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 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

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?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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?

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

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

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

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

Which of these dice are right-handed and which are left-handed?

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 ...

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

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 is wrong with the cogs on a UK 2 pound coin?

Can you fit the tangram pieces into the outlines of the convex shapes?

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

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

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

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

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

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

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

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

Can you fit the tangram pieces into the outline of Mah Ling?

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.

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!

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?

Can you logically construct these silhouettes using the tangram pieces?

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

Can you fit the tangram pieces into the silhouette of the junk?

Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?

Can you fit the tangram pieces into the outline of the playing piece?

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

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

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

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

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

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

Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

Can you fit the tangram pieces into the outlines of the camel and giraffe?

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

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

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

Can you fit the tangram pieces into the outlines of Little Ming and Little Fung dancing?