The lesson starts with a little mental arithmetic, but soon turns into interactive geometry using a computer, projector and input device. It works well on an interactive whiteboard. But you could just use a wireless mouse, which is easier to manage because it can be passed round the class without the need for pupils to come to up to the board.
You'll also need some dynamic geometry software. The commercial leaders are Geometer's Sketchpad and Cabri, both of which run on Mac and Windows; GeoGebra and Kig are good open source alternatives. GeoGebra will run happily inside a learning platform as well as on a desktop.
The idea for the lesson, which is pitched at the top end of key stage 2, comes pretty much straight out of the national curriculum: ". transform images using ICT; visualise and predict the position of a shape following a rotation, reflection or translation".
For the main part of the lesson, I put a blank co-ordinate grid on screen, inside the geometry software (fig 1), and start with revision of the co- ordinate grid - naming axes and asking for the co-ordinates of points, etc.
Passing the mouse round the class, I get the children to move a pointer to co-ordinates I give, discussing each time whether it's the right place or not.
Picking a few points on the line x=4, I'd hope that they'd see what these have in common, before moving on to a second screen (fig 2), with a triangle and x=4 already plotted.
We chat a little about what a reflection is, talking about mirrors and flipping things over, stressing how the image would stay the same distance away from the line. Again passing the mouse round, I ask the children to plot a point at the image of each corner in turn, involving their classmates in a left-a-bit, up-a-bit dialogue. Once all the points are plotted, one of them clicks the reveal button and the image triangle is revealed in all its glory (fig 3).
The fun starts as we hide the image triangle and move the original triangle and then the mirror line around, and repeat the game of finding the image by dragging the corners to where we would predict they end up.
With an IT suite or laptops, pupils could split into pairs and work on reflections hide-and-seek for the rest of the lesson, or even have a go at a few similar puzzles with pencil and paper.
GeoGebra allows interactive diagrams to be posted freely inside a learning platform so pupils could continue to play with the same puzzle at home.
A fun plenary is to link the ideas of reflection and repeated rotation by looking at the symmetry of snowflakes, and a final screen (fig 4) would allow the pupils to design their own snowflake pattern, making sure that the six-fold symmetry holds true.
Miles Berry is headteacher at Alton Convent Prep School in Alton, Hampshire