BOOK
Elementary and Middle School Mathematics: Teaching Developmentally, Global Edition
John A. Van de Walle | Karen S. Karp | Jennifer M. Bay-Williams
(2016)
Additional Information
Book Details
Abstract
For use in Elementary Mathematics Methods or Middle School Mathematics Methods courses (covers Pre-K-8)
Guide teachers to help all Pre-K-8 learners make sense of math
Written by leaders in the field, Elementary and Middle School Mathematics: Teaching Developmentally helps teacher candidates develop a real understanding of the mathematics they will teach and the most effective methods of teaching Pre-K-8 math topics. This text reflects the Common Core State Standards and NCTM’s Principles to Actions, as well as current research. Emphasis is placed on teaching math conceptually, in a problem-based, developmentally appropriate manner that supports the learning needs of all students. Pause and Reflect prompts and Activities engage pre-service teachers as they bolster their own knowledge of the math. Classroom videos and examples of real student work allow teacher candidates to visualize good mathematics instruction and assessment. An important reference to consult throughout a teaching career, this book helps teachers and their students experience the excitement that happens when math makes sense.
Invigorate learning with the Enhanced Pearson eText
The Enhanced Pearson eText provides a rich, interactive learning environment designed to improve student mastery of content with embedded video, assessments, and clickable Activity Sheets and Blackline Masters. The Enhanced Pearson eText is also available without a print version of the textbook.
Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Cover | Cover | ||
| Title Page | 1 | ||
| Copyright Page | 2 | ||
| About the Authors | 3 | ||
| Contents | 7 | ||
| Preface | 15 | ||
| SECTION I: Teaching Mathematics: Foundations and Perspectives | 25 | ||
| CHAPTER 1 Teaching Mathematics in the 21st Century | 25 | ||
| Becoming an Effective Teacher of Mathematics | 25 | ||
| A Changing World | 26 | ||
| Factors to Consider | 27 | ||
| The Movement toward Shared Standards | 28 | ||
| Principles and Standards for School Mathematics | 29 | ||
| Common Core State Standards | 30 | ||
| Principles to Actions | 33 | ||
| An Invitation to Learn and Grow | 34 | ||
| Becoming a Teacher of Mathematics | 34 | ||
| Reflections on Chapter 1 | 36 | ||
| Writing to Learn | 36 | ||
| For Discussion and Exploration | 36 | ||
| Resources for Chapter 1 | 36 | ||
| Recommended Readings | 36 | ||
| CHAPTER 2 Exploring What it Means to Know and Do Mathematics | 37 | ||
| What Does It Mean to Do Mathematics? | 37 | ||
| Verbs of Doing Mathematics | 38 | ||
| An Invitation to Do Mathematics | 39 | ||
| Searching for Patterns | 39 | ||
| Analyzing a Situation | 40 | ||
| Generalizing Relationships | 41 | ||
| Experimenting and Explaining | 42 | ||
| Where Are the Answers? | 44 | ||
| What Does It Mean to Be Mathematically Proficient? | 44 | ||
| Relational Understanding | 45 | ||
| Mathematical Proficiency | 47 | ||
| How Do Students Learn Mathematics? | 50 | ||
| Constructivism | 50 | ||
| Sociocultural Theory | 51 | ||
| Implications for Teaching Mathematics | 51 | ||
| Connecting the Dots | 54 | ||
| Reflections on Chapter 2 | 55 | ||
