Event

India

100 m sprint 1500 m hurdles Shot put Triple jump

a) Which country won the 100 m sprint? b) Write Ethiopia’s time for the 1500 m hurdles in minutes and seconds. c) What is the difference between the shortest and longest triple jump? d) What is the difference between the two longest throws in the shot put?

4 One teaspoon holds 5 ml of milk.

How many teaspoons of milk are there in 2 litres?

How am I doing?

1 mark

Total marks :

Measurement 27895_P064_089.indd 71

4 marks

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Imperial and metric units Challenge 1 1 T ick (✓) the longest length.

1 cm

1 inch 1 mark

2 T ick (✓) the longest length.

1 metre

1 inch

1 foot

1 mark

3 1 kg is approximately 2.2 pounds.

Convert each of these weights into pounds. a) 3 kg =

pounds

b)

400 kg =

pounds

2 marks

4 This table shows equivalent distances in miles and kilometres.

Write in the missing values. miles

km

5

8

10 32 25 72

4 marks

Challenge 2 1 There are 3 feet in 1 yard.

There are 12 inches in 1 foot.

1 inch = 2.5 cm a) How many inches are there in 1 yard?

inches

b) Which is longer – 1 metre or 1 yard? c) What is the difference in length between 1 metre and 1 yard?

Give your answer in centimetres.

cm

3 marks

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2 Write in the missing number.

1 km = 58 miles 130 km = 3

miles

1 mark

1 litre is approximately 74 pints.

Convert each of these amounts into pints. a) 2 litres =

pints

b) 5 litres =

pints

2 marks

4 Peter runs 15 km.

James runs 12 miles. a) Who runs the furthest? b) How many miles further did he run?

2 marks

Challenge 3 1 Write in the missing number.

1 mile = 85 km 28 miles =

km

1 mark

2 1 litre = 134 pints Convert 19 litres to pints.

pints

1 mark

miles

1 mark

miles per hour

1 mark

he distance around the Earth, at the Equator, 3 T is approximately 40 000 km.

How many miles is this?

4 In France, the speed limit in towns is 90 km per hour.

What is this speed limit in miles per hour?

Give your answer to the nearest whole number.

5 How many inches are there in 15 yards?

inches

6 1 mile = 1760 yards a) Convert 25 miles to yards. b) Calculate an estimate for the number of miles equivalent to 10 000 yards.

How am I doing?

yards miles

Total marks :

Measurement 27895_P064_089.indd 73

1 mark

2 marks

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Perimeter and area Challenge 1 1 Here is a rectangle.

8m 4m

Work out: a) the perimeter of this rectangle.

m

b) the area of this rectangle.

m2

2 marks

cm2

1 mark

m2

1 mark

2 This shape is drawn on a centimetre squared grid.

Work out the area of this shape.

3 The perimeter of a square is 36 m.

What is the area of this square?

Challenge 2 1 Draw a rectangle with area 12 cm2 and the largest possible perimeter on this 1 cm grid.

All the side lengths should be whole numbers of centimetres.

1 mark

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2 Work out the perimeter and area of this shape.

8m

10 m 22 m

? ?

30 m

Perimeter =

m

Area =

m2

2 marks

3 The area of a square is 121 cm2.

What is the perimeter of this square?

cm

1 mark

cm2

1 mark

4 A rectangle is 5 cm long and 15 cm wide.

Work out the area of this rectangle in square centimetres.

Challenge 3 1 Draw two different rectangles on the grid, that have the same area as this shape.

2 marks

2 a) Write an equation for the area of this rectangle. a cm Area 70 cm2

b cm 1 mark

b) a and b are whole numbers.

Write all the possible pairs of values of a and b.

2 marks

How am I doing?

Total marks :

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Area of triangles and parallelograms Challenge 1 1 Use the formula to work out the area of the triangle below. area of triangle =

base × height 2

4 cm

10 cm

cm2

1 mark

cm2

1 mark

2 Use the formula to work out the area of the parallelogram below. area of parallelogram = base × height 9 cm 6 cm

Challenge 2 1 Work out the area of each triangle. b)

a)

5 cm

6 cm 7 cm

7 cm

cm2

cm2

2 marks

2 Work out the area of each parallelogram. b)

a)

10 cm

6 cm 9 cm 11 cm

cm2

cm2

2 marks

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3 The area of this parallelogram is 72 cm2.

12 cm

b

Work out the length of b, the base of the parallelogram. cm

1 mark

Challenge 3 1 Work out the area of each shape.

6 cm

a) 4 cm

5 cm

b) 8 cm 4 cm

5 cm

10 cm

cm2

cm2

2 marks

2 The area of this triangle is 28 m2.

h 8m

Work out the height, h, of the triangle. m

1 mark

cm2

1 mark

3 Work out the area of this shape.

7 cm 4 cm

4 cm

How am I doing?

Total marks :

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2-D shapes – triangles, polygons and circles Challenge 1 1 Here is a triangle. a) Tick (✓) the two correct statements.

All of its angles are equal.

It has two equal sides.

It has one line of symmetry.

2 marks

b) Tick (✓) the name of this triangle. equilateral

right-angled

isosceles

scalene 1 mark

2 Three sides of a hexagon are drawn on a squared grid.

The dashed line is a line of symmetry.

Draw the other three sides of the hexagon.

1 mark

Challenge 2 1 a) Make an accurate drawing of this triangle.

Use a ruler and a protractor or angle measurer.

70o

30o 5 cm

b) What type of triangle is it?

2 marks

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2 Here are some 2-D shapes.

A

B

C

D

Write the letters of the shapes for each statement. a) Shape(s) with at least two equal sides. b) Shape(s) with a right angle. c) Shape(s) with at least two parallel sides. d) Shape(s) with at least one obtuse angle. e) Shape(s) that are regular polygons.

5 marks

3 Draw lines to match the labels to the diagrams. circumference

diameter

radius

3 marks

Challenge 3 1 Work out the diameter of this circle.

2 Work out the radius of this circle.

4 cm

cm

1 mark

cm

1 mark

cm

1 mark

11 cm

3 Amelia puts 10 coins next to each other in a row.

Each coin has diameter 25.9 mm.

Work out the length of the row of coins.

Give your answer in centimetres.

How am I doing?

Total marks :

Geometry 27895_P064_089.indd 79

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2-D shapes – quadrilaterals Challenge 1 1 Fill in the description for each quadrilateral. a)

b)

Name

Name pair(s) of equal sides

pair(s) of equal sides

pair(s) of parallel sides

pair(s) of parallel sides d)

c)

Name

Name pair(s) of equal sides

equal sides

pair(s) of parallel sides

pair(s) of parallel sides

12 marks

2 Here are two sides of a parallelogram.

Draw another two sides to complete the parallelogram.

1 mark

Challenge 2 1 Here is a set of trapeziums.

A

B

Write the letters of the isosceles trapeziums.

C

D

1 mark

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2 Here are two sides of an isosceles trapezium.

Draw another two sides to complete the trapezium.

1 mark

3 Complete the description of each quadrilateral. The first one is started for you. b)

a)

Sides:

4 equal

Sides:

Vertices:

Vertices:

Lines of symmetry:

Name:

Lines of symmetry:

Name:

7 marks

Challenge 3 1 Write the name of the quadrilateral that has: 2 pairs of equal sides

2 pairs of parallel sides

no right angles

1 mark

2 Write the name of the quadrilateral that has: 2 pairs of equal sides

no parallel sides

3 obtuse angles

1 mark

3 These diagrams show the diagonals of some quadrilaterals.

Write the name of each quadrilateral. a) b)

c)

How am I doing?

3 marks

Total marks :

Geometry 27895_P064_089.indd 81

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3-D shapes and nets Challenge 1 1 Complete the description for each 3-D shape.

