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

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

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

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?

Build a scaffold out of drinking-straws to support a cup of water

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?

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 clocks?

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

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

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?

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.

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

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

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

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

Can you fit the tangram pieces into the outline of the telescope and microscope?

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

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

Can you fit the tangram pieces into the outline of this plaque design?

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

This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.

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?

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

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 Mai Ling and Chi Wing?

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

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

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

Use the tangram pieces to make our pictures, or to design some of your own!

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

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

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

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Can Jo make a gym bag for her trainers from the piece of fabric she has?

What shape would fit your pens and pencils best? How can you make it?

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

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

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

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

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

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

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