Mathematize It! [Grades K-2]

Kimberly Morrow-Leong is an adjunct instructor at George Mason University in Fairfax, Virginia, a part-time researcher at American Institutes for Research, and a consultant for Math Solutions. She is a former grade 5–9 classroom teacher, K–8 mathematics coach, and coordinator of elementary professional development for the National Council of Teachers of Mathematics (NCTM). She recently completed an elected term as vice president and 2018 program chair for NCSM, Leadership in Mathematics Education. She holds a BA in French language and a masters in linguistics (TESOL). She also holds an MEd and PhD in mathematics education leadership from George Mason University. Kim is the 2009 recipient of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST) from Virginia. She is happiest when working with teachers and students, putting pencils down and getting messy with manipulatives!Sara Delano Moore is an independent mathematics education consultant at SDM Learning.  A fourth-generation educator, her work focuses on helping teachers and students understand mathematics as a coherent and connected discipline through the power of deep understanding and multiple representations for learning. Sara has worked as a classroom teacher of mathematics and science in the elementary and middle grades, a mathematics teacher educator, Director of the Center for Middle School Academic Achievement for the Commonwealth of Kentucky, and Director of Mathematics & Science at ETA hand2mind. Her journal articles appear in Mathematics Teaching in the Middle School, Teaching Children Mathematics, Science & Children, and Science Scope. Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, Linda M. Gojak directed the Center for Mathematics and Science Education, Teaching, and Technology (CMSETT) at John Carroll University for 16 years. She has spent 28 years teaching elementary and middle school mathematics, and has served as the president of the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and the Ohio Council of Teachers of Mathematics.

"One of the most important goals of K–2 math education should be developing a robust understanding of addition and subtraction that can serve as a foundation for later learning. In Mathematize It! Morrow-Leong, Moore, and Gojak help teachers transform solving word problems from an activity focused on getting answers to an activity that supports students’ understanding of the mathematical principles of the operations. Teachingsuggestions are integrated throughout the book in a manner that allows teachers to make adaptations to meet the needs of their students. This book belongs on every primary grade teachers’ bookshelf."

• Publisher′s AcknowledgementsTable of ContentsVideo ListAbout the AuthorsIntroduction: Why You Need to Teach Students to MathematizeProblem Solving Strategies Gone WrongWhat is Mathematizing? Why Is It ImportantFocus on Operation SenseUsing Mathematical RepresentationsTeaching Students to MathematizeBuilding your Understanding of Operations and Related Problem SituationsPlaying in the Mathematizing Sandbox: A Problem-Solving ModelFinal Words Before You DiveChapter 2: Moving From Counting to Addition & SubtractionThinking About Counting, Addition, and SubtractionSandbox Notes: Explore Your ThinkingStudents and Teachers Think About the ProblemThe Development of CourtingCounting or Add-To?Representing Problem Situations or Representing AnswersUsing Children′s Literature to Explore add-To and Take From SituationsTranscribe the Action or RelationshipMoving beyond TwentyStudents and Teachers Think About the ProblemsRepresenting Problem Situations Multiple WaysTranslating the Five Relationships: Try It OutTeaching Students to Use Concrete and Pictorial ModelsKey IdeasTry It Out!Identify the PrincipleWrite the ProblemChange It UpReflectChapter 3: Add-To Problems: Locating the ChangeThinking About Active Addition SituationsThinking About Active Addition SituationsSandbox Notes: Explore Your ThinkingStudents and Teachers Think About the ProblemsFinding the Unknown, Three Story StructuresStory Structures: Implications for TeachingModeling the Active Problem SituationModel ActionsDistinguish Pictures from Pictorial RepresentationIdentify Important FeaturesCreatively Meet Students′ NeedsUsing Children′s Literature to Explore Add-To ProblemsMake PredictionsTranscribe the Action or RelationshipDigging Deeper into Start Unknown SituationsComplicating Things: The Start Unknown VariationStrategies for Making Sense of Start Unknown Problem SituationSeparating Computation from OperationMoving to EquationsKey IdeasTry It Out!Identify the Problem SituationWrite the ProblemChange It UpReflectChapter 4: Take-From Problems: Locating the ChangeThinking About Active Subtraction SituationsSandbox Notes: Explore Your ThinkinStudents and Teachers Think About the ProblemsFinding the Unknown, Three Story StructuresStory Structures: Implications for TeachingModeling the Active Problem SituationDigging Deeper into the Start and Change Unknown SituationsMoving from Concrete to Symbolic RepresentationUsing Children′s Literature to Explore Take-From SituationsCreate Another OutcomeFinding the Unknown QuantityKey IdeasTry It Out!Identify the Problem SituatoonWrite the ProblemChange It UpReflectChapter 5: Part-Part-While: Understanding the RelationshipThinking About Part-Part-Whole SituationsSandbox Notes: Explore Your ThinkingStudents and Teachers Think About the ProblemsDefining the Part-Part-Whole SituationModeling Relationships vs. ActionMoving from Counters to Bar ModelsThe Special Case of Both Parts UnknownModeling Measurement ProblemsA Note About the Commutative PropertyUsing Children′s Literature to Explore part-Part-Whole SituationsMake PredictionsMoving to Larger Whole NumbersStudents and Teachers Think about the ProblemsModeling Measurement ProblemsWriting Equations: Addition or SubtractionWriting Equations: Addition or SubtractionFinding the Equation in the ModelKey IdeasTry It Out!Identify the Problem SitautionWrite the ProblemChange It UpReflectChapter 6: Additive Comparison: Another Kind of RelationshipThinking About Additive Comparison SituationStudents and Teachers Think about the ProblemsEarly Years ComparisonsAdditive Comparison SituationsBuilding Models for ComparisonsStudents and Teachers Think About the ProblemsMaking Use of Models For ThinkingThe Language of ComparisonsLanguage Can Get TrickyBuilding Bar Models for ComparisonsProblem Posing as an Instructional StrategyUsing Children′s Literature to Explore Additive Comparison SituationsCreate Another OutcomeKey IdeasTry It OutIdentify the Problem SituationWrite a ProblemChange It UpReflectChapter 7: Early Multiplication and Division: Patterns and PredictionsThinking about Early Multiplicative ThinkingSandbox Notes: Explore Your ThinkingStudents and Teachers Think About the ProblemModeling Even and Odd NumbersEqual Groups Problem SituationUsing Patterns to Identify Even and Odd NumbersUsing Children′s Literature to Explore Early MultiplicationTranscribe the Action or RelationshipBringing Another Dimension with ArraysRecognizing Area/Array as a Problem SituationBuilding an Understanding of Arrays as StructuresUsing Children′s Literature to Explore ArraysTranscribe the Action or RelationshipSetting the Stage DivisionEquipartitioningTwo Models for DivisionUsing Children′s Literature to Explore Early DivisionTranscribe the Action or RelationshipKey ideasTry It OutIdentify the Problem SituationWrite the ProblemChange It UpReflectChapter 8: Changing How You Teach Word ProblemsGetting into the Mathematizing Sandbox8 Shifts in Instruction for Building Students′ Problem-Solving SkillsDo Word Problems for Sense-MakingTreat Context and Computation SeparatelyCreate More and Varied RepresentationsExplore All the Work Operations can DoAdd Operation Sense Routines with a Variety of Problem SituatonsListen to Students and Be CuriousMake Time for Mathematizing in the SandboxGuidance for Moving Forward: FAQ′sFinding Unexpected Mathematics in Stories