This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
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?
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
This article for students gives some instructions about how to make some different braids.
Learn about Pen Up and Pen Down in Logo
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.
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Build a scaffold out of drinking-straws to support a cup of water
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
Learn to write procedures and build them into Logo programs. Learn to use variables.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
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.
Write a Logo program, putting in variables, and see the effect when you change the variables.
More Logo for beginners. Now learn more about the REPEAT command.
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?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
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?
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
Here is a chance to create some Celtic knots and explore the mathematics behind them.
The Tower of Hanoi is an ancient mathematical challenge. Working on
the building blocks may help you to explain the patterns you
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.
Use the tangram pieces to make our pictures, or to design some of
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
What happens when a procedure calls itself?
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.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
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?
A challenge that requires you to apply your knowledge of the
properties of numbers. Can you fill all the squares on the board?
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?
How can you make an angle of 60 degrees by folding a sheet of paper
Make a clinometer and use it to help you estimate the heights of
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
A game in which players take it in turns to choose a number. Can you block your opponent?
A jigsaw where pieces only go together if the fractions are
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?
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.
Delight your friends with this cunning trick! Can you explain how
Make a spiral mobile.
A game to make and play based on the number line.
A description of how to make the five Platonic solids out of paper.
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?