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Visualization in Primary Mathematics
by
John Gimblett
Visualization activities fit well into the oral and mental starter for a lesson. Here is an example of one you might read
slowly to a Year 6 class (or higher ability Year 5).
Read through the visualization activity. Try to visualize the shape yourself. The children might benefit from sitting
with their eyes closed, though some will prefer to keep their eyes open.
Imagine a square-based pyramid made out of plasticine in the air in front of you. Ask yourself a few questions (but keep
the answers to yourself).
How many corners, or vertices, has the shape?
How many edges?
How many faces? Are the faces all the same shape?
Now imagine a cube, with square faces the same size as the base of your pyramid, also floating in space.
Slide your pyramid until it sits on top of the cube, with its base exactly in line with the top of the cube. Ask yourself
some questions about the new solid:
How many vertices has it?
How many edges?
How many faces? Are they all the same shape?
Now imagine a sharp knife and use it to make a vertical cut through your solid.
Examine one of the pieces you now have and look at the face created by your cut.
Without saying anything, open your eyes and sketch the shape of this new face. Now compare your drawing with others.
Check your solution using the illustrations on this page...
You might think that visualization is just another word for fantasising. In a way, it is; only when we use visualization
in mathematics, it's for a practical purpose.
Visualizing shapes and spaces helps us to gain a very real idea of what is where!
Once you get used to using such a method, you'll find that it has many everyday uses. For example...
You park your bike in the shade when you arrive at school. The sun is on your left. Can you imagine where the sun might
be by lunchtime? Or hometime? Perhaps it would be better to ensure that your bike is shaded in the middle of the day - the
hottest time - even if this means parking it in direct sunlight when you get to school in the morning?
Staying on the subject of shadows: can you imagine what shape shadow might be cast by different 3D solids? Try visualizing
the shape of shadow cast by: a cube; a pyramid; a cylinder; a polyhedron.
Try to imagine yourself on the telephone to a friend, describing the making of a paper plane. You will be imagining -
visualizing - the making of it in your head, but you'll find it's a bit more difficult trying to get your friend to see what
you're seeing!
In pairs, describe a journey on foot within a neighbourhood you both know well. Use landmarks and map directions, as
well as other instructions, to take your partner on an imaginary journey from A to B. Keep a score of how many times each
of you ends up where the other visualized them doing so.
As you can see, there are many uses for visualization methods not only in mathematics, but in day to day life too.
You'll probably find that you can use the same methods in other school subjects - if you don't already do so.
Try finding a use for visualization in each of your other curriculum subjects. And if you do, share your ideas with others!
John Gimblett,
Wales, UK., November 2004.
jgimblett@yahoo.co.uk
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