Translate a word problem into an algebraic expression. |...

SECTION 1

Historical Context & Motivation

Long ago, people used words to solve math puzzles. They needed a way to write unknown amounts with letters. This idea grew into algebra, which helps turn word problems into expressions.

820 AD

Birth of Algebra

Al-Khwarizmi writes the first algebra book. He uses words for unknowns.

1637

Letters for Variables

René Descartes starts using letters like x for unknowns. This makes math clearer.

1800s

Word Problems in School

Schools teach kids to translate stories into algebra. It builds real-world math skills.

Today

SSAT Prep

You use this skill on tests like the SSAT to solve tricky problems fast.

Before algebra, math was hard for stories like "twice as many apples as friends." Now, you can write 2f. This lesson shows you how!

SECTION 2

Core Principles & Definitions

An algebraic expression is math with numbers and letters, like 3x + 2. A variable like x stands for an unknown number. To translate, match words to math symbols.

Addition Words

"more than", "plus", "increased by" mean +.

Subtraction Words

"less than", "minus", "decreased by" mean −.

Multiplication Words

"times", "of", "twice" mean ×.

Division Words

"divided by", "per", "half of" mean ÷.

Equals Words

"is", "equals" mean = (for equations).

✦ Key Takeaway

Think of it like a video game code. Words are the commands, and algebra is the code that makes the game work!

SECTION 3

Visual Explanation

Arrows show how words map to symbols. The variable n holds the place of the unknown.

See how the story breaks into parts? Words like "twice" become numbers times a variable. You can do this with any problem!

SECTION 4

Mathematical Framework

Start with the unknown as a variable like n or x. Then add words step by step. Always read carefully.

COMMON TRANSLATIONS

"a number" → n "three more than n" → n + 3 "twice n" → 2n "n less 4" → n − 4

n is the variable (unknown). Use × for times if needed, but often just next to number.

ORDER MATTERS

"5 less than twice a number" → 2n − 5 NOT 5 − 2n

Read left to right: twice first, then less 5.

SECTION 5

Detailed Breakdown

Phrases point to math operations. Match them to build your expression.

This map helps spot clues in problems. Practice with friends or games to get faster. You're getting great at this!

SECTION 6

Worked Example

Translate: Three times a number plus seven

Step 1: Spot the unknown"a number" is the variable. Let it be n.

Step 2: Find multiplication"Three times" means 3 × n or 3n.

Step 3: Add the rest"plus seven" means + 7. So, 3n + 7.

3n + 7

See? Break it into small steps. You just solved it like a pro!

SECTION 7

Strengths & Common Errors

Avoid these traps to ace your SSAT.

Mistake	Why Wrong	Fix It
Switching order like 5 − 2n for "twice minus 5"	Words go left to right.	Read carefully: 2n − 5.
Forgetting variable like "3 + 7".	No unknown!	Always use n or x.
Using = in expression.	Expressions have no =.	Save = for equations.

✦ KEY TAKEAWAY

Strength: Turns confusing stories into simple math. Like decoding a secret message in a game!

SECTION 8

Connection to Equations

Expression	Equation (Next Level)
2n + 3 (twice plus 3)	2n + 3 = 11 (equals 11)
n − 4 (less 4)	n − 4 = 7
3n (three times)	3n = 21

Expressions are half the story. Add "equals" to make equations and solve for n. You'll learn that next!

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL

What does "a number" represent? A. 5 B. n C. + D. × E. =

PROBLEM 2 — BASIC CALCULATION

"Five more than a number" A. 5 − n B. n + 5 C. 5n D. n − 5 E. 5 + n

PROBLEM 3 — INTERMEDIATE

"Four less than twice a number" A. 4 − 2n B. 2n − 4 C. 4n − 2 D. n − 8 E. 2(n − 4)

PROBLEM 4 — APPLIED

A rectangle's length is 3 more than width w. A. l = w − 3 B. l = 3w C. l = w + 3 D. 3w − l E. w − 3

PROBLEM 5 — CRITICAL THINKING

"The sum of three times a number and 2, decreased by 7" A. 3n + 2 − 7 B. (3n + 2) − 7 C. 3(n + 2 − 7) D. 3n + 2 + 7 E. 3n − 9

SUMMARY

Lesson Summary

You now know how to translate word problems into algebraic expressions. Use variables for unknowns and match words to + − × ÷.

Practice spotting phrases like "more than" for +. Break problems into steps. You're ready for SSAT success—keep practicing!