The purpose of this activity is for students to represent a situation with a multiplication equation that has a symbol for the unknown and find the number that makes the equation true. Students are able to use an earlier representation to help them solve the problem, however some students may just write the equation and skip-count to find the product. Either is okay.

In the Activity Synthesis, share different ways students represented the problem in addition to the equation. If students used repeated addition, avoid saying “Multiplication is repeated addition,” because while repeated addition is one way to find the product, it is not the meaning of multiplication.

To add movement to this activity, students can work in groups of 4 to make a poster for one of the problems. After each group is done, they can do a Gallery Walk to look for things that are the same or different in the posters.

• Display samples of student work for each problem next to each other, including a drawing of equal groups and a tape diagram.
• “Where do we see the parts of the problem in the drawing and the diagram?” (The number of objects in each group are the dots in the drawing, but the number is written in each part of the diagram.)
• “How did you use the factors in each equation to find the product?” (The factors told me how many groups there were and how many were in each group.)
• “How are drawings and diagrams useful for finding the solution to the problem?” (You can count the dots in the drawing. The diagram can be used to count by 10.)

The purpose of this activity is for students to practice solving multiplication problems in which the unknown amount can be the number of groups, the number in each group, or the total. The first three problems have the unknown in each of those locations. The sequence of these problems, the context, and the use of the same factors and product encourages students to use a known fact to find the unknown factor in the “how many in each group?” problem. Students will make the connection between this problem type and division in a future unit. Students are able to choose the representation they use to represent and solve the problems.

• Share student work for each problem and ask students to explain their reasoning. Be sure to share a variety of strategies and representations.
• As students share, consider asking the class:
  • “Why does this strategy make sense?”
  • “Why does this representation make sense?”
  • “Did anyone solve this problem in a different way?”
  • “What do you notice is the same about the representations and strategies that we are using to solve these problems?”