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

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

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

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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

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?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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

Here is a chance to create some Celtic knots and explore the mathematics behind them.

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

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

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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 birds from the egg tangram?

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?

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

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?

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

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 clocks?

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 outlines of the lobster, yacht and cyclist?

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 chairs?

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?

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

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?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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 this junk?

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

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

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

How can you make a curve from straight strips 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.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

The challenge for you is to make a string of six (or more!) graded cubes.

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?