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
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
Make a clinometer and use it to help you estimate the heights of
Make a spiral mobile.
A game to make and play based on the number line.
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
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.
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. . . .
How can you make an angle of 60 degrees by folding a sheet of paper
Turn through bigger angles and draw stars with Logo.
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
Follow these instructions to make a three-piece and/or seven-piece
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
What do these two triangles have in common? How are they related?
This package contains hands-on code breaking activities based on
the Enigma Schools Project. Suitable for Stages 2, 3 and 4.
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
Surprise your friends with this magic square trick.
Make a mobius band and investigate its properties.
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.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Use the tangram pieces to make our pictures, or to design some of
Ideas for practical ways of representing data such as Venn and
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
A jigsaw where pieces only go together if the fractions are
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.
Can you make the birds from the egg tangram?
How can you make a curve from straight strips of paper?
What shape and size of drinks mat is best for flipping and catching?
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Arrange your fences to make the largest rectangular space you can.
Try with four fences, then five, then six etc.
This article for students gives some instructions about how to make some different braids.
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Exploring and predicting folding, cutting and punching holes and
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
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?
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.
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?
Here's a simple way to make a Tangram without any measuring or