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).
- Create a table, graph, or recursive definition of a sequence from given information.
- Let’s look at different ways to represent a sequence.
- I can represent a sequence in different ways.
A sequence in which each term is the previous term plus a constant.
A sequence in which each term is a constant times the previous term.