A word problem is a math problem told as a story. The math is usually easy once you decide what the story is asking. The trick is a calm, repeatable routine.
Try it with your own problem ↓
The steps
- Read it twice. The first time for the story, the second time for the numbers.
- Find the question. Underline what you are asked to find, and write down what the answer will be measured in (dollars, people, hours).
- Pick out the facts. List the numbers and what each one means. Cross out any that aren't needed.
- Choose the operation. Words like "in all" and "total" suggest adding. "Left", "more than", "change" suggest subtracting. "Each" and "groups of" suggest multiplying. "Per" and "shared equally" suggest dividing. "Percent off" means a percent of the price.
- Solve it, then check. Does the answer make sense in the story? Does it have the right units?
A worked example
A coat costs $80 and is 25% off. What is the sale price?
- Question: the sale price, in dollars.
- Facts: the original price is $80 and the discount is 25%.
- Plan: find the discount amount, then subtract it from the price.
- Discount: 25% of 80 = 0.25 × 80 = 20.
- Sale price: 80 − 20 = 60.
- Check: 25% off means you pay 75%, and 0.75 × 80 = 60. ✓
The sale price is $60.
Common mistakes
- Grabbing numbers and operating on them without reading. Decide what you're looking for first.
- Relying on keywords. "More" can mean add or subtract depending on the story. Picture the situation.
- Stopping at the first step. The discount ($20) is not the sale price ($60).
- Skipping the check. Does $60 for an $80 coat on sale make sense? Yes. If you'd got $100, it wouldn't.
Questions people ask
What if there are too many numbers?
Some problems include extra information. Decide what the question needs, and ignore the rest.
How do I know whether to add, subtract, multiply or divide?
Draw a quick picture or act out the story. Joining groups is adding, taking away is subtracting, equal groups are multiplying, and sharing equally is dividing.
What about problems with two steps?
Break them into two small problems and write down the result of the first. The coat example is a two-step problem.
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