The purpose of this activity is to match story problems with equations and tape diagrams. The numbers in this activity were selected so that there are 2 sets of story problems, tape diagrams, and equations that use the same numbers. This sorting task gives students opportunities to analyze story problems, tape diagrams, and equations closely in order to describe how the diagrams and equations represent the context of the story (MP2).

The goal of the Activity Synthesis is to discuss matching representations, highlighting how the tape diagram can help students understand the story and visually represent the equation.

• Invite 2–3 previously selected groups to share a set of matching cards.
• Consider asking:
  • “How did you know these cards go together?”
  • “How do you know that this story doesn’t match some of the other cards that use the same numbers?”
• As needed, display the tape diagrams that match Cards A and B.

• “How are the two diagrams the same? How are they different?” (Both diagrams have a 53, a 25, and a ? One diagram shows two separate rectangles comparing quantities. 53 is the total for one of the rectangles. In the other diagram, 53 is one part and the total is unknown.)
• “Which problem does the first diagram match? How do you know?” (The baseball and tennis ball problem. The first bar shows 53 and the second bar shows 25 less than 53.)
• “How is this different from the pine cone problem?” (53 is how many pine cones are left after 25 were taken away.)
• “Why does the second diagram match the pine cone problem?” (It shows that 53 are left if you take away 25.)

The purpose of this activity is to write story problems that match given tape diagrams (MP2). One diagram represents a one-step Compare problem, while the other two show two-step problems. For the tape diagram with three addends, students might:

• Write Put Together/Take Apart or Add To stories with an unknown addend.
• Write Take Away stories with the change or difference unknown.
• Write a Compare problem that compares the full tape to the sum of the first two sections.

For the tape diagrams that represent Compare problems, students may phrase the question using “How many more . . . ?” or using “How many fewer . . . ?” Although these diagrams are typically used to represent Compare problems, students may also choose to write Put Together/Take Apart or Take Away problems.

The Lesson Synthesis highlights different types of story problems students write that match the same tape diagram.

• Invite previously identified students to share their stories for the same tape diagram or share one story and have the class generate a different story after discussing the student work.
• “How did you know that the second diagram represents a comparison?” (It has two different rectangles. We know the larger amount and the difference, but it shows a question mark for the smaller amount.)
• “How did you solve the problem?” (I subtracted 20 from 63 and then subtracted 6. I added 4 to 26 to make 30, then added 30, and then added 3 more.)