Why do this problem?
This is a tough problem
, ideal for learners who relish the challenge of working with large and difficult numbers. However, using interlocking cubes to create models of the situation will help children form mental images of cube numbers.
It will be necessary to have a large supply of cubes available for this activity, although allow pupils to decide for themselves whether they make use of them.
You could start by describing just a single yellow cube covered in a single layer of red cubes. Ask learners about the number of red cubes that would be needed and invite them to think on their own, then chat with a partner before sharing ideas. You may want to have a model already made to show the group after they have had chance to decide on the number. Pose a few other
questions like this, perhaps asking the group to imagine a few layers, one at a time.
Then you can pose the question itself. You may find it useful to print off and hand out copies of this sheet
which contains the problem.
It may be appropriate to ask pairs or small groups to work together on the challenge and then invite them to create a poster outlining how they approached the task. These could be displayed and time given in the plenary for all pupils to view them.
Have you found out how many cubes are needed to cover the single cube?
Have you remembered that there are only "up to 1000 of each colour"?
What is the cube root of 1000? How does this help you?
What size cubes are possible if the maximum number of cubes in one colour is 1000?
Assuming enough cubes are available, this could be done practically. Calculators may also be helpful.