| Writing to Learn | 55 | ||
| For Discussion and Exploration | 55 | ||
| Resources for Chapter 2 | 56 | ||
| Recommended Readings | 56 | ||
| CHAPTER 3 Teaching through Problem Solving | 57 | ||
| Problem Solving | 57 | ||
| Teaching for Problem Solving | 58 | ||
| Teaching about Problem Solving | 58 | ||
| Teaching through Problem Solving | 61 | ||
| Features of Worthwhile Tasks | 61 | ||
| High Levels of Cognitive Demand | 62 | ||
| Multiple Entry and Exit Points | 62 | ||
| Relevant Contexts | 65 | ||
| Evaluating and Adapting Tasks | 67 | ||
| Developing Concepts and Procedures through Tasks | 68 | ||
| Concepts | 68 | ||
| Procedures | 69 | ||
| What about Drill and Practice? | 71 | ||
| Orchestrating Classroom Discourse | 73 | ||
| Classroom Discussions | 73 | ||
| Questioning Considerations | 75 | ||
| How Much to Tell and Not to Tell | 76 | ||
| Writing to Learn | 77 | ||
| Problem Solving for All | 78 | ||
| Reflections on Chapter 3 | 80 | ||
| Writing to Learn | 80 | ||
| For Discussion and Exploration | 80 | ||
| Resources for Chapter 3 | 80 | ||
| Recommended Readings | 80 | ||
| CHAPTER 4 Planning in the Problem-Based Classroom | 81 | ||
| A Three-Phase Lesson Format | 81 | ||
| The Before Phase of a Lesson | 82 | ||
| The During Phase of a Lesson | 85 | ||
| The After Phase of a Lesson | 87 | ||
| Process for Preparing a Lesson | 89 | ||
| Step 1: Determine the Learning Goals | 90 | ||
| Step 2: Consider Your Students’ Needs | 90 | ||
| Step 3: Select, Design, or Adapt a Worthwhile Task | 91 | ||
| Step 4: Design Lesson Assessments | 91 | ||
| Step 5: Plan the Before Phase of the Lesson | 92 | ||
| Step 6: Plan the During Phase of the Lesson | 93 | ||
| Step 7: Plan the After Phase of the Lesson | 93 | ||
| Step 8: Reflect and Refine | 93 | ||
| More Options for the Three-Phase Lesson | 94 | ||
| Short Tasks | 94 | ||
| Learning Centers | 95 | ||
| Differentiating Instruction | 96 | ||
| Open Questions | 96 | ||
| Tiered Lessons | 97 | ||
| Parallel Tasks | 99 | ||
| Flexible Grouping | 99 | ||
| Planning for Family Engagement | 101 | ||
| Communicating Mathematics Goals | 101 | ||
| Family Math Nights | 102 | ||
| Homework Practices | 104 | ||
| Resources for Families | 105 | ||
| Involving All Families | 106 | ||
| Reflections on Chapter 4 | 107 | ||
| Writing to Learn | 107 | ||
| For Discussion and Exploration | 107 | ||
| Resources for Chapter 4 | 107 | ||
| Recommended Readings | 107 | ||
| CHAPTER 5 Creating Assessments for Learning | 108 | ||
| Integrating Assessment into Instruction | 108 | ||
| What Is Assessment? | 109 | ||
| What Should Be Assessed? | 110 | ||
| Assessment Methods | 111 | ||
| Observations | 111 | ||
| Interviews | 113 | ||
| Tasks | 116 | ||
| Rubrics and Their Uses | 119 | ||
| Generic Rubrics | 120 | ||
| Task-Specific Rubrics | 121 | ||
| Writing as an Assessment Tool | 122 | ||
| Student Self-Assessment | 123 | ||
| Tests | 124 | ||
| Improving Performance on High-Stakes Tests | 125 | ||
| Communicating Grades and Shaping Instruction | 125 | ||
| Reflections on Chapter 5 | 126 | ||
| Writing to Learn | 126 | ||
| For Discussion and Exploration | 126 | ||
| Resources for Chapter 5 | 127 | ||
| Recommended Readings | 127 | ||
| CHAPTER 6 Teaching Mathematics Equitably to All Children | 128 | ||
