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Rolling That Cube

We have a cube which is a bit like a dice, with inky marks on each face.
When it goes on paper it shows these numbers one by one.
The cube just gradually rolls over (NO SLIDING) and prints the following (I've draw squares round each number):
Your challenge is to find where the cube starts and what route it travels to print the numbers exactly as shown above.  You may find it useful to print off a copy of the grid on this sheet.
Can you also say how each face of the cube looks?

Why do this problem?

This activity is one which will particularly appeal to those pupils who enjoy problem solving or have good spatial awareness. It may, therefore, be a useful activity for a whole class - as it will enable you to see more clearly which pupils work well on spatial challenges.  It also offers opportunities for sharing different ways of approaching the task.

Possible approach

Depending on the pupils' experiences, it may be appropriate to start with them all together with a practical simplified example. Using a large cardboard/foam cube with simple shapes on each of the six faces, like this ...
... they could observe what happens as it rolls and try to predict what face will be at the bottom each time.
You could then present the challenge itself and give children time to work independently or in pairs.  A copy of the route can be found on this sheet. Try not to direct the way they work as you may be suprised by the methods they create. 
The plenary can then focus on their different approaches.  Allow time for all the different ways to be explained and then encourage pairs/small groups to discuss which method they might use if they were presented with a similar problem. Can they justify their choice?

Key questions

When working with the simple cube above:
What's happening here?
What can you tell me about the one at the bottom when I roll it this way?
When working on the actual challenge:
How are you working this out?
Will you be able to check that it's ok?

Possible extension

When pupils have managed this activity in a confident way they may like to have a look at Inky Cube which is similar but much harder. You could also give the pupils opportunities to create their own cubes and set challenges for each other.

Possible support

Many pupils may need to have support in rolling a cube over carefully. Be aware though that some pupils who need support in the more numerical aspect of mathematics may not need any support in this spatial work.