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

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

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 fit the tangram pieces into the outline of the house?

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

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

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 fit the tangram pieces into the outline of this teacup?

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

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?

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

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 outlines of the telescope and microscope?

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 the convex shapes?

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?

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

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 Mah Ling?

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

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?

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

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

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 chairs?

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?

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 silhouette of the junk?

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

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

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

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

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

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

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

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

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 outlines of Wai Ping, Wu Ming and Chi Wing?

Can you logically construct these silhouettes using the tangram pieces?