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GCSE Maths exam technique

How to tackle multi-step GCSE Maths problems

Decode the question, represent the relationships, plan the intermediate steps, calculate clearly and check the result—with original worked examples.

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  • Portrait of Robin GibbonsLead authorFounder & CEO·Latimer Tuition
  • Reviewed byHeather LatimerTutor Matching & Customer Service·Latimer Tuition
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Current answer

The five-step method for unfamiliar GCSE Maths problems

For an unfamiliar multi-step question, use five stages: decode, represent, plan, calculate and check. Identify exactly what must be found or decided; turn the information into a useful mathematical form; order the intermediate results; calculate one meaningful step at a time; then test the final answer against the wording, units, size and context.

“translate problems … into a process or a series of mathematical processes” — Department for Education, GCSE Mathematics AO3

This five-stage sequence is a practical Latimer teaching routine, not an official exam-board mnemonic and not a guarantee of marks. The general method is useful across GCSE Maths, but paper structures, formula support and marking details vary by awarding organisation and UK nation.

Multi-step does not always mean unfamiliar

A multi-step problem needs more than one connected mathematical action. A problem-solving question also asks you to decide what mathematics to use, translate information, connect topics or interpret a result. Some questions are difficult because they are long; others are difficult because you must choose the method. In England’s assessment framework, routine multi-step tasks can sit within AO1, while AO3 covers translation, connections, interpretation and evaluation. These are useful distinctions, not labels that every board must use.

Routine multi-step task

The techniques are familiar, but several calculations must be completed in the right order. Concentrate on planning and recording the sequence clearly.

Contextual or worded problem

The information is embedded in prose, a diagram, a table or a graph. Concentrate on decoding the target and representing the relationships.

Unfamiliar problem-solving task

The method is not stated and different areas of maths may need to be connected. Concentrate on planning, checking progress and changing approach when needed.

The five stages at a glance

Use the same questions each time until the sequence becomes familiar.

A five-stage memory aid for GCSE Maths problem solving.

StageQuestion to askWhat to doCommon trap

Decode

What exactly must I find or decide?

Identify the target, units, constraints and required conclusion.

Circling every number without deciding what each one means.

Represent

Which sketch, table, equation or graph shows the relationship?

Choose a form that makes the mathematical structure easier to see.

Forcing the same diagram or model onto every problem.

Plan

Which intermediate results must come first?

Work backwards from the target and order the required techniques.

Calculating only in the order that numbers appear.

Calculate

Can someone follow each meaningful step?

Label intermediate values, use units where helpful and keep suitable precision.

Writing unexplained calculator outputs.

Check

Does my answer fit the question, units and context?

Use an estimate, inverse, substitution or contextual comparison.

Repeating the same calculator entry and calling it a check.

1. Decode the question before touching the calculator

Start by completing this sentence: “I need to find ___, in ___ units, so that I can decide or show ___.”

  • Name the final target

    Is the question asking you to calculate, compare, prove, decide or explain?

  • Identify the answer form

    Note the units, degree of accuracy and whether the answer must be a fraction, percentage, length, area, probability or statement.

  • Separate facts from conditions

    A number may be an input, a maximum, a minimum or irrelevant information. Decide what it represents before using it.

  • Find the constraints

    Look for conditions such as positive values, whole numbers, capacity limits or a required comparison.

  • Return to the final instruction

    A correct intermediate calculation is not enough when the question also asks for a conclusion.

2. Represent the information in a useful form

A mathematical representation is a sketch, table, equation, graph or other form that makes relationships easier to see. Choose it for the structure of the problem, not from habit. NCETM describes a bar model as “not a method for solving problems”; it helps only when it reveals the relevant relationship.

Ways to represent common GCSE Maths problem structures.

Problem structureRepresentation to tryWhat it can revealWhen to switch

Part–whole, ratio or percentage

Ratio table or bar model

The whole, the parts and how quantities compare.

Use an equation if the unknown relationship is clearer algebraically.

Geometry or spatial constraints

Labelled sketch

Known measures, unknowns, angles and geometric limits.

Add an equation when the dimensions are linked algebraically.

Rates, change or repeated values

Table or graph

Unit rates, trends and repeated relationships.

Use a formula if one relationship captures the pattern more clearly.

Unknown quantities and conditions

Equation or inequality

The exact relationship and any upper or lower limit.

Try a simpler numerical case or sketch if the algebra hides the meaning.

Several dependent stages

Known-and-unknown list or arrows

Which intermediate result feeds the next calculation.

Use a table if several cases or repeated stages must be compared.

3. Plan the intermediate results

An intermediate result is a value found partway through because a later calculation depends on it. The Education Endowment Foundation summarises self-regulated learning as “planning, monitoring, and evaluating”. For a short routine question, the plan may be mental; for a longer problem, write a compact sequence.

