This workshop provides and models everything that teachers need to help teach mathematical problem solving for primary school Stages 1-3, high school and beyond.

It models how teachers can transfer this activity direct into your own classroom with minimal effort and maximum effect.

The workshop is comprised of three short videos and related, hands-on activities.

The Tower of Hanoi is a 'stacking tower' game. According to the game story, a group of Buddhist monks believed that by finding the answer to this mystery/problem, they would discover the date that the world would end.

Students try this game and to perform a number of trials and then look for a general formula that will allow them to find the total number of moves for a tower that is 100 disks high.

The steps the students follow in solving the 'mystery', closely parallel some strategies that professional mathematicians use in their work.

The video shows how students put some of these strategies into practice, working together enthusiastically on the challenge of uncovering the mystery of the Tower of Hanoi.

Our introductory video shows that collaboration is an essential part of doing mathematics in the real world.

The metaphor of The Tower of Hanoi game is introduced to students to help them identify, develop and practice the types of strategies that mathematicians might use in solving real-world problems.

The video shows how students naturally develop their own strategies, with guidance from a facilitator who who shows that teachers do not need to provide the answers.

How students put some of these strategies into practice, working together enthusiastically on the challenge of uncovering the mystery of the Towers of Hanoi.

The story is that the Tower of Hanoi is a 'stacking tower' game that was played by Buddhist monks.

According to the rules of the game, the monks had to move 100 disks form one location to another. The amount of time taken to move the disks is the same amount of time left before the world will end. According to the game story, by finding out how long it will take to move the disks, the monks could discover the date when the world would end.

The game starts by placing a number (the actual number can be varied) of disks stacked on top of each other in order of size; with larges disks close to the base/bottom and increasingly smaller disks towards the top of the tower.

To complete the game, all of the disks must be moved from one location to another.

There are two rules about how the disks can be moved:

1. Only move one disk at a time
2. Only place smaller disks on top of a larger disk (you cannot put a large disk on top of a smaller disk)

Record the date and the title 'Towers of Hanoi' on a clean page in your journal (write your name at the top of the page if you are sharing or not using your own journal).

What is the smallest number of moves you can make;

1. to move 3 disks - write down your prediction and draw a circle around it
2. to move 4 disks - write down your prediction and draw a circle around it

Share and compare your solution and justification with others in your group.

Write down the total number of move you found using your solution and draw a square around it.

EXTENDED ACTIVITIES

If there were 100 disks, when would the game story predict that the world would end?

• Write down your prediction of the number of move it will take.
• Draw a circle around the number of moves that you predict

How do you think you can find out how much time it will take to move 100 disks?

Share and compare your solution and justification with others in your group.

• Write down the total amount of time you found using your solution and draw a square around it.
• Write down your justifications/proof, so that you can share and explain it to other students during the next workshop.

• What did you used to think?
• What do you think now?

• Go to Student //Tower of Hanoi// problem page

• Source - Workshop #4 - Thinking like a mathematician
• Reverse Problem Solving - Strategies of a Chess Grand-master
• School of hard sums: https://www.youtube.com/watch?v=I-UHM4IMhGU