Multi-Step Word Problems
Word problems are not arithmetic in disguise — they are detective work. A four-step strategy (understand, plan, solve, check) turns any multi-step story into a sequence of small, safe computations.
1 Understand
The core idea in plain language.
Step 1 — Understand: read the whole story once without touching a pencil. Then underline the question — the exact thing being asked. Circle the numbers that matter and cross out the decoys. If you cannot say what the answer will look like (“an amount of money left over”), you are not ready.
Step 2 — Plan: work backwards from the question. “To find the change, I need the total cost and the amount paid.” Each “I need” becomes one computation step. Write the steps as a numbered list before you compute anything.
Step 3 — Solve: compute one step at a time, labeling each intermediate result (“total cost = $13.50”). Never do two operations in your head at once — that is where most errors hide.
Step 4 — Check: re-read the question. Did you answer what was asked — not just step one? Then sanity-check against the story: change must be less than what you paid; a total must exceed each part.
2 See it
Diagrams that make the idea visual.
The four-step attack plan
Every multi-step problem bows to the same routine:
- Understand — underline the question, circle useful numbers.
- Plan — list the computations, in order.
- Solve — one step at a time, label results.
- Check — answer the actual question; sanity-check the size.
Bar model: see the story
Draw the quantities as bars. A total bar splits into part bars; a comparison puts two bars side by side so the difference jumps out.
If you can draw the bars and label them, the operations choose themselves: parts → add, missing part → subtract, equal groups → multiply or divide.
3 The key rule
After computing, re-read the question word for word. Then ask: is my answer a sensible size for this story? Change < amount paid. A total > each part. A per-item price < the total.
4 Worked examples
Follow each step. The pattern is always the same.
- Understand: Maya buys 3 notebooks at $4.50 each and pays with $20. Question: her change.
- Plan: (1) total cost = 3 × $4.50; (2) change = $20 − total.
- Solve: 3 × $4.50 = $13.50; $20.00 − $13.50 = $6.50.
- Check: answered “change” (not the total); $6.50 < $20. Sensible.
Check: Reverse: $13.50 + $6.50 = $20.00. Correct.
- Understand: Maya has 45 stickers, Leo has 28. Question: how many more does Maya have?
- Plan: one subtraction: 45 − 28.
- Solve: 45 − 28 = 17.
- Check: 17 < 45, and 28 + 17 = 45. Correct.
Check: Parts rejoin: 28 + 17 = 45. Correct.
- Understand: 2 pencils at $3.25, 1 eraser at $5.75, 3 pens at $1.50. Question: total.
- Plan: three multiplications, then add.
- Solve: $6.50 + $5.75 + $4.50 = $16.75.
Check: Estimate: $6 + $6 + $5 = $17 ≈ $16.75. Correct.
- Understand: Start with $20, buy 4 folders at $3.75. Question: money left.
- Plan: (1) spent = 4 × $3.75; (2) left = $20 − spent.
- Solve: 4 × $3.75 = $15.00; $20 − $15 = $5.00.
Check: $15 + $5 = $20. Correct.
5 Common mistakes
These errors show up on almost every quiz. Spot them now and they will never cost you points.
6 Key vocabulary
Say these words like you mean them.
- Multi-step problem
- A story needing two or more computations to reach the answer.
- Intermediate result
- The answer to one step, used by the next step. Label it.
- Decoy number
- A number in the story you do not need. Cross it out.
- Total
- The combined amount of the parts.
- Change
- Amount paid minus total cost — always less than the amount paid.
- Per item
- The price of one item: total ÷ number of items.
7 Quick check
Try each one on paper first, then reveal the answer.
Key points to remember
- Understand → Plan → Solve → Check — in that order, every time.
- Underline the question before you touch the numbers; the question word picks the operation.
- Plan backwards from the question: each “I need” is one computation step.
- Label every intermediate result (“total cost = $13.50”) — never chain two operations mentally.
- Re-read the question after computing: did you answer what was asked?
- Sanity-check the size: change < paid, total > each part, per-item < total.