This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

How many different shapes can you make by putting four right- angled isosceles triangles together?

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?

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.

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

Here are shadows of some 3D shapes. What shapes could have made them?

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?

This activity challenges you to make collections of shapes. Can you give your collection a name?

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.