The first one has been started for you. a)

b)

Name:

12 8

Name: square faces

square faces

edges

rectangular faces

vertices

edges vertices d)

c)

Name:

Name: rectangular faces

triangular faces

edges

rectangular faces

vertices

edges vertices

Challenge 2 1 Complete the description of a hexagonal prism. faces

2

16 marks

Some faces match to more than one 3-D shape.

rectangular faces edges vertices

4 marks

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2 a) Draw lines to match each 3-D shape to the shapes of its faces.

One has been done for you.

2 marks

b) Write the name of each 3-D shape.

6 marks

3 Here is the net of a 3-D shape.

Write the name of this 3-D shape.

1 mark

Challenge 3 1 Here is part of a net of a tetrahedron.

Draw the rest of the net.

1 mark

2 This cube has two shapes drawn on it.

Here is the net of the cube.

Draw the missing pattern on the net.

1 mark

3 Sketch the net of a square based pyramid.

1 mark

How am I doing?

Total marks :

Geometry 27895_P064_089.indd 83

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Volume Challenge 1 1 The volume of this cube is 1 cm3.

1 cm3

Work out the volume of each of these shapes made from 1 cm3 cubes. b)

a)

cm3

cm3

2 marks

2 Work out the volume of this cube.

1 cm

1 cm

cm3

1 mark

cm3

1 mark

m3

1 mark

Challenge 2 1 Work out the volume of this cube.

5 cm

2 Work out the volume of this cuboid.

2m 7m

4m

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3 A cube has volume 8 cm3.

What is the length of one side of this cube?

cm

1 mark

cm3

1 mark

4 Work out the volume of this cuboid shaped fish tank.

10 cm

12 cm

25 cm

Challenge 3 3 cm

1 Here is the net of a cuboid.

3 cm

The net is folded up to make the cuboid.

Work out the volume of the cuboid.

5 cm

cm3

5 cm

3 cm

2 A steel beam is in the shape of a cuboid.

1 mark

3 cm 20 cm

3m

30 cm

Work out the volume of steel in the beam.

Give your answer in m3.

m3

1 mark

cm

1 mark

3 The volume of this cuboid is 104 cm3.

h

10 cm

Work out the height, h of the cuboid.

How am I doing?

2.6 cm

h=

Total marks :

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More practice

Progress test 3 1. Here is a function machine. input

output 9

÷7 What is the input?

1 mark

2. Here is a set of 3-D shapes.

a) Tick (✓) all of the shapes that are prisms. b) Circle all of the shapes that are pyramids.

2 marks

3. Work out the value of the letter in each equation. a) x − 2 = 5

x=

b) 4 × y = 12

y=

c) t + 11 = 17

t=

d) r ÷ 6 = 8

r= 4 marks

4. An online shop uses this formula to work out the total price. total price = price of item + £3.30 postage Work out the total price for this microwave oven.

£79.99

£

1 mark

5. On a separate piece of paper, make an accurate drawing of this trapezium.

Use a ruler and a protractor.

5 cm

130o

130o

50o

5 cm 50o

8 cm

7 marks

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6. x and y are positive whole numbers greater than 0 and less than 15. x−y=4 How many possible pairs of values are there for x and y?

1 mark

7. Here is a net for a 3-D shape.

Write the name of the 3-D shape you can make with this net.

1 mark

8. This shape is drawn on 1 cm squared paper.

Work out: the area of the shape.

cm2

the perimeter of the shape.

cm

2 marks

9. Triangle B is an enlargement of triangle A by scale factor 8.

Not drawn accurately

cm

A

cm

176 cm 96 cm

cm Work out the measurements of triangle A.

B 128 cm

Label them on the diagram.

3 marks

10. Here is a formula: y = 5x − 3 Work out the value of y when x = 8

1 mark

11. The first term in a sequence is 80.

The rule to get from one term to the next is subtract 14.

Write the first four terms in this sequence.

4 marks

Progress test 3 27895_P064_089.indd 87

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12. Work out: 3 1 5 8 + 4 + 16 =

1 mark

13. Here is a sequence of patterns made from squares.

Pattern 1

Pattern 2

Pattern 3

a) Complete the rule to get from one pattern to the next. squares

Add

b) How many squares will there be in pattern 5 in this sequence?

squares

2 marks

14. Label the parts of the circle using the words below. radius

diameter

circumference

3 marks

15. Work out the area of this triangle.

3 cm

8 cm

cm2

1 mark

16. Convert these measures. a) 1200 m =

km

b)

550 g =

c) 245 cm =

m

d)

8 litres =

kg ml

4 marks

cm3

1 mark

17. Work out the volume of this cuboid.

4 cm

2 cm 5 cm

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18. This table shows equivalent distances in kilometres and miles.

Write in the missing values. km

miles

8

5 20

40 96 70

4 marks

19. There are 24 marbles in a bag.

The table shows the number of each colour.

Blue

Red

White

Green

6

12

3

3

Work out the percentage of each colour.

Blue

% Red

% White

% Green

%

4 marks

20. This triangle and parallelogram have the same area.

5 cm

8 cm

10 cm

Work out the height of the triangle. cm

1 mark

cm3

1 mark

21. The formula for the volume of a cube with side length s is: V = s3 Use the formula to work out the volume of this cube.

2 cm

22. Sunita has 8 blue beads and 18 white beads.

She puts some of the beads in patterns, in the ratio blue to white beads 2 : 3 a) How many complete patterns can she make? b) How many beads does she have left over? c) What colour are the leftover beads?

How am I doing?

3 marks

Total marks :

Progress test 3 27895_P064_089.indd 89

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Missing angles Challenge 1 1 W ork out the size of each angle labelled with a letter. a)

b) x

x

65° 65°

y

135°

55°

y

° y =

c)

d) 58°

55°

x

x =

135°

x

°

97°

93°

t w

° w =

t=

°

4 marks

Challenge 2 1 Work out the size of angle x.

35°

x

20°

x=

°

1 mark

y=

°

1 mark

a=

°

1 mark

2 Work out the size of angle y.

35o y

3 Here is a rectangle.

34 o a

Calculate the size of angle a.

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4 Work out the size of angle b.

120o

b

b =

°

1 mark

Challenge 3 1 This shape is 16 of a circle.

f 12 cm

a) Work out the size of angle f.

°

f=

b) Work out the diameter of the circle.

cm

2 marks

°

1 mark

2 Work out the size of angle x.

Not to scale

60o

xo

185o

x=

3 Here is an equilateral triangle. a

b

c

Work out the size of each angle.

a= How am I doing?

°

b=

°

c=

° Total marks :

Geometry 27895_P090_111.indd 91

3 marks

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Angle problems Challenge 1 1 Work out the size of angle x.

95o 130o 60o

xo

x=

°

1 mark

y=

°

1 mark

2 Work out the size of angle y.

45o

135o 135o

y

3 Here is an isosceles trapezium.

Work out the size of: a=

°

b=

°

a

115o b

65o

2 marks

Challenge 2 1 Here is an isosceles triangle. e

Work out the size of: d=

°

e=

°

d

70o

2 marks

2 Here is a regular pentagon.

Work out the size of: u=

°

w=

°

w u

72o

2 marks

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3 This shape is three-eighths of a circle.

r

Work out the size of angle r.

4 The shaded shape is an isosceles triangle. g

r=

° 1 mark

42o

The isosceles triangle is inside a rectangle.

Work out the size of angle g.

g=

°

1 mark

x=

°

1 mark

x=

°

y=

°

p=

°

q=

°

Challenge 3 1 Here is an isosceles triangle.

84 o x

Work out the size of angle x.

2 Work out the size of angle x and angle y.

23°

x 45°

y

2 marks

3 Work out the size of angle p and angle q.

p 5 cm

q 5 cm

How am I doing?

Total marks :

Geometry 27895_P090_111.indd 93

2 marks

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Coordinates Challenge 1 1 a ) Plot these points on the coordinate grid.

A (1, 1)

B (1, 5)

y 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7

C (5, 5)

D (5, 1)

x 4 marks

b) Join the points in order, with straight lines.

What shape have you drawn?

