Lesson 7

In the previous three lessons, students explored the “how many groups?” interpretation of division. Their explorations included situations where the number of groups was a whole number or a mixed number. In this lesson, they extend the work to include cases where the number of groups is a fraction less than 1, that is, situations in which the total amount is smaller than the size of 1 group. In such situations, the question becomes “what fraction of a group?”.

Students notice that they can use the same reasoning strategies as in situations with a whole number of groups, because the structure \(\displaystyle \text{(number of groups)} \boldcdot \text{(size of a group)} = \text{(total amount)}\) is the same as before (MP7). They write multiplication equations of this form and for the corresponding division equations.

Throughout the lesson, students practice attending to details (in diagrams, descriptions, or equations) about how the given quantities relate to the size of 1 group.