Page 148 - IM_Algebra2_FL Print Sample.pdf

Activity Synthesis
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
• “Who can restate [ ]’s reasoning in a di erent way?”
• “Did anyone have the same strategy but would explain it di erently?” • “Did anyone solve the problem in a di erent way?”
• “Does anyone want to add on to [ ]’s strategy?”
• “Do you agree or disagree? Why?”
8.2 Fibonacci Squares
15 minutes
This pattern creates the Fibonacci sequence. One purpose of this task is to make the point that sometimes it is di cult to write a closed-form de nition, so we can just work with the recursive de nition. Another is to make explicit that the domain of a sequence is a subset of the integers, and de ne the term integers if necessary.
Launch
Distribute 1 piece of graph paper to each student. Ask them to complete the rst question and pause. Ensure that they are interpreting the description of the pattern correctly before they proceed with the rest of the activity.
Student Task Statement
1. On graph paper, draw a square of side length 1. Draw another square of side length 1 next to it to create a 2-by-1 rectangle. Next, add a 2-by-2 square, with one side along the sides of both of the rst two squares. Next, add a square where one side goes along the sides of the previous two squares you created. Next, do it again.
2. Write a sequence that records the side lengths of the squares you drew.
3. Predict the next two terms in the sequence and draw the corresponding squares to check your guesses.
4. Write a description for how each square’s side length depends on previous side lengths.
5. Write a recursive function for , the th side length. (Start with the rst term instead of the zeroth term. That is, your de nition should start with )
6. What is the domain of this function?
Unit 1
Lesson 8: What’s the Equation?
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