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?

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

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?

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.

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?

Can you make the birds from the egg tangram?

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

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

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

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

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

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 Little Ming and Little Fung dancing?

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 outlines of the workmen?

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

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 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?

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

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

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.

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

Did you know mazes tell stories? Find out more about mazes and make one of your own.

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

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?

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

Surprise your friends with this magic square trick.

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

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?

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

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

An activity making various patterns with 2 x 1 rectangular tiles.

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

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

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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

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

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 the child walking home from school?

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 the lobster, yacht and cyclist?

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

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