| Mathematics for ALL Students | 128 | ||
| Providing for Students Who Struggle and Those with Special Needs | 130 | ||
| Prevention Models | 130 | ||
| Implementing Interventions | 131 | ||
| Teaching and Assessing Students with Learning Disabilities | 135 | ||
| Teaching Students with Moderate/Severe Disabilities | 137 | ||
| Culturally and Linguistically Diverse Students | 138 | ||
| Culturally Responsive Instruction | 139 | ||
| Focus on Academic Vocabulary | 140 | ||
| Facilitating Engagement during Instruction | 143 | ||
| Implementing Strategies for English Language Learners | 144 | ||
| Providing for Students Who Are Mathematically Gifted | 145 | ||
| Creating Gender-Friendly Mathematics Classrooms | 147 | ||
| Gender Differences | 147 | ||
| What Can You Try? | 148 | ||
| Reducing Resistance and Building Resilience | 149 | ||
| Reflections on Chapter 6 | 150 | ||
| Writing to Learn | 150 | ||
| For Discussion and Exploration | 150 | ||
| Resources for Chapter 6 | 150 | ||
| Recommended Readings | 150 | ||
| CHAPTER 7 Using Technological Tools to Teach Mathematics | 151 | ||
| Tools and Technology | 151 | ||
| Technology-Supported Learning Activities | 152 | ||
| Calculators in Mathematics Instruction | 154 | ||
| When to Use a Calculator | 155 | ||
| Benefits of Calculator Use | 155 | ||
| Graphing Calculators | 156 | ||
| Portable Data-Collection Devices | 158 | ||
| Appropriate and Strategic Use of Digital Tools | 158 | ||
| Concept Instruction | 159 | ||
| Problem Solving | 159 | ||
| Drill and Reinforcement | 159 | ||
| Guidelines for Selecting and Using Digital Resources for Mathematics | 160 | ||
| Guidelines for Using Digital Content | 160 | ||
| How to Select Appropriate Digital Content | 160 | ||
| Mathematics Resources on the Internet | 162 | ||
| How to Select Online Resources | 162 | ||
| Emerging Technologies | 162 | ||
| Reflections on Chapter 7 | 165 | ||
| Writing to Learn | 165 | ||
| For Discussion and Exploration | 165 | ||
| Resources for Chapter 7 | 165 | ||
| Recommended Readings | 165 | ||
| SECTION II: Development of Mathematical Concepts and Procedures | 166 | ||
| CHAPTER 8 Developing Early Number Concepts and Number Sense | 166 | ||
| Promoting Good Beginnings | 167 | ||
| The Number Core: Quantity, Counting, and Knowing How Many | 168 | ||
| Quantity and the Ability to Subitize | 168 | ||
| Early Counting | 169 | ||
| Numeral Writing and Recognition | 172 | ||
| Counting On and Counting Back | 173 | ||
| The Relations Core: More Than, Less Than, and Equal To | 174 | ||
| Developing Number Sense by Building Number Relationships | 176 | ||
| Relationships between Numbers 1 through 10 | 176 | ||
| Relationships for Numbers 10 through 20 and Beyond | 184 | ||
| Number Sense in Their World | 186 | ||
| Calendar Activities | 186 | ||
| Estimation and Measurement | 187 | ||
| Data Collection and Analysis | 188 | ||
| Reflections on Chapter 8 | 189 | ||
| Writing to Learn | 189 | ||
| For Discussion and Exploration | 189 | ||
| Resources for Chapter 8 | 189 | ||
| Literature Connections | 189 | ||
| Recommended Readings | 189 | ||
| CHAPTER 9 Developing Meanings for the Operations | 191 | ||
| Teaching Operations through Contextual Problems | 192 | ||
| Addition and Subtraction Problem Structures | 192 | ||
