The purpose of this activity is to reason, using some examples and the meaning of exponents, that an expression in the form is equivalent to . Monitor for students who reason about the last question by replacing 8 with , or vice versa. When students notice that they can use properties to rewrite expressions, they are noticing and making use of structure (MP7).

The goal of this discussion is for students to remember this property of exponents: .

Use Critique, Correct, Clarify to give students an opportunity to improve a sample written response to why by correcting errors, clarifying meaning, and adding details.

• Display this first draft:
  because 8 is a power of 2.
  Ask, “What parts of this response are unclear, incorrect, or incomplete?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.
• Give students 2–4 minutes to work with a partner to revise the first draft.
• Select 1–2 students or groups to slowly read aloud their draft. Record for all to see as each draft is shared. Then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.

Ensure that students found correct matches for the first question, and invite a few students to articulate how they knew they had found a match without evaluating the expressions. Use at least one example from this activity to make sure students are comfortable with this rule: is equivalent to . For example, demonstrate that because they both equal . Then, for the last question, make explicit a chain of reasoning, such as ,  ,  , and , and point out where this property comes into play. (These steps could also be listed in reverse, first replacing 8 with .)

The purpose of this activity is to familiarize students with the terms “annually,” “semiannually,” “quarterly,” and “monthly,” and use the meaning of these terms to solve some problems. In each problem, students perform a few numerical computations and then generalize by writing an expression, which is an example of expressing regularity in repeated reasoning (MP8).

In this partner activity, students take turns matching a description or expression to a representation. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).