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

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

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 plaque design?

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

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 Mai Ling and Chi Wing?

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 the candle and sundial?

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

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 these rabbits?

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

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

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 do these two triangles have in common? How are they related?

Make a mobius band and investigate its properties.

Follow these instructions to make a three-piece and/or seven-piece tangram.

Surprise your friends with this magic square trick.

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

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

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

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

Follow these instructions to make a five-pointed snowflake from a square of paper.

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

Can you fit the tangram pieces into the outline of the child walking home from school?

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.

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

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

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

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

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?

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?

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

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 brazier for roasting chestnuts?

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 Mai Ling?

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?

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?

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?

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 this telephone?