How To Solve Math Word Problems: Steps And Examples
The short version
- To solve word problems, read the whole problem, find the exact question, sketch what’s happening, choose the operation based on the action in the story, solve, and check that the answer makes sense.
- Keyword lists (“left” means subtract, “in all” means add) fail on a lot of problems. Understanding the story works on all of them.
- A quick drawing, like a bar model, turns most word problems into simple arithmetic.
- When a kid is good at computing but bad at word problems, the gap is usually in reading the situation rather than in the math facts.
The best way to solve word problems is to slow down and understand the situation before touching the numbers. Read the problem all the way through, find what it’s really asking, draw a quick picture, then decide which operation matches what’s happening. Finish by checking that the answer is reasonable and answers the question that was asked.
Below is a step by step method that works from 2nd grade through algebra, worked examples at each level, why keyword tricks backfire, and practice word problems with answers.
How to solve word problems in 6 steps
- Read it twice. The first time, just get the story. The second time, notice the numbers and what they describe.
- Find the question. Underline the actual question, usually the last sentence. Say it back in your own words: “They want to know how many stickers she started with.”
- Draw it. A bar model, a number line, a few boxes, anything. If you can’t draw it, you don’t understand it yet, so reread.
- Choose the operation from the action. Are things being joined, separated, compared, grouped equally, or shared? That tells you what to do.
- Write it and solve it. Write the number sentence or equation, then compute.
- Check it. Plug the answer back into the story. Does it make sense? Does it answer the question, with the right units?
Why keyword tricks backfire
Many kids are taught to hunt for clue words: “altogether” means add, “left” means subtract, “each” means divide. It works on easy problems and falls apart fast. Look at this one:
Example 1: Maya gave away 8 stickers. Now she has 15 stickers left. How many stickers did she have to start?
The words “gave away” and “left” both scream subtraction. A kid who follows the keywords writes 15 – 8 = 7. But think about the story. She had some, lost 8, and ended with 15, so she must have started with more than 15.
15 + 8 = 23 stickers
Check: 23 – 8 = 15. ✓
Example 2: A red rope is 42 inches long. It’s 17 inches longer than a blue rope. How long is the blue rope?
“Longer” tempts kids to add. But the red rope is the longer one, so the blue rope is shorter.
42 – 17 = 25 inches
Check: 25 + 17 = 42. ✓
Keywords can be a hint. They can’t replace understanding what’s going on.
Types of word problems
Most elementary word problems fall into a handful of situations. Once a kid can name the situation, choosing the operation is easy.
| Situation | What’s happening | Example | Operation |
|---|---|---|---|
| Join | Things get added to a group | Sam has 12 cards and gets 9 more | 12 + 9 |
| Separate | Things are taken away | Sam has 21 cards and gives away 9 | 21 – 9 |
| Compare | Two amounts, find the difference | Sam has 21 cards, Ava has 13. How many more does Sam have? | 21 – 13 |
| Equal groups | Several groups the same size | 5 packs with 8 cards each | 5 × 8 |
| Sharing | A total split evenly | 40 cards shared among 5 kids | 40 ÷ 5 |
The catch is that the unknown can be in any spot. In Example 1, the start was missing, which is why subtraction words led to an addition problem.
Worked word problems by grade level
Multi-step problem (grade 4)
Example 3: A school buys 6 boxes of pencils with 24 pencils in each box. The pencils are shared equally among 8 classrooms. How many pencils does each classroom get?
Step 1, total pencils: 6 × 24 = 144
Step 2, share them: 144 ÷ 8 = 18
Each classroom gets 18 pencils.
Check: 18 × 8 = 144. ✓
Remainder problem (grade 4 and 5)
Example 4: 74 students are going on a field trip. Each bus holds 30 students. How many buses are needed?
74 ÷ 30 = 2 remainder 14
Two buses leave 14 students behind, so the school needs 3 buses.
The math is 2 R14. The answer to the question is 3. Deciding what a remainder means is part of the problem.
Fraction problem (grade 5)
Example 5: A recipe uses ¾ cup of flour per batch. How much flour for 2½ batches?
¾ × 2½ = ¾ × 5/2 = 15/8
15/8 = 1⅞ cups
Check: 2 batches is 1½ cups, and another half batch is ⅜ cup, so 1½ + ⅜ = 1⅞. ✓
Percent problem (grade 7)
Example 6: A jacket costs $60. It’s on sale for 25% off, and then 8% sales tax is added. What’s the final price?
Discount: 25% of 60 = 15, so the sale price is 60 – 15 = $45
Tax: 8% of 45 = 3.60
Final price: 45 + 3.60 = $48.60
Algebra problem (grade 7 and up)
Example 7: Two numbers add up to 50. One number is 8 more than the other. What are the numbers?
