The purpose of this activity is to clarify the steps of solving an equation for a variable. This skill will continue to be used and developed in future activities.

This activity uses the Worked Example routine. In this routine, students analyze steps used to solve a problem and discuss specific steps with a partner and the whole class. During the discussions, students construct viable arguments to justify the steps taken by the problem solver (MP3). Later, students can apply these strategies to solve similar problems.

The purpose of this discussion is for students to understand the steps the solver took to solve an equation for a variable.

Tell students to open their books or devices. Display the following questions, and give students 1–2 minutes of quiet think time to consider their responses.

• “How did the solver know to start with subtraction?” (To isolate , the solver needs to remove any other terms from the left side of the equation. Because is added to the term, it needs to be subtracted from each side. This did not have to be the first step, but it is the one they chose.)
• “Why are the 5 and the each divided by 2?” (All parts of each side of the equation must be divided by the same number.)
• “How do you know the solutions are equivalent?” (The second solution distributed the division to each part. The distributive property does not change the value of an expression.)

Ask partners to compare their responses to each question and to decide if either or both answers are correct. During this partner discussion, monitor to select groups who reason about the questions in different ways. Follow with a whole-class discussion, inviting 1–2 selected groups to share their answers for each question.

If time allows, consider displaying next to the first a second worked example that either:

• Shows a different method of solving a similar problem so that students can compare and contrast it with the first example (MP7).
  • For example, divide each term by 2 in Step 1, then subtract from each side in Step 2.
• Shows the same method with an error so that students can critique and correct it (MP3).
  • For example, solve for in , and divide only the and 6 terms by 3.

The mathematical purpose for this activity is to allow students to practice solving for a variable in an equation with two variables. In the associated Algebra 1 lesson, expressing one variable in terms of another is necessary before substituting an expression for a variable in another equation. As students solve for a variable, they can use operations on equations to look for and make use of structure (MP7).