Lesson 9: What’s the Equation?
About this lesson
This is the first of several lessons where students practice modeling sequences using different types of equations and then use their equations to understand different aspects of the sequence, translating between the situations and their representations (MP2). This isn’t meant to be the full modeling cycle, but rather a focus on some practices that students must attend to while modeling (MP4). In this lesson, students describe a reasonable domain for a function representing a context where an unrestricted domain does not make sense. They also encounter a situation where a recursive model is straightforward to write while one for the \(n^{\text{th}}\) term is not, leading to the idea that sometimes the model we use depends on what we are trying to do and the time we have to spend.
Encourage students to represent the sequences in multiple ways to help them make sense of the patterns. These lessons also provide opportunity for students to recall and use techniques they may have learned in earlier courses about modeling linear and exponential functions. It is also important to note that the work students do modeling situations with geometric sequences here will be built upon in a future unit on exponential functions.
Lesson overview
 9.1 Warmup: Math Talk: Multiplying Fractions (10 minutes)
 9.2 Activity: Take the Cake! (15 minutes)

9.3 Activity: Fibonacci Squares (10 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 9.4 Cooldown: Ow, My Jaw (5 minutes)
Learning goals:
 Identify restrictions on the domain of a sequence based on context.
 Use sequences to model situations.
Learning goals (student facing):
 Let’s define sequences.
Learning targets (student facing):
 I can represent situations with sequences.
Required materials:
 graph paper
Required preparation:
 Provide each student with 1 small sheet of graph paper.
Standards:
 This lesson builds toward the standards: CCSS.HSFBF.A.2MS.FBF.2CCSS.HSFLE.A.2MS.FLE.2MO.A1.LQE.B.4MO.A1.LQE.A.3
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