Eyes on Math: A Visual Approach to Teaching Math Concepts

Overview

This new book is an exciting follow-up to the authors' bestsellers on differentiated math instruction, Good Questions and More Good Questions. Eyes on Math is a unique teaching resource that provides engaging, full-color graphics and pictures with text showing teachers how to use each image to stimulate mathematical teaching conversations around key K-8 concepts. Teachers using the book can download the images for projection onto classroom white boards or screens. The questions and answers will help both students...

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Eyes on Math: A Visual Approach to Teaching Math Concepts

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Overview

This new book is an exciting follow-up to the authors' bestsellers on differentiated math instruction, Good Questions and More Good Questions. Eyes on Math is a unique teaching resource that provides engaging, full-color graphics and pictures with text showing teachers how to use each image to stimulate mathematical teaching conversations around key K-8 concepts. Teachers using the book can download the images for projection onto classroom white boards or screens. The questions and answers will help both students and teachers look more deeply and see the math behind the math!

For each of more than 120 visuals, the text identifies the key math concept and the Common Core State Standard being addressed and then provides teachers with:

Mathematical background and context.

Questions to use with students to lead the instructional conversation.

Expected answers and explanations of why each question is important.

Follow-up extensions to solidify and assess student understanding.

This book will be useful to a broad range of teachers who will find new ways to clarify concepts that students find difficult. It can be used as a resource to prepare teachers for the higher mathematical thinking requirements of the CCSS Mathematical Practices. It will also be an invaluable resource for teachers working with students with low reading ability, including English language learners and special education students.

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Product Details

  • ISBN-13: 9780807753910
  • Publisher: Teachers College Press
  • Publication date: 11/28/2012
  • Pages: 240
  • Sales rank: 239,734
  • Product dimensions: 6.90 (w) x 9.90 (h) x 0.60 (d)

Table of Contents

Preface vii

Acknowledgments ix

1 Background 1

Visualization in Math 1

Focusing on the Important Math 2

Building Mathematical Communication 3

2 Grades K-2 5

Counting Up by 1s 6

Counting Back by 1s 8

Counting Up by 2s 10

Counting Back by 2s 12

Counting Up by 5s 14

Counting Back by 5s 16

Counting Up by 10s 18

Counting Back by 10s 20

Comparing Numbers by Matching 22

Benchmark Numbers: All About 5 24

Benchmark Numbers: All About 10 26

Ordinal Numbers 28

Addition as Combining 30

Addition to Describe Part-Part-Whole Situations 32

Adding 0 and Adding 1 34

Addition: Commutativity 36

Addition: Changing Addends, But Not the Sum 38

Adding or Subtracting 10 40

Subtraction as Taking Away 42

Subtraction to Compare 44

Relating Addition and Subtraction 46

Naming Two-Digit Numbers 48

Naming Three-Digit Numbers 50

Place Value: Grouping in Tens 52

Place Value: Positions 54

Comparing Sizes of Numbers 56

Fractions: Halves 58

Fractions: Quarters 60

Measurement: Meaning of Length 62

Measurement: Effect of Unit Size 64

Measurement: Standard Units of Length 66

2-D Shapes Versus 3-D Shapes 68

Comparing 2-D Shapes 70

Comparing 3-D Shapes 72

Composing Shapes 74

Shape Puzzles 76

3 Grades 3-5 79

Multiplication: Equal Groups 80

Multiplication: Commutativity 82

Multiplication: The Distributive Principle 84

Multiplication: 2-Digit by 2-Digit 86

Division as Equal Groups or Sharing 88

Division: Remainders 90

Rounding Numbers 92

Place Value: Multiplying and Dividing by Powers of 10 94

Place Value: Renaming Numbers 96

Factors: What They Are 98

Factors: Come in Pairs 100

Fractions: Representing 102

Fractions: Equivalence 104

Fractions: Comparing 106

Fractions: Mixed Number/Improper Fraction Relationship 108

Fractions: Common Denominators 110

Adding Fractions 112

Multiplying Fractions 114

Fractions: Multiplying as Resizing 116

Fractions as Division 118

Decimals: Relating Hundredths to Tenths 120

Decimals: Equivalence 122

Decimals: Adding and Subtracting 124

Measurement: Time Intervals 126

Measurement: Area of Rectangles 128

Perimeter versus Area 130

Measurement Conversions 132

Graphs with Scales 134

Coordinate Grids 136

Classification of Shapes 138

Parallel and Perpendicular Lines 140

Lines of Symmetry 142

Patterns versus Non-patterns 144

Algebraic Thinking: Growing Additively 146

Algebraic Thinking: Shrinking Additively 148

Algebraic Thinking: Growing Multiplicatively 150

4 Grades 6-8 153

Common Factors 154

Common Multiples 156

Square Roots 158

Fraction Division 160

Ratios: Multiple Ratios Describe Any Situation 162

Equivalent Ratios 164

Equivalent Rates 166

Solving Rate Problems 168

Describing Percent 170

Uses of Integers 172

The Zero Principle 174

Subtraction of Integers as a Directed Distance 176

Multiplication and Division of Integers 178

Area of a Parallelogram 180

Area of a Triangle 182

The Pythagorean Theorem 184

Pi 186

How Measurements Are and Are Not Related 188

Mean 190

Variability 192

Sampling 194

Probability: What It Means 196

Unpredictability 198

Rotations, Reflections, and Translations 200

Scale Drawings 202

Dilatations 204

Angles with Parallel Lines 206

Equivalent Expressions 208

Equation as a Balance 210

Different Types of Equations 212

What Is Linear? 214

Role of the Slope in the Equation of a Line 216

Systems of Equations 218

Function Rules 220

Appendix: Connections Between Topics and Common Core Standards 223

References 225

Index 227

About the Authors 230

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