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Instructional Routines
• Think pair share
What: Students have quiet time to think about a problem and work on it individually, and then time to share their response or their progress with a partner. Once these partner conversations have taken place, some students are selected to share their thoughts with the class.
Why: This is a teaching routine useful in many contexts whose purpose is to give all students enough time to think about a prompt and form a response before they are expected to try to verbalize their thinking. First they have an opportunity to share their thinking in a low-stakes way with one partner, so that when they share with the class they can feel calm and con dent, as well as say something meaningful that might advance everyone’s understanding. Additionally, the teacher has an opportunity to eavesdrop on the partner conversations so that she can purposefully select students to share with the class.
Launch
Ask students to recall from the previous lesson the meaning of geometric sequence, and to give some examples. Write the examples they generate for all to see, and use them to recall the de ning characteristic of geometric sequences (any two consecutive terms have a common ratio).
Arrange students in groups of 2. Give them a few minutes of quiet think time, followed by an opportunity to discuss their responses with a partner before whole-class discussion.
Student Task Statement
For each sequence, Term 0 through Term 4 are listed.
• Sequence A: 30, 40, 50, 60, 70, ... • Sequence B: 0, 5, 15, 30, 50, ... • Sequence C: 1, 2, 4, 8, 16, ...
1. For each sequence, describe a way to produce a new term from the previous term.
2. If the patterns you described continue, in which sequence is Term 10 largest? 3. Which of these could be geometric sequences? Explain how you know.
4. What can you say about the di erences between consecutive terms in Sequence A?
5. What can you say about the di erences between consecutive terms in Sequence B?
Student Response
1. Sample response: For Sequence A, each term is 10 more than the previous term. For Sequence B, each term is 5 times the term number more than the previous term (add 5, then add 10, then add 15...). For Sequence C, each term is double the previous term.
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Teacher Guide Algebra