1 mark

Challenge 2 1 Write the coordinates of each point plotted on this coordinate grid. y 5 4 E A 3 2 1 H F D x 0 –5 –4 –3 –2 –1 1 2 3 4 5 –1 C –2 B –3 –4 G –5 A(

,

)

B(

,

)

C(

,

)

D(

,

)

E (

,

)

F(

,

)

G(

,

)

H(

,

)

8 marks

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Challenge 3 1 a) Plot these points on the coordinate grid.

P (−5, 1)

Q (−3, 5)

R (3, 1)

S (1, −3)

y 5 4 3 2 1 x 0 –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 –4 –5

4 marks

b) Join the points in order, with straight lines.

What shape have you drawn?

1 mark

2 a) Plot these points on the coordinate grid and join them with a straight line.

T (3, 4)

U (−3, −2) y 5 4 3 2 1 x 0 –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 –4 –5

b) Point V is the midpoint of the line TU. Label point V on the diagram. c) Write the coordinates of point V. (

How am I doing?

,

)

4 marks

Total marks :

Geometry 27895_P090_111.indd 95

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Translations Challenge 1 1 T his rectangle is translated 3 squares up.

Draw the rectangle in its new position.

1 mark

2 T his triangle is translated 4 squares right.

Draw the triangle in its new position.

1 mark

3 D escribe the translation that takes shape A on to shape B. A

B 2 marks

Challenge 2 1 Shape C is translated 4 squares left and 2 squares down. y Draw shape C in its new position.

5 4 3 2 C 1 x 0 –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2

1 mark

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2 Here are two shapes, D and E. y 5 4 3 D 2 1 x 0 –5 –4 –3 –2-–1 1 2 3 4 5 –1 –2 E –3 –4 –5 a) Describe the translation that maps shape D on to shape E.

2 marks

b) Describe the translation that maps shape E on to shape D.

2 marks

Challenge 3 1 Shape F is translated so that point A is mapped on to point B. y 5 4 3 2 1 A F 0 –6 –5 –4 –3 –2 –1 –1 1 2 3 4 5 6 –2 B –3 –4 –5

x

Draw the shape after the translation.

How am I doing?

1 mark

Total marks :

Geometry 27895_P090_111.indd 97

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Reflections Challenge 1 1 D raw the reflection of each shape in the mirror line. mirror line

a)

b)

mirror line

c)

mirror line

mirror line

d)

4 marks

2 D raw the mirror line for each reflection. a)

b)

2 marks

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Challenge 2 1 Draw the reflection of this shape in the x-axis.

y 6 5 4 3 2 1 0 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6

x

1 mark

Challenge 3 1 Here are four shapes on a coordinate grid. y 5 4 A B 3 2 1 x 0 –5 –4 –3 –2 –1 1 2 3 4 5 –1 –2 –3 C D –4 –5 a) Which shape is the reflection of shape C in the x-axis? Shape b) Which shape is the reflection of shape C in the y-axis? Shape y 2 a) Draw the reflection of 5 this shape in the y-axis.

4 b) Describe the translation that 3 takes the shape to its reflection.

2 1

x 0 –5 –4 –3 –2 –1 1 2 3 4 5 –1

–2

–3 –4

–5 How am I doing?

Total marks :

Geometry 27895_P090_111.indd 99

2 marks

1 mark

1 mark

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Bar charts Challenge 1 1 T he bar chart shows the number of films people saw in one year.

Number of people

Number of films watched in a year 16 14 12 10 8 6 4 2 0

0–10 11–20 21–30 31–40 41–50 over 50 Number of films

a) How many people saw fewer than 31 films? b) How many people saw more than 20 films? c) How many people are represented in the bar chart? d) One person saw more than 50 films.

Draw a bar for this person on the bar chart.

4 marks

Challenge 2

Number of people

1 This bar chart shows the numbers of ice creams sold by two ice cream shops on different days.

100 90 80 70 60 50 40 30 20 10 0

Key Nice Ices Jolly Lollies

Mon

Tues

Wed

Thur

Days a) Which shop sold most ice creams on Tuesday?

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b) Which shop sold the fewest ice creams on Monday? c) Which shop sold the most ice creams over the four days?

How many more did it sell?

d) Which day had the greatest difference between the numbers of ice creams sold by the two shops?

5 marks

Challenge 3 1 The tally chart shows some people’s scores in a game.

Score

Tally

Frequency

0–20 21–40 41–60 61–80 1 mark

a) Fill in the frequency column. b) How many people’s scores are shown in the table?

1 mark

c) This bar chart shows some of the information from the tally chart.

Complete the bar chart.

Frequency

How am I doing?

24 22 20 18 16 14 12 10 8 6 4 2 0

0–20 21–40 Score

4 marks

Total marks :

Statistics 27895_P090_111.indd 101

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Line graphs Challenge 1

Temperature (°C)

1 T he line graph shows the temperature at different times during a day.

26 24 22 20 18 16 14 12 10 8 6 4 2 0 10:00 11:00 12:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 am am pm pm pm pm pm pm pm pm pm pm pm Time of day

a) What time was the earliest temperature recorded? b) How often was the temperature measured? c) What was the maximum temperature recorded?

°C

d) What time was the hottest temperature? e) How many degrees colder was it at 10pm than at 5pm?

°

f) For how long was the temperature greater than 14°C?

hours

6 marks

Challenge 2 1 The table shows the numbers of teddy bears a shop sells each month.

Month

Number sold

July

Aug

Sept

Oct

Nov

Dec

15

40

25

45

60

80

a) Complete the line graph on the next page to show the information in the table.

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Number sold

Teddy bear sales 100 90 80 70 60 50 40 30 20 10 0

Jul Aug Sept Months

5 marks

b) Between which two months did the sales decrease?

and

1 mark

c) Between which two months was the greatest increase in teddy bear sales?

and

1 mark

Challenge 3

Pounds

his graph converts between 1 T pounds and kilograms.

22 20 18 16 14 12 10 8 6 4 2 0

0 1 2 3 4 5 6 7 8 9 10

Kilograms

a) Use the lines drawn on the graph to convert 10 pounds to kilograms.

10 pounds =

kg

b) Draw lines on the graph to convert 14 pounds to kilograms.

How am I doing?

14 pounds =

kg Total marks :

Statistics 27895_P090_111.indd 103

2 marks

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Pie charts Challenge 1 1 6 0 children have music lessons.

The pie chart shows the instruments they play.Music lessons in Year 6

Recorder Trumpet Drums Piano

a) Which instrument is most popular? b) Which instrument is least popular? c) What fraction of the children play piano? d) How many children play piano?

children

e) Five children play recorder.

Estimate the number of children who play the trumpet. children

5 marks

Challenge 2 1 The table shows the numbers of different fruits for a picnic.

Fruit

Number

Apple

3

Orange

2

Banana

1

Total

6

Colour sections of the pie chart on the next page to represent this information.

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Colour the key to show what each section represents.

Key Apple Orange Banana

4 marks

Challenge 3 1 The table shows children’s pets.

Pet

Number of children

Cat

16

Dog

12

Rabbit

8

Hamster

4

Total

40

Colour sections of this pie chart to represent this information.

Colour the key to show what each section represents.

Key Cat Dog Rabbit Hamster 5 marks

How am I doing?

Total marks :

Statistics 27895_P090_111.indd 105

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The mean Challenge 1 1 F our children have these counters.

Lily

Ben

Ravi

Luca

a) How many counters are there in total? counters

b) Lily collects up all the counters and then shares them out fairly between the 4 children.

How many counters does each child get? counters

2 marks

2 Ryan has 12 sweets, Neil has 11 sweets and Meg has 7 sweets.

Work out the mean number of sweets. total number of sweets ÷ number of children ÷

=

sweets

1 mark

Challenge 2 1 Calculate the mean of these three numbers.

7

8

3

Mean =

1 mark

2 Badger Town Football Club played five matches.

These are the numbers of goals they scored in each match: Match 1

Match 2

Match 3

Match 4

Match 5

5

2

4

6

3

Work out the mean number of goals.

