A step-by-step method for extracting the maths from any worded problem — and why most students never develop this skill properly.
Worded problems are where a lot of GCSE Maths marks get lost. Not because students don't know the maths — but because they can't extract what the question is actually asking. A student who can solve 3x + 7 = 22 instantly might completely freeze when the same equation is hidden inside a paragraph about train tickets and journey times.
This isn't a knowledge gap. It's a reading and translation skill that very few teachers explicitly teach. This guide gives you a systematic method for any worded problem, plus worked examples of the most common question types.
The difficulty isn't mathematical — it's cognitive overload. Your brain is trying to read the English, understand the context, identify the relevant numbers, decide what operation to perform, and execute the calculation all at once. That's too much to hold in working memory simultaneously.
The solution is to separate these tasks. Read first. Extract second. Calculate third. Never try to do all three at once.
Don't start underlining or calculating mid-paragraph. Read the entire question once, slowly. Your only goal on this read is to understand the situation — not to solve it. What is the scenario? Who are the people involved? What's happening?
Read the question again and this time focus only on the final question — often the last sentence. Write down in plain English what you need to find. "Find the total cost." "Calculate how long the journey takes." "Work out how many tiles are needed." This becomes your target.
Go through the question and list every piece of numerical information. Write each one with a label: "Speed = 60 mph", "Distance = 45 miles", "Cost per item = £3.50". Include units every time. Don't write raw numbers without context.
Now look at your list of information and your target. What formula connects them? Speed, distance and time? Area formula? Percentage calculation? Ratio? Define any variables you need: "let x = number of items".
Perform the calculation. Check that your answer is in the right units and makes sense in context. Write a concluding sentence: "The total cost is £47.20." Don't just write a number — state what it represents.
"A plumber charges a call-out fee of £45 plus £28 per hour. She works for 3.5 hours. VAT at 20% is added to the total. How much does the customer pay?"
Step 1: Plumber job, multiple charges, VAT added.
Step 2: Find total cost to customer including VAT.
Step 3: Call-out fee = £45. Hourly rate = £28. Hours worked = 3.5. VAT = 20%.
Step 4: Total before VAT = 45 + (28 × 3.5). Then add 20% VAT.
Step 5: 28 × 3.5 = 98. Total before VAT = 45 + 98 = £143. VAT = 143 × 0.20 = £28.60. Total = 143 + 28.60 = £171.60.
"Jake has x sweets. Lily has three times as many as Jake. Together they have 48. How many sweets does Jake have?"
Step 2: Find x (Jake's sweets).
Step 3: Jake = x. Lily = 3x. Total = 48.
Step 4: x + 3x = 48.
Step 5: 4x = 48 → x = 12. Jake has 12 sweets.
"A rectangular garden is 12 m long and 8 m wide. A square patio of side 3 m is built in the corner. Grass seed costs £2.50 per m². How much does it cost to grass the remaining area?"
Step 2: Cost to grass the area excluding the patio.
Step 3: Garden: 12 m × 8 m. Patio: 3 m × 3 m. Seed cost: £2.50/m².
Step 4: Grass area = garden area − patio area. Cost = grass area × 2.50.
Step 5: Garden = 96 m². Patio = 9 m². Grass area = 87 m². Cost = 87 × 2.50 = £217.50.
Part of translating worded problems is recognising which English words signal which mathematical operations. These appear so consistently across GCSE papers that learning them is genuinely useful.
When a question says "show that" or "show your working", you must write every step — including ones that feel obvious. The marks are for the method, not just the answer. A correct answer with no working scores zero on a "show that" question.
Before writing your final answer, spend five seconds asking whether it makes sense in context. If the question is about the cost of a cinema ticket and your answer is £847, something has gone wrong. If it's about how many buses can carry 240 people with 48 seats each, an answer of 3.something needs rounding up to 5 — you can't have a fraction of a bus.
Context-checking is something examiners specifically look for in "explain" or "justify" questions. If a question ends with "explain whether your answer is reasonable", they want to see you compare your numerical answer against the real-world situation described.
GCSE worded problems often require contextual rounding that differs from standard mathematical rounding. If you need a whole number of boxes to pack items, always round up — even if the decimal is 0.1. If you need a whole number of cuts from a length of wood, think carefully about whether to round up or down based on what the question is actually asking.
PaperPlus generates worded GCSE Maths questions across all topics, with mark schemes that show exactly how to structure your working. Free for AQA, Edexcel and OCR.
Start Practising Free →Most worded problems at GCSE are multi-part — part (a), part (b), part (c). A critical habit: don't abandon a question because you can't do part (a). Parts (b) and (c) are often independent or use the method from (a) rather than the specific answer. If (a) asks you to show something, and you can't, make a reasonable assumption and use it in (b). You may still get marks for correct method in (b) even if (a) is wrong — this is called "follow-through marking" and it's used consistently across all exam boards.
The AQA examiner reports for GCSE Maths explicitly note that students who attempt all parts of worded questions consistently outperform those who skip them. The full reports are available free on the AQA GCSE Mathematics page.