This Math Talk focuses on strategies for manipulating equations while preserving equality. It encourages students to think about expressions or equations and to rely on properties of operations and equality to mentally solve problems. The understanding elicited here will be helpful later in the lesson when students will need to be able to solve complex equations and justify why certain moves preserve equality.

In explaining their strategies, students need to be precise in their word choice and use of language (MP6).

The goal of this discussion is to review students’ strategies for solving multistep equations.

To involve more students in the conversation, consider asking:

• “Who can restate ’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to ’s strategy?”
• “Do you agree or disagree? Why?”
• “What connections to previous problems do you see?”

Emphasize that the expressions on both sides of the equals sign should have the same value, and point out strategies that make explicit use of the equivalence. If the following strategies are not mentioned, ask students about these strategies, and demonstrate if necessary:

• Compensation strategies, such as noticing that 25 is 4 more than 21, so the number that goes in the blank should be 4 more than 3.
• “Doing the same thing to each side” strategies, such as subtracting 21 from each side to get the blank alone.

The purpose of this activity is to further remind students of the different forms that equations representing relationships can take, and to begin to focus students’ attention on equivalent forms of equations in two variables. This will be useful in their Algebra 1 class when students learn to solve equations for a variable.

It’s not critical that students justify why the equations are equivalent to one another. It is more important that they connect each equation back to how it relates to the context. By relating each equation to the context, students are reasoning abstractly and quantitatively (MP2).

Monitor for students who notice that the equations are equivalent and the moves that could be used to relate one to another.

Identify students who struggle with connecting contexts to expressions.

The purpose of this activity is for students to identify why equations are not equivalent. In an associated Algebra 1 lesson, students rewrite equations to express one variable in terms of the other. The work in this activity prepares students to be successful in the associated Algebra 1 lesson by allowing them to gain a deeper understanding of what makes two equations equivalent and to practice making appropriate moves to maintain the balance in an equation.

In this partner activity, 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).