Number Sense and Nonsense: Building Math Creativity and Confidence Through Number Play

Contents......Page 8
Acknowledgments......Page 12
A Note to the Reader......Page 14
A Note to Parents and Teachers......Page 16
1 Odds and Evens......Page 18
When Is an Even Number Odd?......Page 19
When Is an Odd Number Even?......Page 21
The Dating Problem......Page 23
Number Sense About Odds and Evens......Page 25
Puzzles About Odd and Even Numbers......Page 28
Multiplication by Doubling: The Ancient Egyptian Way......Page 29
2 Prime and Not Prime......Page 32
Number Rectangles......Page 33
Prime and Composite Numbers......Page 37
All About Numbers......Page 39
What's Odd About Adding Odd Numbers?......Page 40
Hunt for Primes......Page 42
Those Even Numbers......Page 45
Factors of a Number......Page 47
Casting Out Nines......Page 49
Your Fingers as a Calculator......Page 50
3 Zero—Is It Something? Is It Nothing?......Page 52
That Funny Number......Page 53
When Is Zero Something?......Page 56
Make Your Own Odometer......Page 58
The Many Uses of Zero......Page 60
Is 0 a Number or a Letter?......Page 62
The Missing Year......Page 63
Who Wrote the First Zero?......Page 64
Zero Is a Special Number......Page 66
What Is a Googol?......Page 67
4 Money, Measures, and Other Matters......Page 68
Choose the Better Deal......Page 69
Sharing the Apples......Page 70
Making Sense of the Cents......Page 71
Count the Change......Page 74
A Head for Numbers......Page 75
Tom Fuller, the African Calculator......Page 76
The Missing Dot......Page 77
Number Sense and Common Sense......Page 79
Whose Foot?......Page 80
An Expensive Mistake......Page 81
5 Riddles, Puzzles, and Other Mind Bogglers......Page 82
Which Is Bigger?......Page 83
Keisha's Collection......Page 84
Guess My Number......Page 85
Liberian Stone Game......Page 86
Guess the Digit......Page 88
Guess Two Digits......Page 89
A Calendar Trick......Page 90
Calendar Magic Square......Page 91
The Monkey's Age......Page 92
6 Counting—Fingers, Words, Sticks, Strings, and Symbols......Page 94
Notches on a Bone......Page 95
How Many Fingers?......Page 96
Names for Numbers: Base Ten......Page 99
Names for Numbers: Base Twenty......Page 100
Our Indo-Arabic Numerals......Page 101
Numbers in Stone in Ancient Egypt......Page 102
Chinese Stick Numerals......Page 104
The Chinese Abacus......Page 105
Roman Numerals: Old and New......Page 106
The Inca Quipu: Knots on a String......Page 107
The Bars and Dots of the Maya......Page 108
7 The Calculator and Number Sense......Page 110
A New Kind of Number......Page 111
Calculator Games for Two or More......Page 112
More Calculator Games......Page 113
What Comes First?......Page 114
A Number Trick......Page 116
Number Patterns......Page 117
Different Names for the Same Number......Page 119
Making Sense of Cents......Page 120
Cents and Fractions......Page 121
Going in Circles......Page 123
Our Base-10 System of Numbers......Page 124
8 Numbers Grow, and Grow, and Grow......Page 126
Hanukkah Candles......Page 127
The Twelve Days of Christmas......Page 128
Young Gauss, the Math Genius......Page 130
Multiply by Dividing......Page 131
More Bugs......Page 132
Bugs Multiply Even Faster......Page 133
How Many Ancestors?......Page 134
The King's Chessboard......Page 136
Double the Allowance......Page 137
Going to St. Ives......Page 138
Pennies Grow to Save Lives......Page 139
Answers to Selected Questions......Page 140
Books for Kids......Page 144
Books for Adults......Page 147
Other Resources......Page 150
G......Page 152
S......Page 153
Z......Page 154
For Teachers: Alignment with the National Council of Teachers of Mathematics 2000 Standards......Page 156