  • Work backwards from the target

    Ask which value you need immediately before the final answer.

  • Continue until every step is possible

    Link each required value to information already given or to an earlier calculation.

  • Name the technique

    Decide whether each stage uses percentage change, ratio, area, algebra, a rate, probability or another method.

  • Write a compact sequence

    Words, symbols or arrows can show how the intermediate values connect.

  • Estimate the likely answer

    Predict the sign, scale or approximate region before calculating.

  • Monitor the approach

    If the current representation or sequence is not helping, deliberately change it.

4. Calculate one meaningful step at a time

The aim is traceable working, not decorative working. Each line should show what changed and why.

  • Use one line per meaningful step

    For example, write 0.85 × 80 = 68 rather than an unexplained list of calculator results.

  • Label intermediate values

    Write “discounted price”, “area” or “time” when the meaning would otherwise be unclear.

  • Carry useful units

    Units can expose a mistaken operation and help distinguish length, area, volume, rate and money.

  • Show substitution when it helps

    Writing the formula or the substituted form can make the method clear.

  • Keep suitable precision

    Retain enough digits during intermediate calculations and round when the question requires it. Exact values, bounds and explicit instructions may need different treatment.

  • Copy calculator values carefully

    Check brackets, negative signs, powers and decimal places before using the result in the next stage.

5. Check the answer from a different angle

A reasonableness check tests whether an answer makes sense independently. England’s GCSE Mathematics content includes estimation and checking by approximation, so checking should be more than repeating the same entry.

  • Final target

    Did you answer the question that was asked, rather than stop at an intermediate result?

  • Units and form

    Are the units, answer form and degree of accuracy correct?

  • Sign and size

    Is the result plausible? A length cannot be negative and a probability must lie between 0 and 1.

  • Independent estimate

    Round the inputs and check that the exact answer lies in the expected region.

  • Inverse or substitution

    Reverse the final operation or substitute the result back into the equation or formula.

  • Contextual conclusion

    If the question asks whether something is enough, possible or correct, compare your number with the stated limit and write the decision.

Worked example 1: percentage, rate and capacity

Question: A water tank holds 240 litres and is 35% full. Water enters at 6 litres per minute for 18 minutes. Will the tank overflow?

A worked multi-step problem combining percentage, rate and a capacity decision.

StageReasoning

Decode

Find the final volume, compare it with the 240-litre capacity and state whether it overflows.

Represent

Initial water + added water = final water.

Plan

Find 35% of 240; find 6 × 18; add the results; compare with 240.

Calculate

Initial water: 0.35 × 240 = 84 litres. Added water: 6 × 18 = 108 litres. Final volume: 84 + 108 = 192 litres.

Check

192 < 240, so the tank does not overflow. It has 240 − 192 = 48 litres of space.

Worked example 2: percentage, money and ratio

Question: A jacket costs £80. It is reduced by 15%, then delivery costs £4.50. Two people share the final cost in the ratio 3:2. How much does the person with the larger share pay?

A worked multi-step problem in which the order of the calculations changes the meaning.

StageReasoning

Decode

Find the larger share of the cost after both the discount and delivery have been applied.

Represent

Discounted price → add delivery → divide into five equal ratio parts → take three parts.

Plan

Calculate £80 × 0.85; add £4.50; multiply the final cost by 3/5.

Calculate

Discounted price: £80 × 0.85 = £68. Final cost: £68 + £4.50 = £72.50. Larger share: 3/5 × £72.50 = £43.50.

Check

The smaller share is 2/5 × £72.50 = £29.00, and £43.50 + £29.00 = £72.50. Splitting before adding delivery would answer a different question.

Worked example 3: algebra, geometry and contextual rejection

Question: A rectangle has width x cm, length (x + 3) cm and area 40 cm². Find its perimeter.

A Higher-tier example requiring an algebraic solution and a contextual check.

StageReasoning

Decode

The final target is the perimeter, but the dimensions must be found first.

Represent

Area gives x(x + 3) = 40.

Plan

Form and solve a quadratic, reject any impossible length, then calculate 2(width + length).

Calculate

x² + 3x − 40 = 0, so (x + 8)(x − 5) = 0. Therefore x = −8 or x = 5. A physical width cannot be negative, so the width is 5 cm and the length is 8 cm. Perimeter = 2(5 + 8) = 26 cm.

Check

5 × 8 = 40, matching the area, and both dimensions are positive.

What to do when you get stuck

Do not repeat the same unsuccessful attempt unchanged. Use the reset that best matches the difficulty.

  • You do not know where to start

    Re-read the final sentence and restate the target, answer form and units.

  • There are too many facts

    Make a known-and-unknown table. Remove only information that is genuinely irrelevant.

  • No operation is obvious

    Draw or rewrite the relationship instead of searching for a keyword.

