11+ Multi-Step Word Problems: A Method and Eight Practice Questions

Original learning material for families preparing for 11-plus exams taken in 2027. These examples are not official exam questions; check your school’s current assessment guidance for the skills and format it uses.

The arithmetic in a word problem may be familiar while the route to it is not. Before calculating, decide what the final answer must describe. A correct total is still the wrong answer if the question asks for change. This guide makes those decisions visible.

Make a plan before you calculate

1. 1Read the whole situation, then restate the final question: “I need the money left” or “I need the number of vehicles”.
2. 2List the quantities you need, with their units. Convert metres to centimetres or pounds to pence when the calculation requires a common unit.
3. 3Write short labels for the intermediate answers. A label such as “cost of all tickets” stops that number being mistaken for the final result.
4. 4Calculate in the order your plan requires, retaining working and avoiding early rounding.
5. 5Read the final sentence again. Check the size, unit and whether a remainder changes what the answer means.

A sketch, a bar or a small table can show the relationships without being elaborate. If you know the total and what has been used, the missing part is a subtraction. If equal groups are being combined, multiplication may help. Let the situation decide rather than treating a word as an automatic operation command.

Worked example: total cost is not change

A garden club buys four seed trays at £3.65 each and compost costing £6.80. It pays with £30. How much change is due? First label tray cost: 4 × £3.65 = £14.60. Next label total cost: £14.60 + £6.80 = £21.40. Finally calculate change: £30 − £21.40 = £8.60.

£21.40 is a sensible intermediate answer, but it describes the purchase rather than the change. Check by adding: £21.40 + £8.60 = £30. An estimate also helps: trays cost around £16 and compost around £7, so change should be several pounds, not £20.

Worked example: a fraction of what remains

A club has 72 stickers. It gives away one third of them, then uses half of the remaining stickers on posters. How many are left? One third of 72 is 24, leaving 48. Half of the remaining 48 is 24, leaving 24 stickers. The second fraction applies to 48, not to the original 72.

Compare a different instruction: if the club used half of the original stickers on posters, it would use 36 and have 72 − 24 − 36 = 12 left. Both calculations are reasonable for different stories. Underline “remaining” or “original” because these change the mathematical relationship.

Worked example: interpret a remainder

Ninety-four pupils and eight adults need transport. Each minibus has room for 16 passengers, excluding its driver. How many minibuses are needed? There are 94 + 8 = 102 passengers. Six minibuses hold 96, which leaves six people without seats. Seven are needed. Rounding 102 ÷ 16 to the nearest whole number would give six and fail the actual requirement.

Eight original problems

Work without a time limit first. For each question, write one short sentence explaining your plan. The answer panels include the calculations, but try to identify the required steps before revealing them.

Repair the plan, not just the arithmetic

If an answer is wrong, ask which line changed the meaning of the question. Was a fraction applied to the wrong whole? Were minutes treated as hundredths of an hour? Was the calculation stopped at a subtotal? Repeating the same arithmetic faster will not fix a misunderstood relationship.

Words alone are unreliable shortcuts. In “£12 is shared equally between three people”, “equally” leads to division. In “three people each receive £12”, the total is found by multiplication. Explain what is being counted before choosing the operation.

Build the component skills

Use fraction, decimal and percentage conversions when forms are mixed, ratio sharing for unequal groups, and algebra basics when a missing number can be named. The Maths hub links to further practice.

Skill reference: DfE mathematics programme, checked 21 October 2026. Curriculum guidance does not determine every school’s entrance-test content. These are original questions with worked checks, not an official paper or an exam-score prediction.