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 invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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 Mai Ling?

Exploring and predicting folding, cutting and punching holes and making spirals.

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

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

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

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

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 cut up a square in the way shown and make the pieces into a triangle?

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 the rocket?

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

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

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!

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

Can you fit the tangram pieces into the outlines of the workmen?

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

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outline of this goat and giraffe?

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

Can you make the birds from the egg tangram?

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

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 fit the tangram pieces into the outline of Little Fung at the table?

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 Mai Ling and Chi Wing?

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

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outlines of the chairs?

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 fit the tangram pieces into the outline of Granma T?

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

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.

How many models can you find which obey these rules?

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

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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

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

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?