ABSTRACT

This chapter focuses on three mathematical ideas that are foundational for developing flexibility and procedural fluency when multiplying and dividing whole numbers: Unitizing, Place value understanding and Properties of operations. It reiterates the essential components of procedural fluency. Procedural fluency includes: Knowledge of the steps in a procedure; Knowledge of when to use the procedures appropriately; Skill in applying a procedure flexibly, accurately, and efficiently; Underlying conceptual understanding of mathematical ideas. The chapter focuses on how to build conceptual understanding of the important mathematical ideas that underlie multiplication and division in order to develop procedural fluency. This chapter examines the mathematical ideas and includes discussion of instructional strategies that focus on these concepts and properties to develop students' multiplicative reasoning, flexibility, and fluency. Further, the chapter presents the inherent problems with the rule, "When you multiply a number by 10, just add a zero to the end of the number".