SECTION 1
Why Do We Solve Word Problems?
People have been solving word problems for thousands of years. Long before calculators existed, merchants, farmers, and builders needed to figure out real-life math. They had to combine different operations — adding, subtracting, multiplying, and dividing — all in one problem.
The four basic operations (addition, subtraction, multiplication, and division) are the building blocks of all math. When you combine them in a single problem, you get a multi-step word problem. These problems are a big part of the ISEE because they test whether you can think through a situation step by step.
1650 BCE • Rhind Papyrus
800 CE • Al-Khwarizmi's Algebra
1500s • Merchant Arithmetic
Today • Standardized Tests
The big question is: how do you take a paragraph of words and turn it into math you can solve? That's exactly what this lesson will teach you.
SECTION 2
Core Principles for Multi-Step Problems
Before you start calculating, you need a game plan. Every multi-step word problem follows a pattern. Once you learn to spot that pattern, these problems become much easier. Here are the key ideas to keep in mind.
Read the Whole Problem First
Identify What's Being Asked
Pick the Right Operations
Work in Order
Check Your Answer
KEY TAKEAWAY
SECTION 3
Visualizing the Problem-Solving Process
Let's look at a flowchart that shows the exact steps you should follow every time you see a multi-step word problem on the ISEE. This diagram is your roadmap.
Notice that you don't start doing math until step 4. Most mistakes happen because students jump into calculating before they fully understand the problem. On the ISEE, you have about one minute per question, so spending a few seconds reading carefully actually saves you time in the long run.
SECTION 4
The Math Behind Multi-Step Problems
Multi-step problems combine two or more operations. Let's review what each operation does and the key words that signal which one to use.
ADDITION
Use addition when you are combining amounts. Key words: total, sum, combined, altogether, in all, increased by.
SUBTRACTION
Use subtraction when you are finding what's left or comparing. Key words: remaining, left over, fewer, less than, difference, how many more.
MULTIPLICATION
Use multiplication when you have equal groups. Key words: each, every, per, times, twice, triple, of.
DIVISION
Use division when you are splitting into equal parts or finding a rate. Key words: per, each, shared equally, divided among, average.
ISEE Test Tip
SECTION 5
Key Word Guide & Visual Reference
One of the trickiest parts of word problems is figuring out which operation to use. The table below shows common signal words (words in the problem that hint at a specific operation). Be careful, though — context matters. Always think about what the problem is really asking.
Watch Out!
SECTION 6
Worked Example: Step by Step
Let's walk through a real ISEE-style problem together. Follow each step carefully and see how the flowchart from Section 3 comes to life.
Sample Problem
Solving Maria's Babysitting Problem
- 1
Step 1 — Read and Find the Question
The question asks: "How much money does Maria have left?" The word "left" tells us the final step will be subtraction. - 2
Step 2 — List the Key Numbers
We know: $12 per hour, 5 hours on Saturday, 3 hours on Sunday, and $18 spent on a book. - 3
Step 3 — Find Total Hours Worked
Maria worked two days, so we add the hours: 5 + 3 = 8 total hours.Total hours = 8 - 4
Step 4 — Calculate Total Earnings
She earns $12 "per" hour. That's our signal for multiplication: $12 × 8 = $96.Total earnings = $96 - 5
Step 5 — Subtract the Book Purchase
She spent $18, so we subtract: $96 − $18 = $78.Money left = $78 - 6
Step 6 — Check
Does $78 make sense? Maria earned close to $100 and spent $18, so having $78 left is reasonable. ✓
This problem used three operations: addition (combining hours), multiplication (finding total pay), and subtraction (removing the book cost). That's what makes it a multi-step problem!
SECTION 7
Strategies & Common Mistakes
Even strong math students make mistakes on multi-step problems. The good news is that most mistakes follow patterns. If you know what to watch for, you can avoid them.
| Strategy | What It Helps With | Common Mistake It Prevents |
|---|---|---|
| Underline the question | Keeps you focused on what's actually being asked | Solving for the wrong thing (e.g., finding total cost when they asked for change) |
| Write intermediate results | Tracks your work across multiple steps | Losing track of a number and having to start over |
| Estimate first | Gives you a ballpark answer to check against | Choosing an answer that's way too big or too small |
| Check units | Makes sure your answer is in the right form (dollars, hours, items, etc.) | Giving the answer in the wrong unit (e.g., hours instead of minutes) |
| Use answer choices | Helps you eliminate wrong options or work backward | Spending too long on a problem when you could narrow it down quickly |
Five key strategies to boost your accuracy on multi-step word problems
KEY TAKEAWAY
SECTION 8
Connecting to Harder Problem Types
The multi-step skills you're learning now are the foundation for more advanced math. As problems get harder, the steps get longer, but the approach stays the same. Here's how today's skills connect to what's coming next.
| What You're Learning Now | Where It Leads |
|---|---|
| Adding and subtracting to find totals and differences | Solving equations with variables (algebra) |
| Multiplying a rate by a quantity (e.g., $12 × 8 hours) | Using formulas like d = r × t (distance = rate × time) |
| Dividing to find a per-person or per-unit amount | Working with ratios, proportions, and unit rates |
| Combining multiple operations in the right order | Order of operations (PEMDAS) and multi-step equations |
How multi-step word problem skills build toward advanced math
On the ISEE, you'll also see Quantitative Comparison questions. These give you two quantities (Column A and Column B) and ask you to figure out which is bigger. You'll still need to do multi-step math — the only difference is that you're comparing two results instead of finding one answer. We'll practice both types in the next section.
ISEE Quantitative Comparison Reminder
SECTION 9
Practice Problems
Now it's your turn! Try these five problems. They start easier and get harder as you go. Remember to follow the flowchart: read carefully, find the question, list the numbers, pick your operations, and check your answer.
Question 1: CONCEPTUAL
Show answer
Question 2: BASIC CALCULATION
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Question 3: INTERMEDIATE
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Question 4: APPLIED
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Question 5: CRITICAL THINKING
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SUMMARY
Lesson Summary
Summary
Multi-step word problems ask you to combine addition, subtraction, multiplication, and division in a single problem. The key to success is following a clear process: read carefully, find the question, list the numbers, choose your operations, solve one step at a time, and check your answer.
Look for signal words like "total," "remaining," "each," and "shared equally" to identify which operation to use. On the ISEE, use process of elimination to rule out answer choices that don't make sense. For Quantitative Comparison questions, calculate both columns separately and then compare. Remember: there's no penalty for guessing, so always answer every question!