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

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

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

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

Here are some ideas to try in the classroom for using counters to investigate number patterns.

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 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?

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 Wai Ping, Wah Ming and Chi Wing?

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 outline of this junk?

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?

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 outlines of the lobster, yacht and cyclist?

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

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

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

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 the telescope and microscope?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

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

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 shape. How would you describe it?

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

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

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

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

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

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

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?

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 ...

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

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

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

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?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

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?

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

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?