Let the smaller number be x. The larger is x + 8.
x + (x + 8) = 50
2x + 8 = 50
2x = 42
x = 21, so the numbers are 21 and 29.
Check: 21 + 29 = 50, and 29 – 21 = 8. ✓
Common mistakes with word problems
- Grabbing keywords instead of reading the situation, as in Examples 1 and 2.
- Using every number. Some problems include extra information. If a number doesn’t fit the story, it may not belong in the math.
- Answering the wrong question. A problem asks for change from $20, and the kid stops at the total cost.
- Ignoring remainders or reporting “2 R14 buses.”
- Skipping the check. An answer of 7 stickers when she ended with 15 would get caught in five seconds.
- Dropping units. “25” isn’t a full answer when the question asks about inches.
Practice problems
- A class has 28 students. 13 are boys. How many are girls?
- Leo read 36 pages on Monday and some more on Tuesday. He read 61 pages in all. How many pages did he read on Tuesday?
- Movie tickets cost $7 each. Dana buys 9 tickets and pays with $70. How much change does she get?
- A bakery packs 150 cupcakes into boxes that hold 12 each. How many boxes does it need to pack all of them?
- Jen is 4 times as old as her brother. Their ages add up to 35. How old is each?
- A shirt costs $32 after a 20% discount. What was the original price?
- A train travels 180 miles in 3 hours. At the same speed, how long will it take to go 300 miles?
- A rectangle’s length is 3 more than twice its width. Its perimeter is 48 cm. Find the length and width.
Answers
- 28 – 13 = 15 girls.
- 61 – 36 = 25 pages.
- 9 × 7 = $63, and 70 – 63 = $7 in change.
- 150 ÷ 12 = 12.5, so 12 boxes aren’t enough. It needs 13 boxes.
- Brother = x, Jen = 4x. 5x = 35, so x = 7. The brother is 7 and Jen is 28.
- After 20% off, the shirt costs 80% of the original. 32 ÷ 0.8 = $40. Check: 20% of 40 is 8, and 40 – 8 = 32.
- 180 ÷ 3 = 60 miles per hour, and 300 ÷ 60 = 5 hours.
- Width = w, length = 2w + 3. 2(w + 2w + 3) = 48, so 3w + 3 = 24, 3w = 21, w = 7. The width is 7 cm and the length is 17 cm. Check: 2 × (7 + 17) = 48.
If your child is stuck on word problems
A child who can do 144 ÷ 8 on a worksheet but freezes on the pencil problem above is missing something specific, and it’s usually one of three things. Some kids don’t really know what the operations mean, so they can compute division but can’t recognize a sharing situation. Some are still slow on facts, and all their attention goes to the arithmetic with none left for the story. And some have a reading gap, where the words themselves are the barrier.
Word problems also tend to trigger stress, since there’s no obvious first step. If homework time ends in tears, our guide to math anxiety in children explains what helps. If trouble with word problems comes with other warning signs, check Is My Child Behind In Math? And to figure out which of those three gaps it is, a math assessment beats guessing.
Frequently asked questions
What are the steps to solve word problems?
Read the problem twice, find the question, draw a picture, choose the operation from what’s happening in the story, solve, and check that the answer makes sense and has the right units.
Why is my child good at math but bad at word problems?
Computing and understanding are separate skills. A worksheet tells kids which operation to use. A word problem makes them decide, which takes knowing what each operation means. Reading level and working memory play a part too.
Should kids use keywords to solve word problems?
Only as a hint. Keywords point the wrong way on many problems, especially when the starting amount is the unknown or the comparison is flipped. Picturing the situation is more reliable.
What is a bar model in math?
A bar model (also called a tape diagram) uses rectangles to show amounts. For “Jen is 4 times as old as her brother,” you’d draw 1 bar for the brother and 4 equal bars for Jen. Five equal bars make 35, so each bar is 7.
How can I help my child solve these word problems at home?
Ask questions instead of giving steps: “What’s happening in the story?” “What are they asking?” “Can you draw it?” “Does your answer make sense?” Short practice most days works better than long sessions, as we explain in why 20 minutes a day works.
Find the actual gap
If word problems are a weekly battle, it’s worth finding out whether the problem is facts, operation sense, or reading the setup. Math Anon starts with a short adaptive assessment that identifies the exact skills that are missing and gives you a written report.
Your child then gets about 20 minutes a day of practice built around those skills, and you get a progress report every week. The $49 assessment is credited back in full on the first month. Start the assessment or read about pricing.
