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Word problems

A word problem is not a different kind of arithmetic. It is arithmetic you have to find first: the numbers are on the page and what to do with them is not. Nearly all of the difficulty lives in the reading, which is why the strategy deserves as much practice as the sums do.

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Finding the operation

Maya has 24 stickers. She gives 7 of them to her brother. How many does she have left?

  1. Ask what the question wants: how many are LEFT.
  2. Something has gone, so this is a take-away.
  3. The numbers are 24 and 7, and 24 is what she started with.
  4. 24 take away 7 is 17. She has 17 stickers left.

Worth knowing. The words that hint at an operation — left, altogether, each, shared, more — are worth knowing, but they are hints and not rules. "How many more does Devi have than Sam?" is a subtraction with the word "more" in it.

Two steps, in the order they happen

Maya buys 3 packs of stickers with 8 in each pack, then gives 5 away. How many does she have?

  1. Take one step at a time, in the order the story tells them.
  2. First: 3 packs of 8 is 3 x 8, which is 24.
  3. Then she gives 5 away, so 24 take away 5.
  4. The answer is 19 stickers.

Worth knowing. The order belongs to the story, not to the rules. This is not a question about whether multiplication comes before subtraction — she bought the packs and then gave some away, so that is the order you work in. Order of operations is a different topic, and it is about expressions rather than about events.

Where it usually goes wrong

  • Taking the two numbers and guessing the operation. "The hall has 6 rows of 12 chairs" and "the hall has 6 more chairs than the 12 in the corridor" hold the same two numbers and want different sums.
  • Answering a different question from the one asked — finding the total when the question wanted what was left.
  • Doing the second step first in a two-step problem, which changes the answer: 3 packs of (8 take away 5) is 9, not 19.

The Professor reads the whole problem once before he picks up a pencil, then reads it again and underlines what is actually being asked. Working out the right answer to the wrong question is the most expensive mistake there is.

Practise it

All level paths

Questions teachers and parents ask

How do I know which operation to use?

Start from what is being asked rather than from the numbers. "Altogether" and "in total" usually add; "left" and "how many more" usually subtract; "each" and "rows of" usually multiply; "shared equally" and "split into" usually divide. Usually — the words are hints, and the question is the authority.

What should I do with a two-step problem?

Work the steps in the order the story tells them, and write down what you get after the first one. A two-step problem is two one-step problems with a number carried between them, and nearly all the lost marks come from trying to hold that number in your head.

Are these questions about reading or about maths?

Both, and that is the point. A child who can do 24 take away 7 can still fail to notice that a problem is a 24 take away 7, and noticing is a skill that has to be practised on its own.

When are word problems taught?

Addition and subtraction word problems are grade 2 (2.OA.A.1) and multiplication and division ones grade 3 (3.OA.A.3). Two-step problems using the four operations sit in grades 3 and 4 (3.OA.D.8, 4.OA.A.3).

Where this shows up

Standards

  • 2.OA · Operations and algebraic thinking
  • 3.OA · Operations and algebraic thinking
  • 4.OA · Operations and algebraic thinking

Formats