Bill Handley - Speed Mathematics: Secrets of Lightning Mental Calculation

Contents Dedicated to Benyomin Goldschmiedt Also by Bill Handley: Teach Your Children Tables, Speed Maths for Kids and Fast Easy Way to Learn a Language (published by and available from Wrightbooks) Third edition first published 2008 by Wrightbooks an imprint of John Wiley & Sons Australia, Ltd 42 McDougall Street, Milton Qld 4064 Office also in Melbourne First edition 2000 Second edition 2003 Typeset in 11.5/13.2 pt Goudy Bill Handley 2008 The moral rights of the author have been asserted National Library of Australia Cataloguing-in-Publication data:

Author:	Handley, Bill.
Title:	Speed mathematics / author, Bill Handley.
Edition:	3rd ed.
Publisher:	Camberwell, Vic. : John Wiley and Sons Australia, 2008.
ISBN:	9780731407811 (pbk.)
Subjects:	Mental arithmetic Study and teaching.
Dewey Number:	513.9

All rights reserved. Except as permitted under the Australian Copyright Act 1968 (for example, a fair dealing for the purposes of study, research, criticism or review), no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher at the address above. Cover design by Rob Cowpe Author photograph by Karl Mandl Preface I made a number of changes to the book for the second edition of Speed Mathematics ; many minor changes where I, or my readers, thought something could be explained more clearly. The more important changes were to the chapters on direct long division (including a new chapter), calculating square roots (where I included replies to frustrated readers) and to the appendices.

I included an algebraic explanation for multiplication using two reference numbers and an appendix on how to motivate students to enjoy mathematics. I decided to produce a third edition after receiving mail from around the world from people who have enjoyed my book and found it helpful. Many teachers have written to say that the methods have inspired their students, but some informed me that they have had trouble keeping track of totals as they make mental calculations. In this third edition, I have included extra material on keeping numbers in your head, memorising numbers, working with logarithms and working with right-angled triangles. I have expanded the chapters on squaring numbers and tests for divisibility and included an idea from an American reader from Kentucky. I have produced a teachers handbook with explanations of how to teach these methods in the classroom with many handout sheets and problem sheets.

Please email me or visit my website for details. Many people have asked me if my methods are similar to those developed by Jakow Trachtenberg. He inspired millions with his methods and revolutionary approach to mathematics. Trachtenbergs book inspired me when I was a teenager. After reading it I found to my delight that I was capable of making large mental calculations I would not otherwise have believed possible. From his ideas, I developed a love for working, playing and experimenting with numbers.

I owe him a lot. My methods are not the same, although there are some areas where our methods meet and overlap. We use the same formula for squaring numbers ending in five. Trachtenberg also taught casting out nines to check answers. Whereas he has a different rule for multiplication by each number from 1 to 12, I use a single formula. Whenever anyone links my methods to Trachtenbergs, I take it as a compliment.

My methods are my own and my approach and style are my own. Any shortcomings in the book are mine. Some of the information in Speed Mathematics can be found in my first book, Teach Your Children Tables . I have repeated this information for the sake of completeness. Teach Your Children Tables teaches problem-solving strategies that are not covered in this book. The practice examples in my first book use puzzles to make learning the strategies enjoyable.

It is a good companion to this book. Speed Maths For Kids is another companion which takes some of the methods in this book further. It is a fun book for both kids and older readers, giving added insight by playing and experimenting with the ideas. My sincere wish is that this book will inspire my readers to enjoy mathematics and help them realise that they are capable of greatness. Bill Handley Melbourne, Australia, January 2008 < http://www.speedmathematics.com > Introduction Imagine being able to multiply large numbers in your head faster than you could tap the numbers into a calculator. Imagine being able to make a lightning mental check to see if you have made a mistake.

How would your colleagues react if you could calculate square roots and even cube roots mentally? Would you gain a reputation for being extremely intelligent? Would your friends and colleagues treat you differently? How about your teachers, lecturers, clients, management? People equate mathematical ability with intelligence. If you are able to do multiplication, division, squaring and square roots in your head in less time than your friends can retrieve their calculators from their bags, they will believe you have a superior intellect. I taught a young boy some of the strategies you will learn in Speed Mathematics before he had entered Grade 1 and he was treated like a prodigy throughout primary and secondary school. Engineers familiar with these kinds of strategies gain a reputation for being geniuses because they can give almost instant answers to square root problems. Mentally finding the length of a hypotenuse is childs play using the methods taught in this book. As these people are perceived as being extremely intelligent, they are treated differently by their friends and family, at school and in the workplace.

And because they are treated as being more intelligent, they are more inclined to act more intelligently. Why teach basic number facts and basic arithmetic? Once I was interviewed on a national radio programme. After my interview, the interviewer spoke with a representative from the mathematics department at a leading Melbourne university. He said that teaching students to calculate is a waste of time. Why does anyone need to square numbers, multiply numbers, find square roots or divide numbers when we have calculators? Many parents telephoned the network to say his attitude could explain the difficulties their children were having in school. I have also had discussions with educators about the value of teaching basic number facts.

Many say children dont need to know that 5 plus 2 equals 7 or 2 times 3 is 6. When these comments are made in the classroom I ask the students to take out their calculators. I get them to tap the buttons as I give them a problem. Two plus three times four equals..? Some students get 20 as an answer on their calculator. Others get an answer of 14. Which number is correct? How can calculators give two different answers when you press the same buttons? This is because there is an order of mathematical functions.

You multiply and divide before you add or subtract. Some calculators know this; some dont. A calculator cant think for you. You must understand what you are doing yourself. If you dont understand mathematics, a calculator is of little help. Here are some reasons why I believe an understanding of mathematics is not only desirable, but essential for everyone, whether student or otherwise: