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About teaching mathematics : a K-8 resource / Marilyn Burns.

By: Material type: TextTextPublication details: Sausalito, California : Math Solutions, [2015]Edition: Fourth editionDescription: xxix, 506 pages ; illustrations (some color) ; 28 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 1935099329
  • 9781935099321
Subject(s):
Contents:
pt. 1 Starting Points -- Overview -- General Pedagogical Issues -- Starting Point 1 Getting Started: Connecting Content, Practices, and Instruction -- Starting Point 2 Uncovering the Curriculum -- Starting Point 3 You Can't Teach What You Don't Understand -- Starting Point 4 Helping Students Become Effective Math Learners -- Number and Operations: The Mathematical Cornerstone -- Starting Point 5 Reasoning: A Perspective on Arithmetic -- Starting Point 6 Why Do Students Make Common Arithmetic Errors? -- Starting Point 7 The Equal Sign: What It Really Means -- Starting Point 8 Word Problems: Developing Understanding of Arithmetic Operations -- From Arithmetic to Problem Solving -- Starting Point 9 From Word Problems to Problem Solving: A Broader View -- Starting Point 10 Tackling Problem-Solving Strategies and Issues -- Starting Point 11 Building Number Sense -- Starting Point 12 Developing Mental Math Skills -- Assessing Understanding and Skills -- Starting Point 13 Making Formative Assessment Integral to Instruction -- Starting Point 14 The Importance of Classroom Discussions -- Starting Point 15 Incorporating Writing into Math Instruction -- Starting Point 16 The Benefits of One-on-One Interviews -- Suggestions for Classroom Instruction -- Starting Point 17 Using Games in Math Class -- Starting Point 18 The Role of Manipulative Materials -- Starting Point 19 Strategies for Intervention Instruction -- Starting Point 20 Four Structures for Organizing and Managing Classroom Instruction -- Connecting to English Language Arts Instruction -- Starting Point 21 Building a Teaching Bridge from Reading to Math -- Starting Point 22 Teaching Math Vocabulary -- Starting Point 23 Using Children's Literature to Teach Math -- pt. 2 Problem-Solving Investigations -- Overview -- Planning Whole-Class Lessons with Problem-Solving Investigations -- A Three-Phase Structure for Planning Lessons -- Introducing -- Exploring -- Summarizing -- A Sample Lesson Using the Three-Phase Structure -- The Consecutive Sums Problem -- Planning Lessons Using the Three-Phase Structure Template -- Problem-Solving Investigations: Measurement -- Why Teach Measurement? -- Stages in Learning About Measurement -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- A Nonstandard Measuring Investigation (Body Ratios) -- Measuring with Standard Units (Introducing the Metric System) -- Additional Investigations for Whole-Class Lessons -- Round Things -- The Perimeter Stays the Same -- Independent Investigations -- Longer, Shorter, or About the Same -- Are You a Square? -- A Half-Size Me -- Index Card Portrait -- Statue of Liberty Measurements -- Practicing Measuring -- Writing a Measurement Story -- Foot Measuring #1: Foot Cutout -- Foot Measuring #2: Area and Perimeter -- Foot Measuring #3: Squaring Up -- Standing Broad Jumps -- Book Measuring -- Box Measuring -- Your Height in Money -- How Thick Is Paper? -- Wraparound -- How Long Is a Minute? -- Ratio with Cuisenaire Rods -- Yarn Shapes -- Perimeter with Cuisenaire Rods -- Double the Circumference -- The Area Stays the Same -- Problem-Solving Investigations: Data -- Why Teach Data? -- Stages in Learning About Data -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Spinner Experiments -- Graphing in the Classroom -- Additional Investigations for Whole-Class Lessons -- Junk Sorting -- Tiles in the Bag (Version 1) -- Tiles in the Bag (Version 2) -- Sampling Bean Populations -- The 1-2-3-4 Investigation -- Alphabetical Probability -- Independent Investigations -- Two-Person Spin -- Design Your Own Spinner -- Got a Match? -- Birthday Twins -- The Left-Handed Experiment -- The X-O Problem -- The Two-Dice Sum Game -- How Many Throws? -- How Many Ways? -- How Many Rolls to Get a 1? -- What's the Record? -- Fair Game -- Even and Odd Sums -- Tile Trading -- Shake and Peek -- Shake and Spill -- Two-Coin Toss -- The Game of Pig -- Fair Game -- Paper, Scissors, Rock -- The Popcorn Problem -- Problem-Solving Investigations: Geometry -- Why Teach Geometry? -- Stages in Learning About Geometry -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Pentominoes -- The Four-Triangle Problem -- Additional Investigations for Whole-Class Lessons -- Introductory Investigations with Pattern Blocks -- The Tangram Puzzle -- Investigations with Four Toothpicks -- Introductory Investigations with Geoboards -- Sorting Shapes on the Geoboard -- Independent Investigations -- No-Lift Letters -- Area and Perimeter -- Square Partitioning -- Penticubes -- The Banquet Table Problem -- Interior Regions -- Straight or Curved? -- Geometry Building -- Extending Metric Lengths to Volume and Capacity -- Pool Hall Math -- That's Just Half the Story -- More Geoboard Investigations -- Area on the Geoboard -- Geoboard Line Segments -- Areas of Four on the Geoboard -- Pick's Theorem -- Shape Construction on the Geoboard -- Geoboard Square Search -- Geoboard Triangle Search -- Square Up -- Mirror Cards -- The Fold-and-Cut Investigation -- Rotating Shapes -- Hexagon Fill-in Puzzle -- Hexiamonds -- Angles with Pattern Blocks and Hinged Mirrors -- Making Topless Boxes -- The Pentomino Game -- Pentomino One-Difference Loop -- Problem-Solving Investigations: Patterns and Algebraic Thinking -- Why Teach Patterns and Algebraic Thinking? -- Stages in Learning About Patterns and Algebraic Thinking -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Two of Everything -- Painting Towers -- Additional Investigations for Whole-Class Lessons or Independent Work -- Paper Folding -- Dot Connecting -- More Painting Towers -- Paper Tearing -- The Diagonal Problem -- Points Dividing a Line -- The Ice-Cream-Cone Problem -- Squares from Squares -- More Squares from Squares -- Rod Stamping -- More Rod Stamping -- A Row of Triangles -- A Row of Squares -- A Row of Hexagons -- A Row of Pentagons -- Interlocking Trains -- Toothpick Building -- The Handshake Problem -- Problem-Solving Investigations: Number and Operations -- Why Teach Number and Operations? -- Stages in Learning About Number and Operations -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Number Sums -- Palindromes -- Additional Investigations for Whole-Class Lessons -- Investigations with Raisins -- Coin Riddles -- The Border Problem -- The Game of Poison -- Decision Making -- Riddles with Tiles -- Independent Investigations -- Making Change -- How Many Sums? -- Change from a $10.00 Bill -- Multiplication Possibilities -- The Postage Stamp Investigation -- Arrow Arithmetic -- King Arthur's Problem -- The Prison Problem -- Race for 20 -- Number Bracelets -- The 0 -- 99 Chart -- Pascal's Triangle -- Addition Table Investigations -- Where Does 100 Land? -- On Which Day of the Week Were You Born? -- Sally and the Peanuts -- Number Sorting -- A Mathematical Tug-of-War -- Digit Place -- pt. 3 Teaching Arithmetic -- Overview -- Arithmetic: The Three-Legged Stool -- About the Three-Legged Stool -- Computation -- Problem Solving -- Number Sense -- Putting It All Together -- Teaching What to Do (Procedures) Versus Teaching What to Do and Why (Procedures and Understanding) -- Justifications for Teaching What to Do (Procedures) -- Justifications for Teaching What to Do and Why (Procedures and Understanding) -- The Role of Algorithms -- Teaching Arithmetic: Scenarios from the Classroom -- Scenario 1 Fourth Graders Solve 19 x 21 -- Scenario 2 Fifth Graders Solve 47 x 23 -- Scenario 3 A Study with Fourth, Fifth, and Sixth Graders -- Scenario 4 Third Graders Learn Division -- Scenario 5 Seventh and Eighth Graders Work with Percents -- Relating Arithmetic to