Page 84 - IM_Algebra2_FL Print Sample.pdf

Note that future lessons will focus on a reasonable domain for sequences represented by a function. Students may “connect the dots” in the graphs with lines, but it’s not crucial to address, at this time, whether or not that’s a sensible thing to do.
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
Ideally, arrange students in groups of 2 and distribute scissors and blank paper (or copies of the blackline master, if using). Invite them to read the beginning of the task and work with their partner to carry out the paper cutting while completing the rst few rows of the table. (As an option that would take less time, conduct a demonstration of the paper cutting, instead.) Ask students to pause after completing the rst few rows of the table and then ask,
• “What happens to the number of pieces after each cut?” • “What happens to the area of each piece after each cut?”
Ask students to share their responses with a partner, and then invite a few students to share their response with the class. Ensure students can articulate that as a result of a cut, the number of pieces doubles, and the area of each piece is halved. Students then proceed with the remainder of the activity.
Student Task Statement
Clare takes a piece of paper, cuts it in half, then stacks the pieces. She takes the stack of two pieces, then cuts again to form four pieces, stacking them. She keeps repeating the process.
Unit 1 Lesson 2: Introducing Geometric Sequences 19