| Change Problems | 193 | ||
| Part-Part-Whole Problems | 194 | ||
| Compare Problems | 194 | ||
| Problem Difficulty | 195 | ||
| Teaching Addition and Subtraction | 196 | ||
| Contextual Problems | 196 | ||
| Model-Based Problems | 198 | ||
| Properties of Addition and Subtraction | 201 | ||
| Multiplication and Division Problem Structure | 203 | ||
| Equal-Group Problems | 203 | ||
| Comparison Problems | 203 | ||
| Area and Array Problems | 205 | ||
| Combination Problems | 205 | ||
| Teaching Multiplication and Division | 205 | ||
| Contextual Problems | 206 | ||
| Remainders | 207 | ||
| Model-Based Problems | 207 | ||
| Properties of Multiplication and Division | 210 | ||
| Strategies for Solving Contextual Problems | 212 | ||
| Analyzing Context Problems | 212 | ||
| Multistep Problems | 214 | ||
| Reflections on Chapter 9 | 216 | ||
| Writing to Learn | 216 | ||
| For Discussion and Exploration | 216 | ||
| Resources for Chapter 9 | 216 | ||
| Literature Connections | 216 | ||
| Recommended Readings | 216 | ||
| CHAPTER 10 Developing Basic Fact Fluency | 218 | ||
| Developmental Phases for Learning the Basic Facts | 219 | ||
| Teaching and Assessing the Basic Facts | 220 | ||
| Different Approaches to Teaching the Basic Facts | 220 | ||
| Teaching Basic Facts Effectively | 221 | ||
| Assessing Basic Facts Effectively | 222 | ||
| Reasoning Strategies for Addition Facts | 223 | ||
| One More Than and Two More Than | 224 | ||
| Adding Zero | 225 | ||
| Doubles | 226 | ||
| Combinations of 10 | 227 | ||
| Making 10 | 227 | ||
| Using 5 as an Anchor | 228 | ||
| Near-Doubles | 228 | ||
| Reasoning Strategies for Subtraction Facts | 230 | ||
| Think-Addition | 230 | ||
| Down Under 10 | 231 | ||
| Take from 10 | 231 | ||
| Reasoning Strategies for Multiplication and Division Facts | 232 | ||
| Foundational Facts: 2, 5, 0, 1 | 232 | ||
| Nifty Nines | 234 | ||
| Derived Multiplication Fact Strategies | 235 | ||
| Division Facts | 237 | ||
| Reinforcing Basic Fact Mastery | 238 | ||
| Games to Support Basic Fact Fluency | 238 | ||
| About Drill | 241 | ||
| Fact Remediation | 242 | ||
| Reflections on Chapter 10 | 245 | ||
| Writing to Learn | 245 | ||
| For Discussion and Exploration | 245 | ||
| Resources for Chapter 10 | 245 | ||
| Literature Connections | 245 | ||
| Recommended Readings | 245 | ||
| CHAPTER 11 Developing Whole-number Place-Value Concepts | 246 | ||
| Pre-Place-Value Understandings | 247 | ||
| Developing Whole-Number Place-Value Concepts | 248 | ||
| Integrating Base-Ten Groupings with Counting by Ones | 248 | ||
| Integrating Base-Ten Groupings with Words | 249 | ||
| Integrating Base-Ten Groupings with Place-Value Notation | 249 | ||
| Base-Ten Models for Place Value | 250 | ||
| Groupable Models | 250 | ||
| Pregrouped Models | 251 | ||
| Nonproportional Models | 252 | ||
| Developing Base-Ten Concepts | 252 | ||
| Grouping Activities | 252 | ||
| Grouping Tens to Make 100 | 255 | ||
| Equivalent Representations | 255 | ||
| Oral and Written Names for Numbers | 257 | ||
| Two-Digit Number Names | 257 | ||
| Three-Digit Number Names | 258 | ||
| Written Symbols | 259 | ||
| Patterns and Relationships with Multidigit Numbers | 261 | ||
| The Hundreds Chart | 261 | ||
| Relationships with Benchmark Numbers | 264 | ||