Real Life -- A Real-Life Arithmetic Problem: The Thanksgiving Turkey -- A Real-Life Arithmetic Problem: Raising a Dog -- Other Examples of Real-Life Arithmetic Problems: Classroom or School Situations -- Beginning Number Concepts -- About Beginning Number Concepts -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- Creating Math Moments -- A Number Game: Red + Black -- A Number Game: Empty the Bowl -- Introducing Addition and Subtraction with Word Problems -- A Problem-Solving Lesson: Making Necklaces -- Using Children's Literature -- Additional Instructional Suggestions -- Build a Stack -- Snap It -- Grow and Shrink -- Yarn Shapes -- Trace and Compare -- Grab-Bag Subtraction -- Assessing Understanding of Beginning Number Concepts -- Observing Students -- Individual Assessments -- Place Value -- About Place Value -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- A Problem-Solving Lesson: How Many Fingers? -- A Problem-Solving Lesson: How Many Pockets? -- Additional Counting Investigations -- A Money Game: Race for $1.00 -- A Logic Game: Digit Place -- Patterns on the 0 -- 99 Chart -- Additional Instructional Suggestions -- Stars in 1 Minute -- Fill the Cube (Version 1) -- Number Puzzle -- Five-Tower Game -- Pinch a 10 -- Make a Shape -- Coloring 0 -- 99 Patterns -- Assessing Understanding of Place Value -- Observing Students -- Individual Assessments -- Addition and Subtraction -- About Addition and Subtraction -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction
Note continued: A Statistical Investigation: Name Graphs -- A Problem-Solving Lesson: How Much Ribbon? -- A Problem-Solving Lesson: How Big Is Your Hand? -- A Number Game: Roll 15 -- A Number Game: The Game of Pig -- Additional Instructional Suggestions -- How Old Is Ramona the Pest? -- Estimate and Measure -- In 1 Minute -- Billy Goes Shopping -- Covering Covers -- Fill the Cube (Version 2) -- 101 and Out -- Cross Out Singles -- Assessing Understanding of Addition and Subtraction -- Observing Students -- Individual Assessments -- Introducing Multiplication -- About Introducing Multiplication -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- A Problem-Solving Lesson: The Chopstick Problem -- A Problem-Solving Lesson: Things That Come in Groups -- A Problem-Solving Lesson: Candy Boxes -- A Multiplication Game: Circles and Stars -- Additional Instructional Suggestions -- Patterns in Multiples -- Billy Wins a Shopping Spree -- Calculator Patterns -- Multiplication Stories -- Times Table Plaids -- How Many Were Eaten? -- How Long? How Many? -- The Factor Game -- Assessing Understanding of Multiplication -- Observing Students -- Individual Assessments -- Introducing Division -- About Introducing Division -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- A Problem-Solving Lesson: Division Sharing Problems -- A Problem-Solving Lesson: Division Grouping Problems -- A Problem-Solving Lesson: The Doorbell Rang -- A Division Game: Leftovers -- Additional Instructional Suggestions -- Leftovers with 20 -- Division Stories -- The Kings-and-Elephants Problem -- Chocolate Bars -- Assessing Understanding of Division -- Observing Students -- Individual Assessments -- Extending Multiplication and Division -- About Extending Multiplication and Division -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- Multiplying by Ten and Powers of Ten -- Using the Distributive Property -- A Problem-Solving Lesson: Beans and Scoops -- Multiplication and Division Through Real-World Problems -- A Multiplication Game: Hit the Target (Version 1) -- A Division Game: Leftovers from 100 -- Additional Instructional Suggestions -- The Greatest Product -- Leftovers Revisited -- Remainders of Zero -- Factor Fiddling -- Hit the Target (Version 2) -- Assessing Understanding of Multiplication and Division with Large Numbers -- Observing Students -- Individual Assessments -- Fractions -- About Fractions -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- Introducing Fractions in