Building With Solid Shapes
1 out of 3
We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?
Problem
Building With Solid Shapes printable sheet
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?
Getting Started
You could test out your ideas with some real shapes.
Student Solutions
Alistair and his sisters Rachel and Abigail, all from Histon and Impington Infants School, sent a joint solution:
Rachel and Abigail discussed the shapes, and said that shape B would fall down - because balancing on the pointy bits would be hard.
Shape F would roll down.
Shape I has only got one "leg" at one edge, and there is no weight on the other side to balance it. (Their mum believes they were thinking of a T shape without the right arm.)
Alistair said:
Shape I has a fulcrum at the top right, and a weight on the top left so the cuboid will turn downwards and fall over.
Shape D has sort of wheels so if it is made on a flat surface it should be OK, but if it is tilted, the cuboid will roll off.
Rachel and Abigail suggested that if the shapes were given a little "shove", E might fall over. (Mum's translation: unstable)
Alistair, Rachel and Abigail don't mention shapes A, C, G or H. I wonder if this is because they think these are stable?
Adriana's son from Australia sent in this lovely picture which shows solutions and ways of fixing the unstable ones.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
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.