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

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

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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?

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

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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.

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?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

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

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Move just three of the circles so that the triangle faces in the opposite direction.

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

An activity centred around observations of dots and how we visualise number arrangement patterns.

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

How many loops of string have been used to make these patterns?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

How many pieces of string have been used in these patterns? Can you describe how you know?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outline of the rocket?

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

Can you fit the tangram pieces into the outline of these convex shapes?

Can you fit the tangram pieces into the outline of this junk?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outlines of the candle and sundial?