Exploring shape and its mathematical language through sorting activities/Resource

From OER in Education
Module Number: 2
Module Title: Exploring Shape and Space
Section number: 1
Section title: Exploring shapes
Key Focus Question: How can you help pupils develop and use a mathematical vocabulary for shape?
Keywords: object; shape; geometry; language; classification; open-ended activities

Learning Outcomes

By the end of this section, you will have:

  • used open-ended sorting activities to explore knowledge of shape,
  • explored practical ways to introduce pupils to the language or ‘register’ of mathematical terms,
  • used practical activities to develop pupils’ understanding and use of mathematical descriptions of basic geometric shapes.


Investigating shapes or exploring geometry with your pupils can be very rewarding. Using a practical approach and objects from the pupils’ environment can help to raise their motivation and interest.

In this section, you will be using objects from everyday life to help pupils develop important geometrical skills, such as recognising, visualising, describing, sorting, naming, classifying and comparing.

Webpage 1 – An sorting activity

To begin with, you will need to collect a range of resources that you could use for the activities in this section (see File:SortingShape Resource 1.doc: 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 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 File:SortingShape Resource 1.doc.
  • 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.
  • 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, 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.

Webpage 2 – moving from everyday, to mathematical language

Having introduced the concept of sorting objects, and asking pupils to describe the characteristics in ‘everyday’ language, it is now time to develop a more mathematical way of describing some of the objects’ features.

In every area of activity, people develop special words and terms to describe what they are doing. The special language of mathematics is sometimes referred to as the mathematical register. Introducing pupils to the language of shape will take time and needs to be built into your lessons over time. As your pupils understand the concepts behind the names, this is the time to introduce the mathematical words. As well as using these words in practice, you might also like to ask your pupils to begin making a ‘mathematical dictionary’ to help them remember the meanings of such terms. File:SortingShape Resource 2.doc: A mathematical dictionary gives six examples of the kinds of words that pupils might use to describe the shapes they are working with.

Case Study 2: Using mathematical terms to sort objects

Mrs Nsofu asked her pupils to sort a collection of different shaped objects that she had provided. Some pupils decided to group the objects according to where they would be used in the home, such as the bedroom, kitchen and bathroom. Other pupils were looking at whether the objects looked alike. Some groups found it difficult to describe the features of their objects, for example, they said that some shapes were flat, but could only describe the other shapes as ‘not flat’.

Drawing the whole class around her, Mrs Nsofu examined some of these problematic ‘not flat’ objects with the pupils. Not using the mathematical terms at first, she began pointing out certain features (like curves, edges and corners) and asked pupils to describe these in their own words. Then, when a few pupils had described these features, and thought of all the words they could use, Mrs Nsofu began to introduce the correct mathematical terms, and agreed with the class how they would describe such terms in their own words. She explained that they were beginning to learn ‘the beautiful language of mathematics’ (see File:SortingShape Resource 2.doc for some terms to use).

Mrs Nsofu made a large sheet for the wall and wrote the new mathematical words on it, and the definitions they had agreed. She asked the pupils to start to write their own mathematical dictionary at the back of their exercise books, drawing diagrams to show the meanings of these words. They added to this dictionary during subsequent mathematics lessons.

Activity 2: Describing shapes

  • Introduce and practise using words for shapes through a ‘sorting’ activity (see Activity 1).
  • Use a game to give pupils more practice. The game should be at the right level of difficulty for your pupils. File:SortingShape Resource 3.doc: Pictures for cards and File:SortingShape Resource 4.doc: Games give examples of the kinds of games that can be easily adjusted for different ability levels.
  • Use the pictures in File:SortingShape Resource 3.doc to make sets of cards.
  • Using the instructions from File:SortingShape Resource 4.doc: Games, demonstrate how the games are played.
  • Put the pupils into pairs (or small groups if you have a large class) and give each pair/group a set of cards.
  • After doing the activity with one set of cards, the sets can be passed around so that everyone has a new set.
  • As the pupils play the games, go around the room and monitor what they say. Don’t interrupt unless they ask for help, but make a note of anything you want to tell the whole class afterwards.

Webpage 3 – assessing use of mathematical language, using 'feely bags'

One way to assess how well your pupils have learned to understand and use language to describe shapes is to use ‘feely bags’ (see File:SortingShape Resource 1.doc for more detail). One pupil must carefully describe an object hidden inside a bag. The pupil should use the special words they have learned, and other pupils must try and guess which object is being described.

In this way, pupils have to visualise the shape in the bag, and correctly use the simple geometric terms they have learned, if they are to ‘win’ in the feely bag game. How you organise this, so that all pupils are engaged in the activity, is important because if done well, the learning of more pupils will be enhanced.

Case Study 3: Playing a feely bag game to practise mathematical terms

Mrs Nsofu made some cloth bags big enough for a pupil’s hand to fit into, and with a drawstring around the top to close the bag up.

She put one of the objects from her collection into each bag, having carefully chosen the objects to give variation.

Mrs Nsofu explained the game to her class and chose the pupil who would feel and describe the shape of the object in the first bag. This pupil had to describe the object using their newly learned words. The other pupils had to put their hands up when they thought they knew what the object was. Being able to feel and describe the object in the next feely bag was the reward for the pupil who guessed correctly.

When doing the activity, Mrs Nsofu made sure all the pupils were paying attention, only allowing one to speak at a time so that pupils could think about what each person was saying.

Key Activity: Using a feely bag to think about shapes

First prepare your feely bag or box. You need a bag or box in which you put an object and the pupil can put a hand in to feel the object but not see it (see File:SortingShape Resource 1.doc).

You could have one feely bag for the class or, if your class is big, have more than one so that several groups can work at once. This will help more pupils participate.

Then proceed with the game.

  • One pupil should feel one object in the bag/box and, without taking it out, describe it very carefully to the others. The pupil must not name the object.
  • They should say things like, ‘it has all flat surfaces, it has so many corners, it has so many flat surfaces,’ etc.
  • This carries on until one pupil thinks they can name the object.
  • If it is the correct answer, the object is pulled out of the bag and the successful pupil is the next to do the feeling (but allowing only one chance per pupil).

Encourage your pupils to use the vocabulary they have learned in the previous activities to describe their objects. Ask them to add them to their mathematical dictionaries.