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

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

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

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.

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

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

Make a mobius band and investigate its properties.

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

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

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.

Can you visualise what shape this piece of paper will make when it is folded?

Surprise your friends with this magic square trick.

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

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?

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

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?

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.

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

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?

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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?

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

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 Fung at the table?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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?

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

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

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 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 Little Ming and Little Fung dancing?

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

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

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?

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

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

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

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

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