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.

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

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

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

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?

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

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

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?

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?

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

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

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

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

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

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

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

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

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?

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

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?

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?

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

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

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!

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

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

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

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

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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

Can you fit the tangram pieces into the outlines of these clocks?

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

Can you fit the tangram pieces into the outline of Little Fung at the table?

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?

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

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

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

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

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

Here's a simple way to make a Tangram without any measuring or ruling lines.

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

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

Can you fit the tangram pieces into the outline of this sports car?

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

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