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

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

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

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Here are some ideas to try in the classroom for using counters to investigate number patterns.

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

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

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

How can you make a curve from straight strips of paper?

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

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

Surprise your friends with this magic square trick.

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

Make a mobius band and investigate its properties.

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.

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

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 fit the tangram pieces into the outline of these rabbits?

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 the telescope and microscope?

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

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

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

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

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

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 outline of this plaque design?

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

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 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?

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

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

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

Can you make the birds from the egg tangram?

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

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 outlines of the lobster, yacht and cyclist?

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?

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

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

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 outlines of these people?