Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 5 (Paperback)

Introduction 1

Low-Floor, High-Ceiling Tasks 2

Youcubed Summer Camp 3

Memorization versus Conceptual Engagement 4

Mathematical Th inking, Reasoning, and Convincing 5

Big Ideas 9

Structure of the Book 10

Activities for Building Norms 17

Encouraging Good Group Work 17

Paper Folding: Learning to Reason, Convince, and Be a Skeptic 21

Big Idea 1: Thinking in Cubes 23

Visualize: Solids, Inside and Out 25

Play: City of Cubes 33

Investigate: A Box of Boxes 44

Big Idea 2: Estimating with Fractions 53

Visualize: Making Snowfl akes 55

Play: Fraction Blizzard 61

Investigate: Wondering with Fractions 67

Big Idea 3: Using Fraction Equivalence 81

Visualize: Picking Paintings Apart 83

Play: Make a Fake 94

Investigate: Squares with a Diff erence 101

Big Idea 4: Exploring the Coordinate Plane 115

Visualize: Getting around the Plane 118

Play: Ship Shape 124

Investigate: Table Patterns 133

Big Idea 5: Seeing and Connecting Patterns across

Representations 143

Visualize: Two-Pattern Tango 145

Play: Pattern Carnival 153

Investigate: Seeing Growth on a Graph 159

Big Idea 6: Understanding Fraction Multiplication Visually 169

Visualize: Fractions in a Pan 172

Play: Pieces and Parts 180

Investigate: Th e Sum of the Parts 187

Big Idea 7: What Does It Mean to Divide Fractions? 199

Visualize: Creating Cards 201

Play: Cuisenaire Trains 209

Investigate: Fraction Division Conundrum 217

Big Idea 8: Thinking in Powers of 10 223

Visualize: Th e Unit You 225

Play: Filling Small and Large 233

Investigate: Museum of the Very Large and Small 239

Big Idea 9: Using Numbers and Symbols Flexibly 247

Visualize: Seeing Expressions 250

Play: Inside Pascal’s Triangle 261

Investigate: Th e 1492 Problem 268

Appendix 279

Centimeter Dot Paper 280

Isometric Dot Paper 281

About the Authors 283

Acknowledgments 285

Index 287