Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 5

  • ID: 4411222
  • Book
  • 304 Pages
  • John Wiley and Sons Ltd
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Engage Your Students in Visual, Creative Explorations of the Big Ideas in Mathematics

The Mindset Mathematics series offers a unique, research–based visual approach to exploring the big ideas in mathematics, which is essential to future mathematics success. This hands–on resource is for any teacher who wants to engage their fifth grade students in reasoning and persisting through problems, and provides activities that will engage students′ interest and show them the many ways that mathematics is important in their lives.

During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message: Teachers want to incorporate more brain science into their mathematics instruction, but they need guidance in the techniques that work best to promote learning of mathematics concepts. In this much–needed volume, the authors clearly show what the big ideas are at this grade level, why they are important to know, and how students can best learn those big ideas.

Filled with engaging questions, open–ended tasks, and four–color visuals, Mindset Mathematics is designed to be flexible so that it can be used with any current curriculum. All of the activities and tasks include instructions for launching in the classroom, suggestions for facilitating dynamic discussions, and guidance for what to look for in student thinking as it develops.

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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

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Jo Boaler
Jen Munson
Cathy Williams
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