Mean =

goals

1 mark

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3 Here are four parcels.

150 g

50 g

300 g

100 g

Work out the mean weight of these parcels.

g

Mean =

1 mark

4 Here are the heights of six children, in centimetres.

121 cm

135 cm

142 cm

129 cm

146 cm

137 cm

Work out the mean height.

Mean =

cm

1 mark

Challenge 3 he mean of four numbers is 14.

1 T Here are three of the numbers.

13

16

17

1 mark

What is the 4th number?

2 a) Greg practices long jumps.

Here are the lengths of his jumps.

1.5 metres

2.3 metres

1.7 metres

Work out the mean length of his jumps.

b) Romy practices long jumps.

Here are the lengths of her jumps.

1.6 metres

1.9 metres

1.85 metres

2.15 metres

1.35 metres

Mean =

m

2.2 metres

1.95 metres

Who has the longest mean jump length: Romy or Greg?

Show working to explain.

How am I doing?

1 mark

Total marks :

Statistics 27895_P090_111.indd 107

1 mark

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More practice

Progress test 4 1. Work out the value of x. y

135°

55°

x

x=

°

1 mark

r=

°

1 mark

2. Work out the size of angle r.

32°

r

3. This regular 12-sided shape has a number at each vertex.

2 3 4 5 1 6 0 7

11 10

9

8

Jules turns the pointer from 0, clockwise through 210° Which number is the pointer at now?

1 mark

4. Here are Jen’s scores in five tests.

12

15

16

12

10

Work out Jen’s mean mark.

Mean =

1 mark

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5. 32 children were asked: What is your favourite party food?

Each child chose one food.

The pie chart shows the results. burger hot dog nuggets veggie burger chips

a) What percentage of the children chose burger? b) How many children chose hot dog? c) What fraction of the children chose chips?

3 marks

6.

0 –1

–8 –7 –6 –5 –4 –3 –2

1

2

3

4

5

6

7

8

x

X B

–2 –3 –4 –5

A

X

y

Write the coordinates of: Point A (

,

)

Point B (

,

)

The midpoint of the line AB (

,

)

3 marks

7. Work out the radius of this circle.

18 cm

cm

1 mark

°

1 mark

8. Work out the size of angle y.

70o 145o

y

y=

Progress test 4 27895_P090_111.indd 109

109 27/03/2025 11:24

y 11 10 9 8 7 6 A 5 4 3 2 1 0 0 1 2 3 4 5 6 7

9. Triangle A is translated 4 squares right and 2 squares down.

Draw triangle A in its new position.

x 1 mark

10. A gardener records the number of tomatoes on each tomato plant she grows. y

a) How many tomato plants had 16–20 tomatoes?

b) How many tomato plants had more than 20 tomatoes?

Frequency

The bar chart shows the results.

16 14 12 10 8 6 4 2 0

16–20

21–25

26–30

31–35

x

Number of tomatoes

2 marks

11. Draw the reflection of triangle B in the y-axis.

y 4 3 B 2 1 x 0 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 –4

12. The ratio of red to blue to yellow buttons is 4 : 3 : 1

1 mark

There are 81 blue buttons.

How many counters are there in total?

counters

1 mark

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13. The line graph shows the minimum temperature each month in York.

Temperature °C

10 8 6 4 2 0 –2 –4 –6

Jan

Feb

Mar

April

May

June

a) What was the minimum temperature in York in February?

°C

b) What was the minimum temperature in York in May?

°C 1 mark

c) What is the difference between the minimum temperatures in March and June?

°C

d) The table shows the minimum temperatures in Poole in the same months.

1 mark

Jan

Feb

Mar

April

May

June

0°C

2°C

3°C

3°C

5°C

8°C

Draw a line graph on the same axes to show the Poole temperatures.

1 mark

7 marks

14. Here are the weights of four kittens.

2.3 kg

2.5 kg

2.6 kg

2.2 kg

Work out the mean weight of these kittens.

15. A theatre sells tickets at three different prices.

Mean =

kg

1 mark

3 of the tickets are price A 10

14 of the tickets are price B

The rest of the tickets are price C

What fraction of the tickets are price C?

How am I doing?

1 mark

Total marks :

Progress test 4 27895_P090_111.indd 111

/ 29

111 07/04/2025 15:11

Answers For questions worth 1 mark with several answer spaces, all answers should be correct to achieve the mark, unless otherwise indicated.

Pages 4–11 Starter test 1. £1.55 2. a) Terri b) 166 c) 36 3. 2.44 2.45 2.5 2.54 5.25 [2 marks if all correct, 1 mark if one incorrect] 4. one hundred and twenty-six thousand, three hundred and ninety-seven 5. a) 48 b) 2014 6. 8.10 am 7. 750 ml 8. 15 shelves

33. 3 and 31 circled 34. a) 3.3 b) 100

c) 33

1 116

35.

36. a) 360 b) 1.06 c) 3500 d) 145 37. a) Cardiff b) 5°C 38. a) 104° b) 35° 39. A (1, 4) B (4, 2) C (0, 1) D (3, 0) 40. a) 30 b) 20 c) Thursday Mirror line 41.

29

9. 8 10. 12 171 11. 6 sides 12. any 2 squares coloured 13. 150, 400 14. a) B and C ticked b) D A B C [2 marks if all correct, 1 mark if

one incorrect] 15. 307 001 16. 32 cm3 1

17. 53 18. 72 19. £3450 20. 5 21. 15 22. 14 kg 23. a) 42 m2 b) 26 m 24. 1, 2, 4, 8, 16, 32 [2 marks if all correct, 1 mark

if one incorrect or missing] 1

25. 3 26. 330 minutes 27. 400 ml 1

7

2

42. a)

5180

b) 5200

c) 5000

Pages 12–13 Challenge 1 1.

a) seven hundred and ninety-four thousand, three hundred and two b) 2 000 000 c) 34.06 2. 29 517 31 517 32 517 3. 0.002 0.03 0.07 0.125 0.14 0.6 [2 marks if all correct, 1 mark if one incorrect]

Challenge 2 1.

2.

a) nine million, nine hundred thousand and ninety-nine b) 8 452 000 a) 40 000 or 40 thousands or 4 ten thousands b) 60 or 6 tens c) 9 thousandths

3.

5

28. 2 [2 marks if all correct, 1 12 3 6

mark if one incorrect] 29. a) 0.74 b) 0.1 c) 0.057 30. 652 g 31. any 12 squares coloured 32. a) 9 b) 121 c) 1000

10 thousand less

Number

1 million more

57 450

67 450

1 067 450

472 000

482 000

1 482 000

1 490 030

1 500 030

2 500 030

1 995 000

2 005 000

3 005 000

112 27895_P112_127.indd 112

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Challenge 3 1.

2.

3.

4.

4.

3200 tens and 320 hundreds circled [2 marks if both correct, only 1 mark if other values circled] 3 250 000, 4 500 000 a) 2.68 b) 2.57 c) 2.669 a) 237 519 b) 2375.19 c) 2 400 000 d) 856 025

Pages 14–15 Challenge 1 1. −8°C −6°C −2°C 3°C 7°C [2 marks if all correct, 1 mark if one incorrect] 2. −9°C 3. –1°C

Challenge 2 1.

2.

3.

4.

5.

6.

7.

15° −8°C 16° 9°C 26° −10°C a) –1 b) 0 c) –5

e) –3

f) 5

−26°C −15°C −4°C A −25°C B 10°C 51 metres a) –5 b) 1 d) –6 e) –14

7°C

18°C

c) 3 f) –7

Pages 16–17 Challenge 1 1.

a) 250 000 b) 324 999 a) 23 000, 20 000, 16 000, 21 000, 24 000, 15 000, 10 000 [2 marks if all correct,

1 mark if one incorrect] b) 129 000 c) 130 000

Pages 18–19 Challenge 1 1.

