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?

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

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?

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?

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

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?

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.

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 birds from the egg tangram?

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.

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?

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?

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

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 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?

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?

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

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

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.

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

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

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.

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

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

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?

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?

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 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.

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 this junk?

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

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

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

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

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

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

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?

How can you make a curve from straight strips of paper?

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 outline of the child walking home from school?