Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

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

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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

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?

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

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?

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.

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?

Explore the triangles that can be made with seven sticks of the same length.

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

For this activity which explores capacity, you will need to collect some bottles and jars.

In this activity focusing on capacity, you will need a collection of different jars and bottles.

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

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

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 make five differently sized squares from the tangram pieces?

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

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

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

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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?

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

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

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

These practical challenges are all about making a 'tray' and covering it with paper.

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

Can you make the birds from the egg tangram?

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

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 Little Ming playing the board game?

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 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 this telephone?

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

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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

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

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?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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?

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