# Tower of Hanoi

An age-old exercise in finding a mathematical pattern.

#### by Olga Pesantes and edited by Suzanne Alejandre

CA Mathematics Standards Alignment
Algebra and Functions 3.0
Mathematical Reasoning 1.0
Algebra and Functions 1.1
Mathematical Reasoning 1.0
Algebra I 16.0, 25.0

Students use the properties of the number system to judge the validity of results, to justify each step of a procedure, and to determine how many moves it takes to get from the leftmost to the rightmost peg. After working with specific cases, students are asked to look at the pattern and generalize algebraically.

#### MATERIALS:

1. 4 Tower of Hanoi puzzles (wooden sets)
2. 1 data sheet for the group
3. 2 computers
4. Tower of Hanoi software

#### DIRECTIONS:

1. The Materials Manager checks that all the towers are complete. Each tower should have 6 wooden disks.
2. The Reader reads the Legend of the Tower of Hanoi out loud to the group.
3. There is a game based on this legend. You have a small collection of disks and 3 pegs on which you can place them. You can only move one disk at a time. You cannot put a larger disk on top of a smaller disc. Now you are ready to start.
• Start by placing 1 disk on the left peg.
• How many moves does it take to move it to the right peg?
• Consult with your group members.
• Now place 2 disks on the left peg.
• How many moves does it take to move them to the right peg?
• Consult with your group members.
• Continue this procedure until you have found the solution for 6 disks. Remember that you are trying to move all the disks in the smallest number of moves. Good luck!
4. When everyone in your group has finished, try moving the tower on the computer. This tower has 7 disks.
• Move the mouse on the computer to take the screen saver off the screen.
• At this point there should be an icon labeled Tower of Hanoi on the left hand side of your screen.
• Drag your mouse over to the icon and double-click on Tower of Hanoi.
• Using the mouse, select the button that says "TAKE" to move a disk.
• Using the mouse, select the button that says "PLACE" to place the disk in that stack.
• The computer will keep track of how many moves you have made.
• When you have finished, press the button that says "QUIT" to leave the program.

#### PRODUCT:

In this center you will complete 1 worksheet as a group.

#### CLEAN-UP:

1. Make sure that all the towers are complete and that the disks are placed properly on the pegs.
2. Make sure that the screen on your computer has the Tower of Hanoi icon on it so that the next group is ready to go when they arrive.