The purpose of this activity is for students to make connections between different representations of story problems. A sorting task gives students opportunities to analyze stories, equations, number lines, and tape diagrams closely and make connections (MP2, MP7). The Synthesis focuses on how the representations are alike and different. Students recognize some representations help to make sense of the story, while others help to show their thinking when finding solutions.

• Display Story Problem A with Tape Diagram F, Number Line K, and Equation B.
• “How are these representations of the same problem the same? How are they different?” (They all show the numbers given in the problem, 37 and 63. They all show 63 is the total and 37 is one part. They all show an unknown-addend problem. The diagram and equation show a ? for the unknown, but the number line shows the value of the unknown—the number where the arrow ends. The equation and diagram show addition, but the number line shows subtraction.)

The purpose of this activity is for students to solve story problems using any strategies and representations that make sense to them. In previous lessons, students have used number lines, tape diagrams, and equations to represent situations and solve problems. Now they have the opportunity to apply their understanding and make choices about how to make sense of problems and show their thinking. In the Synthesis, students reflect on which representations are most helpful to them and make connections across representations (MP2). The last question in the Synthesis will likely elicit a variety of responses from students, which can emphasize the point that students should use representations that make sense to them.

• Invite previously selected students to display their work side by side for all to see.
• “What is the same or different between _____ and _____ representations?”
• Help students make connections across representations by highlighting the places where they see the solution in each.
• “Which representations do you find most helpful?”