Building with Solid Shapes

'Building with Solid Shapes' printed from https://nrich.maths.org/

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Building with Solid Shapes

We have a box of solid shapes. In it there are cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons.

Which of the buildings below would fall down if we tried to make them? Which ones would be unstable and possibly collapse?

Why do this problem?

This problem helps children begin to understand the various properties of common geometric solid shapes. It also promotes discussion and experimentation concerning their features, and requires them to justify their ideas. Naming the shapes should be a help in discussion and description of what has been done, rather than as an exercise in its own right.

Possible approach

Before doing this problem children should have plenty of free play building with sets of solid shapes so that they begin to have feel for their properties. They should be encouraged to talk about their buildings and ask questions about them.

You could start working on the actual problem with the whole group by asking an individual to balance one of the shapes - perhaps the cone or the triangular prism - on one of its sides. Ask if they can do it in any other way up. You could then repeat this with other children and other shapes. Ask why certain ways do not balance whereas others do. Also get the children to balance one shape on top of another. Always press the children to explain why there is a certain result.

After this, the children could work in pairs on the problem itself, either by referring to the pictures projected from a computer or by using this sheet (colour) printed out. If you want to photocopy, this sheet (black and white), might be better. If at all possible children should have opportunity to experiment with real shapes as they work on the problem. Again, press the children to explain why they think they get a certain result.

Key questions

Do you think these two shapes would balance like that? Why?

Why do you think that this building would fall down?

Possible extension

Children could build and draw their own buildings which balance.

Possible support

If children are having difficulties with this problem then real solid shapes are essential. Encourage them to predict whether a building will fall down before asking them to make it (or something like it) to see if it does. Continue in this way until they are confident working on their own.