Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

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

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

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?

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?

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?

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

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

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

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

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?

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

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 Mah Ling?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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

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 outline of the butterfly?

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!

An activity centred around observations of dots and how we visualise number arrangement patterns.

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 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?

Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

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

Can you fit the tangram pieces into the outlines of the camel and giraffe?

Can you logically construct these silhouettes using the tangram pieces?

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 the numbers?

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 Little Ming?

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 sports car?

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

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

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