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 timer?
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 practical activity involves measuring length/distance.
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
A game to make and play based on the number line.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Make an equilateral triangle by folding paper and use it to make patterns of your own.
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?
Make a spiral mobile.
Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.
How is it possible to predict the card?
Make a ball from triangles!
How can you make a curve from straight strips of paper?
Make a clinometer and use it to help you estimate the heights of tall objects.
Follow these instructions to make a three-piece and/or seven-piece tangram.
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.
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.
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.
Did you know mazes tell stories? Find out more about mazes and make one of your own.
Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.
Surprise your friends with this magic square trick.
Make a mobius band and investigate its properties.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?
Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.
Learn about Pen Up and Pen Down in Logo
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.
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
Follow these instructions to make a five-pointed snowflake from a square of paper.
Make some celtic knot patterns using tiling techniques
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Write a Logo program, putting in variables, and see the effect when you change the variables.
What happens when a procedure calls itself?
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?
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
Here are some ideas to try in the classroom for using counters to investigate number patterns.
A description of how to make the five Platonic solids out of paper.
Can you describe what happens in this film?
What shape and size of drinks mat is best for flipping and catching?
What shapes can you make by folding an A4 piece of paper?
What do these two triangles have in common? How are they related?
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
This article for students gives some instructions about how to make some different braids.
Build a scaffold out of drinking-straws to support a cup of water