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

The challenge for you is to make a string of six (or more!) graded cubes.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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

Can you fit the tangram pieces into the outline of the telescope and microscope?

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

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

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 candle and sundial?

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

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

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

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

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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?

Surprise your friends with this magic square trick.

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

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

Follow these instructions to make a five-pointed snowflake from a square of paper.

Did you know mazes tell stories? Find out more about mazes and make one of your own.

Can you deduce the pattern that has been used to lay out these bottle tops?

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

What shape is made when you fold using this crease pattern? Can you make a ring design?

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

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 these clocks?

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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

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

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

Make a cube out of straws and have a go at this practical challenge.

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

Can you make the birds from the egg tangram?

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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 this brazier for roasting chestnuts?

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

Make a mobius band and investigate its properties.

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

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?