The purpose of this activity is for students to recall how to write expressions using exponents. Students apply what they know about exponents to represent money doubling each week. They use multiplication to express a different quantity growing linearly each week. This will be useful when students represent two situations and compare them in the associated Algebra 1 lesson. When students write an expression in terms of , they express regularity in repeated reasoning (MP8).

The goal is to discuss how students created their expressions for finding the amount of money that Clare and Tyler had at the end of each week, and if each plan is reasonable. Ask students to discuss how they developed their expressions. Here are some questions for discussion:

• “Is Clare’s plan reasonable? Explain your reasoning.” (It is reasonable for Clare to save $5 each week. If she is being paid a reasonable wage, that should be less than 1 hour’s earnings being saved each week, and she is probably working more than 1 hour per week.)
• “Is Tyler’s plans reasonable? Explain your reasoning.” (Tyler’s plan starts off reasonably and becomes less realistic later on, depending on how much he is paid and how many hours he is working. For example, if he is being paid $15 an hour and works 20 hours each week, that is $300 each week, so he would have trouble saving more than that amount in a week, as he does in week 10.)

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 practice will prepare students to compare growth patterns and interpret graphs to answer questions from a context in the associated Algebra 1 lesson.

Much discussion takes place between partners. Invite students to share how they determined which expressions were matches. Select groups to share their matches and how they sorted their expressions. Ask if other groups have different matches of expressions. Choose as many different groups as time allows. Attend to the language that students use to describe their pairing, and give them opportunities to describe their relationships more precisely. Highlight the use of terms like “expanded notation,” “exponents,“ “factors,“ “multiplication,“ and “addition.“ The purpose of this discussion is to highlight the meaning of an exponent. Here are some questions for discussion:

• “What’s a simpler way to write ? What’s a simpler way to write ?” ( and )
• “Explain how is equivalent to .” (If you expand each exponent, it creates the equivalent expression . The expanded expression shows that there are actually 6 factors being multiplied, so we can rewrite this as .)
• “For what value of will equal 125?” (5)
• “For what value of will equal 64?” (4)
• “Describe any difficulties you experienced and how you resolved them.”