1. Using practical work

In geometry, ‘transformation’ means altering some geometric property of a shape, (such as rotating it or moving its position on the page) while keeping other properties of the shape the same (we say the shapes are ‘congruent’).

An excellent way for pupils to model transformation is by using physical objects or looking at shapes in everyday life and how they are transformed e.g. in fabric patterns. While pupils are doing this, encourage them to talk with you and each other about what they are doing. Talking about how they are trying to manipulate the objects will improve their understanding of geometry and the language associated with it.

Case Study 1: Planning a lesson in geometry with a colleague

Mrs Ogola, a teacher in a primary school in Masindi, Uganda, was discussing her experience in teaching geometry to her pupils with a senior associate, Mrs Mwanga. She complained that pupils do not like this topic. Her pupils complained that geometry is very abstract, requiring much imagination. Apart from that, it bears little or no relation to real life. Therefore, she herself was not always enthusiastic about teaching it.

Mrs Mwanga admitted to similar experiences, but encouraged her to try using a practical investigative approach and to encourage her pupils to talk about what they were doing. Together they planned a lesson in which pupils would carry out step-by-step activities using samples of fabrics with patterns that contain translations and variations of shapes (see Resource 1: Some Tanzanian fabric patterns). This can lead to pupils discovering the concepts to be learned themselves.

Mrs Mwanga and Mrs Ogola both taught the lesson to their classes and then met afterwards to discuss how it went. Mrs Ogola was surprised at the level of her pupils’ thinking and how much they wanted to talk about what they were doing. Mrs Mwanga agreed that allowing pupils to talk about their work not only excited them, but also gave them confidence in their ability to do mathematics.

Activity 1: Investigating congruent shapes

To complete this activity, you will need a piece of cardboard and a pencil and ruler for each pair or small group of pupils, and several pairs of scissors.

  • Ask your pupils to draw three different straight-sided shapes on their card and then cut out their shapes. They should number each of their cardboard shapes 1, 2 or 3.
  • Next, on a separate piece of paper, ask your pupils to draw around each shape; then move the shapes any way they like without overlapping what they have already drawn, and draw round them again. Repeat this until the page is full of shapes, then label inside each outline with a letter (e.g. a, b, c…). (The finished work should be similar to Resource 2: Examples of congruent shapes.)
  • Ask pupils to swap their work with another group. Can they find the outlines that were made with the same shape? (Younger children might need to use the cardboard shapes to help them.) Ask them to write down what they think is the answer – e.g. shape 1, outlines a, b, d, g.
  • Using the cut-out shape, can they show you what has to happen in moving from one outline to another? Can they describe this in their own words?
  • Early finishers can colour in their work, using one colour for outlines from the same shape. You could display these on the classroom walls, headed ‘Congruent shapes’.

Section 5: Teaching transformations

2. Differentiating work