Word problems aren’t just “hard math”, they're short stories with numbers. Once students learn to read for relationships (not “key words”), problems turn into simple, repeatable steps.
1) Read & paraphrase → 2) List knowns/unknowns/units → 3) Visualize (bar/tape/table/line) → 4) Choose operations by relationships → 5) Plan steps → 6) Compute & estimate → 7) Check & explain.
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Why Word Problems Feel Hard (and what fixes it)
The real blocker is language + logic, not arithmetic. Students need to slow down and paraphrase the question to lock in the goal. Avoid “number grabbing” and rigid “key word = operation” tricks. Instead, look for relationships: part–whole, compare, and scale.
Mini routine: Do a Three-Read: (1) read for gist; (2) read for quantities/units; (3) read for the question.
Visual to include: a small callout box titled “Don’t Chase Key WordsChase Relationships.”
The 7-Step Method (works for any problem)
Step 1. Read & Paraphrase the Question
Circle the question. Say it in your own words.
Sentence frame: “I am finding ___ because the question asks ___.”
Step 2. List Knowns, Unknowns, and Units
Make a quick list: what’s given, what’s missing, and the units.
Step 3. Visualize the Situation
Pick a model that fits the relationship:
Bar/Tape diagram: fractions, ratios, percent, part–whole.
Table: rates, patterns, function rules.
Number line: differences, intervals, integers.
Quick sketch: geometry, mixture, work problems.
Step 4. Choose Operations by Relationships (not key words)
Part–whole → add/subtract
Compare → difference
Scale/repeat groups → multiply/divide
Step 5. Plan the Steps
Turn the model into equations. Note if it’s one-step or multi-step.
Step 6. Compute Carefully (with an Estimate First)
Do a quick front-end estimate first; then compute precisely.
Step 7. Check & Explain
Ask: “Does this make sense?” Finish with a sentence answer + units.
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Strategy Showdown CUBES, RUCSAC, Polya, Bar Models
CUBES (Circle, Underline, Box, Evaluate, Solve): focuses attention but can encourage number-grabbing if used rigidly.
RUCSAC (Read, Understand, Choose, Solve, Answer, Check): good for sequencing.
Polya’s Four Steps (Understand, Plan, Carry out, Look back): excellent big-picture structure.
Bar/Tape models: fast clarity on ratios, fractions, percent.
Use what fits the task, and pair any acronym with a visual model for sense-making.
Worked Examples by Grade & Topic (high-intent clusters)
Elementary (2nd-5th)
Example | Topic | Problem | Steps / Plan | Answer |
A | Two-Step Addition/Subtraction (4th) | Liam read 38 pages on Monday and 47 on Tuesday. He wants to read 100 pages this week. How many pages are left? | 1) Paraphrase: “How many pages to reach 100?”2) Knowns/Unknowns: 38, 47; target 100; unknown = pages left.3) Model: Part–whole bar (100 split into “already read” and “left”).4–5) Plan: Already read = 38 + 47 = 85; Left = 100 − 85.6) Compute: 100 − 85 = 15.7) Check & Explain: “He has 15 pages left to reach 100 pages.” | 15 pages |
B | Fractions (5th) | A jug is 3/4 full. After pouring out 1/8 of the jug, what fraction remains? | Model: Bar split into 8 equal parts; 6 parts shaded after removal.Plan & Compute: 3/4 = 6/8; 6/8 − 1/8 = 5/8. | 5/8 of the jug |
C | Multiplication/Division (equal groups) | There are 6 bags with 8 marbles each. If 10 marbles are given away, how many remain? | Compute: 6 × 8 = 48; 48 − 10 = 38. | 38 marbles |
Middle School (6th-8th)
Example | Topic | Problem | Steps / Plan | Answer |
D | Ratio & Unit Rate | A smoothie uses fruit to yogurt in a ratio of 3:2. If you have 5 cups of yogurt, how much fruit keeps the same ratio? | Model: 3 parts fruit : 2 parts yogurt.Scale factor: 5 ÷ 2 = 2.5.Fruit = 3 × 2.5 = 7.5. | 7.5 cups of fruit |
E | Percent Increase (7th) | A jacket costs $40 and is increased by 25%. What is the new price? | Increase: 0.25 × 40 = 10.New price: 40 + 10 = 50. | $50 |
F | Integers (gain/loss) | A submersible is at −120 m. It ascends 85 m, then descends 20 m. What is its final depth? | −120 + 85 = −35.−35 − 20 = −55. | −55 m |
Algebra & Test Prep (SAT/ACT)
Example | Topic | Problem | Steps / Plan | Answer |
G | Linear Rate | A car rental costs $25 plus $0.40 per mile. How much for 120 miles? | Equation: C = 25 + 0.40m.Compute: C = 25 + 0.40(120) = 25 + 48 = 73. | $73 |
H | Systems from Context | At a school play, 200 tickets sold for $1,270. Adult tickets cost $8 and student tickets cost $5. How many of each? | System: { a + s = 200; 8a + 5s = 1270 }.From first: s = 200 − a.Substitute: 8a + 5(200 − a) = 1270 → 3a = 270 → a = 90.Then s = 110. | 90 adults, 110 students |
I | Work/Mixture (structure) | A 20-L solution is 15% acid. How many liters of pure acid must you add to make it 20%? | Let x = liters of pure acid added.Acid amount: 0.15·20 + x = 3 + x.New volume: 20 + x.Equation: (3 + x)/(20 + x) = 0.20 → 3 + x = 4 + 0.2x → 0.8x = 1 → x = 1.25. | 1.25 L |
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Classroom & At-Home Routines That Boost Success
Three-Read Protocol → sense-making first.
Partner Talk → “What model would you choose and why?”
Error Analysis → show a common wrong path; ask students to diagnose it.
Word-Problem Journals with frames: “First I… Then I… Finally I…”
Avoid These Common Myths
“Key words = operation.” Works sometimes, fails often. Use structure.
“Speed = mastery.” Value reasoning and explanation over speed.
Free Practice & Printables
Use the 2-page Strategy Pack below for daily warmups, exit tickets, and homework.
Build topic banks: addition/subtraction, multiplication/division, fractions/decimals, ratio/percent, algebra/linear, systems.
AI/step-by-step solvers are great for checking a plan and seeing another approach. Have students explain the steps in their own words to avoid shortcutting learning.
FAQs (PAA-style)
What is the easiest way to solve word problems?
Use a 7-step routine: read & paraphrase, list knowns/unknowns/units, visualize, choose operations by relationships, plan steps, compute with an estimate, check & explain.
How do I teach multi-step word problems?
Model the relationships (bar/tape). Write a short plan (Step 1, Step 2…), then compute and explain.
Are key words a good strategy?
They’re not reliable. Focus on structure and models instead.
Which strategy is best: CUBES, RUCSAC, or Polya?
All can help. Pair any acronym with a bar model or table to make thinking visible.
How can I build reading comprehension for math?
Use Three-Read, paraphrasing, and sentence frames for explanations.
