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Turn everyday words into the language of algebra so you can solve real problems with confidence.
Have you ever tried to describe a math problem to a friend using only words? It gets complicated fast! For thousands of years, people struggled with this exact issue. Ancient civilizations solved tricky problems, but they wrote everything out in long sentences. Eventually, mathematicians invented a shorthand — algebra — that lets us write math ideas quickly and clearly.
On the ISEE, you'll see questions that describe a situation in words and ask you to pick the matching algebraic expression. The key skill is learning to translate English into math. Let's learn how!
Translating a situation into algebra is like translating between two languages. English has its own words for math operations, and once you learn the "dictionary," you can convert any sentence into a neat expression. Here are the four big ideas you need.
The diagram below is your cheat sheet. It shows common English words and the math operations they represent. Study it closely — you'll see these words again and again on the ISEE.
An algebraic expression (a math phrase that uses numbers, variables, and operations) doesn't have an equals sign — that would make it an equation. Let's look at some common patterns.
Notice that we always pick a variable for the unknown first. Then we build the expression around it, one operation at a time. On the ISEE, always check: does the order match the words?
Some phrases on the ISEE are designed to trip you up. The diagram below shows the most common traps and how to avoid them. Pay special attention to the order-reversal phrases — they are the #1 source of mistakes.
| English Phrase | Common Mistake | Correct Expression |
|---|---|---|
| "10 less than a number" | 10 − n | n − 10 |
| "twice the sum of n and 4" | 2n + 4 | 2(n + 4) |
| "a number divided into 20" | n ÷ 20 | 20 ÷ n |
Let's walk through a full ISEE-style problem together. We'll go step by step so you can see exactly how to think through it.
Students sometimes confuse expressions and equations. The ISEE may test both, so it helps to know the difference. Here's a quick comparison.
| Feature | Expression | Equation |
|---|---|---|
| Has an = sign? | No | Yes |
| Example | 3n + 7 | 3n + 7 = 22 |
| Can you solve for n? | Not by itself — you can evaluate it for a given n | Yes — you can find the exact value of n |
| Think of it like… | A recipe (a set of instructions) | A balanced scale (both sides match) |
Learning to translate situations into expressions is your first big step. Once you're comfortable with expressions, you'll be ready for more advanced topics. Here's where this skill leads.
| This Lesson | Next Level |
|---|---|
| Write expressions: 2n + 5 | Solve equations: 2n + 5 = 17 |
| Use one variable: n | Use two variables: n and m |
| Translate a single situation | Write inequalities: 3n + 2 > 14 |
| Simple operations (+, −, ×, ÷) | Exponents and roots: n² + 3 |
Every one of those advanced skills starts with the same first move: read the words, pick a variable, and build the expression. Master that now, and the rest will come much more easily later.
Try these five problems. They start easy and get harder. Remember: there's no penalty for guessing on the ISEE, so always pick an answer! Use process of elimination to cross out choices that don't make sense.
To translate a situation into an algebraic expression, start by choosing a variable for the unknown quantity. Next, identify the operation words — words like "more than" (addition), "less than" (subtraction), "times" (multiplication), and "divided by" (division). Pay special attention to order-reversal phrases like "less than" and "subtracted from," which flip the position of the variable and the number.
Use parentheses when a phrase like "twice the sum" means you must group operations together. Always plug in a test number to check your expression — this quick strategy catches most errors. Remember: an expression has no equals sign, and on the ISEE, there is no penalty for guessing, so always answer every question!