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

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

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

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

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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.

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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

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

Make a cube out of straws and have a go at this practical challenge.

Here is a version of the game 'Happy Families' for you to make and play.

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

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

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 Mai Ling?

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

Exploring and predicting folding, cutting and punching holes and making spirals.

Make a mobius band and investigate its properties.

Can you make the birds from the egg tangram?

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 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?

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

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

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

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?

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

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 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 these rabbits?

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

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

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 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 this goat and giraffe?

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