Real-World Contexts -- Fractions with Two-Color Counters -- The Fraction Kit -- A Fraction Game: Cover Up -- A Fraction Game: Uncover -- Completing Fraction Equations -- Using Graphs to Build Understanding of Fractions -- A Problem-Solving Lesson: Sharing Cookies -- A Problem-Solving Lesson: Sharing Brownies -- A Fraction Investigation: Put in Order -- Mental Calculation with Fractions -- Additional Instructional Suggestions -- Fractions Close to 1/2 -- Building Rectangles -- Fraction Riddles -- Rod Relationships -- Build the Yellow Hexagon -- Wipeout -- Assessing Understanding of Fractions -- Observing Students -- Individual Assessments -- Decimals -- About Decimals -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- A Problem-Solving Lesson: Sharing Cookie Problems to Introduce Decimals -- A Problem-Solving Lesson: Decimals on Grids -- Mental Calculation with Decimals -- Additional Instructional Suggestions -- Decimals in the Newspaper -- Multiplication Puzzlers -- Adding to 1 -- The Place-Value Game -- Assessing Understanding of Decimals -- Observing Students -- Individual Assessments -- Percents -- About Percents -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- A Problem-Solving Lesson: Sense or Nonsense -- A Problem-Solving Lesson: What Percent Is Shaded? -- Using Graphs to Build Understanding of Percents -- Mental Calculation with Percents -- Additional Instructional Suggestions -- Percents in the Newspaper -- Figuring Tips in Restaurants -- Comparing Advertisements -- The Photocopy Problem -- Block Letters -- The Discount Coupon -- The Warehouse Problem -- Percent Stories -- Assessing Understanding of Percents -- Observing Students -- Individual Assessments -- pt. 4 Questions Teachers Ask -- Overview -- 0 -- 99 Chart versus 1 -- 100 Chart -- Addition -- Algorithms and Basic Facts -- Changing Instruction -- Decimals -- Connecting Decimals and Fractions -- Long Division -- Using Fingers for Computing -- Formative Assessment in the Classroom -- Homework -- The Language of Math -- Math Centers -- Math Portfolios -- Meeting the Needs of All Students -- Money -- Learning Multiplication and Division Facts -- Interpreting Multiplication -- Multidigit Multiplication -- Order of Operations -- Patterns -- Patterns and Addition -- Patterns in Multiples -- Rounding -- Supporting Small-Group Work -- Subtraction -- Test Prep -- Timed Tests -- Multiplication and Division Word Problems.
Summary: In this fourth edition of her signature resource, Marilyn presents her current thinking and insights and includes ideas from her most recent teaching experiences. Part 1, Starting Points, reflects the major overhaul of this book and addresses twenty-three issues important to thinking about teaching mathematics today. Part 2, Problem-Solving Investigations, opens with how to plan problem-solving lessons; followed by whole-class, small-group, and individual investigations organized into five areas of the curriculum: Measurement, Data, Geometry, Patterns and Algebraic Thinking, and Number and Operations. Part 3, Teaching Arithmetic, focuses on the cornerstone of elementary mathematics curriculum, offering ideas and assessments that build students understanding, confidence, and competence in arithmetic. In Part 4, Questions Teachers Ask, features Marilyn's responses to pedagogical questions she's received from teachers over the years.
Holdings
Item type Home library Collection Call number Materials specified Status Date due Barcode Item holds
Children's Book Children's Book Main Library Parent/Teacher Resource Collection-Children's 372.7 B967 Available 33111009176468
Total holds: 0

Enhanced descriptions from Syndetics:

In this fourth edition of her signature resource, Marilyn presents her current thinking and insights and includes ideas from her most recent teaching experiences.

Part 1, "Starting Points," reflects the major overhaul of this book and addresses twenty-three issues important to thinking about teaching mathematics today.

