1. Exploring and classifying shapes
To begin with, you will need to collect a range of resources that you could use for the activities in this section (see Resource 1: Using feely bags). It may be helpful to gather and keep a box of such objects as a permanent resource. Your pupils may enjoy helping you collect the resources, and ‘looking out for shapes’ in everyday life. (Remember to praise the pupils who contribute, and to take the opportunity to discuss the shape of any objects they bring.)
Case Study 1: Planning to study shape
Some primary mathematics teachers in Umtata, South Africa, were planning a geometry scheme of work for the term. As part of their in-service development, they wanted to prepare good, hands-on geometry activities for their pupils.
They decided to invite a mathematics education expert from their nearby higher education institution to help them write their scheme. She agreed, and suggested they start with a sorting activity. They needed to collect as many different objects as possible, such as empty cans, cotton reels, toilet roll tubes and pictures of different shapes in the environment e.g. buildings, fabric patterns and so on. In pairs, they planned an activity using these shapes and tried it themselves.
Back in their classes, the teachers asked their pupils to help them collect similar objects. When they had enough for the pupils to work in groups of five or six, with each group having ten or more different objects to sort, they tried out the activities.
The tasks were all about putting objects into groups that had similar properties, to record what property they shared, and which items had that property. The teachers were surprised and encouraged by the interest and thinking that the activity produced in their pupils.
At the next in-service meeting, each teacher reported back on what happened.
Activity 1: Helping pupils sort real objects
Collect together as many objects of different shapes as you can. You will need at least two objects for every pupil. You could use pictures of shapes from the environment as well.
- Divide the class into groups of five or six and give each group a selection of objects (see Resource 1).
- Explain what a ‘set’ is – a collection of items with some common features, for example, the class is a ‘set’ of children, who are all taught by you. This ‘large set’ can be grouped into smaller sets – one example would be a set of boys, and a set of girls. (You may like to physically separate the pupils into these two sets to illustrate this point.)
- Explain to the groups that they have a set of different objects. You want them to sort these objects into smaller sets. Ask them the following question: How many different ways can you sort these objects into sets? This makes the task an open task, so do not specify how many sets or any criteria.
- Ask them to explain their reasons for their sorting each set.
- As they work, observe them and listen to the discussions they have in their groups, noting carefully what they say. This will help you find out who has clear ideas and who is still exploring the ideas.
- Ask each group to share the different ways they sorted their objects and note the main features on the board.
You may wish to use a double lesson for this activity.