This Math Talk focuses on evaluating expressions with exponents. It encourages students to think about the meaning of exponents and to rely on the properties of operations to mentally solve problems. The understanding elicited here helps students develop fluency and will be helpful later in this lesson when students will need to be able to make sense of expressions with exponents.

The expressions were chosen to highlight some nuances such as , and . Additionally, students can recall that a number raised to the first power equals itself. The last question is meant to highlight that when multiplication and division appear in the same expression, there are different ways to write the operations with the same result.

In describing their answers, students need to be precise in their word choice and use of language (MP6).

The goal of this discussion is to review students’ strategies for solving expressions involving exponents.

To involve more students in the conversation, consider asking:

• “Who can restate ’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to ’s strategy?”
• “Do you agree or disagree? Why?”
• “What connections to previous problems do you see?”

In this activity, students complete tables showing expressions, expanded form, and exponent form. They then use the patterns from the tables to generalize properties of exponents. As students generalize properties of exponents, they look for and express regularity in repeated reasoning (MP8).

The purpose of this activity is for students to apply the exponent rules to evaluate expressions or write them with fewer terms.

The structure of a row game encourages students to check their thinking because their partners should get the same answer to different questions. When students’ answers aren’t the same, students must make sense of each other’s questions and thinking to figure out whose answer is correct. Through this process they construct viable arguments and critique the reasoning of others (MP3).