Stations 1 and 2
Tower of Hanoi
An ageold exercise in finding a mathematical pattern.
by Olga Pesantes and edited by Suzanne Alejandre
Table of Contents 
Versión español 
Looking at the Mathematics
CA Mathematics Standards Alignment
 6th grade
Algebra and Functions 3.0
Mathematical Reasoning 1.0
 7th grade
Algebra and Functions 1.1
Mathematical Reasoning 1.0
 8th grade
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:
 4 Tower of Hanoi puzzles (wooden sets)
 1 data sheet for the group
 2 computers
 Tower of Hanoi software
DIRECTIONS:
 The Materials Manager checks that all the towers are
complete. Each tower should have 6 wooden disks.
 The Reader reads the Legend of
the Tower of Hanoi out loud to the group.
 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.
 Write the answer down on your worksheet.
 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.
 Write the answer down on your worksheet.
 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!
 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 doubleclick 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.
CLEANUP:
 Make sure that all the towers are complete and that the disks are
placed properly on the pegs.
 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.
versión español