Part 2, "Problem-Solving Investigations," opens with how to plan problem-solving lessons; followed by whole-class, small-group, and individual investigations organized into five areas of the curriculum: Measurement, Data, Geometry, Patterns and Algebraic Thinking, and Number and Operations.

Part 3, "Teaching Arithmetic," focuses on the cornerstone of elementary mathematics curriculum, offering ideas and assessments that build students' understanding, confidence, and competence in arithmetic.

In Part 4, "Questions Teachers Ask," features Marilyn's responses to pedagogical questions she's received from teachers over the years.

More than forty reproducibles for About Teaching Mathematics are available to download in a printable format.

Includes bibliographical references (pages 497-498) and index.

In this fourth edition of her signature resource, Marilyn presents her current thinking and insights and includes ideas from her most recent teaching experiences. Part 1, Starting Points, reflects the major overhaul of this book and addresses twenty-three issues important to thinking about teaching mathematics today. Part 2, Problem-Solving Investigations, opens with how to plan problem-solving lessons; followed by whole-class, small-group, and individual investigations organized into five areas of the curriculum: Measurement, Data, Geometry, Patterns and Algebraic Thinking, and Number and Operations. Part 3, Teaching Arithmetic, focuses on the cornerstone of elementary mathematics curriculum, offering ideas and assessments that build students understanding, confidence, and competence in arithmetic. In Part 4, Questions Teachers Ask, features Marilyn's responses to pedagogical questions she's received from teachers over the years.

pt. 1 Starting Points -- Overview -- General Pedagogical Issues -- Starting Point 1 Getting Started: Connecting Content, Practices, and Instruction -- Starting Point 2 Uncovering the Curriculum -- Starting Point 3 You Can't Teach What You Don't Understand -- Starting Point 4 Helping Students Become Effective Math Learners -- Number and Operations: The Mathematical Cornerstone -- Starting Point 5 Reasoning: A Perspective on Arithmetic -- Starting Point 6 Why Do Students Make Common Arithmetic Errors? -- Starting Point 7 The Equal Sign: What It Really Means -- Starting Point 8 Word Problems: Developing Understanding of Arithmetic Operations -- From Arithmetic to Problem Solving -- Starting Point 9 From Word Problems to Problem Solving: A Broader View -- Starting Point 10 Tackling Problem-Solving Strategies and Issues -- Starting Point 11 Building Number Sense -- Starting Point 12 Developing Mental Math Skills -- Assessing Understanding and Skills -- Starting Point 13 Making Formative Assessment Integral to Instruction -- Starting Point 14 The Importance of Classroom Discussions -- Starting Point 15 Incorporating Writing into Math Instruction -- Starting Point 16 The Benefits of One-on-One Interviews -- Suggestions for Classroom Instruction -- Starting Point 17 Using Games in Math Class -- Starting Point 18 The Role of Manipulative Materials -- Starting Point 19 Strategies for Intervention Instruction -- Starting Point 20 Four Structures for Organizing and Managing Classroom Instruction -- Connecting to English Language Arts Instruction -- Starting Point 21 Building a Teaching Bridge from Reading to Math -- Starting Point 22 Teaching Math Vocabulary -- Starting Point 23 Using Children's Literature to Teach Math -- pt. 2 Problem-Solving Investigations -- Overview -- Planning Whole-Class Lessons with Problem-Solving Investigations -- A Three-Phase Structure for Planning Lessons -- Introducing -- Exploring -- Summarizing -- A Sample Lesson Using the Three-Phase Structure -- The Consecutive Sums Problem -- Planning Lessons Using the Three-Phase Structure Template -- Problem-Solving Investigations: Measurement -- Why Teach Measurement? -- Stages in Learning About Measurement -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- A Nonstandard Measuring Investigation (Body Ratios) -- Measuring with Standard Units (Introducing the Metric System) -- Additional Investigations for Whole-Class Lessons -- Round Things -- The Perimeter Stays the Same -- Independent Investigations -- Longer, Shorter, or About the Same -- Are You a Square? -- A Half-Size Me -- Index Card Portrait -- Statue of Liberty Measurements -- Practicing Measuring -- Writing a Measurement Story -- Foot Measuring #1: Foot Cutout -- Foot Measuring #2: Area and Perimeter -- Foot Measuring #3: Squaring Up -- Standing Broad Jumps -- Book Measuring -- Box Measuring -- Your Height in Money -- How Thick Is Paper? -- Wraparound -- How Long Is a Minute? -- Ratio with Cuisenaire Rods -- Yarn Shapes -- Perimeter with Cuisenaire Rods -- Double the Circumference -- The Area Stays the Same -- Problem-Solving Investigations: Data -- Why Teach Data? -- Stages in Learning About Data -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Spinner Experiments -- Graphing in the Classroom -- Additional Investigations for Whole-Class Lessons -- Junk Sorting -- Tiles in the Bag (Version 1) -- Tiles in the Bag (Version 2) -- Sampling Bean Populations -- The 1-2-3-4 Investigation -- Alphabetical Probability -- Independent Investigations -- Two-Person Spin -- Design Your Own Spinner -- Got a Match? -- Birthday Twins -- The Left-Handed Experiment -- The X-O Problem -- The Two-Dice Sum Game -- How Many Throws? -- How Many Ways? -- How Many Rolls to Get a 1? -- What's the Record? -- Fair Game -- Even and Odd Sums -- Tile Trading -- Shake and Peek -- Shake and Spill -- Two-Coin Toss -- The Game of Pig -- Fair Game -- Paper, Scissors, Rock -- The Popcorn Problem -- Problem-Solving Investigations: Geometry -- Why Teach Geometry? -- Stages in Learning About Geometry -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Pentominoes -- The Four-Triangle Problem -- Additional Investigations for Whole-Class Lessons -- Introductory Investigations with Pattern Blocks -- The Tangram Puzzle -- Investigations with Four Toothpicks -- Introductory Investigations with Geoboards -- Sorting Shapes on the Geoboard -- Independent Investigations -- No-Lift Letters -- Area and Perimeter -- Square Partitioning -- Penticubes -- The Banquet Table Problem -- Interior Regions -- Straight or Curved? -- Geometry Building -- Extending Metric Lengths to Volume and Capacity -- Pool Hall Math -- That's Just Half the Story -- More Geoboard Investigations -- Area on the Geoboard -- Geoboard Line Segments -- Areas of Four on the Geoboard -- Pick's Theorem -- Shape Construction on the Geoboard -- Geoboard Square Search -- Geoboard Triangle Search -- Square Up -- Mirror Cards -- The Fold-and-Cut Investigation -- Rotating Shapes -- Hexagon Fill-in Puzzle -- Hexiamonds -- Angles with Pattern Blocks and Hinged Mirrors -- Making Topless Boxes -- The Pentomino Game -- Pentomino One-Difference Loop -- Problem-Solving Investigations: Patterns and Algebraic Thinking -- Why Teach Patterns and Algebraic Thinking? -- Stages in Learning About Patterns and Algebraic Thinking -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Two of Everything -- Painting Towers -- Additional Investigations for Whole-Class Lessons or Independent Work -- Paper Folding -- Dot Connecting -- More Painting Towers -- Paper Tearing -- The Diagonal Problem -- Points Dividing a Line -- The Ice-Cream-Cone Problem -- Squares from Squares -- More Squares from Squares -- Rod Stamping -- More Rod Stamping -- A Row of Triangles -- A Row of Squares -- A Row of Hexagons -- A Row of Pentagons -- Interlocking Trains -- Toothpick Building -- The Handshake Problem -- Problem-Solving Investigations: Number and Operations -- Why Teach Number and Operations? -- Stages in Learning About Number and Operations -- Mathematical Practices -- Mathematical Content -- Sample Whole-Class Lessons -- Number Sums -- Palindromes -- Additional