2.

3.

a) 49 b) 1 c) 36 a) 27 b) 1 c) 9 2 and 19 circled [2 marks if both correct, 1 mark if incorrect values included]

Challenge 2 1.

a) > b) = c) > d) < e) > f) < 36, 49, 100 and 121 circled [2 marks if all correct, 1 mark if incorrect values included] a) 8 b) 9 c) 3 d) 12 e) 10 f) 2 1, 27, 64 and 125 circled [2 marks if all correct, 1 mark if incorrect values included] 101

Challenge 3 1.

2.

4 a) 29 d) 0

b) 73 e) 14

3.

prime number

square number

OR

Number

Rounded to nearest 1000

23 419

23 000

148 600

149 000

1 218 450

1 218 000

5.82 and 5.76 circled [2 marks if both correct, 1 mark if incorrect values included] a) 526.4 b) 526 c) 530

OR

4.

prime number

square number

5.

600, 300 30, 12 a) 5 556 000

2

13 17

4 8

16

square number

=

25

6 9

3 12 10

15 18 14 16 20

[4 marks: 1 mark for each section completely correct]

Answers 27895_P112_127.indd 113

multiples of 3

7 1

=

16

11 19

5

600 × 300 = 180 000 30 × 12 = 360 b) 5 560 000 c) 6 000 000

+

4 square number

square number

prime number

=

9

9 square number

square number

+

9

=

1

900 54

square number

square number

+

7

c) f)

4

prime number

Challenge 2 1.

2.

3.

+

5

3

5500 6000

2.

3.

1.

2.

4.

5.

Challenge 3 1 2 3 4

Challenge 3

2.

3.

d) 2

Estimate 60. Jack is wrong because the total cost must be close to £60, but his cost is close to £600.

113 28/03/2025 15:59

Pages 20–21 Challenge 1 1.

2.

a) a)

6 24

Challenge 2 1.

b) 10 b) 6

c) 11 c) 3

d) 5 d) 4

Challenge 2 1.

2.

3.

4.

5.

a) 32 b) 16 c) 11 d) 13 a) 14 b) 9 c) 10 d) 30 a) 21 b) 6 c) 29 d) 2 (4 + 5) × 7 – 2 = 61 [2 marks: 1 mark for a correct calculation with a lower answer] a) 68 b) 28

Challenge 3 1.

2.

3.

4.

a) 13 b) 49 c) 19 d) 25 a) 8 b) 36 c) 0 d) 35 Jay 26 – 3 + 2 × (4 + 3) ✓ 2² + 4 × (5 + 7) ÷ 3

Pages 22–23 Challenge 1 1.

2.

3.

a) 5350 b) 3650 c) 157 500 a) £4.69 b) £5.31 1995

d) 1 004 800

2.

3.

4.

a) 15 000 b) d) 20 e) a) 22.7 b) d) 171.4 e) 4800

20 000 50 4080 0.98

70

a) d)

0.7

4.

a) a) a) d) a) d)

100

3.5 180

b) 0.24 e) 6

c) 36 f) 1400

b) b) b) e) b) e)

c) f) c) f)

2604 100 246 275 2000 2.4

740 10 40 2.7 5000 4.85

3.

4.

26 300

Yes, with working, e.g. 63 + 85 + 72 + 59 + 78 = 357 kg, or estimate: 60 + 90 + 70 + 60 + 80 = 360 kg 1.034 and 0.966 a) 16.25 b) 6.315

Challenge 3 1.

2.

2.4 m £17.15

Pages 26–27 Challenge 1 1.

2.

3.

3.

4.

5.

370 3.36 5 600 000 0.84

1.

2.

3.

4.

5.

8, 16, 24, 32, 40 a) 1, 2, 4, 7, 14, 28 b) 1, 2, 4, 5, 8, 10, 20, 40 c) 1, 2, 4 102, 105 and 108 circled [2 marks if all correct, 1 mark if incorrect values included] 1, 2, 4, 8 a) 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 b) 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 c) 20, 40 (or any other multiple of 5 and of 4, e.g. 400) a) 1, 2 b) 24, 48, 72 36 and 108 circled [2 marks if all correct, 1 mark if incorrect values included] 13 ny two common multiples of 2, 3 and 5, e.g. two A of 30, 60, 90,…

1, 2, 4 120 28 (factors 1, 2, 4, 7, 14) 24

Pages 28–29 Challenge 1 1.

2.

a)

b) 5658

336 2 3 3

1

a) 4988 b) 20 141 c) 777 747 d) 860 298 £98.26 a) 12.483 b) 13.91

9 1

3.

c) 128 832

4 5 ×

Pages 24–25 Challenge 1 1.

2.

3.

442

Challenge 3

0.04

Challenge 3 1.

2.

3.

2.

1.

2

280 4

5.

c) f) c) f)

4 000 000 3600 34.9 5000

26 742

1187 745

Challenge 2

Challenge 2 1.

27 929

0

0 3

5 0 5

504 hours

114 27895_P112_127.indd 114

28/03/2025 15:59

Challenge 2 1.

2.

3.

4.

3.

7020 Indian rupees 86 400 a) 32.8 b) 29.4 4092

Challenge 3 1.

2.

3.

4.

a) 53 a) 2 37

b) 74 c) 327 b) 1

d) 345

3

6

21 7

5

6

6

3

1

2

6

1

2

6 0

a) 15 6 6

2.

3.

4.

5.

4

3

4 0

5

4

5

4

5 0

a) 12 22 a) 14 a)

1 652

b)

b) 18

c) 215

b) 24 cm 8

b) 21311

Challenge 3 1.

2.

3.

4.

£98.75 0.625 a) 52 b) 223 833

Pages 32–33 Challenge 1 1.

2.

3.

4.

a) 11 880 3665 ml 24 2022

b) 1650

Challenge 2 1.

2.

3.

4.

5.

12 595 a) 26 19 £131.50

b) 50 g

Challenge 3 1.

2.

Pages 34–37 80, 280 6 423 506 ×

5

7

9

6

30

42

54

8

40

56

72

9 45 63 81

Challenge 2 1.

Progress test 1 1.

2.

3.

2025 2197 111 150 m2 <

Pages 30–31 Challenge 1 1.

2.

3.

4.

N o, because 903 ÷ 14 = 64.5, which is not a whole number 32

9 1344 kg

4.

5.

910 0.003 0.02 0.032 0.203 0.23 0.3 [2 marks if all correct, 1 mark if one incorrect] 200 800 6. −400 7. a) 1 2 3 4 6 9 12 18 36

[2 marks if all correct, 1 mark if up to

two factors missing or incorrect] b) 1 2 3 4 6 12

[2 marks if all correct, 1 mark if any

factors missing or incorrect] 8. 2299 9. a) 2 thousands or 2000 b) 2 tenths or 0.2 c) 2 hundred thousands or 200 000 10.

1426 875 1176 or 574 551

301

250

11. 37, 43, 67 and 97 circled [2 marks if all

correct, 1 mark if one incorrect or missing] 12. a) 28 b) 4 13. A ny three multiples of 6 and of 10, e.g. three of 30, 60, 90, 120, 150, 180, ….

14. 13°C 15. 16 16. 10 950 17. thirty-seven thousand, six hundred and nine 18. 9350 19. 109 20. 386 21. 16, 81, 25 and 64 circled [2 marks if all correct,

1 mark if one incorrect or missing] 22. 13.86 23. −9°C 2

24. 265 25. 6

Answers 27895_P112_127.indd 115

115 28/03/2025 15:59

26. a) 46 238 b) 46 240 c) 46 000 d) 50 000 27. 33 28. A ny calculation with correctly rounded numbers, e.g. 80 × 2 = 160 or 82 × 2 = 164 29. Answer between 13 and 15 m 30. £66.75 31. 27.3 cm

Pages 38–39 Challenge 1 1.

2.

3.

a) b)

Any two sections shaded.

Any four sections shaded.

a) a) d)

3 4

2 5

b) = >

4.

