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

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

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

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

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

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

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?

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

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

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?

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?

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

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?

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

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.

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.

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

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

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

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

Turn through bigger angles and draw stars with Logo.

Learn about Pen Up and Pen Down in Logo

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?

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

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

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

What happens when a procedure calls itself?

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?

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

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

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. . . .

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

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

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

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

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

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.

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

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

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

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

Which of the following cubes can be made from these nets?

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?

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

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.