Investigations for Whole-Class Lessons -- Investigations with Raisins -- Coin Riddles -- The Border Problem -- The Game of Poison -- Decision Making -- Riddles with Tiles -- Independent Investigations -- Making Change -- How Many Sums? -- Change from a $10.00 Bill -- Multiplication Possibilities -- The Postage Stamp Investigation -- Arrow Arithmetic -- King Arthur's Problem -- The Prison Problem -- Race for 20 -- Number Bracelets -- The 0 -- 99 Chart -- Pascal's Triangle -- Addition Table Investigations -- Where Does 100 Land? -- On Which Day of the Week Were You Born? -- Sally and the Peanuts -- Number Sorting -- A Mathematical Tug-of-War -- Digit Place -- pt. 3 Teaching Arithmetic -- Overview -- Arithmetic: The Three-Legged Stool -- About the Three-Legged Stool -- Computation -- Problem Solving -- Number Sense -- Putting It All Together -- Teaching What to Do (Procedures) Versus Teaching What to Do and Why (Procedures and Understanding) -- Justifications for Teaching What to Do (Procedures) -- Justifications for Teaching What to Do and Why (Procedures and Understanding) -- The Role of Algorithms -- Teaching Arithmetic: Scenarios from the Classroom -- Scenario 1 Fourth Graders Solve 19 x 21 -- Scenario 2 Fifth Graders Solve 47 x 23 -- Scenario 3 A Study with Fourth, Fifth, and Sixth Graders -- Scenario 4 Third Graders Learn Division -- Scenario 5 Seventh and Eighth Graders Work with Percents -- Relating Arithmetic to Real Life -- A Real-Life Arithmetic Problem: The Thanksgiving Turkey -- A Real-Life Arithmetic Problem: Raising a Dog -- Other Examples of Real-Life Arithmetic Problems: Classroom or School Situations -- Beginning Number Concepts -- About Beginning Number Concepts -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- Creating Math Moments -- A Number Game: Red + Black -- A Number Game: Empty the Bowl -- Introducing Addition and Subtraction with Word Problems -- A Problem-Solving Lesson: Making Necklaces -- Using Children's Literature -- Additional Instructional Suggestions -- Build a Stack -- Snap It -- Grow and Shrink -- Yarn Shapes -- Trace and Compare -- Grab-Bag Subtraction -- Assessing Understanding of Beginning Number Concepts -- Observing Students -- Individual Assessments -- Place Value -- About Place Value -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- A Problem-Solving Lesson: How Many Fingers? -- A Problem-Solving Lesson: How Many Pockets? -- Additional Counting Investigations -- A Money Game: Race for $1.00 -- A Logic Game: Digit Place -- Patterns on the 0 -- 99 Chart -- Additional Instructional Suggestions -- Stars in 1 Minute -- Fill the Cube (Version 1) -- Number Puzzle -- Five-Tower Game -- Pinch a 10 -- Make a Shape -- Coloring 0 -- 99 Patterns -- Assessing Understanding of Place Value -- Observing Students -- Individual Assessments -- Addition and Subtraction -- About Addition and Subtraction -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction

Note continued: A Statistical Investigation: Name Graphs -- A Problem-Solving Lesson: How Much Ribbon? -- A Problem-Solving Lesson: How Big Is Your Hand? -- A Number Game: Roll 15 -- A Number Game: The Game of Pig -- Additional Instructional Suggestions -- How Old Is Ramona the Pest? -- Estimate and Measure -- In 1 Minute -- Billy Goes Shopping -- Covering Covers -- Fill the Cube (Version 2) -- 101 and Out -- Cross Out Singles -- Assessing Understanding of Addition and Subtraction -- Observing Students -- Individual Assessments -- Introducing Multiplication -- About Introducing Multiplication -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- A Problem-Solving Lesson: The Chopstick Problem -- A Problem-Solving Lesson: Things That Come in Groups -- A Problem-Solving Lesson: Candy Boxes -- A Multiplication Game: Circles and Stars -- Additional Instructional Suggestions -- Patterns in Multiples -- Billy Wins a Shopping Spree -- Calculator Patterns -- Multiplication Stories -- Times Table Plaids -- How Many Were