Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

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 brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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

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

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

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

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 the candle and sundial?

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 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 fit the tangram pieces into the outlines of the workmen?

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?

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.

Follow these instructions to make a three-piece and/or seven-piece tangram.

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.

Surprise your friends with this magic square trick.

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

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

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

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

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

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

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

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?

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

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.

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

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

Can you make the birds from the egg tangram?

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

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

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

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 this brazier for roasting chestnuts?

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

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

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 telephone?

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 this junk?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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

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