In this partner activity, students take turns matching a tape diagram to an equation. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

If students don’t know where to begin, encourage them to describe the diagrams and equations in words. For example, Diagram D could be described as “two groups of equal 19,” and so could the equation

Once all groups have completed the matching, discuss the following:

• “Which matches were tricky? Explain why.”
• “Did you need to make adjustments in your matches? What might have caused an error? What adjustments were made?”

If students express uncertainty about , spend some time here. Some students are likely to match it to exactly one diagram and some students match it to both A and B. The point isn’t that only one of these is right; it is to have the conversation about the idea of expressions or equations being identical vs. equivalent. Equivalent expressions or equivalent equations can have different literal interpretations, but when matching equations to tape diagrams, all that matters for the purposes of solving is that the equations are equivalent.

In this activity, students create a tape diagram after interpreting an equation. Students take turns sharing their initial ideas and first drafts. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3). As students revise their writing, they have an opportunity to attend to precision in the language they use to describe their thinking (MP6).

In the digital version of the activity, students use an applet to create their tape diagrams. The applet allows students to divide the tape into parts and label the parts and total. The digital version may be helpful for students who struggle with drawing their own diagrams. However, even if the class is using the digital version, some students may prefer to draw the diagrams in their notebooks or on scratch paper.

The purpose of this discussion is for students to describe how their diagrams represent the two equations. Invite students to share their diagrams and explain their reasoning. If possible, display the students’ diagrams for all to see. To involve more students in the conversation, consider asking:

• “Who can restate ’s reasoning in a different way?”
• “Do you agree or disagree? Why?”
• “What does this part of the diagram represent?”
• “What is the same about these diagrams? What is different?”
• “How else could we show this relationship?”

Draw students’ attention to the structural differences in the diagrams that correspond to the presence or absence of parentheses in the equation.