When a pupil is unsure how to calculate, teaching several methods at once can increase confusion. Select one appropriate strategy that aligns with the school’s calculation policy. Model it clearly, practise it together and remove equipment or prompts gradually.

Accuracy and understanding come before speed.

Select the method carefully

Choose a method that:

• matches the mathematical structure;

• is consistent with prior teaching;

• is used by the school or class;

• can be represented clearly;

• prepares the pupil for later learning.

Check whether the main difficulty is understanding the operation, recalling a fact, interpreting place value or following the procedure. The response should address the actual barrier.

Model every step

Use a worked example and think aloud. Explain what is done and why.

For 8 + 7 using make ten:

1. Show 8 and 7 with counters or a ten frame.

2. Split 7 into 2 and 5.

3. Move 2 to complete 10.

4. Combine 10 and 5.

5. Record 8 + 7 = 8 + 2 + 5 = 15.

The pupil should connect the equipment, spoken reasoning and written calculation.

Move through guided practice

Use a gradual sequence:

• teacher models;

• teacher and pupil complete an example together;

• pupil completes a closely matched example with prompts;

• pupil completes one independently;

• pupil applies the method in a short problem.

Change the numbers but preserve the structure. Avoid moving directly from one demonstration to a full page of unsupported questions. The guided steps could happen, for example, at the pupil’s table while the rest of the class starts independent work.

Respond to errors without changing the method

If the pupil makes an error, identify the exact step. Return temporarily to the representation or worked example and ask for a corrected retry.

Do not introduce a different strategy immediately. The pupil needs a fair opportunity to secure the selected method.

Change the approach only if the method is poorly matched, the underlying concept is insecure or repeated teaching shows that another representation is needed.

Fade equipment and prompts

Progress from:

• concrete equipment;

• a drawing or diagram;

• a complete worked example;

• a partially completed example;

• a short verbal prompt;

• independent calculation.

Remove one layer at a time. Equipment should remain available while it reveals the structure, but it should not become a sequence the pupil follows without understanding.

Introduce another strategy when ready

The pupil is ready to compare methods when they can:

• use the current method accurately;

• explain why it works;

• recognise the calculation type;

• retain it after a gap;

• apply it in a different example.

Then introduce another efficient method and compare when each is useful. Flexibility should grow from secure methods, not replace them.

Common mistakes to avoid

• Teaching several strategies at once.

• Choosing a method that conflicts with the school calculation policy.

• Demonstrating steps without explaining the mathematics.

• Removing equipment because of age rather than readiness.

• Changing method after one error.

• Expecting speed before accuracy.

• Keeping the full scaffold after the pupil can calculate independently.

Evidence and further reading

The Department for Education’s Primary mathematics guidance sets out progression in calculation and representations. The Education Endowment Foundation’s Improving Mathematics in Key Stages 2 and 3 discusses representations, worked examples and development of mathematical independence.