In this activity, students continue to investigate division problems in context, think of them in terms of equal-size groups, and represent them using diagrams and equations.

Both division problems result in quotients that are not whole numbers, but because they represent concrete quantities, students can make sense of the fractional values (number of groups and size of each group) in terms of each situation.

As students work, monitor for students who draw diagrams as they reason about the situations. Any diagram (concrete or abstract) is fine as long as it enables students to make sense of the relationship between the number of groups, the size of one group, and a total amount. Select students whose diagrams clearly show the meanings of division, and ask those students to share later. During class discussion, students will have an opportunity to look more closely at how tape diagrams can support thinking about division.

Some students may round their answers to the nearest whole number rather than including a fraction of a scoop or of a gram. Ask students to consider if it is possible to have a part of a scoop or a part of a unit of volume. Encourage them to think about how to show a part of a whole unit on a diagram.

The goals of the discussion are to solidify students' understanding of the two interpretations of division (“How many groups?” and “How much in a group?”) and to clarify that division may not result in a whole-number quotient.

Invite students to share their responses and reasoning. Ask students who drew effective diagrams to display and explain them.

If no students drew tape diagrams, display the following diagrams as another way to reason about division.

Discuss what each part of the diagram and each label represent:

• The entire length of the tape represents the total amount.
• Each segment of the tape that is the same size represents one group (a packet or a scoop).
• The number inside each rectangle represents the size of one group, which can be a fraction. 14 grams in 4 packets means grams in 1 packet.
• The number of segments tells us how many groups there are, which can also be a fraction. There are 6 full scoops and 2 extra fl oz in 26 fl oz. The 2 extra fl oz is scoop. There are scoops in 26 fl oz.

Ask students how they can tell if the results they get from dividing 14 by 4 and 26 by 4 are correct. If no students mention multiplying each result by 4 to see if the product is 14 and 26, respectively, discuss this idea.

This activity offers an opportunity to practice making sense of situations involving division and representing them in different ways. Students choose one of four situations they encountered in the Warm-up. They create a visual or verbal representation of the situation, write multiplication and division equations to represent the relationships between the quantities, and then answer the question.

Students may use a diagram that they create or the equations that they write to reason about the answer or to find a quotient, but they may also reason in other ways. As students work, monitor for various diagrams, equations, and ways of reasoning. Select students with different representations and reasoning strategies and ask those students to share later.

The purpose of this discussion is to help students see more clearly characteristics of division situations and make connections across representations of division.

For each situation, select 1–2 students to share the responses and reasoning. Display their equations and diagrams (or descriptions) for all to see. Then, discuss questions such as:

• “Why is it possible to think about each situation in terms of division? What is it that they all have in common?” (They all involve equal-size groups or some quantity put into equal groups.)
• “What is one group in each situation?” (In A, it is the length of each segment. In B, it is the volume of each jar. In C, it is one container represented by a segment in the diagram. In D, it is the 4-liter jug.)