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 outline of the house?

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

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 telescope and microscope?

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

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 butterfly?

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

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

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

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

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?

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?

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 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 candle?

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

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

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 child walking home from school?

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?

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?

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 outlines of the people?

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

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 camel and giraffe?

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

Can you logically construct these silhouettes using the tangram pieces?

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

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

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

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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 Little Ming?

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

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

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

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