CONTENTS Preface Introduction Chapter 1: Multiplication: Getting Started What is Multiplication? The Speed Mathematics Method Chapter 2: Using a Reference Number Reference Numbers Double Multiplication Chapter 3: Numbers Above the Reference Number Multiplying Numbers in The Teens Multiplying Numbers Above 100 Solving Problems in Your Head Double Multiplication Chapter 4: Multiplying Above & Below the Reference Number Numbers Above and Below Chapter 5: Checking Your Answers Substitute Numbers Chapter 6: Multiplication Using Any Reference Number Multiplication by factors Multiplying numbers below 20 Multiplying numbers above and below 20 Using 50 as a reference number Multiplying higher numbers Doubling and halving numbers Chapter 7: Multiplying Lower Numbers Experimenting with reference numbers Chapter 8: Multiplication by 11 Multiplying a two-digit number by 11 Multiplying larger numbers by 11 Multiplying by multiples of 11 Chapter 9: Multiplying Decimals Multiplication of decimals Chapter 10: Multiplication Using Two Reference Numbers Easy multiplication by 9 Using fractions as multiples Using factors expressed as division Playing with two reference numbers Using decimal fractions as reference numbers Chapter 11: Addition Adding from left to right Breakdown of numbers Checking addition by casting out nines Chapter 12: Subtraction Numbers around 100 Easy written subtraction Subtraction from a power of 10 Checking subtraction by casting nines Chapter 13: Simple Division Simple division Bonus: Shortcut for division by 9 Chapter 14: Long Division by Factors What Are Factors? Working with decimals Chapter 15: Standard Long Division Made Easy Chapter 16: Direct Long Division Estimating answers Reverse technique — rounding off upwards Chapter 17: Checking Answers (Division) Changing to multiplication Bonus: Casting twos, tens and fives Casting out nines with minus substitute numbers Chapter 18: Fractions Made Easy Working with fractions Adding fractions Subtracting fractions Multiplying fractions Dividing fractions Changing vulgar fractions to decimals Chapter 19: Direct Multiplication Multiplication with a difference Direct multiplication using negative numbers Chapter 20: Putting it All into Practice How Do I Remember All of This? Advice For Geniuses Afterword Appendix A: Using the Methods in the Classroom Appendix B: Working Through a Problem Appendix C: Learn the 13, 14 and 15 Times Tables Appendix D: Tests for Divisibility Appendix E: Keeping Count Appendix F: Plus and Minus Numbers Appendix G: Percentages Appendix H: Hints for Learning Appendix I: Estimating Appendix J: Squaring Numbers Ending in 5 Appendix K: Practice Sheets Index First published 2005 by Wrightbooks an imprint of John Wiley & Sons Australia, Ltd 42 McDougall Street, Milton, Qld 4064 Office also in Melbourne © Bill Handley 2005 The moral rights of the author have been asserted. National Library of Australia Cataloguing-in-Publication data: Handley, Bill. Speed maths for kids: Helping children achieve their full potential. Includes index. For primary school students. ISBN 0 7314 0227 8. 1. Mental arithmetic. 2. Mental arithmetic – Study and teaching (Primary). I. Title. 513.9 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 the publisher. Cover design by Rob Cowpe PREFACE I could have called this book Fun With Speed Mathematics. It contains some of the same material as my other books and teaching materials. It also includes additional methods and applications based on the strategies taught in Speed Mathematics that, I hope, give more insight into the mathematical principles and encourage creative thought. I have written this book for younger people, but I suspect that people of any age will enjoy it. I have included sections throughout the book for parents and teachers. A common response I hear from people who have read my books or attended a class of mine is, ‘Why wasn’t I taught this at school?’ People feel that, with these methods, mathematics would have been so much easier, and they could have achieved better results than they did, or they feel they would have enjoyed mathematics a lot more. I would like to think this book will help on both counts. I have definitely not intended Speed Maths for Kids to be a serious textbook but rather a book to be played with and enjoyed. I have written this book in the same way that I speak to young students. Some of the language and terms I have used are definitely non-mathematical. I have tried to write the book primarily so readers will understand. A lot of my teaching in the classroom has just been explaining out loud what goes on in my head when I am working with numbers or solving a problem. I have been gratified to learn that many schools around the world are using my methods. I receive emails every day from students and teachers who are becoming excited about mathematics. I have produced a handbook for teachers with instructions for teaching these methods in the classroom and with handout sheets for photocopying. Please email me or visit my website for details. Bill Handley, Melbourne, 2005 [email protected] www.speedmathematics.com INTRODUCTION I have heard many people say they hate mathematics. I don’t believe them. They think they hate mathematics. It’s not really maths they hate; they hate failure. If you continually fail at mathematics, you will hate it. No-one likes to fail. But if you succeed and perform like a genius you will love mathematics. Often, when I visit a school, students will ask their teacher, can we do maths for the rest of the day? The teacher can’t believe it. These are kids who have always said they hate maths. If you are good at maths, people think you are smart. People will treat you like you are a genius. Your teachers and your friends will treat you differently. You will even think differently about yourself. And there is good reason for it — if you are doing things that only smart people can do, what does that make you? Smart! I have had parents and teachers tell me something very interesting. Some parents have told me their child just won’t try when it comes to mathematics. Sometimes they tell me their child is lazy. Then the child has attended one of my classes or read my books. The child not only does much better in maths, but also works much harder. Why is this? It is simply because the child sees results for his or her efforts. Often parents and teachers will tell the child, ‘Just try. You are not trying.’ Or they tell the child to try harder. This just causes frustration. The child would like to try harder but doesn’t know how. Usually children just don’t know where to start. Sometimes they will screw up their face and hit the side of their head with their fist to show they are trying, but that is all they are doing. The only thing they accomplish is a headache. Both child and parent become frustrated and angry. I am going to teach you, with this book, not only what to do but how to do it. You can be a mathematical genius. You have the ability to perform lightning calculations in your head that will astonish your friends, your family and your teachers. This book is going to teach you how to perform like a genius — to do things your teacher, or even your principal, can’t do. How would you like to be able to multiply big numbers or do long division in your head? While the other kids are writing the problems down in their