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

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

Investigate the number of faces you can see when you arrange three cubes in different ways.

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

Use the isometric grid paper to find the different polygons.

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

This problem explores the shapes and symmetries in some national flags.

How would you move the bands on the pegboard to alter these shapes?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

How many different triangles can you make on a circular pegboard that has nine pegs?