Cubes and cuboids

problem
Nicola's jigsaw

Age

11 to 14

Challenge level

Nicola has lost a piece of her 3D jigsaw. Can you work out the shape of the missing piece?
problem
Changing areas, changing volumes

Age

11 to 14

Challenge level

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?
problem
Four layers

Age

5 to 11

Challenge level

Can you create more models that follow these rules?
problem
Troublesome dice

Age

11 to 14

Challenge level

When dice land edge-up, we usually roll again. But what if we didn't...?
problem
Inky cube

Age

7 to 14

Challenge level

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
problem
Three sets of cubes, two surfaces

Age

7 to 11

Challenge level

How many models can you find which obey these rules?
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
Which solid?

Age

7 to 16

Challenge level

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
problem
Castles in the middle

Age

7 to 14

Challenge level

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
problem
Solids

Age

11 to 16

Challenge level

A task which depends on members of the group working collaboratively to reach a single goal.