Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 8 - Cathy Williams

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Résumé :

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 eighth 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....

Biographie:

Introduction 1

Low-Floor, High-Ceiling Tasks 2

Youcubed Summer Camp 3

Memorization versus Conceptual Engagement 4

Mathematical Thinking, Reasoning, and Convincing 5

Big Ideas 9

Structure of the Book 9

Note on Materials 17

Manipulatives and Materials Used in This Book 18

Activities for Building Norms 21

Encouraging Good Group Work 21

Paper Folding: Learning to Reason, Convince, and Be a Skeptic 22

Big Idea 1: Moving Shapes 27

Visualize: What Does It Mean to Be the Same? 29

Play: Pixel Puzzles 35

Investigate: Slide It, Flip It, Turn It 45

Big Idea 2: Zooming In and Out 53

Visualize: What is Similarity? 55

Play: Find the Fakes 60

Investigate: Growing on a Grid 65

Big Idea 3: Analyzing Proportional Relationships 71

Visualize: Dropping the Altitude 73

Play: Seeing Triangles under the Line 79

Investigate: Stairway to Eleven 85

Big Idea 4: Comparing Patterns of Growth 91

Visualize: Squared Squares 93

Play: Skip-Counting Arrays 100

Investigate: Stacking Pennies 107

Big Idea 5: The Ins and Outs of Functions 117

Visualize: Growing Functions 120

Play: Getting Warmer! 134

Investigate: The Functions of Near Squares 140

Big Idea 6: Finding Patterns in the Clouds 149

Visualize: What's Going On in This Graph? 151

Play: What's the Story Here? 158

Investigate: Creating Data Visualizations 166

Big Idea 7: Completing the Real Number System 177

Visualize: Square Sides 179

Play: Between 4 ? 4 and 5 ? 5 187

Investigate: The Hypotenuse Hypothesis 193

Big Idea 8: Discovering Pythagoras 201

Visualize: Unpacking Pythagoras 204

Play: Pythagorean Triples 209

Investigate: Approximating Square Roots 214

Big Idea 9: Exploring the Geometry of Ice Cream 221

Visualize: Building Intuition about Volume 223

Play: Comparing Cylinders 227

Investigate: Scooping Up Volume 233

Appendix 239

Centimeter Grid Paper 240

Grid Paper 241

Isometric Dot Paper 242

Dot Paper 243

About the Authors 245

Acknowledgments 247

Index 249