The purpose of this activity is to extend the definition of exponents to include negative exponents. The meaning of an exponent of 0 is also revisited. When students use tables to explore expressions with negative exponents, they are noticing and making use of structure (MP7). 

The goal of this discussion is to clarify the meaning of negative exponents. Display the completed table, and resolve any questions students have. Here are some questions for discussion:

• “How would you make sense of ?” (I know , and I know that would be the result of multiplying by another . So, .)
• “How could we figure out the value of ?” (We could rewrite it as , and then .)

In this partner activity, students take turns using exponent rules to analyze expressions and identify equivalent ones. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

The goal is to discuss strategies students used to match equivalent expressions.

Direct students’ attention to the reference created using Collect and Display. Ask students to share how they decided which expressions are equivalent. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.

Much discussion takes place between partners. Invite students to share how they decided which expressions were equal to the given expressions.

• “What were some ways you handled ?”
• “Describe any difficulties you experienced and how you resolved them.”

Once all groups have completed the matching, discuss the following:

• “Which matches were tricky? Explain why.”
• “Did you need to make adjustments in your matches? What might have caused an error? What adjustments were made?”
• “What mistakes might lead to the expressions that are not equivalent to the original expression?”
• “How do you know that expression is not equivalent to the original?”
• “Did anyone think about that expression in a different way?”