Why do this problem?
is fundamentally a practical one which involves careful measuring and drawing. But by making a string of graded cubes for themselves, children's understanding of length and volume will be deepened far more than through just calculating volumes of hypothetical cubes. The problem could be used as a group or team activity where
learners work together for a common purpose.
You could begin by showing the group the string of cubes pictured in the problem and invite them to talk in pairs about what they see. Open up the discussion so that the whole group participates and eventually comes to a consensus about what is pictured. You can then introduce the challenge to make a set of cubes for themselves.
This problem could be a good way to introduce the idea of a net of a cube, or you could choose to set the challenge having already worked on nets. The group's prior experience of nets will influence the way you facilitate the activity and the frequency with which you bring them all together to share progress.
Invite groups of learners to work together on this task and try not to be too prescriptive in terms of the way they approach it and the materials they use. It might be worth ensuring that sharp pencils, rulers, thin card (preferably squared), glue and sticky tape are available, should a group require them. (This squared
sheet for printing onto thin card might be useful.) Some groups might want to use the computer to create their net. Thin thread and a needle will also be needed to hang up the shapes.
It might be that the whole class decides to distribute the work amongst the groups so that one or two sets are produced in total.
How will you make a cube from paper/card?
What can you tell me about a cube?
How do you know how big each cube will be?
How will you share out the work?
Learners could make a string of other more ambitious shapes such as tetrahedra or octahedra although calculating the exact volume of these might be too tricky.
Some children will find this net
a useful starting point.