How to Solve Math Word Problems: When You Don’t Know Where to Start

To solve math word problems, read the problem twice, name the unknown as a number, translate one sentence at a time into an equation, solve it line by line, then check the answer back in the story.

Step 5: Check and Label. Put the answer back into the story, write the unit, and ask whether the number makes sense.

Step 1: Read It Twice. First read for the story, second read to mark the numbers, the conditions and the question. Say the question back in your own words.

Step 2: Name the Unknown. Write “Let x = the number of ___” in full, with units. A letter is a number, not a label.

Step 3: Translate and Test. One sentence at a time. Ask what you must do to one quantity to make it equal the other, then test the equation with small numbers before solving.

Step 4: Solve the Math. One operation per line, using inverse operations, showing every line.
This guide walks you through all five steps and explains how to solve math word problems, with a worked example for each.

What Are the 5 Steps to Solving a Word Problem?

To solve a math word problem, read it twice and say the question in your own words. Name the unknown, with its units. Translate one sentence at a time into an equation, and test that equation with small numbers you pick. Solve it, showing every line.

Then put the answer back into the original story and label it.

Step	What you do	On the professors problem
1. Read twice	First read with no pen. Second read: mark every number and the question.	“How many students are there compared with professors?”
2. Name the unknown	Write “Let ___ = the number of ___”.	Let S = the number of students, P = the number of professors
3. Translate and test	One sentence at a time, then plug in small numbers.	S = 6P. Test: P = 1 gives S = 6.
4. Solve	One operation per line.	(This one is a setup question, so it ends at step 3.)
5. Check and label	Answer in the story’s words, with units. Does it make sense?	6 students for every professor

Your textbook may call them story problems or problem sums; the steps don’t change.

Step 1: Read It Twice, Then Say the Question Back

The first read is for the story. The second is for the data: every number (including hidden ones like “half” or “a dozen”) and every condition like “at least”. Then say the question in one sentence of your own. If you can’t, you’re not ready to write anything yet.

Step 2: Name the Unknown as a Number

Write “Let S = the number of students”, in full. The study above found a second source of the reversal: students knew there were more students than professors but treated S as a label for “students”, like a unit stuck to the 6. A letter in an equation is always a number. Saying “the number of” out loud keeps it that way.

Step 3: Translate One Sentence at a Time, Then Test It

Build the equation clause by clause. The researchers called the faulty version “word order matching”, copying English words into symbols in the order they appear. People who got problems like this right thought about it another way: what do I have to do to P to get a number equal to S? Multiply it by 6. Then run the small-numbers test before you solve anything.

Step 4: Solve It Line by Line

Use inverse operations, one per line. Skipping lines is the easiest way to drop a minus sign or a whole term.

Step 5: Check It in the Story and Label It

Put the answer back into the original words, not just into your equation, and write the unit. A negative number of apples or a car doing 5,000 mph means go back to step 3.

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Can You Trust Keywords Like “Total”, “Times” and “Less Than”?

Signal words point you to the sentence that matters, but they can’t tell you what to write there. Math educators writing for the National Council of Teachers of Mathematics put “use keywords to solve word problems” on a list of 13 rules that expire, because shortcuts that skip understanding break once problems get harder. The usual list is below, with the place each word goes wrong.

Word	Usually points to	Where it misleads
total, sum, altogether	addition	“The total is 40 and one part is 15” needs subtraction to find the other part
more than	addition	“Maya has 5 more stickers than Leo. Maya has 12.” Leo has 12 − 5 = 7, not 17
less than	subtraction	The order flips: “7 less than n” is n − 7
times	multiplication	“Six times as many students as professors” is S = 6P
of	multiplication	Right with fractions and percents: 2/5 of 30 is 2/5 × 30 = 12
per, each	division	“60 miles per hour for 3 hours” multiplies: 180 miles

So the word “times” tells you a multiplication is somewhere in the sentence. Where it goes comes from the sentence itself and the small-numbers test.

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What If You Can’t See an Equation at All?

