In the oral/mental part of the lesson, you can direct some questions towards the most able pupils, just as you can direct some specifically towards the children who find mathematics difficult. Able pupils can also contribute by suggesting and explaining alternative methods of calculation.
In the main part of the lesson you will often introduce a new topic with some direct teaching of the whole class. You will consolidate previous ideas and develop and use the correct mathematical language. For able pupils, the amount of practice and consolidation needed is less than that required by other pupils. Within whole-class teaching, you can set different tasks for pupils to undertake, for example:
a common task, starting from the common experience of pupils, leading to different outcomes - this is typical of open investigations;
a stepped task that helps pupils build on their own learning strategies - each step needs to be relevant and purposeful, and able pupils can omit earlier steps;
separate tasks for each group of pupils, but linked to a common theme.
You should give all pupils opportunities to apply their mathematical knowledge. Able pupils can often move quickly beyond basic knowledge and skills and begin to use these in a range of contexts. Problems need not involve difficult mathematics but may require insight, reasoning and higher order thinking skills in order to reach a solution.
The plenary session gives you opportunities to extend as well as consolidate work. Methods of solution can be compared and explanations shared.
Homework can provide the opportunity for pupils to tackle challenging questions and puzzles. The results can form the basis of the next lesson with either the whole class or a group. Opportunities also exist for pupils to read about mathematical topics.
In all parts of the lesson, the quality of questioning is crucial in helping pupils develop mathematical ideas and improve their thinking skills. The National Numeracy Strategy Mathematical vocabulary contains guidance on types of questioning appropriate to all parts of the mathematics lesson. The range of questioning should include recalling and applying facts, hypothesising and predicting, designing and comparing procedures, interpreting results and applying reasoning. You can use some open questions to allow more pupils to respond at their own level. Such questions often provide a greater challenge for able pupils, who can be asked to think of alternative solutions and, in suitable cases, to list all the different possibilities: 'Can you suggest another method you might have used?' 'Would it work with different numbers?' 'How do you know you have included all the possibilities?'
