Wednesday, 17 July 2013

Line symetry, rotational symmetry and works of art

Works of art

Symmetry, rotational and line
Symmetry is one of the easiest topics to teach. The idea of line symmetry is probably innate and is cultivated from an early age. What parent does not have proudly displayed their 4 or 5 year old's first attempt at combing art and maths; paint splashed on a piece of paper and folded over to produce a glorious symmetrical design. How many homes throughout the world have these masterpieces attached to fridges or other suitable surfaces?

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 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 1800. 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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