A jigsaw where pieces only go together if the fractions are
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.
Watch the video to see how to fold a square of paper to create a
flower. What fraction of the piece of paper is the small triangle?
What shapes can you make by folding an A4 piece of paper?
It might seem impossible but it is possible. How can you cut a
playing card to make a hole big enough to walk through?
Make a mobius band and investigate its properties.
Surprise your friends with this magic square trick.
What is the greatest number of counters you can place on the grid
below without four of them lying at the corners of a square?
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. . . .
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
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.
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
Make a clinometer and use it to help you estimate the heights of
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
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?
Make a spiral mobile.
Follow these instructions to make a three-piece and/or seven-piece
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
What do these two triangles have in common? How are they related?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Use the tangram pieces to make our pictures, or to design some of
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?
How can you make a curve from straight strips of paper?
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
Use the lines on this figure to show how the square can be divided
into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
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?
Ideas for practical ways of representing data such as Venn and
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
Have a go at drawing these stars which use six points drawn around
a circle. Perhaps you can create your own designs?
How many triangles can you make on the 3 by 3 pegboard?
This activity investigates how you might make squares and pentominoes from Polydron.
What is the greatest number of squares you can make by overlapping
How can you make an angle of 60 degrees by folding a sheet of paper
Arrange your fences to make the largest rectangular space you can.
Try with four fences, then five, then six etc.
Cut a square of paper into three pieces as shown. Now,can you use
the 3 pieces to make a large triangle, a parallelogram and the
How is it possible to predict the card?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Here's a simple way to make a Tangram without any measuring or
Where can you put the mirror across the square so that you can
still "see" the whole square? How many different positions are
An activity making various patterns with 2 x 1 rectangular tiles.
Make a cube out of straws and have a go at this practical