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

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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

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

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

Can you split each of the shapes below in half so that the two parts are exactly the same?

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?

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 the telescope and microscope?

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

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 outline of this plaque design?

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

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

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

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

Can you put these shapes in order of size? Start with the smallest.

These pictures show squares split into halves. Can you find other ways?

Can you fit the tangram pieces into the outline of Mai Ling?

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

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

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 outlines of the lobster, yacht and cyclist?

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

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

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

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

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Can you make the birds from the egg tangram?

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

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

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

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 game to make and play based on the number line.

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

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

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

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

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 shape. How would you describe it?

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