Contest problems often don’t hand you a clean equation. When that happens, work through these five strategies in order.

1. Draw it. A line for a journey, boxes for parts of a whole, a table for two people’s ages. The US Institute of Education Sciences rates teaching visual representations as backed by strong evidence in its guide to problem solving in grades 4–8.
2. Guess and check, in order. Two numbers add to 15 and multiply to 56. Try 5 and 10: product 50, too small. Try 6 and 9: 54, closer. Try 7 and 8: 56. Each guess tells you which way to move.
3. Work backwards. “Ana spent half her money on a book, then $6 on lunch, and has $9 left. How much did she start with?” Undo each step from the end: 9 + 6 = 15, then 15 × 2 = 30. Check: half of 30 is 15, minus 6 is 9.
4. Try a smaller version. Swap the big numbers for 1, 2 or 10 and solve that first. The pattern usually carries over.
5. Use the answer choices. On multiple choice, put each option back into the story and see which one fits every condition.

The same guide rates helping students monitor their own problem solving as strong evidence too. In practice that’s one question halfway through: does what I’m doing still answer what was asked?

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How to Solve Math Word Problems: Five Worked Examples With Answers

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Your Teacher Uses a Different Acronym. Does It Matter?

Keep whatever your class uses. What matters is that it has a translate step and a check step. Here’s how the common ones line up with the five steps above.

The 5 steps	Pólya’s 4 steps	OpenStax 7 steps	CUBES	GUESA
1. Read twice	Understand the problem	Read, Identify	Circle key information, Underline the question	Given
2. Name the unknown	Understand the problem	Name	(no step)	Unknown
3. Translate and test	Devise a plan	Translate	Box clues, Eliminate extra information	Equation
4. Solve	Carry out the plan	Solve	Solve	Substitute or Solution
5. Check and label	Look back	Check, Answer	Only where S means “Solve and check”	Answer

Pólya’s four steps come from his 1945 book How to Solve It. The seven-step version is from OpenStax’s Elementary Algebra 2e, a free textbook you can read online or download as a PDF if you want a printable chapter. CUBES, GUESA and GAPESA are classroom acronyms, and the exact letters vary from teacher to teacher. If yours turns “translate” into “box the keywords”, add the small-numbers test after it.

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How Do You Get Better at Word Problems?

Sort your misses by the step where they broke. If they look like 6S = P, the step is translation, so practice translation on purpose.

• Keep a translation log. When you miss one, write down the sentence you mistranslated and the equation you should have written. Skip the arithmetic slips. Read it the night before a test; after ten entries you will usually see the same two or three sentence shapes.
• Write your own problem. Start from an equation like 24 − x = 10 and wrap it in a story: Sam has 24 apples, gives some away and has 10 left. How many did he give away? (14.)
• Mix the types. Once rate problems feel easy, stop doing ten in a row. A mixed set makes you decide which kind of problem you’re looking at, and on a test nobody tells you the type in advance.

Helping a younger brother or sister? The same steps work with pictures, and our word problems for kids with answers start at that level. If you’re past school-level problems, try contest-style word problems with full solutions, and if you want to go further, read about building problem-solving habits for olympiad contests.

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What You Can Do on the Next Word Problem

You came in not knowing where to start. Now you have an order: read it twice, name the unknown as a number, translate one sentence at a time, solve and check it in the story.

You also have the ten-second test that catches 6S = P before it costs you anything, and five moves for the problems that won’t turn into an equation. Run all of it on the next word problem you see, starting with the professors.

When you want more reps, Gonit has 10,000+ original olympiad-style questions for grades 1–12. They’re multiple choice and sorted by grade, topic and difficulty, so you can practice translating and then check yourself against the options. Hints before you answer and step-by-step explanations after a wrong answer are part of Premium.

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FAQ

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Related guides

• How to Solve Math Olympiad Problems: The Complete Guide
• Math Olympiad Questions: Types, Topics and Sample Problems by Grade
• AIME Problems: What They Look Like and How to Practice

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