Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
This problem can have more than one
solution, depending on what you decide 'different' means. Thomas,
Lydia and Bethan from Old Earth Primary School described a
quadrilateral by the number of dots you move around the circle as
you join its four corners. For example, a 1115 quadrilateral would
look like this:
They thought there were eight different
possible quadrilaterals although they didn't explain exactly how
they found them. This way of recording the quadrilaterals is very
useful - a good idea! Here is the list of eight that Thomas, Lydia
and Bethan found:
Some children at Breckland Middle School
also worked on this problem. They said:
Here is a picture of the solutions they
It is interesting now to compare these
two sets of solutions. Can you match Thomas, Lydia and Bethan's
solutions to the pictures above? So, if we decide that 'different'
means that one shape cannot fit on another, even if it is rotated,
then there would be ten as children at Breckland have
But, if we decide that reflections are the
same too, then I think there are eight, as Thomas, Lydia and Bethan
suggest. Here is a picture of the eight that Thomas, Lydia and
Bethan found but I have drawn them in a particular order to make
sure I didn't miss any out. Can you see what my system was?
If we define 'different' in one of the
ways above, the problem is quite manageable. Some of you made life
very challenging by opening up the possibilities. Kerim, working at
home, and Maiya, from Marist College, approached the problem
differently. Kerim wrote:
So, Kerim found thirty-five quadrilaterals
which all have two corners next to each other. She then began to
think about quadrilaterals where none of the corners
was immediately next to another on the
circle. She says:
Kerim has been very systematic in the way she
has listed the quadrilaterals, which is very helpful. If you've had
a go at this problem, how did you think about 'different'
quadrilaterals? Do you agree with what Kerim has found? It is
interesting that Kerim said she thought about the square because
she'd played around with the problem to start with. It might be
that using a combination of drawings and other ways of describing
the quadrilaterals (eg using numbers or letters) works well for