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

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

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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

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

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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 Little Ming playing the board game?

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 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 outline of this telephone?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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

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?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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

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

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?

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?

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 outlines of the candle and sundial?

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 outline of the child walking home from school?

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?

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 deduce the pattern that has been used to lay out these bottle tops?

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

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

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

Can you split each of the shapes below in half so that the two parts are exactly the same?

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

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

Can you lay out the pictures of the drinks in the way described by the clue cards?

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

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?

These pictures show squares split into halves. Can you find other ways?

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

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