Cubes Cut Into Four Pieces

'Cubes Cut Into Four Pieces' printed from https://nrich.maths.org/

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Cubes Cut Into Four Pieces

Eight children sat round the big table at the end of the classroom. They each had a cube made from modelling clay.

"Cut your cube into four pieces which are all exactly the same shape and size," said their teacher, "and try to make your pieces different from everyone else's!"

When the children had cut the cubes up they put some of the pieces on the table in two rows with their names by them.

Pieces of cubes

"Someone didn't cut theirs into four!" said Belinda pointedly.

Who was that and how many pieces were there?

"Two of us have made the same shapes!" shouted Charlie.

Who were they?

Here are six cubes showing the way the children cut them.

6 cubes

Whose are they?

Why do this problem?

This problem requires some visualisation, and knowledge of 3D shapes. It gives children experience of identifying shapes from pictures of them in different positions and orientations.

Possible approach

Ideally, it would be good to have some modelling clay/plasticene available for this activity (wooden or plastic 3D shapes might also be useful).

You could start by showing the group a cube of clay and asking them to describe the shape. Ask them to imagine how they could cut the cube into four pieces which are exactly the same size and shape. Give them time to think on their own, then to share their ideas with a partner. You could then give each pair their own cube of clay and invite them to test out their cuts.

Gather all the cut cubes together to compare the different cuts, encouraging the children to talk about what they notice. You may find that some pairs have not got four pieces, some may have differently-shaped or differently-sized pieces and so this will promote much discussion.

From there, you can introduce the problem as it is written, showing the group the pictures of the children's pieces. You may find this sheet useful which has each picture as a separate card so pupils can match the picture of the cut cubes to each child's pieces. It may be helpful to have more cubes of clay available in case it is necessary to re-create some of the cuts in the problem.

Key questions

Which cube do you think that shape came from?

How would you cut a cube to make that shape?

Possible extension

Learners could try different ways of cutting cubes into more than four pieces, and draw the results.

Possible support

Having modelling clay cubes available for the children to cut in the ways drawn will help them access this problem.