How to solve math word problems: a 5-step method
TutorAura guide · Updated
Word problems are hard because they add a step before the maths: working out what calculation the situation needs. The good news is that a consistent method makes that step much easier. The one below is based on George Pólya's classic problem-solving stages (understand, plan, carry out, look back), and the Education Endowment Foundation's guidance on maths recommends teaching pupils problem-solving strategies and using representations such as diagrams.
It works for a grade 2 sharing problem and for a grade 9 system of equations.
Key takeaways
- Read twice: once for the story, once for the question.
- List what you know and what you need to find.
- Draw a model: a bar, a table or a sketch.
- Check that your answer is reasonable and answers the question.
The 5 steps
- Understand. Read the whole problem, then read the question sentence again. Say in your own words what you're finding.
- List. Write the numbers and what they mean, with units. Cross out information you don't need.
- Model. Draw it: a bar model, a number line, a table or a diagram.
- Solve. Choose the operation or write an equation from the model, and calculate.
- Check. Is the answer sensible? Does it answer the actual question? Put it back into the story.
Example: a bar model (grade 4)
Ali has 3 times as many stickers as Ben. Together they have 48. How many does Ali have?
- Understand: we need Ali's stickers.
- List: Ali = 3 × Ben; total = 48.
- Model: Ben is 1 bar, Ali is 3 bars of the same size: 4 bars altogether = 48.
- Solve: 1 bar = . Ali = .
- Check: , and 36 is 3 times 12. Correct.
The model makes the structure visible, and it leads naturally to algebra later: .
Example: rates (grade 7)
A car travels 150 km in 2.5 hours. At the same speed, how long will 240 km take?
- Understand: time for 240 km.
- List: 150 km in 2.5 h.
- Model: a table with distance and time.
- Solve: speed km/h; time hours.
- Check: 240 km is a bit more than 1.5 times 150 km, and 4 hours is a bit more than 1.5 times 2.5 hours. Sensible.
Don't rely on key words
Key word lists ("more" means add, "left" means subtract) often mislead:
"Maya has 15 shells. That's 6 more than Leo. How many does Leo have?" contains "more", but you need to subtract: .
Drawing the situation (Maya's bar is longer than Leo's by 6) shows what to do more reliably than any key word.
Common mistakes and fixes
| Mistake | Fix |
|---|---|
| Answering a different question | Underline the question; check the answer against it |
| Using every number given | Ask whether each number matters |
| Mixing units | Write units at every step; convert first |
| Unrealistic answers (2.5 people) | Check: does the answer make sense in the story? |
| Getting stuck at the start | Draw something, even a rough sketch |
Practise the method, not just answers
Do a few word problems regularly rather than many at once, and mix types so you practise choosing the operation; see interleaved practice. For each one, say the five steps out loud. If you're stuck, an AI tutor can guide you through the setup without giving the answer away; see help with math word problems.
Frequently asked questions
What are the steps to solve a word problem?
Understand the question, list what you know, draw a model, choose the operation or write an equation and solve, then check the answer makes sense.
Why are word problems so hard?
Because you have to work out which calculation the situation needs before doing the maths. Drawing a model and listing what you know make that easier.
Do key words help with word problems?
They can mislead. Picturing or drawing the situation is more reliable.
What is a bar model?
A diagram using rectangles to represent quantities and their relationships. It helps show which operation to use and leads naturally into algebra.
Sources
- How to Solve It. Princeton University Press (George Pólya).
- Improving Mathematics in Key Stages 2 and 3 (guidance report). Education Endowment Foundation.
Keep reading
Help with math word problems: turn the words into math, step by step
Learn to turn word problems into math: what you know, what you need, which operation or equation, and a check.
How to study math: do problems, mix them up, and learn from mistakes
Practise problems instead of re-reading, mix topics, keep a mistakes log and space it out, with a sample study week.
An AI math tutor that teaches, not just answers
Step-by-step maths help from times tables to calculus: it asks questions, checks each step and reads your handwriting.
Interleaved practice: why mixing topics helps you learn
Mixing problem types in practice helps you learn to choose the right method. Here's how to use it.