A jigsaw where pieces only go together if the fractions are
Delight your friends with this cunning trick! Can you explain how
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
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?
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
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 game to make and play based on the number line.
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.
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.
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.
How can you make an angle of 60 degrees by folding a sheet of paper
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?
The Tower of Hanoi is an ancient mathematical challenge. Working on
the building blocks may help you to explain the patterns you
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 tangram pieces to make our pictures, or to design some of
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?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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?
Here is a chance to create some Celtic knots and explore the mathematics behind them.
How is it possible to predict the card?
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.
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. . . .
This article for students gives some instructions about how to make some different braids.
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
A challenge that requires you to apply your knowledge of the
properties of numbers. Can you fill all the squares on the board?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Make a spiral mobile.
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 package contains hands-on code breaking activities based on
the Enigma Schools Project. Suitable for Stages 2, 3 and 4.
Make some celtic knot patterns using tiling techniques
It might seem impossible but it is possible. How can you cut a
playing card to make a hole big enough to walk through?
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
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.
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
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.
What shape and size of drinks mat is best for flipping and catching?
What shape would fit your pens and pencils best? How can you make it?
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?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Make a clinometer and use it to help you estimate the heights of
A description of how to make the five Platonic solids out of paper.
What happens when a procedure calls itself?
A game in which players take it in turns to choose a number. Can you block your opponent?
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.