Make some celtic knot patterns using tiling techniques

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

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.

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

This article for students gives some instructions about how to make some different braids.

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

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 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?

A game to make and play based on the number line.

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

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?

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

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

Make a mobius band and investigate its properties.

Make a clinometer and use it to help you estimate the heights of tall objects.

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

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

Make an equilateral triangle by folding paper and use it to make patterns of your own.

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.

Write a Logo program, putting in variables, and see the effect when you change the variables.

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

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

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

Learn to write procedures and build them into Logo programs. Learn to use variables.

Surprise your friends with this magic square trick.

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

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

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

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

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!

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.

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 blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Learn about Pen Up and Pen Down in Logo

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

Turn through bigger angles and draw stars with Logo.

Delight your friends with this cunning trick! Can you explain how it works?

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

What happens when a procedure calls itself?