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?

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

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

Can you fit the tangram pieces into the outline of these convex shapes?

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

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

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

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

Can you cut up a square in the way shown and make the pieces into a triangle?

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

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 the telescope and microscope?

Can you fit the tangram pieces into the outline of these rabbits?

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

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

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

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

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

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

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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

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 this brazier for roasting chestnuts?

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 these people?

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

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

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.

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

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

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

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

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

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?

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.

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

Exploring and predicting folding, cutting and punching holes and making spirals.

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

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

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?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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?

Exchange the positions of the two sets of counters in the least possible number of moves

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

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.