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KS2 9–10 Years Master Maths at Home Multiplication and Division Scan the QR code to help your child’s learning at home. mastermathsathome.com 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 11 1144//0022//22002222 1111::1166 How to use this book Maths — No Problem! created Master Maths at Home to help children develop fluency in the subject and a rich understanding of core concepts. Key features of the Master Maths at Home books include: • Carefully designed lessons that provide • Exercises that allow a flexible approach and structure, but also allow flexibility in how can be adapted to suit any child’s cognitive they’re used. or functional ability. • Speech bubbles containing content designed • Clearly laid-out pages that encourage children to spark diverse conversations, with many to practise a range of higher-order skills. discussion points that don’t have obvious • A community of friendly and relatable ‘right’ or ‘wrong’ answers. characters who introduce each lesson and • Rich illustrations that will guide children come along as your child progresses through to a discussion of shapes and units of the series. measurement, allowing them to make connections to the wider world around them. You can see more guidance on how to use these books at mastermathsathome.com. We’re excited to share all the ways you can learn maths! Copyright © 2022 Maths — No Problem! Maths — No Problem! mastermathsathome.com www.mathsnoproblem.com [email protected] This book was made with Forest Stewardship Council™ First published in Great Britain in 2022 by certified paper – one small Dorling Kindersley Limited step in DK's commitment to a sustainable future. For One Embassy Gardens, 8 Viaduct Gardens, London SW11 7BW more information go to www. A Penguin Random House Company dk.com/our-green-pledge The authorised representative in the EEA is Dorling Kindersley Verlag GmbH. Arnulfstr. 124, 80636 Munich, Germany 10 9 8 7 6 5 4 3 2 1 001–327097–May/22 All rights reserved. Without limiting the rights under the copyright reserved above, no part of this publication may be reproduced, stored in, or introduced into a retrieval system, or transmitted, in any form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior written permission of the copyright owner. A CIP catalogue record for this book is available from the British Library. ISBN: 978-0-24153-942-2 Printed and bound in the UK For the curious www.dk.com Acknowledgements The publisher would like to thank the authors and consultants Andy Psarianos, Judy Hornigold, Adam Gifford and Dr Anne Hermanson. The Castledown typeface has been used with permission from the Colophon Foundry. 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 22 1144//0022//22002222 1111::1166 How to use this book Contents Maths — No Problem! created Master Maths at Home to help children develop fluency in the subject and a rich understanding of core concepts. Page Key features of the Master Maths at Home books include: Multiples 4 • Carefully designed lessons that provide • Exercises that allow a flexible approach and structure, but also allow flexibility in how can be adapted to suit any child’s cognitive Factors 6 they’re used. or functional ability. Common factors 8 • Speech bubbles containing content designed • Clearly laid-out pages that encourage children to spark diverse conversations, with many to practise a range of higher-order skills. Composite, square and prime numbers 10 discussion points that don’t have obvious • A community of friendly and relatable ‘right’ or ‘wrong’ answers. Square numbers 12 characters who introduce each lesson and • Rich illustrations that will guide children come along as your child progresses through Cube numbers 14 to a discussion of shapes and units of the series. measurement, allowing them to make Multiplying by 10, 100 and 1000 16 connections to the wider world around them. Multiplying 2- and 3-digit numbers 18 You can see more guidance on how to use these books at mastermathsathome.com. Multiplying 4-digit numbers (part 1) 22 We’re excited to share all the ways you can learn maths! Multiplying 4-digit numbers (part 2) 26 Multiplying 2-digit by 2-digit numbers (part 1) 30 Multiplying 2-digit by 2-digit numbers (part 2) 32 Copyright © 2022 Maths — No Problem! Maths — No Problem! Dividing by 10, 100 and 1000 34 mastermathsathome.com www.mathsnoproblem.com Dividing 3-digit numbers 36 [email protected] This book was made with Forest Stewardship Council™ First published in Great Britain in 2022 by certified paper – one small Dividing 4-digit numbers 38 Dorling Kindersley Limited step in DK's commitment to a sustainable future. For One Embassy Gardens, 8 Viaduct Gardens, London SW11 7BW more information go to www. Dividing with remainder 42 A Penguin Random House Company dk.com/our-green-pledge The authorised representative in the EEA is Dorling Kindersley Review and challenge 44 Verlag GmbH. Arnulfstr. 