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

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

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.

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?

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?

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

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

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?

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

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 make the birds from the egg tangram?

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

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?

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 Little Fung at the table?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

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

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

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

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?

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?

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 these rabbits?

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 the telescope and microscope?

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?

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?

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

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

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

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 outlines of these clocks?

If you'd like to know more about Primary Maths Masterclasses, this is the package to read! Find out about current groups in your region or how to set up your own.

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Make a flower design using the same shape made out of different sizes of paper.

What shape is made when you fold using this crease pattern? Can you make a ring design?

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

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 visualise what shape this piece of paper will make when it is folded?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.