Lesson 82: Expressions in Word Problems

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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

Word problems allow algebra to be applied to real-world situations. In this lesson, students learn how to translate written scenarios into algebraic expressions and evaluate them using variables and mathematical operations.

Learning Objectives

• Translate word problems into algebraic expressions.
• Identify key words that signal mathematical operations.
• Evaluate algebraic expressions derived from real-world situations.

Topics Covered

• Identifying variables in real-world contexts
• Translating verbal phrases into algebraic expressions
• Evaluating expressions from word problems

Key Terms

• Variable: A symbol that represents an unknown or changeable value.
• Algebraic Expression: A mathematical phrase that contains numbers, variables, and operations.
• Translation: Converting verbal statements into mathematical expressions.

Lesson Examples

Example 1: Writing an Expression from a Word Problem

A taxi charges a $4 starting fee plus $2 for each mile traveled. Write an expression for the total cost if m miles are traveled.

1. Identify the starting fee → 4
2. Identify cost per mile → 2m
3. Combine both parts → 4 + 2m

Example 2: Evaluating an Expression from a Word Problem

A movie ticket costs $8, and snacks cost $3 per item. Find the total cost if a person buys 2 tickets and 3 snacks.

1. Write the expression → 8(2) + 3(3)
2. Multiply → 16 + 9
3. Add → 25

Practice Problems

1. A gym charges $20 per month plus a $15 sign-up fee. Write an expression for total cost after m months.
2. A store sells notebooks for $2 each. Write and evaluate the expression if a student buys n notebooks.
3. A ride costs $5 plus $1.50 per mile. Write the expression and evaluate it for 6 miles.
4. A streaming service costs $12 per month. Write and evaluate the cost for 9 months.

Tips & Common Mistakes

• Look for keywords like "per," "each," "plus," or "total."
• Assign variables clearly before writing expressions.
• Check units to ensure the expression represents the correct quantity.

Summary

Expressions in word problems allow mathematical models to describe real-world situations. By identifying variables, translating language into mathematical operations, and evaluating expressions, students develop essential algebra skills.

Challenge Problems

1. A rental company charges $40 per day plus $0.25 per mile driven. Write and evaluate the expression for 3 days and 120 miles.
2. A fundraiser sells tickets for $6 each and raises $300 in donations. Write an expression for total money raised if t tickets are sold.
3. A phone plan costs $25 per month plus $10 for each extra data package. Write and evaluate the expression for 5 months and 3 packages.