Mine the Gap for Mathematical Understanding, Grades K-2

John J. SanGiovanni is a mathematics coordinator in Howard County, Maryland. There, he leads mathematics curriculum development, digital learning, assessment, and professional development. John is passionate about growing new mathematics leaders in the district and through McDaniel College. In addition to the Figuring Out Fluency series, some of his many Corwin books include Daily Routines to Jump-Start Problem Solving, Grades K–8; Answers to Your Biggest Questions About Teaching Elementary Math; the Daily Routines to Jump-Start Math series; and Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance. John is a national mathematics curriculum and professional learning consultant who also speaks frequently at national conferences and institutes. He is active in state and national professional organizations, recently serving on the board of directors for the National Council of Teachers of Mathematics (NCTM) and on the board of directors for NCSM.

• Big Ideas & Tasks at a GlanceAcknowledgmentsPublisher’s AcknowledgmentsAbout the AuthorIntroductionCHAPTER 1. RICH MATHEMATICS TASKS, STUDENT MISCONCEPTIONS, USING TASKSCHAPTER 2. COUNTING AND REPRESENTING NUMBERSBIG IDEAS1. Counting on From Any Number (0–120)2. Counting on a Number Line3. Skip-Counting4. Representing Numbers5. Representing Numbers to 1,000 With Models6. Understanding Relationships Between NumbersCHAPTER 3. NUMBER RELATIONSHIPS AND COMPARISONBIG IDEAS7. Comparing Numbers Within 1008. Comparing Numbers Within 1,0009. Comparing Numbers Within 1,00010. Number Relationships Through Number Lines11. Decomposing Numbers Less Than 10012. More Decomposing NumbersCHAPTER 4. ADDITION AND SUBTRACTIONBIG IDEAS13. Representing Addition14. Properties of Addition15. Reasoning About Addition16. Representing Subtraction17. Connecting Addition and Subtraction18. Reasoning About Subtraction19. The Meaning of the Equal Sign20. Problem Solving With Addition and SubtractionCHAPTER 5. ADDITION AND SUBTRACTION WITHIN 100BIG IDEAS21. Addition Within 10022. More With Addition Within 10023. Reasoning About Addition Within 10024. Subtraction Within 10025. Reasoning About Subtraction Within 10026. Problem Solving Using Addition and Subtraction Within 100CHAPTER 6. ADDITION AND SUBTRACTION WITHIN 1,000BIG IDEAS27. Adding Within 1,00028. Reasoning About Addition Within 1,00029. Subtraction Within 1,00030. Reasoning About Subtraction Within 1,00031. Problem Solving Within 1,000CHAPTER 7. MEASUREMENT WITH MONEY AND TIMEBIG IDEAS32. Working and Problem Solving With Money33. Working and Problem Solving With Money34. Telling Time35. Elapsed TimeCHAPTER 8. MULTIPLICATION AND DIVISIONBIG IDEAS36. Representing Multiplication and Division37. Reasoning About Multiplication38. Properties of Multiplication39. Representing Division40. Problem Solving With Multiplication and DivisionCHAPTER 9. WHAT DO WE DO NEXT?References and Additional Resources

"Wow! Mine the Gap for grades K–2 teachers really unpacks! Not only does the book providedozens of great mathematical tasks, but—perhaps more important—it gives teachers the chanceto consider each task; anticipate student responses—a critical first step in formative assessment;analyze actual student responses; and then consider what they would do in the classroom.Thoughts about modifying each task provide another option for each task. At a time when teachersare encouraged to regularly provide students with tasks that promote reasoning and problemsolving, this book will help teachers dig deeper as they mine for understandings."