| Connections to Real-World Ideas | 265 | ||
| Numbers Beyond 1000 | 266 | ||
| Extending the Place-Value System | 266 | ||
| Conceptualizing Large Numbers | 267 | ||
| Reflections on Chapter 11 | 269 | ||
| Writing to Learn | 269 | ||
| For Discussion and Exploration | 269 | ||
| Resources for Chapter 11 | 270 | ||
| Literature Connections | 270 | ||
| Recommended Readings | 270 | ||
| CHAPTER 12 Developing Strategies for Addition and Subtraction Computation | 271 | ||
| Toward Computational Fluency | 272 | ||
| Connecting Addition and Subtraction to Place Value | 273 | ||
| Three Types of Computational Strategies | 278 | ||
| Direct Modeling | 278 | ||
| Invented Strategies | 279 | ||
| Standard Algorithms | 281 | ||
| Development of Invented Strategies | 282 | ||
| Creating a Supportive Environment | 283 | ||
| Models to Support Invented Strategies | 283 | ||
| Development of Invented Strategies for Addition and Subtraction | 285 | ||
| Single-Digit Numbers | 285 | ||
| Adding Two-Digit Numbers | 286 | ||
| Subtraction as “Think-Addition” | 288 | ||
| Take-Away Subtraction | 288 | ||
| Extensions and Challenges | 290 | ||
| Standard Algorithms for Addition and Subtraction | 291 | ||
| Standard Algorithm for Addition | 291 | ||
| Standard Algorithm for Subtraction | 293 | ||
| Introducing Computational Estimation | 294 | ||
| Understanding Computational Estimation | 294 | ||
| Suggestions for Teaching Computational Estimation | 295 | ||
| Computational Estimation Strategies | 296 | ||
| Front-End Methods | 296 | ||
| Rounding Methods | 296 | ||
| Compatible Numbers | 297 | ||
| Reflections on Chapter 12 | 299 | ||
| Writing to Learn | 299 | ||
| For Discussion and Exploration | 299 | ||
| Resources for Chapter 12 | 299 | ||
| Literature Connections | 299 | ||
| Recommended Readings | 300 | ||
| CHAPTER 13 Developing Strategies for Multiplication and Division Computation | 301 | ||
| Student-Invented Strategies for Multiplication | 302 | ||
| Useful Representations | 302 | ||
| Multiplication by a Single-Digit Multiplier | 303 | ||
| Multiplication of Multidigit Numbers | 304 | ||
| Standard Algorithms for Multiplication | 306 | ||
| Begin with Models | 306 | ||
| Develop the Written Record | 308 | ||
| Student-Invented Strategies for Division | 310 | ||
| Standard Algorithm for Division | 312 | ||
| Begin with Models | 312 | ||
| Develop the Written Record | 313 | ||
| Two-Digit Divisors | 315 | ||
| Computational Estimation in Multiplication and Division | 317 | ||
| Suggestions for Teaching Computational Estimation | 317 | ||
| Computational Estimation Strategies | 318 | ||
| Reflections on Chapter 13 | 322 | ||
| Writing to Learn | 322 | ||
| For Discussion and Exploration | 322 | ||
| Resources for Chapter 13 | 322 | ||
| Literature Connections | 322 | ||
| Recommended Readings | 322 | ||
| CHAPTER 14 Algebraic Thinking, Equations, and Functions | 323 | ||
| Strands of Algebraic Thinking | 324 | ||
| Structure in the Number System: Connecting Number and Algebra | 324 | ||
| Number Combinations | 324 | ||
| Place-Value Relationships | 325 | ||
| Algorithms | 336 | ||
| Structure in the Number System: Properties | 327 | ||
| Making Sense of Properties | 327 | ||
| Applying the Properties of Addition and Multiplication | 330 | ||
