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?

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

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

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?

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

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

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

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

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.

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?

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

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

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

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

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?

Can you make five differently sized squares from the tangram pieces?

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

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

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

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

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?

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?

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

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?

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 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 outlines of these people?

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

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of the child walking home from school?

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?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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

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

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

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 fit the tangram pieces into the outline of this junk?

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 visualise what shape this piece of paper will make when it is folded?

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.