Framework for teaching mathematics

A typical lesson

A typical 45 to 60 minute lesson in Years 1 to 6 will be structured like this:

oral work and mental calculation (about 5 to 10 minutes)
whole-class work to rehearse, sharpen and develop mental and oral skills
the main teaching activity (about 30 to 40 minutes)
teaching input and pupil activities
work as a whole class, in groups, in pairs or as individuals
a plenary to round off the lesson (about 10 to 15 minutes)
work with the whole class to sort out misconceptions and identify progress, to summarise key facts and ideas and what to remember, to make links to other work and discuss the next steps, and to set work to do at home

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Oral work and mental calculation

The first 5 to 10 minutes of a lesson can be used in a variety of ways to rehearse and sharpen skills, sometimes focusing on the skills that will be needed in the main part of the lesson. On different days you might choose to do one or more of these:

counting in steps of different sizes, including chanting as a whole class and counting round the class;
practising mental calculations and the rapid recall of number facts in varied ways (for example, by playing an interactive number game, by giving examples of 'a number one less than a multiple of 5' or 'a calculation with the answer 12');
figuring out new facts from known facts and explaining the strategies used;
building on a previous strategy, and then developing it;
identifying facts which children can learn by heart and discussing ways of remembering them;
reviewing an activity done at home.

In this first part of the lesson you need to:

get off to a clear start and maintain a brisk pace;
provide a variety of short oral and mental activities throughout each week;
prepare a good range of open and closed questions to ask the class;
ensure that all children can see you easily and can and do take part;
target individuals, pairs or small groups with particular questions;
use pupils' responses to make an informal assessment of their progress;
brief any support staff to position themselves and give discreet help to any children who need particular support;
avoid disruption from too much movement of pupils about the room;
avoid running over time and move smoothly to the next part of the lesson.

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The main teaching input and pupil activities

The main part of the lesson provides time for:

introducing a new topic, consolidating previous work or extending it;
developing vocabulary, using correct notation and terms and learning new ones;
using and applying concepts and skills.

In this part of the lesson you need to:

make clear to the class what they will learn;
make links to previous lessons, or to work in other subjects;
tell pupils what work they will do, how long it should take, what, if anything, they need to prepare for the plenary session and how they are to present it;
maintain pace and give pupils a deadline for completing their work.

When you are working directly with the whole class you need to:

demonstrate and explain using a board, flip chart, computer or OHP;
involve pupils interactively through carefully planned questioning;
ensure that pupils with particular learning needs in mathematics are supported effectively with appropriate resources and wall displays, and adult help;
identify and correct any misunderstandings or forgotten ideas, using mistakes as positive teaching points;
highlight the meaning of any new vocabulary, notation or terms, and get pupils to repeat these and use them in their discussions and written work;
ask pupils to offer their methods and solutions to the whole class for discussion.

When you are working directly with groups you need to:

have a manageable number of groups (usually a maximum of four), so that you know what each group should be doing at any time;
decide how groups will be introduced to tasks and how the group work will end;
control the degree of differentiation (for example, provide tasks on the same theme and usually at no more than three levels of difficulty);
provide activities, tasks and resources that don't involve children in a long wait for turns and which keep them all interested, motivated and on-task;
sit and work intensively with one or two of the groups, not flit between them all;
brief any support staff or adult helpers about their role, making sure that they have plenty to do with the pupils they are assisting and will not interrupt you;
avoid interruption by pupils by making sure that those working independently in a group know where to find further resources, what to do before asking you for help and what to do if they finish early.

When you are providing work for individuals or pairs you need to:

keep the class working on related activities, exercises or problems;
target individuals or pairs for particular questioning and support;
during paired work, encourage discussion and co-operation between pupils.

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The plenary session

The plenary is an important part of the lesson. It is a time when you can help pupils to assess their developing knowledge and skills against any targets they have been set and to see for themselves the progress they are making. It is also a time when you can relate mathematics to their work in other subjects: for example, how their work on calculation will be used in science, or how their measuring skills will be practised in physical education.

For example, this part of the lesson can be used to:

ask pupils to present and explain their work, or mark a written exercise done individually during the lesson, so that you can question pupils about it, assess it informally and rectify any misconceptions or errors;
discuss and compare the efficiency of pupils' different methods of calculation;
help pupils to generalise a rule from examples generated by different groups, pairs or individuals;
draw together what has been learned, reflect on what was important about the lesson, summarise key facts, ideas and vocabulary, and what needs to be remembered;
discuss the problems that can be solved using the ideas and skills that have been learned;
make links to other work and discuss briefly what the class will go on to do next;
remind pupils about their personal targets and highlight the progress made;
provide tasks for pupils to do at home to extend or consolidate their class work.

In this part of the lesson you need to:

have a clear idea of the purpose of the plenary session and what you want to achieve in it;
make sure that the main part of the lesson does not over-run, so that there is enough time for the plenary;
plan carefully how pupils are to present their work, if they are to do this, and how long it will take;
bring the lesson to a close and evaluate its success.

The outline structure of a typical lesson should not be seen as a mechanistic recipe to be followed. You should use your professional judgement to determine the activities, timing and organisation of each part of the lesson to suit its objectives.

In the main part of the lesson, in particular, there is scope for considerable variety and creativity, with a different mix of work with the whole class, groups, pairs and individuals on different days, although each lesson should include direct teaching and interaction with the pupils, and activities or exercises that pupils do. Overall, there should be a high proportion of work with the whole class but there may be more in some lessons than in others. For example, at the start of a new unit of work you might need more time for explanation and discussion with everyone together for the whole lesson, and the plenary may be very short. On the other hand, where you have identified general errors or misunderstanding during the main part of a lesson, you might need a longer plenary to sort them out. At the end of a unit of work it can be useful to use the plenary to look back with the whole class over a number of lessons to draw together what has been learned and to identify the key points and methods that you want pupils to remember and use in the future. For this kind of plenary session, you may need a much longer time than usual.

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