The purpose of this activity is for students to represent and solve a two-step story problem involving multiplicative comparison, in ways that make the most sense to them. As they make connections between strategies for solving multi-step problems, they also compare representations that show multiplicative comparison more discretely (diagrams) and those that show the comparison more abstractly (expressions).

• “Tell me more about how you organized the information from the problem.”
• “How can knowing ______ (quantity in step 1 of the problem) help us find the amount of total sales for that day?

• Invite previously selected students to share their representations and their reasoning for problem 1. 
• “How does ______’s diagram or expressions relate to the problem?” (The diagram and the expressions showed and 8 times as much.) 
• “How was solving this problem like the second problem? How is it different?” (The question, the numbers, and multiplicative comparison “8 times as much” were the same in both problems. The diagram from the first problem could also work with the second problem. The calculations were different because of what the problems were about.)
• “How were both of these problems different from other problems we solved in this unit?” (We had to do more than one calculation to solve the problem.)
• “Both problems asked for the amount of total sales and involved multiplying and adding. How did you know which operation to use and with which numbers?” (One problem involves adding first, and then using multiplicative comparison to find the amount of total sales. In the other problem, multiplicative comparison is first, and then you add to find the amount of total sales for the day. It’s important to pay attention to the information given in the problem and the multiplicative comparisons.)

The purpose of this activity is for students to apply what they learned about interpreting and representing multiplicative comparison to solve multi-step problems. They must interpret what values are unknown and make a plan for how to represent these values.

Students reason abstractly and quantitatively when they make sense of the given information and use it to find the different numbers of books (MP2).

• Invite previously selected students to share their diagrams or equations.
• “How does __'s diagrams or equations match the story problem?”
• “Why might someone choose to show their work with equations instead of drawing diagrams for this particular problem?”
• “What did you learn about paying attention to what the question is asking?”
• If time, invite previously selected students to share how they revised their thinking.
  • “What did you notice during the partner discussion and how did you change your work after noticing it?”
  • Consider asking a different student to rephrase this revision in their own words.