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

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

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?

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

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

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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

Can you deduce the pattern that has been used to lay out these bottle tops?

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

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

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 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?

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

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 outline of the telescope and microscope?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Can you fit the tangram pieces into the outline of this goat and giraffe?

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

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 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 playing the board game?

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 this junk?

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?

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

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

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?

Can you make the birds from the egg tangram?

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

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?

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

An activity making various patterns with 2 x 1 rectangular tiles.

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

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?

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?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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

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?