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

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

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

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

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

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

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

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?

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

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

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

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

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

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?

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

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?

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 clock?

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

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

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

Can you split each of the shapes below in half so that the two parts are exactly the same?

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.

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

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?

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

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

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

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

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

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

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

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

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

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.

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!

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 outline of Little Ming?

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 outline of Granma T?

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