  • The method stops halfway

    Ask which missing intermediate value would connect your current result to the final target.

  • The algebra feels unclear

    Try a diagram, table, numerical example or simpler case to expose the structure.

  • The answer looks wrong

    Estimate, check units, substitute back or reverse the final operation.

  • The same attempt keeps failing

    Change representation, leave clear working and return later if needed.

Practise the failed stage, not only the topic

A wrong answer does not always mean the underlying topic is unknown. Diagnose where the thinking first broke down.

  • Attempt

    Try a mixed or exam-style problem without looking at the solution.

  • Mark

    Compare your work with the answer and accepted method.

  • Identify

    Find the first failed stage: decoding, representation, planning, calculation or checking.

  • Correct

    Repair that stage without immediately copying the full worked solution.

  • Transfer

    Try a structurally similar problem using the corrected approach.

  • Retest

    Return to the same structure later and record the failed stage as well as the topic.

Sources and further reading

These official, research and Latimer sources support the assessment, learning and service information used in this guide.

  • GOV.UK — GCSE mathematics: subject content and assessment objectives

    Department for Education · Published 1 November 2013 · Accessed 4 August 2026

    Open source 1

  • Ofqual — Formula-sheet decisions for 2025, 2026 and 2027

    Updated 13 November 2024 · Accessed 4 August 2026

    Open source 2

  • Ofqual — Formula-sheet decision from 2028

    Published 5 May 2026 · Accessed 4 August 2026

    Open source 3

  • Education Endowment Foundation — Metacognition and Self-Regulated Learning

    Published 13 November 2025 · Accessed 4 August 2026

    Open source 4

  • NCETM — Representation and Structure

    Accessed 4 August 2026

    Open source 5

  • NCETM — The Bar Model

    Accessed 4 August 2026

    Open source 6

  • AQA — GCSE Mathematics subject content

    Accessed 4 August 2026

    Open source 7

  • AQA — Mathematics assessment guidance

    Accessed 4 August 2026

    Open source 8

  • OCR — Clarification to GCSE Mathematics mark schemes

    Accessed 4 August 2026

    Open source 9

  • OCR — Updated GCSE Mathematics sample assessment materials

    Published 27 September 2024 · Accessed 4 August 2026

    Open source 10

  • Latimer Tuition — GCSE Mathematics Tutors

    Last reviewed 16 May 2026 · Accessed 4 August 2026

    Open source 11

  • Latimer Tuition — Match Me With a Tutor

    Accessed 4 August 2026

    Open source 12

Related guidance

More guidance from this section

More guidance from this part of the Ed Centre that may help with the same decision, stage or next step.

Support and clarity

Frequently asked questions

Straight answers to the questions people ask most often.

What is a multi-step problem in GCSE Maths?

It is a question that requires more than one connected mathematical action. Some use familiar procedures in sequence; harder problem-solving questions also require you to choose methods, translate information, connect topics or interpret the result. In England’s framework, routine multi-step tasks and unfamiliar problem solving are treated differently, although other qualifications may use different wording.

Are all GCSE Maths word problems multi-step?

No. A worded context may require only one operation. A multi-step problem may also be presented through a diagram, table, graph or algebraic relationship rather than prose.

How do I know which maths method to use?

State the final target, choose a representation that shows the relationships, then work backwards to the intermediate value needed immediately before the answer. Continue until every stage can be linked to the information given. When the first approach does not clarify the structure, change representation or try a simpler case.

How much working should I show in a multi-step question?

Show enough for another person to follow the mathematical method and identify important intermediate values. Clear working can preserve evidence of a valid method after an arithmetic mistake, but the available credit depends on the individual question and mark scheme; every line does not automatically earn a mark.

Can I use a different method from the model answer?

A mathematically valid alternative may be acceptable when it is communicated clearly. OCR explicitly recognises alternative correct methods and representations where possible, but exact credit is governed by the relevant mark scheme and this wording should not be assumed for every board.

How can I check whether a GCSE Maths answer is reasonable?

Check the final target, units, answer form, sign and size. Use an independent estimate, an inverse operation or substitution, and compare the result with any contextual limit. Finish by writing the conclusion the question asks for.

Does the GCSE Maths formula sheet solve a multi-step problem?

No. A formula sheet can supply a formula, but you still have to select it, substitute correctly, connect it with other calculations and interpret the result. Current formula-sheet arrangements are nation- and board-specific, so practise with the materials for your awarding organisation and exam series.

Should I round after every step?

Usually, keep sufficient precision during intermediate calculations and round when the question requires it. Do not apply this as an absolute rule: exact values, bounds and explicit instructions about intermediate answers can require a different treatment.

Sources and references

Sources and references

Official guidance

Peer-reviewed research

Internal pages

Other sources