3. A practical approach to ‘reflection’

Translation is relatively simple, because it affects the coordinates of all vertices in the same way (for example, all x coordinates will increase or decrease by the same amount).

Reflection is more mathematically complex, because you must treat each coordinate separately and in relation to another item – the location of the mirror line. Reflection therefore requires pupils to hold quite a number of different ideas in their minds at the same time (see Resource 4).

Think about what familiar examples of reflection you might be able to use to help your pupils with this topic – perhaps some work you may have done on symmetry or patterns and designs in art using local traditional ideas. Consider how pupils could use cut-out shapes as they develop the ability to manipulate such shapes mentally.

In addition, this part suggests you continue to encourage pupils to discuss their thinking – an important key in unlocking their understanding of mathematics.

Case Study 3: Using group work to help think about reflections

Mrs Nkony, an experienced teacher in a primary school in Kilimanjaro, has taught the basics of reflection to her class. She now decides to help them discuss their activity and their findings.

She knows that discussion is not merely answering short, closed questions, so she decides to set up a structure to help discussion among her pupils. She arranges them into pairs. They are asked to look at each other’s work, and make three observations about reflection that they will report back. For each observation, they must both be happy that they have found a way to describe or explain it as clearly as they can. When both members of the pair are in agreement that they have three clear observations, they are to put their hands up.

Mrs Nkony then puts the pairs together to make fours, asking each pair to explain their observations to the other. She then asks the fours to decide on the three best or most interesting observations to feed back to the class.

She realises that she could use this way of working in lessons other than mathematics. To find out what your pupils know and can do see Key Resource: Assessing learning [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .