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

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

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

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

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?

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?

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

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.

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?

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

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

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

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

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

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?

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

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

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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 the chairs?

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?

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?

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.

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 fit the tangram pieces into the outline of this junk?

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

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?

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 Little Ming playing the board game?

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

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?

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

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

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

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

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Can you lay out the pictures of the drinks in the way described by the clue cards?

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?