In this activity, students rewrite a subtraction operation as adding the opposite. Then they rearrange terms in an expression that involves only addition. This concept is applied to get students used to the idea that the subtraction sign has to stay with the term it is in front of. Making this concept explicit through a numeric example will help students see its usefulness and help them avoid common errors in working with expressions that involve subtraction.

To explain why it is valid to rewrite terms in a different order, students need to attend to precision (MP6).

The purpose of this discussion is to review rewriting subtraction as “adding the opposite,” and to reinforce understanding that rewriting an expression using addition means that it’s valid to rearrange the terms.

Ensure everyone agrees that is equivalent to is equivalent to . Use the language “commutative property of addition.”

In this activity, students express the area of a rectangle in different ways using the distributive property. Students learn that even when the terms are negative, we can still organize our work with the distributive property in a way that is similar to using area diagrams.

Students must notice and make use of structure to rewrite an expression in different ways (MP7).

The purpose of this discussion is to recognize and justify different, valid ways to write equivalent expressions. 

Solicit responses to the second question and demonstrate thinking about one product at a time:

Then ask students to share how they approached the last question. Highlight responses where students noticed that can be rewritten like because of what they talked about in the Warm-up. So, the two questions could have the same answer.