In this partner activity, students take turns sorting equations into categories of their own choosing. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

Once all groups have completed the Card Sort, discuss:

• “How do you describe the categories you chose?”
• “Did you need to make adjustments in your categories? What adjustments were made and why?”
• “Were any equations difficult to categorize? What made them difficult?”

The purpose of this discussion is to uncover that  equations of the form have a different structure than those of the form . Select 2–3 groups to share their categories and how they decided to sort their equations. Discuss as many different sets of categories as the time allows.

In this activity, students match two tape diagrams with two situations, explain what the variable represents, write equations, and then solve them. This activity is an opportunity to put together the learning of the past several lessons: correspondences between tape diagrams, equations, and stories, and using representations to reason about a solution. The focus of this activity is still contrasting the two main types of equations that students encounter in this unit. In order to coordinate the tape diagrams with the situations and write equations, students need to notice and make use of structure (MP7).

The purpose of this discussion is to understand why a particular diagram and equation represents a situation, and why the solution is true. For each story, select 1 or more groups to present the matching diagram, their equation, and their solution method. Possible questions to ask:

• “How were the diagrams alike? How were they different?” (They have the same numbers and a variable. One has 3 equal groups and an extra bit, the other just has 3 equal groups, but each group is a sum.)
• “How were the stories alike? How were they different?” (They were both about distributing 90 flyers. In one story, Lin makes a series of moves to each volunteer. In the other story, she gives each volunteer the same amount, but then there are some left over.)
• “What parts of the story made you think that one diagram represented it?”
• “Explain how you reasoned about the story, diagram, or equation to find the value of the variable.”