[eBook Code] Awesome Math (eBook Code, 1st)

Acknowledgments xi

About the Authors xiii

Introduction xvii

I. Why Problem Solving?

Chapter 1: Rewards for Problem-Based Approach: Range, Rigor, and Resilience 5

Range Ignites Curiosity 5

Rigor Taps Critical Thinking 9

Resilience is Born Through Creativity 10

Chapter 2: Maximize Learning: Relevance, Authenticity, and Usefulness 13

Student Relevance 13

Mathematical Relevance 14

Mathematical Relevance: The Math Circle Example 16

Curriculum Relevance 18

Authenticity: The Cargo Cult Science Trap 21

Authenticity in Learning 22

Usefulness 25

Chapter 3: Creating a Math Learning Environment 27

Know Yourself: Ego and Grace 27

Know Your Students 30

Know Your Approach 35

Chapter 4: What is the Telos? 47

Autonomy to Solve Your Problems 47

Mastery Through Inquiry 48

Purpose with Competitions 50

Quadrants of Success 52

Chapter 5: Gains and Pains with a Problem-Based Curriculum 57

Teachers 58

Students 61

Parents 67

II. Teaching Problem Solving

Chapter 6: Five Steps to Problem-Based Learning 75

Start with Meaningful Problems 75

Utilize Teacher Resources 79

Provide an Active Learning Environment 91

Understand the Value of Mistakes 97

Recognize That Everyone is Good at Math 99

Chapter 7: The Three Cs: Competitions, Collaboration, Community 103

Competitions 103

Collaboration 107

Community 117

Aspire to Inspire: Stories from Awesome Educators 121

Chapter 8: Mini-Units 147

Relate/Reflect/Revise Questions 147

Roman Numeral Problems 148

Cryptarithmetic 151

Squaring Numbers: Mental Mathematics 155

The Number of Elements of a Finite Set 157

Magic Squares 159

Toothpicks Math 163

Pick’s Theorem 165

Equilateral versus Equiangular 168

Math and Chess 170

Area and Volume of a Sphere 172

III. Full Units

Chapter 9: Angles and Triangles 177

Learning Objectives 177

Definitions 177

Angles and Parallel Lines 177

Summary 180

Chapter 10: Consecutive Numbers 185

Learning Objectives 185

Definitions 185

Chapter 11: Factorials! 191

Learning Objectives 191

Definitions 191

Chapter 12: Triangular Numbers 199

Learning Objectives 199

Definitions 199

Chapter 13: Polygonal Numbers 205

Learning Objectives 205

Definitions 205

Chapter 14: Pythagorean Theorem Revisited 213

Learning Objectives 213

Definitions 213

Pythagorean Theorem 214

Rectangular Boxes 214

Euler Bricks 216

Assessment Problems 219

Chapter 15: Sequences 221

Learning Objectives 221

Definitions 221

Introduce a Geometric Progression 222

Chapter 16: Pigeonhole Principle 227

Learning Objectives 227

Definitions 227

Chapter 17: Viviani’s Theorems 235

Learning Objectives 235

Definition 235

Chapter 18: Dissection Time 239

Learning Objectives 239

Definitions 239

Chapter 19: Pascal’s Triangle 245

Learning Objective 245

Summary 249

Chapter 20: Nice Numbers 255

Learning Objectives 255

Definitions 255

Index 259