In this partner activity, students take turns matching a sequence to a definition. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

One sequence and one definition do not have matches. Students are tasked with writing the corresponding match.

Monitor for students using clear reasoning as they create a recursive definition for the sequence 18, 20, 22, 24 to share during the discussion.

Making a spreadsheet available gives students an opportunity to choose appropriate tools strategically (MP5).

Some students may not be sure how to begin matching sequences to definitions. Encourage them to start by picking a definition and calculating the first few terms of the sequence it represents.

The goal of this discussion is for students to share what features of the sequences and definitions they used to make their matches.

Once all groups have completed the matching, ask “How did you decide which definitions to match to sequence 3, 6, 12, 24 and sequence 18, 36, 72, 144, given they both involve doubling?” (They are both geometric with a growth factor of 2, but since they have different first terms, we could use those to match the sequences to and .)

Next, invite previously identified students to share the recursive definition they created for the sequence 18, 20, 22, 24 and their strategy for writing it.

If time allows and students need extra practice graphing functions, assign students one function each from the Task Statement to sketch a graph for. After work time, select students to share their sketches. Display them for all to see and compare.

The purpose of this task is for students to write a recursive definition for a sequence that represents a mathematical context and to create other representations of the sequence.

Monitor for groups who create their recursive definitions in different ways to share during the whole-class discussion. For example, some students may first create a table showing step number and the associated values, while others may draw additional steps.

Allow students to use graph paper to sketch their graphs if needed. Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).

Students may not be sure where to begin with the graph since no axes are provided in the Task Statement. Encourage these students to first figure out what values they need to plot before drawing, scaling, and labeling their axes.

The goal of this discussion is for students to share how they reasoned about a recursive definition for and how they created their graph for Steps 1 to 7. Invite previously identified groups to share how they created their definitions and to include any additional representations, such as tables or drawings of additional steps, they used to help their thinking. After these students have shared, ask "Did anyone use a different strategy for writing their definition?" and invite any new students to share their thinking.

Conclude the discussion by reviewing graphing strategies as needed. Select 2–4 students to share how they created their sketch of . In particular, focus on how the scale of each axis was chosen.