Page 74 - IM_Algebra2_FL Print Sample.pdf

The ultimate purpose of this activity is to de ne the term sequence. A recursive rule is generated, but only informal notation is required. Other purposes are to start to establish that students are expected to try things out, look for patterns, explain their thinking, justify their responses, and listen respectfully to their classmates.
This activity works best when each student has access to devices that can run the GeoGebra applet because students will bene t from seeing the relationship in a dynamic way. If students don't have individual access, projecting the applet during the launch would be helpful.
Launch
Distribute objects with which to experiment with the puzzle. Alternatively, help students access the digital applet.
Ask students to read the rules to the puzzle, and give them a few minutes to solve the puzzle with 2 discs. Ask a student to demonstrate why it takes 3 moves to solve the puzzle with 2 discs. Before students start working, remind them they need to keep track of the number of moves needed for each new number of discs, and that they need to try to nd the smallest number of moves. Encourage them to check in with those around them to see if anyone found a solution with fewer moves.
Student Task Statement
In the Tower of Hanoi puzzle, a set of discs sits on a peg, while there are 2 other empty pegs.
A move in the Tower of Hanoi puzzle involves taking a disc and moving it to another peg. There are two rules:
• Only move 1 disc at a time.
• Never put a larger disc on top of a smaller one.
You complete the puzzle by building the complete tower on a di erent peg than the starting peg.
1. Using 2 discs, complete the puzzle. What is the smallest number of moves needed?
2. Using 3 discs, complete the puzzle. What is the smallest number of moves you can nd? 3. Using 4 discs, complete the puzzle. What is the smallest number of moves you can nd?
Unit 1
Lesson 1: A Towering Sequence 9