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. . . .

Challenge Level

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

Challenge Level

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

Challenge Level

Learn about Pen Up and Pen Down in Logo

Challenge Level

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

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

Challenge Level

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

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

Challenge Level

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

Challenge Level

Turn through bigger angles and draw stars with Logo.

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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.

Challenge Level

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

Challenge Level

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

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

Challenge Level

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.

Challenge Level

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

Challenge Level

What happens when a procedure calls itself?

Challenge Level

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?

Challenge Level

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

Challenge Level

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?

Challenge Level

Make some celtic knot patterns using tiling techniques

Challenge Level

You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

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

Challenge Level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Challenge Level

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

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

Challenge Level

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.

Challenge Level

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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