| Study of Patterns and Functions | 331 | ||
| Repeating Patterns | 332 | ||
| Growing Patterns | 334 | ||
| Relationships in Functions | 336 | ||
| Graphs of Functions | 337 | ||
| Describing Functions | 339 | ||
| Linear Functions | 340 | ||
| Meaningful Use of Symbols | 343 | ||
| Equal and Inequality Signs | 344 | ||
| The Meaning of Variables | 352 | ||
| Mathematical Modeling | 358 | ||
| Algebraic Thinking across the Curriculum | 359 | ||
| Geometry, Measurement and Algebra | 359 | ||
| Reflections on Chapter 14 | 361 | ||
| Writing to Learn | 361 | ||
| For Discussion and Exploration | 361 | ||
| Resources for Chapter 14 | 362 | ||
| Literature Connections | 362 | ||
| Recommended Readings | 362 | ||
| CHAPTER 15 Developing Fraction Concepts | 363 | ||
| Meanings of Fractions | 364 | ||
| Fraction Constructs | 364 | ||
| Why Fractions Are Difficult | 365 | ||
| Models for Fractions | 366 | ||
| Area Models | 367 | ||
| Length Models | 368 | ||
| Set Models | 369 | ||
| Fractional Parts | 370 | ||
| Fraction Size Is Relative | 371 | ||
| Partitioning | 371 | ||
| Sharing Tasks | 375 | ||
| Iterating | 377 | ||
| Fraction Notation | 380 | ||
| Equivalent Fractions | 382 | ||
| Conceptual Focus on Equivalence | 382 | ||
| Equivalent Fraction Models | 383 | ||
| Developing an Equivalent-Fraction Algorithm | 386 | ||
| Comparing Fractions | 389 | ||
| Comparing Fractions Using Number Sense | 389 | ||
| Using Equivalent Fractions to Compare | 391 | ||
| Estimating with Fractions | 391 | ||
| Teaching Considerations for Fraction Concepts | 392 | ||
| Reflections on Chapter 15 | 393 | ||
| Writing to Learn | 393 | ||
| For Discussion and Exploration | 393 | ||
| Resources for Chapter 15 | 394 | ||
| Literature Connections | 394 | ||
| Recommended Readings | 394 | ||
| CHAPTER 16 Developing Fraction Operations | 395 | ||
| Understanding Fraction Operations | 396 | ||
| A Problem-Based Number-Sense Approach | 396 | ||
| Addition and Subtraction | 398 | ||
| Contextual Examples and Invented Strategies | 398 | ||
| Models | 399 | ||
| Estimation and Informal Methods | 402 | ||
| Developing the Algorithms | 403 | ||
| Fractions Greater Than One | 405 | ||
| Addressing Misconceptions | 406 | ||
| Multiplication | 408 | ||
| Contextual Examples and Models | 408 | ||
| Estimation and Invented Strategies | 414 | ||
| Developing the Algorithms | 414 | ||
| Factors Greater Than One | 415 | ||
| Addressing Misconceptions | 415 | ||
| Division | 416 | ||
| Contextual Examples and Models | 417 | ||
| Answers That Are Not Whole Numbers | 421 | ||
| Estimation and Invented Strategies | 422 | ||
| Developing the Algorithms | 422 | ||
| Addressing Misconceptions | 424 | ||
| Reflections on Chapter 16 | 425 | ||
| Writing to Learn | 425 | ||
| For Discussion and Exploration | 425 | ||
| Resources for Chapter 16 | 426 | ||
| Literature Connections | 426 | ||
| Recommended Readings | 426 | ||
| CHAPTER 17 Developing Concepts of Decimals and Percents | 427 | ||
| Extending the Place-Value System | 428 | ||
| The 10-to-1 Relationship—Now in Two Directions! | 428 | ||
| The Role of the Decimal Point | 429 | ||
| Connecting Fractions and Decimals | 431 | ||
| Say Decimal Fractions Correctly | 431 | ||
| Use Visual Models for Decimal Fractions | 431 | ||
| Multiple Names and Formats | 433 | ||
