The purpose of this activity is for students to formalize the relationship between multiplication and division equations. They see that the unknown quantity in a division situation can be represented as an unknown factor in a multiplication equation or as an unknown quotient in a division equation. The Activity Synthesis should emphasize that both equations are appropriate ways to represent a situation that involves equal groups.

This activity gives students an opportunity to make sense of each quantity and how it relates to the situation (MP2). As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).

• “After discussing your ideas with your partner, who do you agree with? Explain your reasoning.” (They are both correct because the situation can be represented with a multiplication equation with an unknown factor or a division equation with an unknown result. Both equations show the number of onions in each box as the unknown number.)
• If students don’t see that both Lin and Mai are correct, consider asking, “How could both equations represent this situation?”

The purpose of this activity is for students to understand how multiplication equations correspond to diagrams and equations used to represent division situations. The focus should be on relating the unknown factor to the unknown number of groups or the unknown number of objects in each group. In their explanations, students should make direct connections between the situations, representations, and equations (MP2).

• “How did you decide what type of equation to write?”
• “How could we represent this diagram (or situation) with a multiplication (or division) equation? Where do we see each part of the equation in the diagram (or situation)?”

• Share student responses for each row.
• Consider asking “How does the equation (or drawing) show the numbers or amounts in the situation?”
• “What relationship did you see between the multiplication equations and the division equations?” (The equations used the same numbers to represent the situation. The answer for the division equation was always one of the unknown factors for the multiplication equation.)