Table Of Content

KS2 9–10 Years Master Maths at Home Extra Challenges Scan the QR code to help your child’s learning at home. mastermathsathome.com 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 11 2244//0022//22002222 0077::3300 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 This book was made with [email protected] 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 1 001–327102–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: 978-0-24153-946-0 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. 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 22 2244//0022//22002222 0077::3300 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: Numbers to 1 000 000 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 Adding and subtracting 6 they’re used. or functional ability. Factors and multiples 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. Prime numbers 10 discussion points that don’t have obvious • A community of friendly and relatable Multiplying 3-digit numbers 12 ‘right’ or ‘wrong’ answers. characters who introduce each lesson and Dividing 4-digit numbers 14 • Rich illustrations that will guide children come along as your child progresses through to a discussion of shapes and units of the series. Adding and subtracting fractions 16 measurement, allowing them to make connections to the wider world around them. Multiplying fractions 18 Multiplying mixed numbers 20 You can see more guidance on how to use these books at mastermathsathome.com. Ordering and comparing decimals 22 We’re excited to share all the ways you can learn maths! Adding and subtracting decimals 24 Percentages 28 Copyright © 2022 Maths — No Problem! Line graphs 30 Maths — No Problem! mastermathsathome.com Capacity 34 www.mathsnoproblem.com [email protected] This book was made with Perimeter 36 Forest Stewardship Council™ First published in Great Britain in 2022 by certified paper – one small Dorling Kindersley Limited step in DK's commitment Area 38 to a sustainable future. For One Embassy Gardens, 8 Viaduct Gardens, London SW11 7BW more information go to www. A Penguin Random House Company Angles 40 dk.com/our-green-pledge The authorised representative in the EEA is Dorling Kindersley Position 44 Verlag GmbH. Arnulfstr. 124, 80636 Munich, Germany 10 9 8 7 6 5 4 3 2 1 Answers 46 001–327102–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: 978-0-24153-946-0 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 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 22 2244//0022//22002222 0077::3300 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 33 2244//0022//22002222 0077::3300 Numbers to 1 000 000 Lesson 1 Starter Jacob is making numbers using digit cards. This is the last number he makes. 2 1 6 9 3 4 He then decides to swap the places of some digit cards and makes 3 swaps. What is the greatest number he can make? What is the smallest number he can make? Example 2 1 6 9 3 4 To make the The greatest greatest number digit is 9. we need to have 9 1 6 2 3 4 as many hundred thousands, ten thousands and 9 1 6 2 3 4 The second thousands as greatest digit possible. is 6. 9 6 1 2 3 4 9 6 1 2 3 4 The last digit we can change should be 4. 9 6 4 2 3 1 964 231 is the greatest number Jacob can make by making 3 swaps. 4 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 44 2244//0022//22002222 0077::3300 Numbers to 1 000 000 Lesson 2 1 6 9 3 4 To make the smallest 1 number we place the 1 in the Change 1 1 2 6 9 3 4 hundred thousands place. Starter Change 2 1 2 3 9 6 4 Jacob is making numbers using digit cards. This is the last number he makes. Change 3 1 2 3 4 6 9 2 1 6 9 3 4 123 469 is the smallest number Jacob can make by making 3 swaps. He then decides to swap the places of some digit cards and makes 3 swaps. What is the greatest number he can make? Practice What is the smallest number he can make? 1 Swap the places of 2 digits in each number with 2 others to make Example a number as close as possible to 500 000. (a) 328045 2 1 6 9 3 4 To make the The greatest (b) 429375 greatest number digit is 9. we need to have 9 1 6 2 3 4 (c) 743021 as many hundred thousands, ten (d) 521997 thousands and 9 1 6 2 3 4 The second thousands as greatest digit possible. 2 Use the following digits to make the number closest to: is 6. 9 6 1 2 3 4 7 2 3 5 2 3 9 6 1 2 3 4 The last digit (a) 200000 we can change should be 4. (b) 350000 9 6 4 2 3 1 964 231 is the greatest number Jacob can make by making 3 swaps. (c) 490000 4 5 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 44 2244//0022//22002222 0077::3300 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 55 2244//0022//22002222 0077::3300 Adding and subtracting Lesson 2 Starter Emma and her family are on holiday in Indonesia. Emma has Rp1000000 (Indonesian Rupiah) to spend (approximately £50). Rp375 659 Rp240 999 How much will she have left after buying the 2 items? Example Start by ﬁnding the cost of the 2 items. ? 1 1 1 1 3 7 5 6 5 9 + 2 4 0 9 9 9 6 1 6 6 5 8 375 659 240 999 375659 + 240999 = 616658 The total cost of the 2 items is Rp616658. 6 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 66 2244//0022//22002222 0077::3300 Adding and subtracting Lesson Subtract the total cost of the 2 items 2 from the amount Emma started with. Starter 9 9 9 9 9 1 000 000 10 10 10 10 10 10 1 0 0 0 0 0 0 Emma and her family are on holiday in Indonesia. Emma has Rp1000000 − 6 1 6 6 5 8 (Indonesian Rupiah) to spend (approximately £50). 3 8 3 3 4 2 616 658 ? 1000000 – 616658 = 383342 Emma will have Rp383342 left after buying the 2 items. Practice Rp375 659 Rp240 999 Emma’s dad buys the following items. How much will she have left after buying the 2 items? How much money will he have left if he starts with Rp1000000? Example Start by Rp482 199 Rp337 805 ﬁnding the cost of the 2 items. ? 1 1 1 1 3 7 5 6 5 9 + 2 4 0 9 9 9 6 1 6 6 5 8 375 659 240 999 375659 + 240999 = 616658 The total cost of the 2 items is Rp616658. Emma’s dad will have Rp left. 6 7 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 66 2244//0022//22002222 0077::3300 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 77 2244//0022//22002222 0077::3311 Factors and multiples Lesson 3 Starter A group of pupils take part in 3 outdoor activities: kayaking, climbing and archery. They are put into groups of 4 for kayaking, groups of 8 for climbing and groups of 14 for archery. Each activity has more than 1 group. What is the minimum number of pupils taking part in the outdoor activities? Example 8 ÷ 4 = 2 8 ÷ 8 = 1 What is the 8 is the lowest common multiple smallest number divisible of 4 and 8. by 4 and 8? We know that each activity has more than 1 Find the group so climbing must have multiples of more than 8 pupils. 4 and 8. Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56 Multiples of 8: 8, 16, 24, 32, 40, 48, 56 There may be 16 pupils. Four groups of 4 pupils kayaking. Two groups of 8 pupils climbing. 8 332277110022__MMNNPP__EExxttrraa CChhaalllleennggeess__99--1100__KKSS22..iinndddd 88 2244//0022//22002222 0077::3311