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Learn to turn everyday word problems into equations you can solve with confidence.
People have been solving word problems for thousands of years. Ancient merchants needed to figure out prices, farmers needed to split land, and builders needed exact measurements. The trick was always the same: turn a real-life situation into math you can work with.
For most of history, people described problems in long sentences. It was not until mathematicians invented variables (letters that stand for unknown numbers) that writing equations became fast and powerful. Today, writing an equation is like creating a shortcut for a word problem.
On the ISEE, you will not need to solve the equation every time. Sometimes the question just asks you to pick the equation that correctly matches the story. That means the most important skill is translating words into math. Let's learn how!
An equation is a math sentence that uses an equal sign (=) to show that two things have the same value. When a problem describes a situation with an unknown number, you can write an equation to represent it. Here are the key ideas you need.
The diagram below shows how a word problem breaks apart into pieces. Each piece becomes part of an equation. Follow the arrows to see how the English words turn into math symbols.
The purple box identifies the unknown (what we want to find). The cyan box shows the operations (multiply and subtract). The pink box gives us the result (what everything equals). Once you find these three pieces, putting the equation together is straightforward.
Certain words almost always mean the same math operation. Learning these keyword translations will help you move quickly on the ISEE. Below are the most common ones you will see.
Most ISEE word problems follow a handful of patterns. If you recognize the pattern, you can write the equation quickly. The diagram below shows the five patterns you are most likely to see.
The most common ISEE pattern is number 3: the two-step equation. It combines multiplication with addition or subtraction. When you see a rate (like dollars per item) and a flat fee or starting amount, you are dealing with a two-step equation.
Let's walk through a full ISEE-style problem step by step.
The ISEE is designed so that wrong answer choices match common mistakes. If you know what mistakes to watch for, you can avoid traps and eliminate wrong answers faster.
| Common Mistake | What It Looks Like | How to Fix It |
|---|---|---|
| Reversing subtraction | Writing 7 − n instead of n − 7 for "7 less than n" | "Less than" means you subtract FROM the variable. Think: "7 less than 20" is 20 − 7 = 13. |
| Wrong operation | Using addition when the problem says "times" or "each" | Circle the keyword in the problem. Match it to your operation chart before writing the equation. |
| Putting the result on the wrong side | Writing 55 = 5c − 20 instead of 5c + 20 = 55 | Both sides of an equation are equal, so 55 = 5c + 20 is actually the same as 5c + 20 = 55. Check the operation, not just the order. |
| Forgetting a step in a two-step problem | Writing 5c = 55 and leaving out the $20 fee | After writing your equation, check: does it include ALL the numbers from the problem? If a number is missing, you probably skipped a step. |
Right now, you are learning to write equations using an equal sign. As you move into higher math, you will also see inequalities (using symbols like < and > instead of =). The skills you build now — identifying unknowns, spotting operations, and translating carefully — are the exact same skills you will use later.
| What You Learn Now | What Comes Next |
|---|---|
| One-step equations (x + 5 = 12) | Multi-step equations (3x + 5 − 2 = 18) |
| Two-step equations (2n + 7 = 21) | Equations with variables on both sides (2n + 7 = n + 14) |
| Modeling with = (equals) | Modeling with <, >, ≤, ≥ (inequalities) |
| Translating words into one equation | Systems of equations (two equations at once) |
The great news is that the ISEE Middle Level focuses on the skills in the left column. If you master these, you are not only ready for the test — you are also building a strong foundation for algebra in high school.
Try these five problems on your own. They go from easier to harder. Remember: there is no penalty for guessing on the ISEE, so always pick an answer! Use process of elimination if you are not sure.
To choose an equation that models a situation, follow four steps. First, identify the unknown and assign it a variable. Second, spot the operations by looking for keywords like "more than" (add), "less than" (subtract), "each" or "per" (multiply), and "split among" (divide). Third, find the result — the number that everything equals, usually signaled by words like "is," "total," or "left." Fourth, build and verify your equation by re-reading the problem to confirm every part matches.
Watch out for common ISEE traps: reversed subtraction ("7 less than n" is n − 7, not 7 − n), swapped numbers in the rate and the constant, and missing steps in two-step problems. Use process of elimination to cross out answers with wrong operations, and always guess if you are unsure — there is no penalty on the ISEE!