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through these activities. Specifying that students take turns deciding, explaining, and listening limits the phenomenon where one student takes over and the other does not participate. Taking turns can also give students more opportunities to construct logical arguments and critique others’ reasoning (MP3).
Launch
Arrange students in groups of 2. Tell students that for each sequence, one partner nds its matching recursive de nition and explains why they think it matches. The partner's job is to listen and make sure they agree. If they don't agree, the partners discuss until they come to an agreement. For the next sequence, the students swap roles. If necessary, demonstrate this protocol before students start working. Ensure that students notice that one sequence and one de nition do not have matches, and they are tasked with writing the corresponding match.
If students have access to a spreadsheet, suggest that it might be a helpful tool in this activity.
Student Task Statement
For each sequence:
• Determine whether it could be geometric or arithmetic, or whether it cannot be either.
• Match the sequence to a recursive de nition.
There is one sequence and one de nition that do not have matches. Create their
corresponding match. Sequences:
1. 2. 3. 4. 5. 6.
De nitions: 1.
2. 3. 4. 5.
Unit 1
Lesson 5: Recursive De nitions 53