What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Learn about Pen Up and Pen Down in Logo

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

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

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?

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

More Logo for beginners. Now learn more about the REPEAT command.

Turn through bigger angles and draw stars with Logo.

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

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

What happens when a procedure calls itself?

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

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.

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

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

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

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.

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?

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

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

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

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

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

Make some celtic knot patterns using tiling techniques

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

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

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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

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

A game in which players take it in turns to choose a number. Can you block your opponent?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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?

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

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

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?

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

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?

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

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

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

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.

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

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 description of how to make the five Platonic solids out of paper.

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.