11 plus Multi-Step Word Problems questions

What a Multi-Step Word Problems question looks like

A Multi-Step Word Problem is a short everyday situation with numbers in it, set as a multiple choice with five options and no sum written out anywhere. Before a child can calculate anything they have to decide what the calculations are and what order they go in. That decision is the whole question, and it is the part of 11 plus maths where a confident calculator can still lose marks.

Two things mark this type out from the other maths formats. The sum is never handed over, so the child builds it themselves from the sentences, and money is only one of the quantities in play. Lengths, weights, capacities, times, cooking rates, speeds and prices all appear, and a unit change is often hidden in the middle of the working.

Example one: a hidden unit change

A ribbon is 5 m long. Fatima cuts off three pieces each 80 cm long. How much ribbon is left? Give your answer in centimetres.

The question asks for centimetres, so change the ribbon into centimetres first: 5 m is 500 cm. Now the three pieces: 3 x 80 = 240 cm cut off. Finally take that away from what she started with: 500 - 240 = 260 cm.

The answer is 260 cm.

The tempting wrong answer is 420 cm. That is 500 - 80, which is what happens when a child converts correctly, sees the 80 and subtracts it before noticing the word “three”. The arithmetic is perfect and the answer is still wrong, which is the pattern to watch for in this whole question type.

Example two: find one first

A market stall sells oranges at 4 for £1.20. Nadia buys 10 oranges. How much does she pay?

Ten is not a whole number of fours, so the price of four is not enough on its own. Find the price of one orange instead: £1.20 divided by 4 is 30p. Then ten oranges cost 10 x 30p = £3.00.

The answer is £3.00.

Two wrong options are built here. £2.40 is two lots of £1.20, which pays for eight oranges and quietly forgets the other two. £3.60 is three lots of £1.20, which pays for twelve. Both come from trying to work in fours instead of dropping down to one, and finding the cost of one item is the move that unlocks most rate questions.

Example three: working backwards

A dog walker charges a £4 booking fee, then £2.50 for every 15 minutes of walking. A bill comes to £19. How long was the walk?

This one gives the answer to the sum and asks for a number from the middle of it, so the steps run in reverse. Take off the booking fee first, because it does not depend on the length of the walk at all: £19 - £4 = £15. Every 15 minutes costs £2.50, so £15 divided by £2.50 is 6 lots of 15 minutes. That is 6 x 15 = 90 minutes, or 1 hour 30 minutes.

The answer is 1 hour 30 minutes.

The trap is 2 hours, which comes from dividing the whole £19 by £2.50, getting 7.6, and rounding up to 8 lots of 15 minutes, all because the booking fee was never taken off. The other slip is stopping at 6, the number of 15-minute blocks, and giving “6 minutes” as though it were the time.

How to answer it

1. Read to the end, then say what the question actually wants, with its unit attached. “How many centimetres are left” and “how much change” are answers to different questions, and the wrong options are usually the answer to the other one.
2. Make the units match before calculating anything. Metres to centimetres, kilograms to grams, litres to millilitres, hours to minutes. Doing this first turns a two-unit problem into ordinary arithmetic.
3. Find the step you can do straight away, the one where both numbers are already in front of you. Do it, and write the result down with a short label such as “36 rolls” or “£4.50 cakes”. The label is what stops a child using the number for the wrong thing two lines later.
4. Look at what you now have and repeat, until the number you are holding is the one the question asked for.
5. Check the size and the unit. If the question asks how many whole boxes, rolls or bags, round up even when the division is untidy, because 3.75 rolls means buying 4.

Common mistakes

• Stopping one step early. Giving the total cost instead of the change, or how many were sold instead of how many are left. This is the single most common wrong answer in this format, and it is always on the list of options.
• Converting one number and not the other. Taking 80 cm off 5 without turning the 5 into 500, or taking 300 g from 1.5 without turning it into 1500 g. The result looks like a sensible number, which is what makes it dangerous.
• Rounding down on a “how many must you buy” question. Needing 22.5 metres of wallpaper from 6 metre rolls is 3.75 rolls, so the answer is 4. Shops do not sell three quarters of a roll.
• Answering break-even when the question says save. If a card costs £6 and saves £1.20 a visit, five visits leaves the cost the same either way, so saving money takes a sixth visit. The break-even number is always offered as an option.
• Miscounting people or groups in the first line. Tickets for “himself and 2 friends” is three tickets, not two. A first-line slip is invisible afterwards, because every later step is done correctly on the wrong starting number.

How to practise 11 plus Multi-Step Word Problems questions

The useful practice here is talking, not marking. When your child gets one wrong, ask which step they did first and what they thought the question wanted, because nine times out of ten the arithmetic was fine and the plan was not, and that is a fixable thing. Little and often works better than long sessions, which is the pattern we set out in how much 11 plus practice a child needs each day, and it suits a question type where five discussed questions beat twenty silent ones. 11+ Daily has a Multi-Step Word Problems project sitting alongside the other maths topics listed on our 11 plus maths practice page, on laptop, tablet or phone, and it is a sensible place to start eleven plus maths work because the habit it builds carries into every other topic. Every question is original to 11+ Daily, nothing is a past paper and nothing is licensed from another publisher, and the bank is re-checked in rounds.

Questions parents ask