This lesson is optional. If students are proficient working with function notation, creating tables, and sketching graphs, this lesson may be skipped. This lesson also provides more practice writing recursive definitions.
The goal of the lesson is for students to practice interpreting and writing recursive definitions of functions while also representing functions in different ways. Students match sequences and recursive definitions in a matching activity, giving them opportunities to explain their reasoning and critique the reasoning of others (MP3). An important part of the activities is giving students time to share and explain their strategies for creating different representations. This helps emphasize that there is often more than one way to approach problems. It also helps establish that sharing strategies and learning from other students are classroom norms.
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available (MP5).
Lesson overview
 6.1 Warmup: Reading Representations (5 minutes)
 6.2 Optional Activity: Matching Recursive Definitions (15 minutes)

6.3 Optional Activity: Squares of Squares (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 6.4 Cooldown: Represent this Sequence (5 minutes)
Learning goals:
 Create a table, graph, or recursive definition of a sequence from given information.
Learning goals (student facing):
 Let’s look at different ways to represent a sequence.
Learning targets (student facing):
 I can represent a sequence in different ways.
Required materials:
 graph paper
Standards:
 This lesson builds on the standard:CCSS.HSFIF.A.3MS.FIF.3MO.A1.LQE.B.5MO.A1.LQE.B.6
 This lesson builds towards the standards:CCSS.HSFBF.A.2MS.FBF.2MO.A1.LQE.B.4CCSS.HSFLE.A.2MS.FLE.2MO.A1.LQE.A.3
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