5.

6.

Challenge 3

a)

1 4

7

4.

2

3

6

9

5

4

15

12

b) c)

3 12 1 3

c) < f) >

a) d)

2.

1

d) 6

1 2

3.

a)

2.

2

2 3

4 5

a)

2.

a)

3.

5 8

12 20 3 8

8 12

12 16 8

b) 50

3.

4.

1.

3 4

7 20

a) a)

£5 5

23 3 20 = 120 67 7 c) 30 = 230 13 1 12 = 112

a)

2.

c) 3.

e) a) c)

4.

1 5 of 150 = 30

d) 9 litres d) 8

9 1 21 5 b) 8 = 28 4 = 24 (given) 13 1 15 1 4 = 34 d) 7 = 27 25 1 50 6 6 = 46 f) 11 = 411

1500 kg £240

1 5

1 3

30 a)

7

b) 240 km d) £10.66

4 9

114

9

Challenge 2 1.

22

b) 15 = 115 25 1 d) 12 = 212

29 45

13 24

17 24

c) 27

c) 6 m c) 9

13

c) 24 19 f) 60

41 1315

b)

3.

b) 4 kg b) 9

14

a)

2 7

[2 marks if all correct, 1 mark if one incorrect]

1 4 of 100 = 25

1

b) 45 11 e) 15

17 35

2.

1 3 of 120 = 40

15

5

Challenge 3

4 12

Pages 40–41 Challenge 1 1.

2.

3.

3

5 12 3 20

Challenge 3 20 60

b) 30

1 2 1 10 9 1 8 = 18 25 1 12 = 212

[2 marks if all correct, 1 mark if one incorrect] 1.

c) 162

3 10

d)

33

6 12

b) 18

Challenge 2

11

9 12

b) 10 = 12 13 1 d) 6 = 26

4.

3 1535 hours

1.

Any three fractions that simplify to 3, 2 4 6 24 36 e.g. 3, 6, 9, 36, 54 a) 12 8 12 1 4

c) 8 17 f) 100

a)

1.

1 3

21

3.

1

c) 3

b) 8 7 e) 12

3.

c) 1

d) 20

a) 45 19

Pages 42–43 Challenge 1

b) > e) <

b) 5

1

1.

2.

Challenge 2 1.

2.

90 60 35

3 8

1 6

29 30 1 9 23 7 40, 10

Pages 44–45 Challenge 1 1.

a)

2.

a)

3.

a) c)

1 1 b) 12 6 1 1 4✓ 7✓ 1 1 1 2 × 6 = 12 1 1 1 4 × 5 = 20

1

1

c) 40 d) 54 1 1 b) 8 and 7 circled 1

1

1

b) 4 × 8 = 32 3 1 1 d) 4 × 9 = 12

Challenge 2 1.

a) d)

2.

a)

4 35 8 21 1 1 b) 7 6

5

b) 36 21 e) 160 1

c) 4

15

1

c) 88 33 f) 100

d) 15

116 27895_P112_127.indd 116

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3.

2 5 3 5

a) d)

4.

2

1

b) 9 3 e) 7

c) 4 2 f) 5

1 27 2 15

5 18

2 5

1 3

5 6

Challenge 3 1.

a) d)

2.

3.

4.

1 9 9 16

7 2 16 m 4 15 2 a) 315

b) e)

1 36 1 8

c) f)

4 25 27 64

4.

5.

a) a)

3

1

1.

2.

3.

1.

28

5

29

7

29 10

2.

a)

105

2

b) 192

2.

3.

1.

1

b) 10 1 b) 12

2.

d) 2.

3.

4.

3 10 m 1 2 36 m 47 a) 70

b) e)

1

c) 30 1 f) 100

1 1 10 ÷ 2 = 5 ÷ 4 7 c) 40 5 f) 54

1 8 1 12

c) f)

1 14 3 20

a) c)

2.

a)

3.

a)

5 1 4 = 14 7 3 4 = 14 6 b) 5 1 38 b)

1.

b)

2.

3.

a)

3

12 2 5 = 25 11 5 d) 6 = 16 10 19 c) 8 d) 7 3 4 24 c) 49 d)

b) 5

34 3 8

5

d) 157

Percentage 41% 50% 25% 75% 10% 20%

a)

b) 18 cm

£24

c) 42 miles

d) 9 kg

7

12

9

35% = 20

48% = 25

90% = 10

52% = 50

9% = 100

9

2.

10% of £80

5% of £80

15% of £80

£8

£4

£12

10% of £45

20% of £45

40% of £45

£4.50

£9

£18

3.

4.

5.

£7.20 a)

£15.30

85 100 = 85%

£8.25 84 100 = 84%

b) English

b)

2

c) 43 8 6

£54 000 Team B

Pages 52–53 Challenge 1

20 3 1 82

a) dogs 40 children, cats 100 children, rabbits 240 children, hamsters 20 children b) 60 children

2.

a)

3.

4.

1

d) 133

1 12 0

1.

e)

1

33

1

41 100 1 2 1 4 3 4 1 10 1 5 3 5 4 5

26

1.

2.

53 72

Challenge 2 1.

c) 334

Challenge 3

Pages 48–49 Challenge 1 1.

1

[2 marks if all correct, 1 mark if one incorrect]

Challenge 2

1 1 b) 16 8 1 1 d) 35 e) 16 1 1 1 1 4÷8=8÷4 6÷3=2 ÷9 3 5 a) 20 b) 14 4 3 d) 27 e) 40

a)

53 18

60%

80%

Challenge 3 1.

32 11

Fraction

11

a)

1 4 1 12

d) 39 d) <

Pages 50–51 Challenge 1

b) 24

Challenge 2 1.

2

c) 26 c) <

Challenge 3

Pages 46–47 Challenge 1 1 4 1 a) 6 1 a) 8

5

b) 52 b) >

44 >

2

[2 marks if all correct, 1 mark if one correct]

3 10 21 50

53

b) 100 51 f) 125

217

3

c) 1000 d) 5 2 9 g) 25 h) 125

0.375 0.35

Challenge 2 1.

2.

3.

208 60 a) 0.125

b) 0.875

4.

a)

b) 5

84

1

Answers 27895_P112_127.indd 117

117 28/03/2025 15:59

5.

a)

b)

>

c) >

<

d) >

2.

3.

Challenge 3 1.

a)

b)

TVs R Us

£36.20

1

Challenge 2

1

2. a) 0.2 21% 0.23 4 [2 marks if all correct, 1 mark if one incorrect] 9

b) 150% 1.9 1.95 5 [2 marks if all correct, 1 mark if one incorrect]

Pages 54–55 Challenge 1 1.

2.

3

a) 4 b) 4 Max 8 grapes, Tilly 16 grapes b) 6 red pens, 24 black pens

a) b) c)

1 5 3 7

12 blue cars, 9 silver cars 3

a)

3 5

b) 12

1.

a)

2.

3.

Challenge 3

a) 40 b) 14 Any 3 counters coloured black, the rest white

Challenge 2

1.

2.

3.

1.

2.

3.

Progress test 2

Pages 60–63

1.

2.

a) a)

3.

13 5 3 a) 10

The ratio of yellow to purple is 3 : 2 ✓ a) 1 : 3 b) 4 : 1 5:1 1:2 1:5 2:3

4.

16 red, 12 yellow

Challenge 3 1.

2.

a) 3 : 6 9

b) 1 : 3 c) 10 : 2 d) 1 : 6 : 3

Pages 56–57 Challenge 1 1.

2.

3.

Square with sides 6 squares long.

21 cm 9 2

15

12

a) 30 cm b) 10 cm c) 4 cm

Pages 58–59 Challenge 1 4 : 5

2

15. 5 = 25 16. a) 49 b) 8 c) 3 17. 35

c)

4 9

d) 9

1

18. 24 3 19. 37 2

b)

8

11. 18 18 18 (accept also equivalent fractions with denominator 36, 90 or other multiple of 18) 12. 120 kg 13. 2004 14. a) £7 b) 18 kg

1.

a)

12

4. b) 25 5. 106 cards 6. £4.70

7.

