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. . . .
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?
Make some celtic knot patterns using tiling techniques
A game to make and play based on the number line.
Make a clinometer and use it to help you estimate the heights of
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?
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
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.
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
How is it possible to predict the card?
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
Make a spiral mobile.
How can you make an angle of 60 degrees by folding a sheet of paper
This article for students gives some instructions about how to make some different braids.
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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?
Use the tangram pieces to make our pictures, or to design some of
Learn about Pen Up and Pen Down in Logo
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.
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
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?
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
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?
Here is a chance to create some Celtic knots and explore the mathematics behind them.
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Write a Logo program, putting in variables, and see the effect when you change the variables.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
More Logo for beginners. Now learn more about the REPEAT command.
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.
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.
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
Delight your friends with this cunning trick! Can you explain how
What happens when a procedure calls itself?
Can you describe what happens in this film?
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?
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?
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
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.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
A description of how to make the five Platonic solids out of paper.
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.
Build a scaffold out of drinking-straws to support a cup of water
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
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.