In this activity, students compare three methods for solving the same equation. Monitor for students with different, valid reasons for agreeing or disagreeing with each method.

Students are critiquing the reasoning of others (MP3) by finding and describing errors in reasoning.

If students aren’t sure how to begin analyzing Noah’s method, ask them to explain what it means for a number to be a solution of an equation. Alternatively, suggest that they draw a tape diagram to represent .

Invite students to share as many unique reasons they agree or disagree with each method as time allows. The purpose of this discussion is to make explicit a common conceptual error (in Noah’s method) and a common conceptual error in Elena’s work.

Some possible questions to prompt discussion include:

• “What are some ways you can tell that a value is _not_ a solution to an equation?” (Test if it makes the original equation true.)
• “Why isn’t equivalent to ?” (The first 9 is being multiplied by 2. So this expression is actually , which is , not .)
• “Is it possible to solve the original equation without using the distributive property?” (Yes, you could start by dividing each side by 2.)

In this activity, students solve equations of the form , recognize that there are two valid approaches, and make judgments about which one is more sensible for a given equation.

Deciding on the best approach relies on noticing and using the structure of the equation (MP7).

Reveal the solution to each equation and give students a few minutes to resolve any discrepancies with their partner.

Display the list of equations in the task, and ask students to help you label them with which solution method was the better choice, either “divide first” or “distribute first.”

Some are not so clear. For example, for , one person might distribute the -10 to get rid of the decimal, while someone else might divide each side by -10 to solve in fewer steps.

Some possible questions for discussion:

• “For this equation, why is one method preferable to the other?”
• “Which is more important to you—minimizing the number of steps, or getting rid of fractions or decimals?”