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Next Size Up

Age 7 to 11
Challenge Level

Next Size Up

10 cubes
Long ago, I made a string of ten graded cubes.
Each edge of the smallest cube was one centimetre long. Each edge of the largest cube was ten centimetres long.
I labelled each one with its volume in cubic centimetres.
The challenge for you is to make a string of graded cubes. You might do better working in a team, so encourage your friends to help!
We would love to hear how you made your own cubes and to see photos of them.


Why do this problem?

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. 

Possible approach

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.

Key questions

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?

Possible extension

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.

Possible support

Some children will find this net a useful starting point.