A multi-step problem can become difficult before any calculation begins. Pupils need to identify the required outcome, represent the relationships, order the steps and keep intermediate results connected to the original context.

Teach a consistent sequence and model the decisions aloud. Use concise annotations rather than turning the plan into a second extended-writing task.

Unpack the question

Identify:

• the final outcome required;

• known and unknown quantities;

• units;

• constraints or conditions;

• information that may be irrelevant;

• relationships between the quantities;

• whether an exact or approximate answer is needed.

Do not allow individual keywords to determine the operation. The same word can occur in several mathematical structures. For example, “How much more does she need?” asks for a difference, even though it contains the word “more”.

Represent the structure

Choose a suitable equation, diagram, table, graph or annotated model. Label quantities and units.

For a rate problem, a table may show distance, time and speed more clearly than a bar model. For geometry, an annotated diagram may expose the missing dimensions. The representation must fit the mathematics.

Order the steps

Write a short plan that shows what each intermediate result will provide.

For example:

1. Find the discounted price.

2. Add delivery.

3. Compare the total with the budget.

4. State whether the purchase is possible.

This prevents a correct intermediate calculation from being mistaken for the final answer.

A complete Secondary example

Problem: A jacket costs £84. It is reduced by 15%. Delivery costs £4.50. A customer has £75. Can they afford it, and how much money will remain or be needed?

Understand

Need the final cost including delivery and a comparison with £75.

Represent and plan

15% = 10% + 5%.

1. Find 15% of £84.

2. Subtract the discount.

3. Add delivery.

4. Compare with £75.

Calculate

10% of £84 = £8.40
5% of £84 = £4.20
15% = £12.60
Reduced price = £71.40
With delivery = £75.90

Interpret and check

The customer cannot afford it. They need another £0.90. An estimate confirms that a price just above £75 is plausible.

The final sentence matters because £75.90 alone does not answer whether the customer can afford the purchase.

Keep intermediate results meaningful

Write labels such as discount, reduced price and final cost. This reduces the risk of using the right number in the wrong step.

After each stage, ask: “What does this result now tell us, and what remains to be found?”

Keep a short checklist visible

While the pupil practises, keep five short prompts on a card or in the margin:

1. What am I asked to find?

2. What information do I need, and what can I ignore?

3. What order will the steps go in?

4. Solve, labelling each result.

5. Does the answer fit the question?

Fade the support

Move from:

• full teacher think-aloud;

• joint annotation and planning;

• partially completed plan;

• pupil writes two or three concise steps;

• one prompt about the missing condition;

• independent planning and review.

Return to the full model for a new problem type, then fade again.

Common mistakes to avoid

• Choosing operations from keywords.

• Calculating before identifying the requested outcome.

• Using an unsuitable representation by habit.

• Leaving intermediate values unlabelled.

• Ignoring units or constraints.

• Recalculating without reviewing the problem structure.

• Keeping a long checklist after independent planning is secure.

Evidence and further reading

An Education Endowment Foundation blog on developing problem-solving strategies discusses think-aloud modelling and graduated scaffolds. The Department for Education’s Key Stage 3 mathematics guidance provides curriculum-aligned progression and examples.