The purpose of this activity is for students to match story problems, in the context of money, to tape diagrams. Students make sense of stories and determine which diagram represents each situation. One pair of problems are one-step stories while the other pair are two-step stories. The numbers in the stories are the same, so students will have to focus on the relationships between the quantities in the stories to match them to tapes (MP2).

Students may choose and justify matches different from those given in the student responses (MP3). For example, diagram B could match Jada’s story. But this story is a comparison and naturally matches diagram C, whereas both parts of diagram B make up Diego’s money. Both two-step problems as well, could be represented by either diagram A or diagram D. For the basketball story, we know that the basketball costs \$ less than the football and the soccer ball combined. For the clothes, we know that the pants cost \$ and want to know how much more the shirt and the shoes cost. Diagram A matches the clothes story because the price of the pants, 39, is known but the difference is not known. Diagram D matches the basketball story because the difference, 39, is known.

• “How were the diagrams the same or different?”
  • Every diagram has 39 and a 68 and some of them have a 29.
  • The numbers are in different places. 
  • Some of the diagrams look like they are comparing quantities while one of them puts two quantities together.
• “How did you decide which diagram went with each story?” (In two of the stories there was something that cost \$ and something that cost \$ so I could look at tapes A and D and figure out how the stories match. In some stories the greater amount had the prices of two things added together, so I looked for that in the diagrams. The story about Diego was the simplest tape. I just needed to find out how much money he got. For Jada’s story, the diagram compares the amount she had to the price of the building bricks.)
• Share and record responses.
• As needed, invite students to share how some stories could be represented by more than one diagram by explaining how they match the quantities and the context.
• “In the next activity, you will have a chance to solve some of these story problems and a few others.”

The purpose of this activity is for students to solve two-step problems, without the scaffold of having the first step explicitly stated. Students solve in a way that makes sense to them and may use diagrams to help them make sense of the story. In the Activity Synthesis, the tape diagram is highlighted.

• “What is the story about? How could you break the problem into smaller parts?”
• “How could you use a diagram or an equation to represent the smaller parts?”

• Invite previously identified students to share the diagram for comparing Tyler’s money to Andre’s and Noah’s money.
• “How does this diagram represent the story?” (It shows Tyler’s amount and then the amount of Andre and Noah together. I can see that Tyler has less than Andre and Noah. I need to add Andre’s amount and Noah’s amount, and then subtract Tyler’s amount from that.)