2. Introducing 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.

Resource 2: 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 Uwamariya 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 Uwamariya 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 Johnson 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 Resource 2 for some terms to use).

Mrs Uwamariya 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 geometric objects

Using a selection of the objects you have gathered, draw the pupils around you and show them some of the objects.

Show them an object with a flat surface, then another with a curved surface.

Ask the pupils to pick out other objects with flat surfaces, or with curved surfaces.

Ask the pupils to return to their groups, and give each group a selection of objects.

Their task is to put each object into one of four sets;

all flat surfaces;

all curved surfaces;

flat and curved surfaces;


You can extend this activity through introducing the further terms ‘vertex’ and ‘edge’ and using these to sort the objects.

Make a table of their results to display in the classroom.

1. Exploring and classifying shapes

3. Using a game to practice mathematical words