Mathematize It! [Grades K-2]

Publisher's Acknowledgements Table of Contents Video List About the Authors Introduction: Why You Need to Teach Students to Mathematize Problem Solving Strategies Gone Wrong What is Mathematizing? Why Is It Important Focus on Operation Sense Using Mathematical Representations Teaching Students to Mathematize Building your Understanding of Operations and Related Problem Situations Playing in the Mathematizing Sandbox: A Problem-Solving Model Final Words Before You Dive Chapter 2: Moving From Counting to Addition & Subtraction Thinking About Counting, Addition, and Subtraction Sandbox Notes: Explore Your Thinking Students and Teachers Think About the Problem The Development of Courting Counting or Add-To? Representing Problem Situations or Representing Answers Using Children's Literature to Explore add-To and Take From Situations Transcribe the Action or Relationship Moving beyond Twenty Students and Teachers Think About the Problems Representing Problem Situations Multiple Ways Translating the Five Relationships: Try It Out Teaching Students to Use Concrete and Pictorial Models Key Ideas Try It Out! Identify the Principle Write the Problem Change It Up Reflect Chapter 3: Add-To Problems: Locating the Change Thinking About Active Addition Situations Thinking About Active Addition Situations Sandbox Notes: Explore Your Thinking Students and Teachers Think About the Problems Finding the Unknown, Three Story Structures Story Structures: Implications for Teaching Modeling the Active Problem Situation Model Actions Distinguish Pictures from Pictorial Representation Identify Important Features Creatively Meet Students' Needs Using Children's Literature to Explore Add-To Problems Make Predictions Transcribe the Action or Relationship Digging Deeper into Start Unknown Situations Complicating Things: The Start Unknown Variation Strategies for Making Sense of Start Unknown Problem Situation Separating Computation from Operation Moving to Equations Key Ideas Try It Out! Identify the Problem Situation Write the Problem Change It Up Reflect Chapter 4: Take-From Problems: Locating the Change Thinking About Active Subtraction Situations Sandbox Notes: Explore Your Thinkin Students and Teachers Think About the Problems Finding the Unknown, Three Story Structures Story Structures: Implications for Teaching Modeling the Active Problem Situation Digging Deeper into the Start and Change Unknown Situations Moving from Concrete to Symbolic Representation Using Children's Literature to Explore Take-From Situations Create Another Outcome Finding the Unknown Quantity Key Ideas Try It Out! Identify the Problem Situatoon Write the Problem Change It Up Reflect Chapter 5: Part-Part-While: Understanding the Relationship Thinking About Part-Part-Whole Situations Sandbox Notes: Explore Your Thinking Students and Teachers Think About the Problems Defining the Part-Part-Whole Situation Modeling Relationships vs. Action Moving from Counters to Bar Models The Special Case of Both Parts Unknown Modeling Measurement Problems A Note About the Commutative Property Using Children's Literature to Explore part-Part-Whole Situations Make Predictions Moving to Larger Whole Numbers Students and Teachers Think about the Problems Modeling Measurement Problems Writing Equations: Addition or Subtraction Writing Equations: Addition or Subtraction Finding the Equation in the Model Key Ideas Try It Out! Identify the Problem Sitaution Write the Problem Change It Up Reflect Chapter 6: Additive Comparison: Another Kind of Relationship Thinking About Additive Comparison Situation Students and Teachers Think about the Problems Early Years Comparisons Additive Comparison Situations Building Models for Comparisons Students and Teachers Think About the Problems Making Use of Models For Thinking The Language of Comparisons Language Can Get Tricky Building Bar Models for Comparisons Problem Posing as an Instructional Strategy Using Children's Literature to Explore Additive Comparison Situations Create Another Outcome Key Ideas Try It Out Identify the Problem Situation Write a Problem Change It Up Reflect Chapter 7: Early Multiplication and Division: Patterns and Predictions Thinking about Early Multiplicative Thinking Sandbox Notes: Explore Your Thinking Students and Teachers Think About the Problem Modeling Even and Odd Numbers Equal Groups Problem Situation Using Patterns to Identify Even and Odd Numbers Using Children's Literature to Explore Early Multiplication Transcribe the Action or Relationship Bringing Another Dimension with Arrays Recognizing Area/Array as a Problem Situation Building an Understanding of Arrays as Structures Using Children's Literature to Explore Arrays Transcribe the Action or Relationship Setting the Stage Division Equipartitioning Two Models for Division Using Children's Literature to Explore Early Division Transcribe the Action or Relationship Key ideas Try It Out Identify the Problem Situation Write the Problem Change It Up Reflect Chapter 8: Changing How You Teach Word Problems Getting into the Mathematizing Sandbox 8 Shifts in Instruction for Building Students' Problem-Solving Skills Do Word Problems for Sense-Making Treat Context and Computation Separately Create More and Varied Representations Explore All the Work Operations can Do Add Operation Sense Routines with a Variety of Problem Situatons Listen to Students and Be Curious Make Time for Mathematizing in the Sandbox Guidance for Moving Forward: FAQ's Finding Unexpected Mathematics in Stories