Crib Sheet

Our daily guide to educational jargon, teaching methods and the strange things children may bring back from school as homework. If there is a particular aspect of your child's education you wish explaining, use the POL Ask an Expert service.
 Design - Symmetry  
 Symmetry is a property of two dimensional objects. It means that the object is shaped the same on both sides - you could fold it in half along an imaginary axis, and the sides would match. This is called lateral symmetry. There is another type of symmetry - rotational symmetry. The difference is, instead of folding the object, you spin it around a point.

Exploring Symmetry

In school, children are often asked to explore symmetry in two ways - by deciding which objects are symmetrical, and by creating symmetrical objects themselves. They usually have to identify and mark the axis (or point) of symmetry.

Here are some samples of laterally symmetrical objects:
Humans (at least externally - our internal organs aren't arranged symmetrically); a domino; a pair of scissors; a starfish (if you draw the axis so that it divides one arm); the letters B C D E H I K M O T U V W X; a butterfly.

And rotationally symmetrical objects:
A starfish; a butcher's hook; the letters S N X Z.

You'll notice that quite a few objects have more than one axis of symmetry, and that some have both lateral and rotational symmetry.
 Symmetry Investigations Find some objects and ask decide if they are symmetrical or not. Find the axis or point of symmetry. Prove you're right - mark the axis and fold the object, or the point and spin it. If the object isn't something you can fold, draw round it on a piece of paper and cut it out first.
Symmetry butterflies Splash paint (the sort that comes in squeezy bottles is great for this) on a piece of paper. Fold the paper in half and open it out to find a symmetrical 'butterfly'. Can you see other patterns there?

Polyominoes

You'll need some squared paper - 1cm squares is best.
If you cut out one of the squares, there's only one way to do it.
If you cut out two squares (a domino), there is also only one way to do it.
But if you cut out three square's there are two ways - you can make a strip of three; or an 'L' shape.
Ask your child to discover how many ways there are to cut out four squares, and then five and six - always remembering that the squares must be joined along an edge, not just at a corner.
Now - which of these shapes are symmetrical? How many have more than one axis of symmetry? Which have lateral symmetry and which rotational symmetry? How many have both? Neither?
Could you use the polyominoes to make a poster to teach someone about symmetry?