Why Do We Solve Word Problems?
People have been solving math problems in real life for thousands of years! Long before calculators existed, word problems helped people figure out everyday things. Think about it — when you buy snacks at a store, you are solving a word problem!
Math has always been about solving real-life puzzles. Let's look at how word problems have been important throughout history.
Here is the big question: When a problem needs more than one step to solve, how do you figure out what to do first? That is exactly what this lesson will teach you!
The Four Building Blocks
Every multi-step word problem uses a mix of the four operations (that means addition, subtraction, multiplication, and division). Think of them as your four superpowers. Each one does a different job.
Addition (+)
Subtraction (−)
Multiplication (×)
Division (÷)
On the ISEE, you will see word problems that need two or even three steps. The trick is to read carefully, find the clue words, and figure out which operations to use in which order. You've got this!
The Step-by-Step Strategy
Here is a simple plan you can follow every time you see a multi-step word problem. We call it the R.U.N.S. strategy. The diagram below shows you how it works!
Look at the example in the diagram. Sara's problem needed two steps. First, you found the total with multiplication. Then you subtracted. If you tried to do it all at once, you might get confused. Breaking it into steps makes it easy!
How the Operations Work Together
Multi-step problems often combine two or three operations. Here are the most common patterns you will see on the ISEE. Knowing these patterns helps you work faster!
Clue Words That Tell You Which Operation to Use
Word problems are like little mysteries. The clue words hidden inside the sentences tell you exactly which operation to use. Learning to spot these clues is one of the biggest keys to doing well on the ISEE!
Worked Example: Step by Step
Let's solve a real ISEE-style problem together. Follow along and notice how we use the R.U.N.S. strategy!
See how we used three steps? First multiplication, then two subtractions. Each step was simple on its own. That's the power of breaking it down!
Common Mistakes and How to Avoid Them
Even smart students make mistakes on multi-step problems. Here are the most common traps — and how to dodge them!
| Common Mistake | Why It Happens | How to Fix It |
|---|---|---|
| Stopping too early (only doing one step) | You solve the first part and think you are done | Re-read the question at the end. Does your answer match what was asked? |
| Using the wrong operation | You add when you should subtract, or multiply when you should divide | Circle clue words. Ask: Am I putting together or taking away? Equal groups or sharing? |
| Doing steps in the wrong order | You rush and mix up what comes first | Write each step on a new line. Number them 1, 2, 3. |
| Forgetting a number from the problem | You miss a number that was mentioned in the problem | Underline every number in the problem before you start solving. |
Building Toward Harder Math
The skills you are learning right now are the same skills you will use in harder math later! Let's see how multi-step word problems connect to what comes next.
| What You Learn Now | What It Becomes Later |
|---|---|
| Finding a total, then subtracting | Solving equations with two operations (algebra!) |
| Picking the right operation from clue words | Translating word problems into algebraic expressions |
| Breaking big problems into small steps | Solving multi-step equations and proofs |
| Checking if your answer makes sense | Verifying solutions and estimating reasonableness |
Every time you solve a multi-step word problem, you are training your brain to think like a mathematician. The ISEE tests this because schools want to see that you can think through problems logically — not just memorize facts. Keep practicing and you will be ready for anything!
Practice Problems
Time to put your skills to the test! These problems go from easier to harder, just like the real ISEE. Remember to use the R.U.N.S. strategy. Read carefully, underline clue words, set up your number sentences, and solve step by step. You've got this!
Putting It All Together
You now know how to solve multi-step word problems using the four operations: addition, subtraction, multiplication, and division. Remember the R.U.N.S. strategy — Read, Underline, write a Number sentence, and Solve & check. Look for clue words like "each," "left," "total," and "shared equally" to pick the right operation for each step.
The biggest tip for the ISEE: break every problem into small, simple steps. Solve one step at a time and use the answer from each step in the next one. Always re-read the question to make sure you answered what was asked. And remember — on the ISEE there is no penalty for guessing, so never leave a question blank. Eliminate wrong answers, take your best guess, and move on. You are ready!