Number Sense and Nonsense: Building Math Creativity and Confidence Through Number Play
Acknowledgments I want to thank the many educators and authors whose ideas I have adapted for this book Several of their books are listed in the Bibliography In particu lar I am indebted to the Family Math book for the activity Number Rectangles on page 16 Beatrice Lumpkin informed me about the evidence for the concept of zero in ancient Egypt The two headed sheep on page 2 is described in Finders Keepers by Stephen J Gould and Rosamond Wolff Purcell Nor ton 1992 Credit for permission to reprint The Monkey’s Age page 75 goes to Gary Hendren and the Missouri Council of Teachers of Mathematics Bul letin March
Introduction A Note to the Reader This book is about numbers all kinds of numbers Numbers have different personalities just like peo ple Numbers have relationships just as people do A person might be a daughter or son a sister or broth er a cousin and a friend Numbers are also related to other numbers in various ways Some ways of connecting numbers make good number sense Others may make no sense at all they are just nonsense In this book you will meet young people who are trying to tell the difference between number sense and nonsense they Often need some common sense to help them decide I think you will enjoy their discussions and debates You may want to have such discussions with your classmates friends and even grown ups These discussions will help you to build up your own number sense You will develop a good head for numbers the ability to see patterns in groups of numbers and an appreciation of how useful numbers are and how much fun you can have with numbers Most of the topics in each chapter include ideas for activities that you can carry out either alone or with other people There are also many questions for you to think about questions that sometimes have
no definite answers Many of the activities are easy for you to check you will decide whether they are correct See page 123 126 for the answers to some of the activities although you probably won't need to refer to the answer pages very often It's much more satisfying to work out the solutions yourself even if it takes time Some activities are harder than others and may be too difficult for you to complete at present Try them anyhow Discuss them with your friends or a grown up Your number sense will grow as you work on them even if you don't get the final answer correct And you will feel so proud when you do work out a hard problem But if you can't finish some of the activities now come back to them next year or the year after next You probably already know about odd and even num bers But did you know that an odd number might be even and an even number might be odd Chapter 1 is all about odds and evens Chapter 2 introduces other relationships among numbers You will have a chance to work on an idea called a conjecture about even numbers that no one has been able to prove either true or false although mathematicians have worked on it for over 200 years In Chapter 3 you will learn why zero is a very spe cial number For example we cannot divide a non zero number by zero When I try to divide six by zero
on my calculator the display shows the word error Zero is special in other ways too Chapter 4 deals with money and decimal points and measures You will learn how the United States lost hundreds of millions of dollars because of a mix up in units of measurement Riddles and puzzles are the subject of Chapter 5 although you will also find some riddles and puzzles in other chapters You will learn clever tricks with numbers that will make people think you are a genius How did numbers begin How have people used numbers in the past That's what Chapter 6 is all about You will read about finger counting number words in several languages signs for numbers and ways of calculating that have been used in different parts of the world over thousands of years You may wonder what about the calculator Why bother learning about numbers when the calculator can do all the work Not true The calculator has no number sense It takes a human being to tell the calcu lator what to do The same is true of the computer But the calculator can be very useful as you will find out in Chapter 7 You will learn about negative num bers repeating and terminating decimal fractions and a lot more Chapter 8 is about big numbers Would you like your allowance to take the form of one cent on the first day of the month two cents on the second
