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Learn to turn everyday words into math equations so you can solve tricky word problems with confidence!
People have been solving word problems for thousands of years! Long before we had the math symbols we use today, people wrote out their math puzzles using only words. Let's look at how math language grew over time.
So here's the big question: how do you figure out which math operation a word problem is asking you to do? That's exactly what this lesson will teach you. By the end, you'll be a word-problem detective!
Every word problem hides a math equation inside it. Your job is to find the clue words that tell you which operation to use. Think of it like a secret code! Certain words always point to addition, subtraction, multiplication, or division.
Here is your secret decoder chart! It shows the most common clue words and which math operation each one means. Study this chart — it will help you on the ISEE!
Notice that some words can be tricky. The word "per" can mean multiplication or division, depending on the problem. Always read the whole sentence before deciding!
Let's learn the step-by-step way to turn a sentence into an equation. An equation is a math sentence that uses numbers, symbols, and an equals sign. Here are some common patterns you'll see on the ISEE.
Let's see the whole process in a picture! This flowchart shows how to go from reading a word problem to writing a complete equation. Follow each arrow from start to finish.
Let's try an example with these steps. Imagine the problem says: "Sam has 8 toy cars. He gets 5 more for his birthday. How many toy cars does Sam have in all?"
Let's walk through a problem just like you'd see on the ISEE. Follow along with each step!
Some words on the ISEE can fool you if you're not careful. Let's look at a few tricky words and learn how to handle them.
| Tricky Word | What It Seems Like | What It Really Means |
|---|---|---|
| "less than" | Subtract the second number from the first | Flip the order! "5 less than 12" means 12 − 5, not 5 − 12 |
| "more than" | First number + second number | Also flip! "3 more than 10" means 10 + 3 |
| "twice" | Something happens two times | Multiply by 2! "Twice 7" means 2 × 7 = 14 |
| "how many more" | Maybe addition? | It's subtraction! Find the difference between two amounts |
Now that you can translate one-step word problems, let's peek at what comes next. Some ISEE problems need two steps to solve. You use the same skills — you just do them twice!
| One-Step Problem | Two-Step Problem |
|---|---|
| "Tom has 8 balls. He gets 4 more. How many in all?" | "Tom has 8 balls. He gets 4 more, then gives away 3. How many now?" |
| Equation: 8 + 4 = 12 | Equations: 8 + 4 = 12, then 12 − 3 = 9 |
| One clue word: "more" | Two clue words: "more" and "gives away" |
The great news is that two-step problems are just two one-step problems glued together. Solve the first step, use that answer in the second step, and you're done. You already have all the skills you need!
Time to practice! Remember: read the problem, find the clue words, pick the operation, and write the equation. You've got this!
You now know how to translate word relationships into equations! Start by reading the problem carefully and finding the clue words. Words like "in all" and "altogether" mean addition. Words like "left over" and "fewer" mean subtraction. Words like "each" and "groups of" mean multiplication. Words like "shared equally" and "split" mean division.
Watch out for tricky words like "less than" and "more than" — they flip the order of the numbers. Use the five-step process every time: Read, Find clue words, Pick the operation, Write the equation, and Solve. On the ISEE, always answer every question — there's no penalty for guessing. You've got this!