A weaker class pattern in applying maths may mean pupils know individual methods but struggle to recognise relationships, constraints and a suitable approach in an unfamiliar problem.

Teach the decision-making process openly. Do not reduce problem solving to spotting a keyword and choosing an operation.

Model the approach, not only the calculation

Think aloud while you:

1. identify what is known and unknown;

2. annotate units, conditions and constraints;

3. choose a representation;

4. select and justify a method;

5. carry out the mathematics;

6. check the result against the original problem.

For example, in a ratio problem, draw a bar or ratio table to show the relationship before calculating. Explain why that representation fits this structure and what each part means.

At Secondary level, make assumptions and limits explicit. Ask whether the answer fits the expected range, uses the correct units and satisfies every condition.

Compare approaches

Use completed examples to compare two valid methods or identify why an approach fails. Ask pupils which method is more efficient here and whether it would still work if one condition changed.

NRICH (University of Cambridge, free) publishes problem-solving tasks with teacher support for ages 3 to 18. Choose one with more than one sensible route and use it for this comparison.

Where applying maths is slightly weaker, focus on the final check or method justification. Where the class pattern is lower, model the complete sequence and provide guided practice on problems with related structures.

Avoid teaching a script without meaning

A planning routine is useful only when it directs attention to the mathematics. Pupils should be able to explain why they selected a representation or method.

When some pupils need more

This is whole-class modelling of mathematical problem solving. A pupil who needs a written personal plan or extra rehearsal requires Focused support.

Further guidance

• EEF: Improving Mathematics in Key Stages 2 and 3

• NCETM: The Bar Model

Talamo has no commercial relationship with any of the organisations named here. We suggest them only because we think they could be useful to schools.