Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?
A game in which players take it in turns to choose a number. Can you block your opponent?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Here is a chance to create some Celtic knots and explore the mathematics behind them.
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
How is it possible to predict the card?
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.
Write a Logo program, putting in variables, and see the effect when you change the variables.
What happens when a procedure calls itself?
Turn through bigger angles and draw stars with Logo.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
Learn to write procedures and build them into Logo programs. Learn to use variables.
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
More Logo for beginners. Now learn more about the REPEAT command.
Learn about Pen Up and Pen Down in Logo
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
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?
Delight your friends with this cunning trick! Can you explain 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.
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?
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
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 your own!
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.
Make some celtic knot patterns using tiling techniques
Can you describe what happens in this film?
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.
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
This article for students gives some instructions about how to make some different braids.
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.
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
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?
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?
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?
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
A description of how to make the five Platonic solids out of paper.
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 a spiral mobile.
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.
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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 package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.