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I don't know about you, but as a teacher I used to love teaching
coordinates. I frequently found that children who struggled with
other branches of mathematics seemed to pick up this topic
relatively easily. Coordinates lend themselves well to activities
which pupils often find engaging. We're all familiar with
traditional games like Battleships and you don't need to look far
to find coordinate practice involving the creation of pictures,
shapes or patterns. However, a more imaginative approach to the
teaching and consolidation of coordinates is possible!
At a teacher conference I was lucky enough to attend the sessions
given by Sue Lowndes and Elaine Sellars. They were full of ideas
designed to promote and develop mathematical thinking in the
classroom, ranging from investigational problems to end of term
type games. The opening activities were all based on coordinates
and it is these that I shall now describe. The appeal for me was
the fact that everything was practical - we were physically
participating in the maths ourselves.
Chairs were arranged in rows, a short distance apart, all facing
the same way:
There were in fact a few more chairs than people so that when
we had all sat down, there were some empty. This was deliberate -
to make the activities more "interesting"! The "teacher" stood
facing us, although that is not strictly necessary.
We were told that one of the chairs (in the representation
above it would be the blue one) was in the first row and the first
column. From this information we could then work out which row and
column our particular chair was in. Row 1, column 1 was given the
position 1,1 so we could assign ourselves a set of numbers
Instructions were called out and we responded accordingly. For
- 4,1 and 2,3 stand up and swap places
- Stand up everyone in row 3
- Stand up everyone in column 5
Here it would be beneficial to explain to the children that
each chair is a point, having a particular position. The label
which each chair has depends on the reference point (in this case
the blue chair).
The reference point was then changed and the blue chair above
became (0,0). We adjusted our own coordinates accordingly. We began
with a similar place-swapping exercise to the one described above.
Then particular people were asked to stand, for example (1,0) (1,1)
(1,2) and (1,3). They were invited to:
- Say their own coordinates
- Notice what they all had in common i.e. first coordinate of
- Observe that they formed a straight line
This led on to the fact that because all the points on that
line have an x coordinate of 1, the line is called x = 1.
After a few practices of this, we were used to assigning a line its
equation and the activities progressed into mirror symmetry. We
were told that a particular line was the "mirror line". One point
was called, that person stood up and then their reflection in the
given line had to stand too. I have to admit that by this stage we
had become much slower at jumping to our feet, not simply because
of weary muscles but rusty brains too!!
The final challenge was to incorporate rotational symmetry. A point
was chosen as the centre of rotation and everyone had to move into
their new position after rotation of a given angle in a given
direction. This was quite chaotic at first! We then tried another
rotation but holding hands with two neighbours. This really
emphasised the fact that we had all moved exactly the same amount
in the same direction so that our spatial relationships with each
other had not changed.
On a practical note, it may be helpful to place (0,0) in the
diagonally opposite corner to the blue chair so that pupils have
the origin at their left hand side. Depending on the space you have
available, you may have to limit numbers and have a group of
children at a time.
I came away itching to find a class to try this with! I am
convinced that the "hands (or should that be bodies?) on" approach
can only enhance our teaching methods. Obviously these activities
are progressive so that you could not possibly include everything
described in a single lesson, but do have a go and let us know how
you get on. If you're feeling brave, why not extend it to
Many thanks to Sue and Elaine for
a wonderful session and allowing us to use their