Maths word problems for ages 7 to 11: a method that works

The five-step method

1. Read the whole problem twice. Underline the actual question, which is often in the last sentence.
2. Draw it. A bar model (rectangles standing for amounts) shows which amounts are parts, which is the whole and which is a comparison.
3. Decide the operation or operations. Ask: am I combining, taking away, finding a difference, sharing or making equal groups?
4. Estimate. Round the numbers and get a rough answer, so a wildly wrong result is obvious.
5. Calculate, then reread the question and check the answer fits the story, including units and remainders.

Worked example 1 (two-step, Year 3 to 4): change from a note

Omar buys 3 notebooks at 12 dirhams each. He pays with a 50 dirham note. How much change does he get?

1. The question is 'how much change', so the final step is a subtraction from 50.
2. Step one: the cost of the notebooks is 3 × 12 = 36 dirhams.
3. Step two: change = 50 - 36 = 14 dirhams.
4. Estimate: 3 notebooks at about 10 dirhams is 30, so change is roughly 20. 14 is sensible.

Worked example 2 (bar model, Year 5 to 6): 'times as many'

Layla has 3 times as many stickers as Adam. Together they have 48 stickers. How many does Layla have?

1. Draw Adam's stickers as one box and Layla's as three boxes of the same size.
2. There are 4 equal boxes altogether, worth 48 stickers.
3. One box is 48 ÷ 4 = 12, so Adam has 12.
4. Layla has 3 boxes: 3 × 12 = 36. Check: 36 + 12 = 48, and 36 is 3 times 12.

Worked example 3 (remainders, Year 5 to 6): round up or down?

A minibus holds 14 children. 100 children are going on a trip. How many minibuses are needed?

1. This is grouping, so divide: 100 ÷ 14 = 7 remainder 2.
2. Seven minibuses carry 98 children, leaving 2 children without a seat.
3. Those 2 children still need a bus, so the answer is 8 minibuses.
4. Compare: 'How many full minibuses can be filled?' would have the answer 7. The context decides whether to round up, round down, or give the remainder.

Worked example 4 (time, Year 5 to 6)

A film starts at 4:45 pm and lasts 1 hour 50 minutes. When does it end?

1. Add the hour first: 4:45 pm + 1 hour = 5:45 pm.
2. Add 15 minutes to reach the next hour: 6:00 pm. That leaves 50 - 15 = 35 minutes.
3. 6:00 pm + 35 minutes = 6:35 pm.
4. Trap: adding 45 + 50 = 95 and writing 5:95 or 6:95. Time does not work in hundreds.

Key words are clues, not rules

Children who hunt only for key words go wrong on problems like example 2. Drawing the problem is more reliable.

Common mistakes

• Starting to calculate before reading to the end of the problem.
• Using every number in the question, including ones that are not needed.
• Answering an earlier step: giving 36 (the cost) instead of 14 (the change).
• Ignoring units, or mixing metres and centimetres in one calculation.
• Writing a remainder when the story needs a whole number, such as 7 r 2 minibuses.
• Skipping the estimate, so an answer like 1,400 for the change from 50 dirhams goes unnoticed.

How one-to-one lessons help with word problems

Word problems are partly a reading skill, so a child who struggles often needs to slow down and talk through what is happening. In a lesson the tutor reads each problem with your child, asks them to retell it in their own words, and draws the bar model together on the shared whiteboard before any calculating. Over a few weeks the tutor hands more of that over until your child does it unprompted. Lessons mix problem types, because recognising which kind of problem it is is the real skill being tested.

Self-check

• A box holds 24 pencils. A school buys 6 boxes and gives out 100 pencils. How many are left? (44)
• Huda reads 15 pages a day. How many days to finish a 100-page book? (7 days, because 6 days is only 90 pages)
• A rope is 3 m long. 85 cm is cut off. How much is left? (215 cm, or 2.15 m)
• Sam has 4 times as many marbles as Ali. Sam has 36 more than Ali. How many does Ali have? (12)