Eaten? -- How Long? How Many? -- The Factor Game -- Assessing Understanding of Multiplication -- Observing Students -- Individual Assessments -- Introducing Division -- About Introducing Division -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- A Problem-Solving Lesson: Division Sharing Problems -- A Problem-Solving Lesson: Division Grouping Problems -- A Problem-Solving Lesson: The Doorbell Rang -- A Division Game: Leftovers -- Additional Instructional Suggestions -- Leftovers with 20 -- Division Stories -- The Kings-and-Elephants Problem -- Chocolate Bars -- Assessing Understanding of Division -- Observing Students -- Individual Assessments -- Extending Multiplication and Division -- About Extending Multiplication and Division -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- Multiplying by Ten and Powers of Ten -- Using the Distributive Property -- A Problem-Solving Lesson: Beans and Scoops -- Multiplication and Division Through Real-World Problems -- A Multiplication Game: Hit the Target (Version 1) -- A Division Game: Leftovers from 100 -- Additional Instructional Suggestions -- The Greatest Product -- Leftovers Revisited -- Remainders of Zero -- Factor Fiddling -- Hit the Target (Version 2) -- Assessing Understanding of Multiplication and Division with Large Numbers -- Observing Students -- Individual Assessments -- Fractions -- About Fractions -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- Introducing Fractions in Real-World Contexts -- Fractions with Two-Color Counters -- The Fraction Kit -- A Fraction Game: Cover Up -- A Fraction Game: Uncover -- Completing Fraction Equations -- Using Graphs to Build Understanding of Fractions -- A Problem-Solving Lesson: Sharing Cookies -- A Problem-Solving Lesson: Sharing Brownies -- A Fraction Investigation: Put in Order -- Mental Calculation with Fractions -- Additional Instructional Suggestions -- Fractions Close to 1/2 -- Building Rectangles -- Fraction Riddles -- Rod Relationships -- Build the Yellow Hexagon -- Wipeout -- Assessing Understanding of Fractions -- Observing Students -- Individual Assessments -- Decimals -- About Decimals -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- A Problem-Solving Lesson: Sharing Cookie Problems to Introduce Decimals -- A Problem-Solving Lesson: Decimals on Grids -- Mental Calculation with Decimals -- Additional Instructional Suggestions -- Decimals in the Newspaper -- Multiplication Puzzlers -- Adding to 1 -- The Place-Value Game -- Assessing Understanding of Decimals -- Observing Students -- Individual Assessments -- Percents -- About Percents -- Mathematical Practices -- Mathematical Content -- Whole-Class Instruction -- A Problem-Solving Lesson: Sense or Nonsense -- A Problem-Solving Lesson: What Percent Is Shaded? -- Using Graphs to Build Understanding of Percents -- Mental Calculation with Percents -- Additional Instructional Suggestions -- Percents in the Newspaper -- Figuring Tips in Restaurants -- Comparing Advertisements -- The Photocopy Problem -- Block Letters -- The Discount Coupon -- The Warehouse Problem -- Percent Stories -- Assessing Understanding of Percents -- Observing Students -- Individual Assessments -- pt. 4 Questions Teachers Ask -- Overview -- 0 -- 99 Chart versus 1 -- 100 Chart -- Addition -- Algorithms and Basic Facts -- Changing Instruction -- Decimals -- Connecting Decimals and Fractions -- Long Division -- Using Fingers for Computing -- Formative Assessment in the Classroom -- Homework -- The Language of Math -- Math Centers -- Math Portfolios -- Meeting the Needs of All Students -- Money -- Learning Multiplication and Division Facts -- Interpreting Multiplication -- Multidigit Multiplication -- Order of Operations -- Patterns -- Patterns and Addition -- Patterns in Multiples -- Rounding -- Supporting Small-Group Work -- Subtraction -- Test Prep -- Timed Tests -- Multiplication and Division Word Problems.

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