ABSTRACT
This chapter focuses on building procedural fluency with understanding through exploring the relationships among the open area model, properties of operations, and different algorithms for multiplication and division. In the CCSSM, fluency with standard algorithms for multiplication and division is not expected until students have developed conceptual understanding of strategies based on place value and properties of operations. The chapter considers the implications of this defining characteristic that standard algorithms can be "reduced to a collection of single digit computations" for developing procedural fluency with understanding, and it explores the importance of developing understanding of multi digit multiplication and division through visual models. The chapter reviews the connections among the open area model, the partial products algorithm, and the traditional US algorithm we will look more closely at student solutions to an equal measures problem that involves multiplying two-digit quantities. It focuses on developing procedural fluency with understanding by connecting algorithms to place value, visual models, and properties of operations.
