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Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 8

Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 8

Authors
Publisher John Wiley & Sons Inc
Year 16/03/2020
Pages 272
Version paperback
Readership level Professional and scholarly
ISBN 9781119358749
Categories Teaching of a specific subject, Educational: Mathematics & numeracy
$39.99 (with VAT)
152.00 PLN / €33.37 / £29.02
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Book description

Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the eighth-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message-that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 8

Table of contents

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 x 4 and 5 x 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

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