Why do this problem?
allows all pupils to have a positive experience of solving problems, as it requires very little mathematical knowledge. It encourages a systematic approach and provides an opportunity for pupils to explain how they know they have all the solutions.
As a class, begin with three large dice. Discuss what the first instruction means - what are 'the touching faces of adjacent dice'? Ask a pupil to demonstrate how to 'stick' the three dice together.
Once the dice are 'stuck' together, discuss what the total of the numbers on the top is. If we switched the numbers around as in the first picture, would this be the same arrangement or a different arrangement? Encourage pupils to discuss their ideas, and then explain that for this activity we will be thinking of both arrangements as being the same.
Once pupils have understood these key ideas, give them time to work in small groups on the four challenges.
Explain what you are doing to find the next arrangement.
Tell me how you are recording your results.
Will you know if you have found them all? How?
Challenge the pupils to change one of the rules about this task, maybe the number of dice, the totals to be obtained... Ask the pupils to set a new and different challenge for someone else to do, making sure that they know what the answers should be.
Some pupils may need help remembering and following the rules throughout the activity. Sharing different ways of thinking about the problem and different ways of recording that thinking can be very useful in developing all learners' problem-solving skills.