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

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!

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

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?

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?

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

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.

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

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

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 the lobster, yacht and cyclist?

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

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 outlines of these people?

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 candle and sundial?

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?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

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 outlines of Mai Ling and Chi Wing?

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

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

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

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Use the tangram pieces to make our pictures, or to design some of your own!

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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?

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

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

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

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

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

Can you make the birds from the egg tangram?

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

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

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?

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