The purpose of this activity is for students to determine whether a situation is about an unknown number of groups or an unknown number of objects in each group. After sorting the situations, students write a division expression to represent each situation. The fact that the structure of the expressions is the same for representing an unknown number of groups or an unknown number of objects in each group further emphasizes that division expressions can be interpreted two ways.

As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3). Encourage students to describe how they would start to solve the problem to help make it clear what is unknown in the situation.

• Invite students to share their expression for each situation.
• Consider asking:
  • “What does each number represent in the expression?”
  • “Where do you see the number of groups in the expression?”
  • “Where do you see the number of objects in each group in the expression?”

In this activity, students consolidate their understanding of the types of division situations and their representations to solve division problems.

During the Activity Synthesis, arrange and display students‘ posters by type, as sorted in the previous activity.

This activity uses MLR7 Compare and Connect. Advances: representing, conversing.

• Ask students to identify which type of division problem each poster shows.
• “What is the same about the two types of division problems?” (They both involve putting things into equal groups. The total is known in both.)
• “What is different about them?” (Sometimes we know how many things are in each group and we need to find how many groups we can make. Sometimes we know how many groups there are, but we need to find how many things are in each group.)