What is the relationship between addition and subtraction? How do you know whether an algorithm will always work? Can you explain why order matters in subraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining an understanding about addition and subtraction is essential as they are the foundation for students later learning of multiplication and division.

Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K–Grade 2

Jennifer Bay-Williams

Janet Caldwell

Karen Karp

Rose Mary Zbiek

NCTM

Move beyond the mathematics you expect your students to learn. Unpacking the ideas related to multiplication and division is a critical step in developing a deeper understanding. To those without specialized training, may of these ideas might appear to be easy to teach. But those who teach in grades 3-5 are aware of their subtleties and complexities. This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3 5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modeled by multiplication have an element that represents the scalar and an element that represents the quantity to which the scalar applies. Big Idea 2 relates to the algorithms that problem solvers have invented some of which have become standard for multiplying and dividing. The authors examine the ways in which counting, adding, and subtracting lead to multiplication and division, as well as the role that these operations play in algebraic expressions and other advanced topics. The book examines challenges in teaching, learning, and assessment and is interspersed with questions for teachers reflection.

Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3–5

Sarah Wallus Hancock

Albert, Otto

Cheryl Lubinski

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Books by Janet Caldwell