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Learn how to turn a word problem into a math equation you can solve!
People have been solving word problems for thousands of years! Long ago, farmers needed to figure out how much grain they had left after selling some. Shopkeepers had to calculate how much money a customer owed. They all needed a way to organize their thinking.
An equation is a math sentence that uses numbers and symbols. It helps us take a story or situation and turn it into math we can solve. Let's see how this idea grew over time!
On the ISEE, you will read a short story or situation. Then you pick the equation that matches it. Let's learn how to do that step by step!
Before we practice, let's nail down some key ideas. These are the building blocks for choosing the right equation.
Let's look at a diagram that shows how to go from a word problem to an equation. Follow the arrows from left to right!
The top row shows the three steps. First, you read the story carefully. Next, you circle or underline the clue words that tell you which operation to use. Finally, you write the equation with the correct numbers and symbol.
The bottom row shows clue words for each operation. Keep these in mind when you read ISEE problems!
On the ISEE, word problems usually need one of four operations. Let's see what each equation looks like. The question mark shows the unknown — the number you need to find.
Clue words are like a treasure map. They point you to the right operation! Let's organize them in a handy table.
| Operation | Clue Words | Example Sentence |
|---|---|---|
| Addition (+) | in all, total, altogether, combined, sum, both, more | Jill has 4 red pens and 6 blue pens. How many pens does she have in all? |
| Subtraction (−) | left, fewer, gave away, remain, difference, less than | Tom had 15 grapes. He ate 7. How many grapes are left? |
| Multiplication (×) | each, every, times, groups of, per, rows of | There are 5 bags with 4 apples in each bag. How many apples in all? |
| Division (÷) | share equally, split, divided, each gets, per group | 24 stickers are shared equally among 6 friends. How many does each friend get? |
Let's walk through a problem together, just like you would on the ISEE. Follow each step carefully!
Problem: There are 6 shelves in a bookcase. Each shelf holds 8 books. Which equation shows how to find the total number of books?
(A) 6 + 8 = ? (B) 8 − 6 = ? (C) 6 × 8 = ? (D) 8 ÷ 6 = ?
Even great students make mistakes on these problems. Here are the most common ones and how to avoid them.
| Mistake | Why It Happens | How to Fix It |
|---|---|---|
| Picking addition when the story says "take away" | Rushing through the problem | Underline the clue words before looking at the answer choices. |
| Confusing multiplication and addition | Both can give a bigger number, so they seem similar | Ask: Are there equal groups? If yes, multiply. If you're just combining two different amounts, add. |
| Putting numbers in the wrong order for subtraction | Not thinking about which number is bigger | In subtraction, the bigger number (the total you started with) always comes first. |
| Not reading all four answer choices | Picking the first choice that looks right | Always read all four choices. Two might use the same numbers but different operations! |
Right now, most ISEE problems ask you to pick an equation with one operation. As you grow as a math student, problems will get more interesting. Let's see how this skill grows.
| What You Know Now | What Comes Next |
|---|---|
| One-step equations (one operation) | Two-step equations (two operations) |
| Using a ? for the unknown | Using letters like x or n for unknowns |
| Choosing the equation from a list | Writing your own equation from scratch |
| Simple whole numbers | Fractions and decimals in equations |
Every big math skill starts with a small step. Choosing the right equation is one of those important first steps. You're building a strong foundation!
Now it's your turn! Read each problem carefully, find the clue words, and pick the equation that matches the story. Remember: there is no penalty for guessing on the ISEE, so always pick an answer!
To choose the right equation for a situation, follow three steps. First, read the problem carefully and find the numbers. Next, look for clue words that tell you which operation to use: addition for combining, subtraction for taking away, multiplication for equal groups, and division for splitting equally. Finally, pick the equation that uses the correct numbers and operation.
Remember to check your answer by asking, "Does this equation match the story?" On the ISEE, always answer every question — there is no penalty for guessing. Use process of elimination to cross out choices that use the wrong operation. You've got this!