CHAPTER ONE PROBLEM SOLVING

1.1 Seeing and Extending Patterns 1

Just for Fun - The Peg Jumping Puzzle

1.2 Geometric Number Patterns 8

Just for Fun - Fibonacci Numbers in Nature

1.3 Patterns with Colored Tile 14

Just for Fun - Spirolaterals

Ideas for the Elementary Classroom 19

Suggested Classroom Activity...Act Out The Problem

Readings for More Classroom Ideas

CHAPTER TWO SETS FUNCTIONS AND REASONING

2.1 Sorting and Classifying 21

Just for Fun - Attribute Identity Game

2.2 Curves of Motion 28

Just for Fun - The Curve of Orbiting Planets

2.3 Logic Problems for Cooperative

Learning Groups 34

Just for Fun - Pica-Centro

Ideas for the Elementary Classroom 37

Suggested Classroom Activity...Math Communication

Readings for More Classroom Ideas

CHAPTER THREE WHOLE NUMBERS

3.1 Models for Numeration 39

Just for Fun - Mind Reading Cards and the Game of Nim

3.2 Adding and Subtracting with Multi-base Pieces 46

Just for Fun - Force Out

3.3 Multiplying with Multi-base pieces 53

Just for Fun - Cross-numbers for Calculators

3.4 Dividing with Multi-base Pieces 58

Just for Fun - Calculator Games and Number Tricks

Ideas for the Elementary Classroom 65

Suggested Classroom Activity...Visualizing Basic Operations

Readings for More Classroom Ideas

CHAPTER FOUR NUMBER THEORY

4.1 Models for Even Numbers, Odd Numbers, Factors and Primes 67

Just for Fun - Number Chart Primes and Multiples

4.2 Models for Greatest Common Factor and Least Common Multiple 76

Just for Fun - Star Polygons

Ideas for the Elementary Classroom 84

Suggested Classroom Activity...Odd- Even Class Models

Readings for More Classroom Ideas

CHAPTER FIVE INTEGERS AND FRACTIONS

5.1 Models for Operations with Integers 86

Just for Fun - Games for Negative Numbers

5.2 Fraction Models for Equality and Inequality 94

Just for Fun - Fraction Games

5.3 Computing with Fraction Bars 101

Just for Fun - Fraction Games for Operations

Ideas for the Elementary Classroom 108

Suggested Classroom Activity...Integer Balloon

Readings for More Classroom Ideas.

CHAPTER SIX DECIMALS: RATIONAL AND IRRATIONAL NUMBERS

6.1 Models for Decimals 111

Just for Fun - Decimal Games

6.2 Operations with Decimal Squares 120

Just for Fun - Decimal Games for Operations

6.3 A Model for Introducing Percent 130

Just for Fun - Number Search

6.4 Irrational Numbers on the Geoboard 140

Just for Fun - Golden Rectangles

Ideas for the Elementary Classroom 148

Suggested Classroom Activity...Base Piece Decimal Model

Readings for More Classroom Ideas.

CHAPTER SEVEN ALGEBRA AND FUNCTIONS

7.1 Solving Story Problems with Algebra Pieces 149

Just for Fun - Algebraic Expression Game

7.2 Geometric Models for Algebraic Expressions 155

Just for Fun - Coordinate Games

Ideas for the Elementary Classroom 161

Suggested Classroom Activity...Pattern Block Perimeters

Readings for More Classroom Ideas.

CHAPTER EIGHT STATISTICS

8.1 Randomness, Sampling and Simulation

in Statistics 163

Just for Fun - Simulated Racing Game

8.2 Scatterplots: Looking for Relationships 171

Just for Fun - Page Guessing

8.3 Statistical Distributions: Observations

and Applications 177

Just for Fun - Cryptanalysis

Ideas for the Elementary Classroom 209

Suggested Classroom Activity...Student-centered Data Collection

Readings for More Classroom Ideas.

CHAPTER NINE PROBABILITY

9.1 Probability Experiments 190

Just for Fun - Probability Games

9.2 Multi-stage Probability Experiments 198

Just for Fun - Trick Dice

Ideas for the Elementary Classroom 209

Suggested Classroom Activity...Race Track Probability

Readings for More Classroom Ideas.

CHAPTER TEN GEOMETRIC FIGURES

10.1 Figures on Rectangular and Circular Geoboards 211

Just for Fun - Tangram Puzzles

10.2 Regular and Semiregular Tessellations 220

Just for Fun - The Game of Hex

10.3 Models for Regular and Semiregular Polyhedra 226

Just for Fun - Instant Insanity

10.4 Creating Symmetric Figures: Pattern Blocks and Paper Folding 232

Just for Fun - Snowflakes

10.5 Computer Games in Logo 240

Ideas for the Elementary Classroom 242

Suggested Classroom Activity...Paper Cutting Symmetries

Readings for More Classroom Ideas.

CHAPTER ELEVEN MEASUREMENT

11.1 Measuring with Metric Units 244

Just for Fun - Metric Games

11.2 Areas on Geoboards 251

Just for Fun - Pentominoes

11.3 Models for Volume and Surface Area 257

Just for Fun - Soma Cubes

Ideas for the Elementary Classroom 264

Suggested Classroom Activity...Folding Boxes

Readings for More Classroom Ideas.

CHAPTER TWELVE MOTIONS IN GEOMETRY

12.1 Locating Sets of Points in the Plane 266

Just for Fun - Line Designs

12.2 Drawing Escher-type Tessellations 274

Just for Fun - Paper Puzzles

12.3 Devices for Indirect Measurement 281

Just for Fun - Enlarging Drawings

12.4 Topological Investigations and Entertainment 291

Just for Fun - Topological Games

Ideas for the Elementary Classroom 299

Suggested Classroom Activity...Analyzing Shapes

Readings for More Classroom Ideas.

Answers to Puzzlers 301

Answers to Selected Activities 303

Index 321

Materials Cards 331