One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

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?

Can you make a 3x3 cube with these shapes made from small cubes?

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?

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?

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

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Exchange the positions of the two sets of counters in the least possible number of moves

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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.

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

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Exploring and predicting folding, cutting and punching holes and making spirals.

What is the greatest number of squares you can make by overlapping three squares?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

Can you find a way of counting the spheres in these arrangements?

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

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

Reasoning about the number of matches needed to build squares that share their sides.

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

Can you cut up a square in the way shown and make the pieces into a triangle?

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

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

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

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Can you fit the tangram pieces into the outlines of the chairs?

Can you visualise what shape this piece of paper will make when it is folded?

Can you fit the tangram pieces into the outline of Granma T?

What shape is made when you fold using this crease pattern? Can you make a ring design?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Make a flower design using the same shape made out of different sizes of paper.

Can you fit the tangram pieces into the outline of Little Ming?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of the child walking home from school?

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

Can you logically construct these silhouettes using the tangram pieces?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?