Lesson 79: Writing Expressions from Words

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson teaches students how to translate word phrases into algebraic expressions. Students will learn to identify keywords that represent mathematical operations and use variables to represent unknown values in real-world situations.

Learning Objectives

• Translate verbal phrases into algebraic expressions.
• Identify operation keywords such as sum, difference, product, and quotient.
• Use variables to represent unknown quantities.

Topics Covered

• Recognizing mathematical keywords in sentences
• Writing algebraic expressions from word phrases
• Representing real-life situations with algebra

Key Terms

• Verbal Phrase: A sentence or group of words that describes a mathematical relationship.
• Algebraic Expression: A mathematical phrase that uses numbers, variables, and operations.
• Operation Keywords: Words that indicate mathematical operations, such as sum (addition) or product (multiplication).

Lesson Examples

Example 1: Translating an Addition Phrase

1. Phrase: "The sum of a number n and 7."
2. Identify keywords: "sum" means addition.
3. Write expression: n + 7

Example 2: Translating a Real-Life Situation

1. A movie ticket costs $9 plus a $2 service fee.
2. Let t represent the number of tickets.
3. Write expression: 9t + 2

Practice Problems

1. Write an expression for "the difference between x and 5."
2. Write an expression for "three times a number y."
3. Write an expression for "8 less than a number p."
4. A gym charges $15 per visit plus a $5 membership fee. Let v represent visits. Write an expression.

Tips & Common Mistakes

• Watch for order when translating phrases like "less than" or "more than."
• Identify operation keywords before writing expressions.
• Use parentheses when expressions contain multiple operations.

Summary

Writing expressions from words requires recognizing keywords that represent mathematical operations and translating them using variables. This skill allows students to model real-life scenarios using algebraic language.

Challenge Problems

1. Write an expression for "twice the sum of a number n and 4."
2. A car rental company charges $40 per day plus $0.25 per mile. Let m represent miles driven. Write an expression.
3. Explain why word phrases like "less than" can change the order of numbers in expressions.