The goal of this discussion is to highlight that both multiplication and division can be reasoned in terms of equal-size groups. Just as we can interpret to mean “3 groups of 5 make 15,” we can think of division equations such as in terms of the number of groups and how much is in each group. Diagrams and equations can help us make sense of the numbers and what they mean.

Ask students questions such as:

• "What are two ways to interpret ?" (“How many groups of 8 are in 20?" or "How much is in each group if there are 20 in 8 equal-size groups?")
• “Suppose we interpret it as 'How much is in each group if there are 20 in 8 groups?' How might we draw a diagram to show this?” (A tape that represents 20 divided into 8 equal parts.) "What multiplication equation can we write?" (Either or can work, as long as we know what each factor represents.)
• "If we think of it as 'How many groups of 8 are in 20?', how would the diagram be different?" (A tape that represents 20 divided into equal parts of 8.) "What multiplication equation can we write?" (Either or can work, as long as we are clear what each factor represents.)

A note about the term “group:”

Students may be most familiar with the idea of a group as a collection of people or objects. Clarify that the term is used more broadly here. A “group” can refer to a part, a batch, a bag, a section, or another quantity with a particular value. So “equal-size groups” can refer to collections with the same number of items or people in each, as well as parts with the same value, sections of equal length, bags of the same weight, and so on. As students reason about various multiplication and division situations, the meaning of “group” in each situation will become more intuitive.