In this lesson, students continue their exploration of situations polynomial functions can model. Students make connections between equivalent expressions for a polynomial function, the function’s graph, and the situation it models.
Students first consider how polynomials let us look at something familiar in a new way by identifying parallel structures between the base10 number system and polynomials (MP7). Students will draw on these parallel structures to better understand polynomial division in later lessons. This activity also gives students an opportunity to practice evaluating polynomials for different inputs; these calculations can be tricky because polynomials have many parts, and careful attention is needed when entering expressions into a calculator. Students then examine a financial context, building a polynomial to model a simple investment account. Students may choose to use a table, equation, graph, or combination of these to make sense of and reason about this situation (MP5). Investment accounts will be revisited at the end of the unit when students calculate the sum of a finite geometric series.
Lesson overview
 2.1 Warmup: Notice and Wonder: Writing Numbers (5 minutes)

2.2 Activity: Polynomials in the Integers (10 minutes)
 Includes "Are you Ready for More?" extension problem
 2.3 Activity: A Yearly Gift (20 minutes)
 Lesson Synthesis
 2.4 Cooldown: A Different Account (5 minutes)
Learning goals:
 Create a polynomial to model a simple investment situation.
 Generalize the structure of integers in order to see similarities to polynomials.
Learning goals (student facing):
 Let’s look at some other things that polynomials can model.
Learning targets (student facing):
 I can use polynomials to understand different kinds of situations.
Required materials:
 Graphing technology
Required preparation:
 Acquire devices that can run Desmos (recommended) or other graphing technology.
 It is ideal if each student has their own device. (Desmos is available under Math Tools.)
Standards:
 This lesson builds on the standard: CCSS.HSFIF.A.2MS.FIF.2MO.A1.IF.A.2
 This lesson builds towards the standards: CCSS.HSAAPR.A.1MS.AAPR.1CCSS.HSASSE.A.1MS.ASSE.1MO.A2.APR.A.3MO.A2.NQ.A.2
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