The purpose of this Warm-up is to elicit the idea that rewriting expressions in different ways allows us to notice different features, which will be useful when students manipulate the structure of polynomial expressions in later activities. While students may notice and wonder many things about the four representations of 329, the use of exponents and parentheses to illuminate the different forms of the number 329 are the important discussion points.

Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the appropriate representation. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the idea that all numbers can be represented the way 329 is here using different powers of 10 does not come up during the conversation, ask students to discuss this idea.

If time allows, ask students to consider what would be true if the small squares were actually 0.1 instead of 1. What number would the squares represent? How could we write that number in the other 3 ways?

The purpose of this activity is to extend student thinking from the Warm-up into polynomial notation and show how the parts of a polynomial expression are similar to the parts of an integer written in base 10 (MP7). While the term “polynomial” won’t be introduced to students until the Lesson Synthesis, this activity gives students a chance to evaluate a polynomial function at specific values of , a skill that often needs practice. If students do not yet correctly evaluate the function because of sign errors, ask them to review their work, focusing on the results of multiplying negative numbers.

In this activity, students write a polynomial function to model a simple investment situation. They decide whether to use a table, equation, graph, or a combination of the three to make sense of and reason about the situation. While students are guided through the steps for writing the expression for 1, 2, and 4 years, careful notation with parentheses may help students make sense of the final equation. Monitor for students writing expressions in different ways or writing out each step, to share their work during the whole class discussion. Highlight any student that wrote out things like for all to see.