The purpose of this activity is for students to solidify what they have learned about the relationship between multiplication and division. Students start by creating a drawing of equal groups. They then get a drawing created by another student in their group and write a division situation to match it. Then, they pass their paper and use the drawing of equal groups and the situation to write a multiplication equation. In the final round of this “carousel” structure, students write a division equation to match the other representations. 

When students relate drawings, situations, and equations they reason abstractly and quantitatively (MP2). As students look through each other’s work, they add to the representations and can defend different points of view. Students are able to critique the work of others and construct viable arguments (MP3).

Students work on the same box on a graphic organizer as the other students in their group, so if they struggle, encourage them to talk to their group. Remind students that what they are creating should match what has already been filled in.

• “What strategies were shared in your group?” (When I wasn’t sure about writing a situation, I looked back at the drawing and tried to imagine something I could be dividing that looks like the drawing. When I was writing an equation it helped me to imagine the situation happening.)
• “As you look at your paper, what are some connections you notice between multiplication and division?” (I can use both multiplication and division to represent the same drawing or situation. The multiplication equations all have an unknown factor, but the division equations all have an unknown quotient.)

The purpose of this activity is for students to represent and solve problems involving equal groups. Students can solve the problem first or write the equation first, depending on the order that makes the most sense to them. Students write equations with a symbol standing for the unknown quantity to represent each problem, but can write either a multiplication equation or a division equation. A multiplication equation and a division equation that represent the same problem are highlighted in the Activity Synthesis.

• “What is this problem about?”
• “How could you represent the problem?”

• Have students share a division equation and a multiplication equation that were written to represent the same division situation and display for all to see.
• Discuss differences in equations students wrote.
• Consider asking:
  • “How does each number in the equations represent the situation?”
  • “_____ wrote _____, and _____ wrote _____ to represent the same problem. How are those equations the same and different?” (Both equations use the same numbers. Both symbols in the equations represent the unknown _____ in the situation. One of the equations is a division equation, but the other equation is a multiplication equation with an unknown factor. They used different symbols for the unknown amount.)
• Have students share strategies they used to solve the problem.