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.

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

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

Make a mobius band and investigate its properties.

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

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

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

Surprise your friends with this magic square trick.

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

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?

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

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

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?

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

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?

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?

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

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

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?

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 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 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 this brazier for roasting chestnuts?

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

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?

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 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 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 Little Fung at the table?

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

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

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?

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

Can you make the birds from the egg tangram?

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