ABSTRACT
This chapter explores the models for the operations and their meanings. It begins with a discussion on division, multiplication, subtraction, and addition. Thinking of difference as distance is a powerful subtraction model. Division is the inverse of multiplication or it can be thought of as repeated subtraction. Partitive division or partitioning involves knowing the total, knowing the number of groups, and finding the number in each group. As with division, there are several models for multiplication such as equal grouping model, array model, area model. Since multiplication and division are inverse operations, if one model for division is separating into equal groups, then one model for multiplication is combining equal groups. There are two primary models for addition. One involves the action of joining or combining. The other involves the relationship of parts to a whole or total. The meanings of the operations and related models provide people with related conceptual language translations.
