1. Using group work to explore symmetry

Introducing the concept of symmetry and reflection needs careful planning. Understanding that a shape is symmetrical if both sides are the same when a mirror line is drawn is best explored using practical activities. You need to think of ways to organise and group your pupils so that they can participate fully. One way to introduce this topic is by using drawings, photos and flat items like leaves. To see the line of symmetry you need to try:

looking at a piece of paper held upright on the line of symmetry – look on one side, then the other;

putting a piece of paper over an item, along the line of symmetry, then turning the paper over to cover the other half;

holding small hand mirrors on the line of symmetry.

When looking at natural objects or images, your pupils need to understand that we are only looking at ‘approximate’ symmetry. For example, the left side of a person’s face is probably not ‘exactly’ the same as the right side. However, by using real examples from the local environment such as fabric patterns or nature, you will motivate pupils more.

Case Study 1: Using group work to explore symmetry

Miss Bwalya, a primary teacher from Juba, Southern Sudan, wanted to introduce her pupils to the concept of symmetry.

She divided her class into groups of four and distributed to each group four pieces of paper that she had cut into the following shapes – rectangle, square, isosceles and equilateral triangles. She asked one pupil from each group to take the rectangle and fold it so that the two parts fitted exactly. The rest of the group could offer advice and support. She noticed that some groups found only one way to fold the rectangle while others found two. Miss Bwalya asked each group to show what they did.

Next, she asked another member of each group to take the square and repeat the exercise. The class agreed that there were four ways for a square. She told the class: ‘These lines are called lines of symmetry. The rectangle has two, while the square has four.’

She drew a table on the chalkboard drawing the shapes and asked them to enter the number of lines of symmetry.

Next, she asked them to explain the meaning of ‘symmetrical’ and ‘line of symmetry’ in words that everyone in the class understood. They then added these terms to their mathematics dictionaries.

For homework, she asked them to collect objects from home or from their journey home that they thought had lines of symmetry to explore in the next lesson.

Activity 1: Observing symmetry in nature

Before the lesson, collect some natural objects that have approximate symmetry: these could include leaves, flowers or vegetables. You could even use local animals (but you must ensure they are well treated) or you could use photos of them (you might ask your pupils to help you). Resource 1: Examples of symmetry found in nature has some useful photos and you may want to collect more from magazines and newspapers, or some samples of local fabrics.

Divide the class into small groups of five or six and ask each group to consider the objects or images and try to identify all the lines of symmetry. Share their answers as a class (see Key Resource: Using group work in your classroom [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]   to plan how to do this).

Ask your groups to think of other objects from everyday life that are symmetrical. Suggest that on the way home they try to find other examples and either note these down or bring a sample in if possible.

In the next lesson, ask each group to make a poster of six different objects that they have found that have lines of symmetry and draw the line(s) of symmetry on them. They could draw or perhaps stick on some objects.

Display the posters for the whole class to see and discuss their ideas after a day or so to remind them.

Section 4: Exploring symmetry

2. A cross-curricular approach