In this lesson, students encounter situations in which the number of groups is known but the size of each group is not. They interpret division expressions as a way to answer “How much in a group?” questions.

Students begin by inventing a situation for a tape diagram in which the number of groups and the total amount are shown but the amount in each group is represented with a “?” symbol.

Next, students solve problems about finding the amount in 1 batch of a recipe given an amount for a different number of batches. They answer questions such as, “If 2 tablespoons are enough for of a batch, how many tablespoons are in 1 batch?” To support their reasoning, students use familiar representations—multiplication and division equations and tape diagrams—and make use of the same structure of equal-size groups (MP7).

Each of the next two activities prompts students to match three tape diagrams and three descriptions representing an unknown group size. Because all three situations involve the same context and the same total number, represented by a segment of the same length on a tape diagram, students need to make sense of the problems carefully and persevere in interpreting them (MP1).

The first of the two activities, “How Much in One Container?” is optional. There, the known total amount is a whole number. Consider doing this activity to scaffold students’ thinking, if needed, before they do “How Much in One Section?” where the total amount is a fraction.