The purpose of this activity is for students to relate equations to multiplication situations and diagrams using a symbol for the unknown number. This sorting task gives students opportunities to analyze these equations, situations, and diagrams closely and make connections (MP2, MP7). Students explain their matches to their peers and revise their language for precision and clarity when they describe how the numbers and symbols in the equations match the representations (MP3, MP6). In the Activity Synthesis, students explain the meaning of the factors and products and what a symbol in an equation represents.

• Invite previously selected students to share how they decided which cards go together.
• Choose 1–2 equations (at least one with a missing factor) and ask:
  • “What does each number in the equation represent?”
  • “What does each question mark (or blank or box) represent?”
  • “How can we figure out which number goes in the blank to make the equation true?”
• Listen for the language students use to describe their matches and the equations, diagrams, and situations clearly and precisely. As needed, ask:
  • “What do you mean when you say _____?”
  • “Was the unknown the product or one of the factors? Explain.”
  • “What did the unknown factor represent? Explain.”
• Highlight the terms “factor” and “product.”

The purpose of this activity is for students to write equations for multiplication situations and diagrams using a symbol for the unknown number. When students write an equation to represent a situation, including a symbol for the unknown number, they model a situation with mathematics (MP4).

Students find an unknown factor or unknown product in multiplication problems. In this task, the unknown factor diagrams and situations only include the “how many groups?” problem type and the factors 2, 5, and 10. This sets up students to skip-count to find the unknown number.

This problem type will be revisited extensively in future lessons and will be related to division. It is not necessary to make the connection to division now. In the Activity Synthesis, students explain how the equations they wrote represent the diagram or situation.

• “How does your equation represent the diagram (or situation)?”
• “How could you show the number that was unknown with a symbol?”

• “What strategies did you use to find the unknown numbers?” (I counted by 2 to get the total. I counted by different numbers until I found a number that gave me the product.)
• “How did each equation change as you found the unknown number?” (The symbol was replaced with the number.)