Lesson 100: Multi-Step 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

Multi-step word problems require more than one mathematical operation. Students must identify relevant information, determine the correct order of operations, and translate words into numerical expressions or equations. This lesson develops structured problem-solving habits essential for algebra.

Learning Objectives

• Break multi-step problems into logical mathematical steps.
• Translate written scenarios into numerical expressions.
• Apply order of operations accurately in real-world contexts.

Topics Covered

• Identifying known and unknown quantities
• Translating words into operations
• Order of operations (PEMDAS)
• Checking solutions for reasonableness

Key Terms

• Multi-Step Problem: A problem requiring more than one operation to solve.
• Order of Operations: The rules that determine the sequence for performing calculations.
• Expression: A mathematical phrase combining numbers and operations.

Lesson Examples

Example 1: School Fundraiser

A class sells 45 tickets at $8 each. They spend $120 on supplies. How much profit do they make?

1. Find total revenue: 45 × 8 = 360
2. Subtract expenses: 360 − 120 = 240
3. Final Answer: The class makes $240 profit.

Example 2: Grocery Shopping

A shopper buys 3 bags of apples at $4 each and 2 cartons of juice at $3 each. They use a $5 coupon. What is the total cost?

1. Apples: 3 × 4 = 12
2. Juice: 2 × 3 = 6
3. Add subtotal: 12 + 6 = 18
4. Apply coupon: 18 − 5 = 13
5. Final Answer: The total cost is $13.

Practice Problems

1. A store sells 25 shirts at $12 each. It costs $150 to produce them. What is the profit?
2. A car travels 60 miles per hour for 3 hours, then 50 miles per hour for 2 hours. What total distance is traveled?
3. A restaurant bill is $85. A 15% tip is added. What is the total amount paid?
4. You buy 4 notebooks at $2.50 each and pay with a $20 bill. How much change do you receive?

Tips & Common Mistakes

• Do not combine steps too quickly—solve systematically.
• Pay attention to units (dollars, miles, hours).
• Always reread the question to ensure you answered what was asked.

Summary

Multi-step word problems require organization, careful reading, and correct application of operations. Breaking problems into smaller steps prevents errors and builds algebra readiness.

Challenge Problems

1. A concert hall sells 320 tickets at $25 each and 180 tickets at $40 each. Expenses total $8,000. What is the net profit?
2. A gym charges a $50 sign-up fee plus $35 per month. What is the total cost after 8 months?
3. A contractor buys 15 boxes of tiles at $18 each and receives a 10% discount on the total. What is the final cost?