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?

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?

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

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

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

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?

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

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?

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

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.

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

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?

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

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

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

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

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

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

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

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

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?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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

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.

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.

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

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

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

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 second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.

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

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.