A pupil should be able to use one accurate method before being expected to choose flexibly between several approaches. Model a method that aligns with the maths department’s teaching, use a worked example and ask the pupil to explain each step during guided practice.

Keep the focus on structure and accuracy. Speed should increase only after the procedure is understood and secure.

Identify the exact method

Use recent work to establish whether the difficulty concerns:

• calculation with fractions;

• percentages;

• negative numbers;

• decimal operations;

• ratio;

• rearranging or simplifying algebra;

• a written arithmetic procedure.

Check that prerequisite number knowledge is available. A pupil may appear to forget a fraction method when the real barrier is insecure multiplication or equivalence.

Align with department practice

Use the language, layout and representations already taught in class. Ask the maths department or consult the calculation policy before introducing a different method.

Consistency matters because the pupil needs to recognise the same structure in lessons, intervention and homework.

Model the procedure explicitly

Use a complete worked example and think aloud.

For adding fractions with different denominators:

1. Identify a common denominator.

2. Rewrite each fraction equivalently.

3. Add the numerators while retaining the denominator.

4. Simplify if appropriate.

5. Estimate whether the result is reasonable.

For 2/3 + 1/4, the common denominator is 12, so the sum becomes 8/12 + 3/12 = 11/12. As an estimate, two thirds plus a quarter is a little less than 1, so 11/12 is reasonable.

Explain why each step is necessary. Avoid phrases such as “just cross-multiply” unless the mathematical relationship has been established.

For algebra, make each transformation visible and preserve equality at every line.

Move into guided practice

Use a gradual sequence:

• teacher models;

• pupil explains a completed example;

• teacher and pupil complete a matched example;

• pupil fills missing steps;

• pupil completes a new calculation independently;

• pupil applies the method in a short problem.

Keep the values manageable while the procedure is new. Increase complexity only when the structure is secure. This can fit into ordinary lessons, for example by working through two or three matched examples at the pupil’s desk while the class starts independent work.

Correct the step, not only the answer

When an error occurs, identify whether it came from:

• selecting the wrong procedure;

• omitting a step;

• misapplying a rule;

• losing a negative sign or unit;

• a basic arithmetic fact;

• failing to sense-check.

Return to the relevant line of the worked example and ask for a corrected retry. Do not replace the method after one error.

Remove support gradually

Fade from:

• a full worked example;

• a partially completed example;

• step headings;

• one brief prompt;

• independent work.

Bring the example back temporarily if the same error returns. This is more useful than leaving a permanent model that the pupil copies without thinking.

Introduce alternatives only when useful

Once the pupil has a dependable method, compare another approach where it is quicker or shows something new.

For 15% of £80, a pupil might calculate 10% and 5%, or use 0.15 × 80. Both are valid, but method choice should follow understanding and task demands rather than novelty.

Common mistakes to avoid

• Teaching a method that conflicts with department practice.

• Expecting flexible choice before one method is secure.

• Demonstrating rules without explaining why they work.

• Increasing numerical complexity too quickly.

• Correcting only the final answer.

• Retaining the complete example indefinitely.

• Treating slower accurate work as failure.

Evidence and further reading

The Education Endowment Foundation’s Improving Mathematics in Key Stages 2 and 3 covers explicit teaching, representations and mathematical independence. The national curriculum mathematics programmes of study set expectations for efficient mental, written and calculator-supported methods.