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)] .
Key Activity: Thinking about reflections
Your pupils could reuse the shapes they cut out of grid paper for Activity 2, or make some more if necessary.
- On a second piece of grid paper, ask pupils to draw and label x-y axes at least 20 squares long (see Resource 4).
- Putting one of their cut-out shapes on the paper so that its corners are on the ‘crosses’ of the grid, they should mark the vertices (a, b, c & d as appropriate) then draw the shape and write down the coordinates of each vertex (corner).
- Ask pupils to draw a vertical or horizontal mirror line on their grid. They should then draw the reflection of the shape on the other side of the mirror line (remind pupils that they may use the cut-out shape if it helps them) and write down the coordinates of the reflection.
- Challenge your pupils to work out the reflection coordinates without using the cut-out shape. Ask them to explain how they did it. Practise using lots of shapes so that pupils become confident.
How well did you introduce and explain this work? How do you know this?
2. Differentiating work
Resource 1: Some Tanzanian fabric patterns