| Developing Decimal Number Sense | 434 | ||
| Familiar Fractions Connected to Decimals | 435 | ||
| Comparing and Ordering Decimal Fractions | 438 | ||
| Density of Decimals | 439 | ||
| Computation with Decimals | 440 | ||
| Addition and Subtraction | 441 | ||
| Multiplication | 442 | ||
| Division | 445 | ||
| Introducing Percents | 446 | ||
| Physical Models and Terminology | 447 | ||
| Percent Problems in Context | 448 | ||
| Estimation | 450 | ||
| Reflections on Chapter 17 | 451 | ||
| Writing to Learn | 451 | ||
| For Discussion and Exploration | 451 | ||
| Resources for Chapter 17 | 451 | ||
| Literature Connections | 451 | ||
| Recommended Readings | 452 | ||
| CHAPTER 18 Ratios, Proportions, and Proportional Reasoning | 453 | ||
| Ratios | 454 | ||
| Types of Ratios | 454 | ||
| Ratios Compared to Fractions | 454 | ||
| Two Ways to Think about Ratio | 455 | ||
| Proportional Reasoning | 456 | ||
| Proportional and Nonproportional Situations | 457 | ||
| Additive and Multiplicative Comparisons in Story Problems | 459 | ||
| Covariation | 461 | ||
| Strategies for Solving Proportional Situations | 466 | ||
| Rates and Scaling Strategies | 467 | ||
| Ratio Tables | 469 | ||
| Tape or Strip Diagram | 470 | ||
| Double Number Line Diagrams | 472 | ||
| Percents | 472 | ||
| Equations | 473 | ||
| Teaching Proportional Reasoning | 474 | ||
| Reflections on Chapter 18 | 475 | ||
| Writing to Learn | 475 | ||
| For Discussion and Exploration | 475 | ||
| Resources for Chapter 18 | 475 | ||
| Literature Connections | 475 | ||
| Recommended Readings | 476 | ||
| CHAPTER 19 Developing Measurement Concepts | 477 | ||
| The Meaning and Process of Measuring | 478 | ||
| Concepts and Skills | 478 | ||
| Introducing Nonstandard Units | 480 | ||
| Introducing Standard Units | 480 | ||
| The Role of Estimation and Approximation | 482 | ||
| Length | 485 | ||
| Comparison Activities | 486 | ||
| Using Physical Models of Length Units | 487 | ||
| Conversion | 488 | ||
| Making and Using Rulers | 489 | ||
| Area | 491 | ||
| Comparison Activities | 491 | ||
| Using Physical Models of Area Units | 492 | ||
| The Relationship between Area and Perimeter | 494 | ||
| Developing Formulas for Area | 496 | ||
| Areas of Rectangles, Parallelograms, Triangles, and Trapezoids | 497 | ||
| Circumference and Area of Circles | 499 | ||
| Volume and Capacity | 500 | ||
| Comparison Activities | 500 | ||
| Using Physical Models of Volume and Capacity Units | 502 | ||
| Developing Formulas for Volumes of Common Solid Shapes | 503 | ||
| Weight and Mass | 504 | ||
| APPENDIX A: Standards for Mathematical Practice | A-1 | ||
| APPENDIX B: NCTM Mathematics Teaching Practices: from Principles to Actions | A-5 | ||
| APPENDIX C: Guide to Blackline Masters | A-7 | ||
| APPENDIX D: Activities at a Glance | A-13 | ||
| References | R-1 | ||
| Index | I-1 | ||
| A | I-1 | ||
| B | I-2 | ||
| C | I-3 | ||
| D | I-5 | ||
| E | I-6 | ||
| F | I-7 | ||
| G | I-9 | ||
| H | I-10 | ||
| I | I-11 | ||
| J | I-11 | ||
| K | I-11 | ||
| L | I-12 | ||
| M | I-12 | ||
| N | I-14 | ||
| O | I-15 | ||
| P | I-15 | ||
| Q | I-17 | ||
| R | I-17 | ||
| S | I-18 | ||
| T | I-20 | ||
| U | I-22 | ||
| V | I-22 | ||
| W | I-22 | ||
| X | I-23 | ||
| Z | I-23 | ||
| Credits | C-1 |