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

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.

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

Make a mobius band and investigate its properties.

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

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

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.

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

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

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?

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

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

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

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

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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

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

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?

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?

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 outlines of the chairs?

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 outline of Little Ming and Little Fung dancing?

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 outlines of Mai Ling and Chi Wing?

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 these clocks?

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 the lobster, yacht and cyclist?

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

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

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Can you lay out the pictures of the drinks in the way described by the clue cards?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Use the tangram pieces to make our pictures, or to design some of your own!

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?