In this partner activity, students take turns matching equations with descriptions of valid moves between them to practice identifying and providing descriptions of moves. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

Students also encounter negative values for the first time in the unit, which are not possible when using hangers.

The purpose of this discussion is to get students using the language of equations and describing changes happening on each side when writing equivalent equations. Select 2–3 groups to share one of their sets of cards and how they matched the pair of equations with a move. Discuss as many different sets of cards as the time allows.

Math Community
Invite 2–3 students to share the norm they chose and how it supported the work of the group or a realization they had about a norm that would have worked better in this situation. Provide a sentence frame to help students organize their thoughts in a clear, precise way:

• “I picked the norm “.” It really helped me/my group because .”
• “I picked the norm “.” During the activity, I realized the norm “” would be a better focus because .”

The purpose of this activity is to get students thinking about strategically solving equations by paying attention to their structure.

Monitor for groups who use these different strategies:

• Distribute a value to the terms in parentheses.
• Divide each side by the coefficient of the parenthetical expression. Both methods are equally valid, but there are advantages and disadvantages to each.

Both methods are equally valid, but there are advantages and disadvantages to each.

Some students may have trouble understanding Noah’s or Lin’s solutions. Ask them to try drawing arrows to describe each move. 

The goal of the discussion is to see the advantages and disadvantages of each strategy.

Display 2–3 approaches/representations from previously selected students for all to see. If time allows, invite students to briefly describe their solution paths for the last two questions, then use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:

• “What are the advantages of choosing to distribute first? To divide first?” (Distributing first eliminates confusion about which terms can be subtracted from each side. Dividing first makes the numbers smaller and easier to mentally calculate.)
• “What makes it easier to distribute versus divide first on the last question?” (In Diego’s equation, dividing by 4 before distributing will result in non-integer terms, which can be harder to add and subtract mentally.)
• “Is one path more right than another?” (No. As long as we follow valid steps, like adding or multiplying by the same thing on each side of an equation, the steps are right and will give a correct solution.)