124, 80636 Munich, Germany 10 9 8 7 6 5 4 3 2 1 Answers 46 001–327097–May/22 All rights reserved. Without limiting the rights under the copyright reserved above, no part of this publication may be reproduced, stored in, or introduced into a retrieval system, or transmitted, in any form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior written permission of the copyright owner. A CIP catalogue record for this book is available from the British Library. ISBN: 978-0-24153-942-2 Printed and bound in the UK For the curious www.dk.com Acknowledgements The publisher would like to thank the authors and consultants Andy Psarianos, Judy Hornigold, Adam Gifford and Dr Anne Hermanson. The Castledown typeface has been used with permission from the Colophon Foundry. Ruby Elliott Amira Charles Lulu Sam Oak Holly Ravi Emma Jacob Hannah 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 22 1144//0022//22002222 1111::1166 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 33 1144//0022//22002222 1111::1166 Multiples Lesson 1 Starter Ravi can count in eights. 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 You are naming multiples of 8. What does Sam mean? Example We can describe multiples of 8 as numbers that divide exactly by 8. When we multiply a whole number by 8, the product is also a multiple of 8. 1 × 8 = 8 1 2 3 4 5 6 7 8 9 10 2 × 8 = 16 11 12 13 14 15 16 17 18 19 20 3 × 8 = 24 21 22 23 24 25 26 27 28 29 30 4 × 8 = 32 5 × 8 = 40 31 32 33 34 35 36 37 38 39 40 6 × 8 = 48 41 42 43 44 45 46 47 48 49 50 The orange 7 × 8 = 56 51 52 53 54 55 56 57 58 59 60 numbers on the 8 × 8 = 64 61 62 63 64 65 66 67 68 69 70 100-square are 9 × 8 = 72 71 72 73 74 75 76 77 78 79 80 all multiples 10 × 8 = 80 of 8. 81 82 83 84 85 86 87 88 89 90 11 × 8 = 88 91 92 93 94 95 96 97 98 99 100 12 × 8 = 96 4 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 44 1144//0022//22002222 1111::1177 Multiples Lesson Practice 1 1 2 3 4 5 6 7 8 9 10 1 (a) Draw a circle around 11 12 13 14 15 16 17 18 19 20 each multiple of 3. Starter 21 22 23 24 25 26 27 28 29 30 (b) Draw a square 31 32 33 34 35 36 37 38 39 40 Ravi can count in eights. around each multiple of 7. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 8, 16, 24, 32, 40, 71 72 73 74 75 76 77 78 79 80 48, 56, 64, 72, 80 You are naming 81 82 83 84 85 86 87 88 89 90 multiples of 8. 91 92 93 94 95 96 97 98 99 100 What does Sam mean? 2 Fill in the blanks with the missing multiples. Example (a) Multiples of 4: 4, 8, , 16, , , , 32, 36, , We can describe multiples of 8 as numbers that divide exactly by 8. When we multiply a whole number by 8, the product is also a multiple of 8. , , ... 1 × 8 = 8 1 2 3 4 5 6 7 8 9 10 (b) Multiples of 6: 2 × 8 = 16 11 12 13 14 15 16 17 18 19 20 3 × 8 = 24 6, , , 24, , , , , 54, 21 22 23 24 25 26 27 28 29 30 4 × 8 = 32 5 × 8 = 40 31 32 33 34 35 36 37 38 39 40 60, , , ... 6 × 8 = 48 41 42 43 44 45 46 47 48 49 50 The orange 7 × 8 = 56 51 52 53 54 55 56 57 58 59 60 3 Fill in the blanks. The first one has been done for you. numbers on the 8 × 8 = 64 61 62 63 64 65 66 67 68 69 70 100-square are (a) 8 is a multiple of 1, 2, 4 and 8. 9 × 8 = 72 71 72 73 74 75 76 77 78 79 80 all multiples 10 × 8 = 80 (b) 6 is a multiple of 1, , and . of 8. 81 82 83 84 85 86 87 88 89 90 11 × 8 = 88 91 92 93 94 95 96 97 98 99 100 12 × 8 = 96 (c) 10 is a multiple of , , and . 4 5 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 44 1144//0022//22002222 1111::1177 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 55 1144//0022//22002222 1111::1177 Factors Lesson 2 Starter Ruby and Charles are playing a card game. Each row must have the same number of cards. How many ways can Ruby and Charles arrange the cards? Example Ruby and Charles can arrange the cards in a single row. There is 1 row of 12 cards. We say that 1 and 12 are factors of 12. 1 × 12 = 12 They can arrange the 2 and 6 are cards into factors of 12. 2 rows of 6. 2 × 6 = 12 They can leave the cards as 3 rows of 4. 3 and 4 are factors of 12. 3 × 4 = 12 6 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 66 1144//0022//22002222 1111::1177 Factors Lesson We can say that all 2 the factors of 12 are 1, 2, 3, 4, 6 and 12. 12 can be divided by its factors and not Starter leave a remainder. Ruby and Charles are playing a card Practice game. Each row must have the same number of cards. Fill in the blanks. How many ways can Ruby and Charles arrange the cards? 1 (a) × 1 = 8 × 2 = 8 Example × 4 = 8 × 8 = 8 Ruby and Charles can arrange The factors of 8 are , , and . the cards in a single row. (b) × 1 = 14 × 2 = 14 There is 1 row of 12 cards. We say that × 7 = 14 × 14 = 14 1 and 12 are factors of 12. 1 × 12 = 12 The factors of 14 are , , and . They can (c) × = 21 × = 21 arrange the 2 and 6 are cards into The factors of 21 are , , and . factors of 12. 2 rows of 6. 2 × 6 = 12 2 (a) The factors of 18 are , , , , They can leave the cards as and . 3 rows of 4. (b) The factors of 16 are , , , 3 and 4 are factors of 12. 3 × 4 = 12 and . 6 7 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 66 1144//0022//22002222 1111::1177 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 77 1144//0022//22002222 1111::1177 Common factors Lesson 3 Starter I’ve found the I’ve found the factors of 10. factors of 15. 1,2,5, 10 1, 3, 5, 15 Which numbers are factors of both 10 and 15? Example 1 is a factor of all whole numbers. 1 × 10 = 10 2 × 5 = 10 1 × 15 = 15 3 × 5 = 15 The factors of 10 are 1, 2, 5 and 10. The factors of 15 are 1, 3, 5 and 15. 1 and 5 are common factors of 10 and 15. This means if we divide 10 or 15 by 1 or 5, we will not be left with a remainder. 8 332277009977__MMNNPP__MMuullttiipplliiccaattiioonn aanndd DDiivviissiioonn__99--1100__KKSS22..iinndddd 88 1144//0022//22002222 1111::1188