Direct students’ attention to the reference created using Collect and Display. Ask students to share their reason each step is equivalent to the last. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases. (For example, the display may have “You can rewrite subtracting as adding so you can rearrange the terms” already on it, which can be updated with the more precise statement “You can rewrite subtraction as adding the opposite so you can use the commutative property.”)

Invite students to justify that the steps taken by Diego do not change the value of the expressions. Emphasize places where he used the distributive property and the commutative property. 

Present a simpler expression, like , and ask students how you could rewrite it with fewer terms. Ensure they see it’s equivalent to , whether justified by or by writing .

Consider using this opportunity to explain the meaning of this lesson’s title. Explain that two terms are called “like terms” when they are both numbers or when they both have the same variable. When we add like terms, we call it “combining like terms.” Use these examples to clarify:

• are like terms because they both have the variable . We can combine them as .
• are like terms because they are both numbers. We can combine them as 8.
• are not like terms because one has a variable and one is a number. We cannot combine them.

In this activity, students use what they have learned so far to find an unknown term or expression that makes two expressions equivalent. Students have many strategies at their disposal to reason about the unknown term or expression in each equation. For example, for the first equation , students might reason as in the previous activity and write out the sum of 6 's and ? on one side, and a string of 10's on the other side, and reason that 4 's are needed to make the sides equivalent. Alternatively, they might reason with the distributive property, and rewrite the left side as .

When students compare their results with a partner and resolve discrepancies, they have an opportunity to justify their thinking and critique the reasoning of others (MP3).

The purpose of the discussion is to highlight alternative ways of reasoning about equivalent expressions.

Ask students to share their expressions for each problem. Record and display their responses for all to see. After each student shares, ask the class if they agree or disagree.

The following questions, when applicable, can be used as students share:

• “Why didn't you combine terms and numbers?” (Rewriting expressions using the properties of multiplication or the distributive property shows why this doesn't result in an equivalent expression.)
• “How did you decide on the components of the unknown term or expression?” 
• “Did you use the commutative property?”
• “Did you use the distributive property?”