A jigsaw where pieces only go together if the fractions are equivalent.

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?

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

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

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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?

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

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

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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

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

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

An activity making various patterns with 2 x 1 rectangular tiles.

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

Can you make the birds from the egg tangram?

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 telephone?

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

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 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 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 this brazier for roasting chestnuts?

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 fit the tangram pieces into the outline of this junk?

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

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

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

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.

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 Wai Ping, Wah Ming and Chi Wing?

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

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

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

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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

How many models can you find which obey these rules?

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

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?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

What shape and size of drinks mat is best for flipping and catching?