Word problems require more than finding numbers and choosing an operation. You need a model linking quantities under stated conditions. Translating the story into relationships helps prevent keywords from substituting for reasoning and keeps the eventual calculation connected to the question.
Read without calculating
Describe the situation in plain language and identify the requested unknown. Name quantities with units and distinguish given facts from assumptions. If a problem involves a fixed fee plus an hourly charge, preserve both components. Do not assume that more always means addition or that per always supplies a complete formula. Words acquire meaning through the relationships in the particular situation, not through an isolated keyword rule.
Build and test the model
Use an equation, table, or diagram to represent the relationship. Explain each term in words. For total cost, a fixed fee and a rate multiplied by time play different roles. Try an easy value, such as zero hours if meaningful, to see whether the model behaves sensibly. Check domain restrictions: fractional people or negative travel time may be invalid even when an equation permits them.
Return to the story
After solving, answer the original question with units and relevant rounding. Substitute the result into the relationship and inspect whether it fits the context. Beginners can annotate every term. Experienced learners can compare alternative models and explain which assumptions produce different answers. A mathematically correct manipulation of an inappropriate equation still solves the wrong problem, so validation must include the story as well as the arithmetic.
Put it into practice
Put it into practice
- Choose a word problem and hide the answer choices.
- Define quantities and write a relationship before computing.
- Explain every term, test a simple value, and verify the final result against both the equation and the original situation.
Sources & further reading
- Carnegie Mellon Eberly Center: Classroom Assessment Techniques ↗
- Carnegie Mellon Eberly Center: Choosing an Appropriate Approach ↗
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