Building with solid shapes
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
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?
For accessibility:
A is a cone on top of a cylinder, on top of a cuboid.
B is three equilateral triangular prisms stacked on top of each other.
C is a triangular prism on top of 3 cubes.
D is a pyramid on top of a cuboid on top of 2 horizontal cylinders.
E is a pyramid on top of 2 cylinders stacked face to face.
F is three cylinders stacked on top of each other, with the curved faces touching.
G is a cone stacked on top of a cube on top of a horizontal cuboid on top of a second, vertical cuboid.
H is a pyramid stacked on top of a cylinder on top of a horizontal cuboid on top of 2 vertical cylinders which are side-by-side, on top of a horizontal cuboid.
I is a cone and cube next to each other on top of a horizontal cuboid stacked on a vertical cuboid which is to the right side of the base of the horizontal cuboid.
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
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
Key questions
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.