4:1

1:3

12

5 9

2

b) 3 b) 0.7 c) 0.54

8. 42 700 9. 3 10. 561 810

Challenge 3

1.

0.31

1:1

2.

1 5

1:4

Challenge 2 1.

2.

36 red 24 blue 12 yellow 4 green 2 blue 20 red 2 yellow 300 ml mango juice 450 ml orange juice 750 ml sparkling water

20. a) 5 b) 12 red balls, 8 blue balls 21. 20°C

c) 4

1

22. 20

118 27895_P112_127.indd 118

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23. 32.43 33.34 33.4 33.43 34.04 [2 marks if all correct, 1 mark if one incorrect] 24. 0.375 25. a) 27 blue marbles b) blue 15, green 25 26. 2 27. 30 cars 28. a) 12 bananas b) 6 mangoes 3

54

5 60 8 = 96

29. 4 = 72

Challenge 2 1.

2.

3.

8 × 3 or + 6 ÷ 3 or − 8 × 2 12

1.

2.

a) 9 b) 6 c) 11 d) 20 output 1, input 25 a) a = 1, b = 8 a = 2, b = 7 a = 3, b = 6 a = 6, b = 3 a = 4, b = 5 a = 5, b = 4 a = 7, b = 2 a = 8, b = 1 [2 marks if all correct, 1 mark if at least six pairs correct] b) 8 input 9, output 22 6 a) 4 b) 10

c) 3.5

d) 42

2.

a) b) a)

£6 £18 4 hours £102.94 b) £24.50

Challenge 2 1.

2.

3.

4.

23 1 a) £21.50 £48.50 b) 3 hats

1.

2.

3.

a) 1 b) 5 d) 2000 e) 3 1.65 litres or 1650 ml 91 cm or 0.91 m

100

y = 2b 14 m2

c) 30 f) 40 000

Challenge 2 1.

3.

4.

240 000 seconds 72 hours 4800 minutes 36 days 6 weeks [2 marks if all correct, 1 mark if one correct] a) 0.75 b) 0.485 c) 1.67 d) 3600 e) 230 f) 10.09 125 g or 0.125 kg 1.258 m or 125.8 cm or 1258 mm

Challenge 3 1.

2.

3.

4.

16:18 or 4.18 pm 30 weeks a) Spain c) 1.63 m or 163 cm 400 teaspoons

b) 6 minutes 12 seconds d) 0.45 m or 45 cm

Pages 72–73 Challenge 1

1. 1 inch ✓ 2. 1 metre ✓ 2 1 3. a) 6.6 pounds 5 10 4. miles 10 25

5 n

Challenge 3 1.

2.

104 and 124 38

Pages 70–71 Challenge 1

2.

Pages 66–67 Challenge 1 1.

580 and 700 circled 1850, 1700, 1550, 1400 a) 4 counters b) 25 counters

Challenge 3

Challenge 3 1.

2.

3.

67, 75, 83 90, 83, 69 a)

b) 16, 21 c) 26

[2 marks if all correct, 1 mark if one incorrect]

Challenge 2 1.

2.

3.

1.

2.

3.

1 8 6 = 48

Pages 64–65 Challenge 1 1.

2.

3.

4.

5.

Pages 68–69 Challenge 1

3n – 5

295

10

b) 880 pounds km 8 16

20

32

25

40

45 72

Answers 27895_P112_127.indd 119

119 28/03/2025 15:59

Challenge 2 1.

2.

3.

4.

a) 36 inches 81.25 miles a) a)

b) 1 metre

1 3.5 or 32 pints

c) 10 cm 3 8.75 or 84 pints

James

a) b)

It has two equal sides. ✓ It has one line of symmetry. ✓ isosceles ✓

2.

1.

44.8 km

2.

3.

4.

5.

6.

33.25 or 334 pints 25 000 miles 56 miles per hour 540 inches a) 44 000 yards b) Estimate 10 000 ÷ 2000 = 5 miles

1

Pages 74–75 Challenge 1 a) 24 m 7 cm2 81 m2

Challenge 2 1.

a)

Accurate drawing of triangle

70 o

b) 32 m2

30 o 5 cm

2.

Challenge 2 1.

2.

3.

4.

1.

b) b) 2.625 miles

Challenge 3

1.

2.

3.

Pages 78–79 Challenge 1

1 cm by 12 cm rectangle drawn on the grid.

Perimeter = 104 m Area = 440 m2 44 cm 75 cm2

3.

b)

scalene

a) d)

A, C, D A, C, D

b) B e) A, C

circumference

diameter

c) C radius

Challenge 3 1.

1 cm by 4 cm rectangle and a 2 cm by 2 cm rectangle (square) drawn on the grid.

2. a) a × b = 70 b) a = 1, b = 70 a = 2, b = 35 a = 5, b = 14 a = 7, b = 10 a = 10, b = 7 a = 14, b = 5 a = 35, b = 2 a = 70, b = 1 [2 marks if all correct, 1 mark if fewer than two incorrect or missing]

Challenge 3 1.

2.

3.

Pages 80–81 Challenge 1 1.

Pages 76–77 Challenge 1 1.

2.

a) b)

20 cm2 54 cm2

c)

Challenge 2 1.

2.

3.

8 cm 5.5 cm 25.9 cm

d)

a) 21 cm a) 66 cm2 6 cm 2

b) 17.5 cm b) 90 cm2

2

(isosceles) trapezium, 1 pair of equal sides, 1 pair of parallel sides parallelogram, 2 pairs of equal sides, 2 pairs of parallel sides kite, 2 pairs of equal sides, 0 pairs of parallel sides rhombus, 4 equal sides, 2 pairs of parallel sides

2.

Challenge 3 1.

2.

3.

a) 30 cm2 7m 22 cm2

b) 20 cm2

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Challenge 2

Challenge 3

1.

2.

A, C

1.

3.

a) b)

Vertices: 4 right angles, Lines of symmetry: 4, Name: square Sides: 4, 1 pair of parallel sides, Vertices: 4, 2 right angles, Lines of symmetry: 0, Name: trapezium

Drawing of 4 equilateral triangles joined along their edges, e.g.

2.

3.

Challenge 3 1.

2.

3.

parallelogram kite a) parallelogram

b) square

c) rhombus

Pages 82–83 Challenge 1 1.

a) b) c) d)

Name: cube, 6 square faces Name: cuboid, 2 square faces, 4 rectangular faces, 12 edges, 8 vertices Name: cuboid, 6 rectangular faces, 12 edges, 8 vertices Name: triangular prism, 2 triangular faces, 3 rectangular faces, 9 edges, 6 vertices

Challenge 2 1.

2.

2 hexagon(al) faces, 6 rectangular faces, 18 edges, 12 vertices a) Rectangle matches to

Pages 84–85 Challenge 1 1.

2.

a) 12 cm3 64 cm3

b) 9 cm3

Challenge 2 1.

2.

3.

4.

125 cm3 56 m3 2 cm 3000 cm3

Challenge 3 1.

2.

3.

45 cm3 0.18 m3 4 cm

Progress test 3 Pages 86–89

Pentagon matches to

1.

2.

63 a)

✓

✓

b) Circle matches to

Square matches to

Triangle matches to

3.

[2 marks if all correct, 1 mark if one or two errors] b) cylinder, cone, cuboid, square-based pyramid, pentagonal prism, triangular prism. pentagon(al) prism

3. a) 7 b) 3 c) 6 d) 48 4. £83.29 5. Accurate drawing of trapezium [1 mark for each correct angle, 1 mark for each side of correct length (3 labelled sides only)] 6. 10 7. triangular prism 8. a) 8 cm2 b) 16 cm 9.

12 cm

A

22 cm 16 cm

10. 37

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11. 80

66

52

15 16

12.

13. a) 14.

3

2.

