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The Path of the Dice

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The Path of the Dice

You have an ordinary dice with $6$ faces:


In this game you can turn the dice onto any face which is already showing. Look at the $4$ ways this can be done:

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In the grid below, you move the dice to another place by clicking on the direction arrow,
OR by clicking on the place you want to move to.

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Can you work out the route from the start to the finishing position by turning the dice in this way?
How many ways can you find of doing it?
Can you explain this?

Starting in the same way, how many different finishing positions can you find? Make up your own routes for a friend.


Why do this problem?

This game is suitable for your pupils who can approach hard challenges. It will give them the opportunity to make use of theirĀ  spatial awareness and their ability to put into action some systems that they think will work. It can also be a useful tool for pupils to learn from their mistakes.

Possible approach

It would be good to have a try at this game yourself first before deciding to present it to the pupils.
Take a dice and show the slow rolling of that dice forwards, backwards, right and left. This can of course be replicated by the first interactivity. The pupil or pupils that you think are ready for this should be invited to explore the changes that take place with these $4$ types of movement.
When they've explored the dice for a while, present the challenge as shown.

Key questions

What sorts of things have you noticed?
Have you come to any decisions? What are they?
Tell ne about what you've done.
Tell me about what you've decided to do to get a solution?

Possible extension

Explore all the possible moves starting from all the different positions a dice can start from.

Possible support

Some pupils with poor motor control may need help when exploring with real dice.