### Works of art

Symmetry, rotational and line |

### What is in a word?

Whenever I have taught symmetry I have referred to it as
just that, symmetry. It was only when I tried to teach rotational symmetry did the
phrase ‘line symmetry’ begin to be used by me in order to differentiate between
the two. No wonder that many of my pupils became confused when asked to reflect
a shape and/or subsequently describe rotational symmetry because the idea that symmetry
was a reflection was so ingrained. It was only when my mistake became apparent
to me did I make a huge effort always to refer ‘reflective’ or ‘line symmetry’
every time. This at least went some way to avoiding confusion. (I believe
rotational symmetry is called pint symmetry in the States, but I await to be
corrected.)

### Repeating the exercise

Pupils must get bored with the same exercises on symmetry,
be it line or rotational so here are a couple of games that will enliven your
lessons, give them a different pace and help pupils identify the difference
between line and rotational symmetry.

They are both taken from the marvellous book ‘Maths for
humans’ by Mark Wahl. This book is full of rich mathematical activities, using
the ideas expressed by Howard Gardner in his book Frames of Mind: The Theory of Multiple Intelligences
. Both books are
well worth having in your resource library whether at home or in school. Go to
Amazon and have a look at the price of Mark Wahl’s book, wince, and then go to
his website www.markwahl.com and buy the
book there (signed by the author). The site will repay a visit anyway, buying
the book or not.

### Activity 1

Mark Wahl calls this ‘Copycat game for two’. You need to
hand out the sheet below, one between two, the players must have two different coloured
pens. The initial sheet would look like the one below.

1. Player 1 colours two squares on one side of the line.

2. Player 2 then copies the pattern but on the opposite side
of the line in the same rows and the same distance from the line.

3. Repeat until the grid is completely covered.

This is a fun way of reproducing line symmetry and makes a
great wall display.

### Activity 2

This is called ‘Rotate game for two’, again from the
excellent ‘Maths for humans’ book. Hand out copies of the sheet below, one
between two.

1. Player
1 colours two squares on the left of the centre line above the dotted line.

2. Player
2 now must colour below the dotted line on the left, the same distance
form the solid line and the same distance

**below the dotted line**as the other shape was above.
3. After
a few shadings encourage the children to put a finger on the centre and
spin the grid through 180

^{0}. What do they notice?
4. Using
two different colours complete each quadrant.

They should now have a fine example of rotational symmetry
and you will have a great wall display.

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