ABSTRACT
This chapter delves deeper into the models for the operations and their meanings. The goal is for students to work flexibly with a variety of these models when computing. This will shift to understanding how they are to operate on the numbers instead of recalling the steps of memorized algorithms. Partitive division or partitioning involves knowing the total, knowing the number of groups, and finding the number in each group. Quotitive division or quotitioning involves knowing the total, knowing the number in each group, and finding the number of groups. Repeated addition is often used to introduce students to multiplication. In the early grades, multiplication is introduced as a specialized form of addition. Understanding the meanings of the operations and the associated models and conceptual language gives students access to what at first sight may look like a complex mathematical idea.
