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Lesson 8: What’s the Equation?
• Understand that sequences are functions and can be used to model situations. • Understand that the domain of a sequence is a subset of the integers.
Lesson Narrative
Over the next several lessons, students model several situations with sequences represented in di erent ways. This isn’t meant to be full-blown modeling, but to touch on some practices that must be attended to while modeling, such as choosing a good model and expressing numbers with an appropriate level of precision.
In this lesson, students write a recursive de nition of the Fibonacci sequence and recognize that this is a function, and its domain is a subset of the integers. (Integers should be de ned for students who are unfamiliar with its meaning.) They see that not all sequences have a straightforward closed-form equation. Then, they write a function to represent a situation characterized by exponential change in both recursive and closed forms. They see that although the inputs are a subset of the integers, the outputs don’t have to be. Students engage in aspects of mathematical modeling (MP4) when they describe a reasonable domain for a function representing this context.
Required Preparation
Each students needs at least 1 sheet of graph paper.
Student Learning Goals
• Let’s use sequences to solve problems.
8.1 Math Talk: Multiplying Fractions
Warm Up: 10 minutes
The purpose of this Math Talk is to elicit strategies and understandings students have for interpreting an exponential function and for multiplying fractions. These understandings help students develop uency and will be helpful later in this lesson when students will need to multiply 1 by several times and create a closed-form de nition for a geometric sequence.
Math Talks build uency by encouraging students to think about expressions and rely on what they know about properties of operations to mentally solve a problem.
If students need a deeper dive in recalling how to multiply fractions, here is string of problems to try:
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Unit 1 Lesson 8: What’s the Equation? 81