3D shapes and their properties

problem

Four Points on a Cube

Age

16 to 18

Challenge level

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?
problem

Construct-O-Straws

Age

7 to 11

Challenge level

Make a cube out of straws and have a go at this practical challenge.
problem

Cereal Packets

Age

7 to 11

Challenge level

How can you put five cereal packets together to make different shapes if you must put them face-to-face?
problem

Triple Cubes

Age

5 to 11

Challenge level

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
problem

Double Your Popcorn, Double Your Pleasure

Age

7 to 11

Challenge level

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.
problem

28 - Upward and Onward

Age

7 to 11

Challenge level

Can you find ways of joining cubes together so that 28 faces are visible?
problem

Little Boxes

Age

7 to 11

Challenge level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
problem

Face Painting

Age

7 to 11

Challenge level

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.
problem

Dodecamagic

Age

7 to 11

Challenge level

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
problem

Child's Play

Age

7 to 11

Challenge level

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?