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Activity Synthesis
Tell students that for this sequence, is the th term of a sequence, and
for is called a recursive de nition of the sequence.
“Recursive” just means that the value of any new term is computed based on the previous term.
Ask a student to demonstrate how they used the rule to nd or if necessary, demonstrate this yourself.
Ask a student to articulate why nding would be di cult (you’d have to nd the number of dots for every stage up through 100). Tell students that we will learn an e cient way to compute
in a future lesson.
If needed, consider presenting and asking students to interpret the recursive de nition for some sequences they have seen so far in this unit. For example, the de nition for the number of pieces after each cut in the paper-cutting sequence would be
5.3 Matching Recursive De nitions
15 minutes
In this activity students take turns with a partner matching a sequence to a recursive de nition. Students trade roles explaining their thinking and listening, providing opportunities to explain their reasoning and critique the reasoning of others (MP3). One sequence and one de nition do not have matches; students are tasked with writing the corresponding match.
Making a spreadsheet available gives students an opportunity to choose appropriate tools strategically (MP5).
Instructional Routines
• Take turns
What: Students work with a partner or small group. They take turns in the work of the activity, whether it be spotting matches, explaining, justifying, agreeing or disagreeing, or asking clarifying questions. If they disagree, they are expected to support their case and listen to their partner’s arguments. The rst few times students engage in these activities, the teacher should demonstrate, with a partner, how the discussion is expected to go. Once students are familiar with these structures, less set-up will be necessary. While students are working, the teacher can ask students to restate their question more clearly or paraphrase what their partner said.
Why: Building in an expectation, through the routine, that students explain the rationale for their choices and listen to another's rationale deepens the understanding that can be achieved
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Teacher Guide Algebra