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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.
“This book provides a way for both teachers and students to get used to talking about mathematics in nonthreatening, open-ended ways. The author’s friendly explanations of the mathematical ideas the pictures are intended to surface give teachers who are less confident about the conceptual aspects of mathematics the support they need to facilitate less-scripted mathematical discourse with their students.”
—Lucy West, education consultant
“A must for any educator who is serious about reaching more students more often and achieving more positive results.”
—Resources for the Mathematics Educator
“A valuable book for mathematics teachers, teacher educators, and faculty involved in differentiated instruction.”
—Choice
“A great resource.”
—Mathematics Teaching in the Middle School
“I highly recommend this user-friendly resource for all mathematics teachers.”
—Teaching Children Mathematics
Product Details
| ISBN-13: | 9780807772362 |
|---|---|
| Publisher: | Teachers College Press |
| Publication date: | 08/19/2013 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| File size: | 8 MB |
About the Author
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
What People are Saying About This
“This book provides a way for both teachers and students to get used to talking about mathematics in nonthreatening, open-ended ways.”—Lucy West, education consultant