Reading like a detective
A word problem tells a story with maths hidden inside. The hardest part is often not the calculation but working out what to calculate. Good problem solvers read slowly and carefully, like detectives.
The read–think–solve routine
| Step | What to do |
|---|---|
| 1. Read | Read the whole problem twice. |
| 2. Restate | Say it in your own words. |
| 3. Find the unknown | What is the question asking? Underline it. |
| 4. Find the given information | Circle the numbers and facts you need. |
| 5. Cross out extra information | Ignore details that don’t help. |
| 6. Plan | Pick the operation(s) and the order. |
| 7. Solve and check | Calculate, then ask: does the answer fit the story? |
Key words (with caution)
Key words can hint at operations:
| Operation | Common clues |
|---|---|
| Add | total, altogether, in all, sum, combined, more than (sometimes) |
| Subtract | difference, how many more, how many fewer, left, remain |
| Multiply | each (with groups), times, per, groups of, product |
| Divide | share equally, split, each (finding one share), per, quotient |
But key words can trick you. "Sam has 5 more marbles than Jo. Sam has 12. How many does Jo have?" uses "more", but you subtract: 12 − 5 = 7. Always think about the story, not just the words.
Visualize the problem
- Draw a picture. Sketch the objects.
- Bar model. Draw bars for the parts and the whole.
- Act it out with objects.
Example walkthrough
Problem: A school bought 6 boxes of markers. Each box has 12 markers. The teacher gave out 45 markers. The boxes are blue. How many markers are left?
- Restate: We had some markers, gave some away; how many remain?
- Unknown: markers left.
- Given: 6 boxes, 12 per box, 45 given out.
- Extra: the boxes are blue.
- Plan: multiply to find the total, then subtract.
- Solve: 6 × 12 = 72; 72 − 45 = 27 markers.
- Check: 27 + 45 = 72 ✓. It makes sense that fewer than 72 remain.
Worked examples
Example 1: Mia has 3 times as many stickers as Leo. Leo has 14. How many does Mia have?
"Times as many" → multiply: 3 × 14 = 42.
Example 2: 84 chairs are set in 7 equal rows. How many chairs in each row?
Equal rows → divide: 84 ÷ 7 = 12.
Example 3: A train travels 245 km in the morning and 180 km in the afternoon. How much farther did it go in the morning?
"How much farther" → difference: 245 − 180 = 65 km.
Common mistakes
- Grabbing all the numbers and adding them without thinking.
- Answering a different question (giving the total when asked how many are left).
- Trusting key words blindly.
- Forgetting units in the answer.
Try it yourself
- A baker makes 9 trays of 8 muffins and sells 50. How many are left?
- Ana is 4 years older than Ben. Ana is 13. How old is Ben?
- 3 friends share $45 equally. How much does each get?
- Find the extra information: "Tom, who is 10, buys 4 pens at $2 each. What does he spend?"
Answers: 1) 22 2) 9 3) $15 4) Tom’s age; he spends $8.
Quick recap
- Read twice, restate, find the unknown and given information.
- Use key words as hints, but think about the story.
- Ignore extra information and check that your answer makes sense.