Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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

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

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.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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?

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.

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?

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

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

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

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

Make a mobius band and investigate its properties.

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

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

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?

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?

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

Surprise your friends with this magic square trick.

What do these two triangles have in common? How are they related?

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

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

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.

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

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?

Can you fit the tangram pieces into the outlines of the candle and sundial?

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

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?

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 Little Fung at the table?

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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

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 make the birds from the egg tangram?

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?

Can you logically construct these silhouettes using the tangram pieces?

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

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?