Page 75 - IM_Algebra2_FL Print Sample.pdf

4. Jada says she used the solution for 3 discs to help her solve the puzzle for 4 discs. Describe how this might happen.
5. How many moves do you think it will take to complete a puzzle with 5 discs?
6. How many moves do you think it will take to complete a puzzle with 7 discs?
Student Response
1. 3 moves
2. 7 moves
3. 15 moves
4. Sample response: Jada moved the tower of discs 1–3, then moved disc 4, then moved the tower of discs 1–3 onto it.
5. Sample response: Double the previous answer, then add 1. The number of moves is 31, because .
6. 127 moves
Activity Synthesis
Display a table for all to see that looks like this:
Ask students to share the smallest number of moves they found for 3 and 4 discs. Each time, ask if anyone in the class solved it with fewer moves. (If no one nds the minimal solution, ask students to keep looking if time allows, or share the minimum number of moves and challenge them to do it, or demonstrate the minimal solution.) Invite students to demonstrate the moves to show that their claim is possible. Ask students to consider how many moves to complete the puzzle with 1 disc. (The answer is 1, since the puzzle speci es the discs have to end up on a different peg.) You should now be showing a table like this:
Ask students for their thoughts about 5 discs and 7 discs. If no one suggests it, steer them toward looking for a pattern in how the number of moves is growing. If the pattern continues, would we expect the number of moves for 5 discs to be more than 30 or less than 30? How many moves would we predict are needed to solve the puzzle with 5 discs? Complete the table with 31, 63, and 127.
number of discs
1
2
3
4
5
6
7
number of moves
3
number of discs
1
2
3
4
5
6
7
number of moves
1
3
7
15
10
Teacher Guide Algebra