If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
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 a mobius band and investigate its properties.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
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.
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
How can you make a curve from straight strips of paper?
Follow these instructions to make a three-piece and/or seven-piece
This package contains hands-on code breaking activities based on
the Enigma Schools Project. Suitable for Stages 2, 3 and 4.
A game to make and play based on the number line.
Make a ball from triangles!
Make a cube with three strips of paper. Colour three faces or use
the numbers 1 to 6 to make a die.
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.
What do these two triangles have in common? How are they related?
Use the tangram pieces to make our pictures, or to design some of
Make a spiral mobile.
Turn through bigger angles and draw stars with Logo.
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
What is the largest number of circles we can fit into the frame
without them overlapping? How do you know? What will happen if you
try the other shapes?
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
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?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
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.
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
This article for students gives some instructions about how to make some different braids.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
These practical challenges are all about making a 'tray' and covering it with paper.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Surprise your friends with this magic square trick.
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?
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
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. . . .
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Write a Logo program, putting in variables, and see the effect when you change the variables.
An activity making various patterns with 2 x 1 rectangular tiles.
Ideas for practical ways of representing data such as Venn and