In this lesson, students extend their exploration of “How many groups?” questions to include cases where the number of groups is a fraction less than 1. In such situations, the total amount is smaller than the size of 1 group, so the question becomes “What fraction of a group?”

Students notice that they can use the same reasoning strategies as before because each situation here still has the same structure of . They continue to write multiplication equations of this form and the corresponding division equations.

Students first reason about “What fraction of a group?” questions in the context of fractional batches of a recipe. Students can make sense of fractions of a group in the optional activity, which provides another concrete situation involving lengths of ropes before answering questions without a context in the last activity.

Throughout the lesson, students need to pay close attention to how their diagram, description, and equations represent the relationship between a given total amount and the size of 1 group. In doing so, they practice reasoning abstractly and quantitatively (MP2).