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

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

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

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?

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

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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

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

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

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?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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?

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

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.

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?

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.

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

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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

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?

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

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

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?

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

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

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Can you make the birds from the egg tangram?

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

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?

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 Wai Ping, Wah Ming and Chi Wing?

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 telephone?

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 clocks?

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

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

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?

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