On the other side of the mirror

Mathematics without a mirror? No way! A model particularly useful for mathematical purposes is a half-transparent one, which both reflects the image and lets us to see the things on the other side through it. This enables us to find, in an interactive way, the symmetry line of a shape. Like this one, for example:

When the reflected image matches ideally a part of the shape seen on the other side of the mirror, the surface of the mirror shows us the line of symmetry. Sometimes there are more of them than one …

… and sometimes there are none.

An unusual use of this half-transparent mirror was found one day by Marcel (7). The children had to complete the spots on a butterfly’s wing, so that both wings would look the same.

The objective of this activity was to reinforce the concept of an even number as a result of doubling or taking the same number twice. There were several drawings of butterflies: some with more spots, some with less. Usually this type of task takes children about ten minutes. Marcel, instead of getting to work, walked decisively to the shelf and took a 'symmetry mirror' from it. To my best knowledge, he had never had it in his hands before (and yet I must have been wrong :-)). Before I had time to say: ‘This will be no use here, I will show you later what this is for…’ the boy aligned the mirror with the symmetry line of the drawing, and the reflected spots appeared on the background of the other wing, as if they were already there.

He then quickly started to mark the spots on the other wing, looking in the mirror from one side and drawing on the other one.

All this in perfect silence, without one needless word, but petty fast. The purpose of this innovation was obviously to finish the task as quickly as possible, which wasn’t accompanied by any special emotions. This I certainly couldn’t say about myself.

This was, actually, the longest day ever, waiting for a quiet moment when I would be finally able to try this new technique of mapping patterns. At last it came! The mirror, the paints, the paintbrush…

… and one last thing: the choice of a pattern to map. Red hearts on a white plastic bag?

Not bad, could do. Lets start!

Done!

Believe it or not, but this was the first shapely heart I ever managed to paint on an egg. And I  did it in the ‘landscape’ mode! :-)