Number Sense and Nonsense: Building Math Creativity and Confidence Through Number Play
concepts remains with a person over the years As I write these words educators and the public are caught in a dilemma On one side are parents who feel that their children are being shortchanged because many of the current math programs do not call for extensive drill on multiplication tables and addition facts the so called basics On the other side are those who object to the kind of rote learning advanced by the older math programs still used in many schools and by teachers who teach as they have been taught using drill and kill methods With the increasing emphasis on standardized test scores teachers are pressured to spend a great deal of time drilling for tests in spite of the fact that research shows that when children learn the basics in the course of doing challenging math work they are far better prepared to cope with new ideas than if they had learned by rote memorization methods This book focuses on numbers their characteris tics and relationships applications of numbers in society and the history of number systems As rec ommended in the NCTM Standards 2000 readers also make connections to geometry and other branches of mathematics they develop skills in esti mation and problem solving they generalize about patterns of numbers and they are encouraged to engage in discussions with peers and adults see pages 139 140 This book provides a model for cre ativity and independence in the learning of mathe
matics and for the development of a positive attitude toward the subject The book is addressed to children in grades three to six and encompasses a wide range of mathemati cal knowledge I prefer not to specify a grade level or a level of difficulty for each activity Children should be encouraged to try as many activities as possible They should not be afraid to make mistakes or to fol low a wrong path Mathematicians do that all the
1 Odds and Evens What This Chapter Is About All whole numbers are divided into two groups odd numbers and even numbers They follow one another in order odd even odd even like the page num bers in this book But sometimes an even number can be odd and an odd number can be even You will read about it in this chapter Knowing how numbers behave can give a big boost to your number sense That knowledge can help you discover when numbers are used in ways that make no sense or are nonsense You will learn when to expect an even number and when to expect an odd number as an answer to a problem in arithmetic The ancient Egyptians almost 4 000 years ago had a way of multiplying numbers using mostly even numbers You will learn it
When Is on Even Number Odd C A sheep with two heads exclaimed Eddie pointing to a picture in the book he was reading That's an odd number of heads for an animal That s nonsense replied his sister Molly as she came over to look No animal has two heads And C what's more nonsense two is not an odd number Two is an even number See there really was such a sheep said Eddie But you re right an animal should have only one head An animal with two heads is unusual When I said an odd number of heads I meant that the sheep had an unusual number of heads Numbers like 1 3 5 7 and 9 are called odd num bers The numbers 2 4 6 and 8 are called even num bers Are the odd numbers unusual No there are just as many odd numbers as even numbers So why are these numbers called