3.

38 b) 16 squares

x = 68° p = 45°

Pages 94–95 Challenge 1 1.

radius

a)

circumference diameter

15. 12 cm2 16. a) 1.2 km c) 2.45 m 17. 40 cm3 18. km

b) 0.55 kg d) 8000 ml

8

5 20

40

25

96

60

b) 45°

c) 29°

d) 263°

Challenge 2 1.

2.

3.

4.

1.

2.

3.

a) 60° b) 24 cm 25° a = 60°, b = 60°, c = 60°

75° 45° a = 115°

b = 65°

Challenge 2 1.

2.

3.

4.

D (0, 0) H (−5, 0)

a)

[1 mark for each point correct] b) parallelogram a) and b)

2.

125° 55° 56° 120°

Pages 92–93 Challenge 1

C (−3, −1) G (0, −4)

1.

y 5 4 3 2 R 1 P x 0 –5 –4 –3 –2 –1 –1 1 2 3 4 5 –2 –3 –4 S –5 Q

y 5 T 4 3 2 1 V x 0 –5 –4 –3 –2 –1 –1 1 2 3 4 5 X –2 –3 –4 –5

Challenge 3 1.

2.

3.

B (4, −2) F (3, 0)

Challenge 3

Pages 90–91 Challenge 1 25°

square

A (2, 3) E (−4, 3)

19. Blue 25% Red 50% White 12.5% Green 12.5% 20. 8 cm 21. 8 cm3 22. a) 4 b) 6 c) white

a)

x

[1 mark for each point correct] b)

1.

112 70

1.

y 7 6 B C 5 4 3 2 A D 1 0 0 1 2 3 4 5 6 7

Challenge 2

miles

32

y = 67° q = 45°

c)

[1 mark for each point correct, 1 mark for V label] V (0, 1)

Pages 96–97 Challenge 1 1.

d = 70° e = 40° u = 108° w = 108° 135° 96°

Challenge 3 1.

48°

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2.

2.

3.

2 squares left and 3 squares down

Challenge 2 1.

2.

y 5 4 3 2 C 1 x 0 –5 –4 –3 –2 –1 –1 1 2 3 4 5 –2

a) b)

b)

4 right, 5 down 4 left, 5 up

Challenge 3 1.

y 5 4 3 2 1 A F 0 –6 –5 –4 –3 –2 –1 –1 1 2 3 4 5 6 –2 B –3 –4

–5

Pages 98–99 Challenge 1 1.

a)

Challenge 2 1.

x

y 6 5 4 3 2 1 0 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 –4 –5

–6

Challenge 3 1.

2.

a)

a) a)

mirror line

b)

mirror line

b)

1.

D

y 5 4 3 2 1 x 0 –5 –4 –3 –2 –1 –1 1 2 3 4 5 –2 –3 –4 –5

5 squares left

a) d)

mirror line

b)

22

22

c)

32

Number of films watched in a year Number of people

mirror line

d)

b)

A

Pages 100–101 Challenge 1

c)

x

16 14 12 10 8 6 4 2 0

0–10 11–20 21–30 31–40 41–50 over 50 Number of films

Challenge 2 1.

a) c) d)

Nice Ices b) Nice Ices Jolly Lollies, 10 Thursday

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Challenge 3 1.

Challenge 3

a)

1.

Score

Tally

Frequency 4

0-20 21-40

13

41-60

22

61-80

16

55

Frequency

b) c)

24 22 20 18 16 14 12 10 8 6 4 2 0

Pages 106–107 Challenge 1 1.

2.

1.

2.

3.

4.

b) every hour e) 12°

10 am 2 pm

c) 24°C f) 8 hours

Challenge 2

1.

2.

100 90 80 70 60 50 40 30 20 10 0

Pages 108–111

Jul Aug Sept Oct Nov Dec Months

[1 mark for each point, 1 mark for correct labels] b) August and September c) July and August

Challenge 3 1.

a) 4.5 kg b) 6.5 kg (accept answers between 6.2 kg and 6.5 kg)

Pages 104–105 Challenge 1 1.

a) d) e)

10 a) 1.8 m b) Romy, Reason Romy’s mean = 1.9 m OR Romy’s jumps total 9.5 m, which is greater than Greg’s total (9 m) [1 mark if all correct, 0 marks if no working or reason given]

Progress test 4

Teddy bear sales

Number sold

a)

6 4 goals 150 g 135 cm

Challenge 3

0–20 21–40 41–60 61–80 Score

Pages 102–103 Challenge 1 a) d)

a) 20 b) 5 30 ÷ 3 = 10

Challenge 2

[1 mark for each bar, 1 mark for correct labels]

1.

ie chart coloured with 4 sections for Cat, 3 sections P for Dog, 2 sections for Rabbit, 1 section for Hamster, plus key completed to show the colour of sections for each pet.

1

1.

2.

3.

4.

125° 58° 7 13

5.

6.

a) 50% b) 8 c) 16 Point A (1, −4) Point B (7, −2) The midpoint of the line AB (4, −3) 9 cm 105°

7.

8.

9.

1

y 11 10 9 8 7 6 A 5 4 3 2 1 x 0 0 1 2 3 4 5 6 7

piano b) recorder c) half 2 30 children 10. a) 10 children (accept answers between 8 and 12)

6

b)

36

Challenge 2 1.

P ie chart coloured with 3 sections for Apple, 2 sections for Orange, 1 section for Banana, plus key completed to show the colour of sections for each fruit.

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11.

y 4 3 B 2 1 x 0 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 –4

12. 216 counters 13. a) −2°C b) d) 10 Temperature °C

8 6 4 2 0 Jan –2 –4 York –6

4°C

c)

14°C Poole

Feb

Mar

April

May

June

[7 marks: 1 mark for each point correctly plotted, 1 mark for joining with straight lines] 14. 2.4 kg 9

15. 20

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Notes

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Progress test charts Use these charts to record your results in the four Progress tests. Colour in the questions that you got right to help you identify any areas that you might need to study and practise again. (These areas are indicated in the ‘See page…’ row in the charts.)

Progress test 1: Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10 Q11 Q12 Q13 Q14 Q15 Q16

See page… 12-13 12-13 22-23 24-25 12-13 14-15 26-27 22-23 12-13 24-25 18-19 32-33 26-27 14-15 20-21 22-23

Q17

Q18

Q19

Q20

Q21

Q22

Q23

Q24

Q25

Q26

Q27

Q28

Q29

Q30

Q31

TOTAL /58

See page… 12-13 28-29 18-19 30-31 18-19 24-25 14-15 30-31 20-21 16-17 32-33 22-23 32-33 32-33 32-33

Progress test 2: Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

Q11

Q12

Q13

Q14

Q15

See page… 12-13 12-13 22-23 24-25 12-13 14-15 26-27 22-23 12-13 24-25 18-19 32-33 26-27 14-15 20-21

Q16 See page…

Q17

Q18

Q19

Q20

Q21

Q22

Q23

Q24

Q25

Q26

Q27

Q28

Q29

TOTAL /51

18-19 24-25 44-45 48-49 52-53 14-15 42-43 12-13 52-53 58-59 52-53 52-53 54-55 38-39

Progress test 3: See page…

See page…

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

Q11

64-65

82-83

66-67

66-67

86-87

66-67

82-83

74-75

56-57

66-67

68-69

Q12

Q13

Q14

Q15

Q16

Q17

Q18

Q19

Q20

Q21

Q22

42-43

68-69

78-79

76-77

72-73

84-85

72-73

50-51

76-77

84-85

54-55

Q7

Q8

Q9

TOTAL /52

Progress test 4: Q1

Q2

Q3

Q4

Q5

Q6

Q10

Q11

Q12

Q13

Q14

Q15

TOTAL /29

See page… 90-91 90-91 92-93 106-107 104-105 94-95 78-79 90-91 96-97 100-101 98-99 54-55 102-103 106-107 40-41

What am I doing well in?

What do I need to improve?

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