Lesson 99: Patterns 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

In this lesson, students learn how to interpret word problems that describe patterns and represent them as tables, coordinate points, and linear equations. The goal is to recognize constant rates of change and model real-world relationships using algebraic expressions.

Learning Objectives

• Translate word problems into tables of values.
• Identify constant rate of change in real-world scenarios.
• Write and graph linear equations from contextual situations.

Topics Covered

• Identifying independent and dependent variables
• Writing equations from verbal descriptions
• Graphing real-world linear relationships

Key Terms

• Independent Variable: The input value that you choose or control (usually x).
• Dependent Variable: The output value that depends on the input (usually y).
• Rate of Change: The amount one variable changes compared to another.

Lesson Examples

Example 1: Movie Ticket Cost

1. A movie ticket costs $8. Write an equation to represent the total cost (y) for x tickets.
2. Since each ticket costs $8, multiply 8 × x.
3. The equation is y = 8x. Plot points such as (1,8), (2,16), (3,24).

Example 2: Gym Membership Fee

1. A gym charges a $20 sign-up fee plus $15 per month.
2. The monthly cost increases by 15 each month. The starting value is 20.
3. The equation is y = 15x + 20. Graph starting at (0,20).

Practice Problems

1. A babysitter earns $12 per hour. Write and graph the equation.
2. A taxi charges $5 plus $2 per mile. Write the equation.
3. A plant grows 3 inches per week starting at 4 inches tall. Model the pattern.
4. A streaming service costs $9 per month. How much after 6 months?

Tips & Common Mistakes

• Always identify the starting value (y-intercept).
• Look for key phrases like “per,” “each,” or “every.”
• Do not confuse the rate of change with the starting value.

Summary

Word problems often describe linear patterns. By identifying the starting value and rate of change, you can write equations, create tables, and graph the relationship on the coordinate plane.

Challenge Problems

1. A cell phone plan costs $40 plus $5 per GB of data. Write the equation and graph it.
2. A savings account starts with $100 and increases by $25 per week. Model the growth.
3. A company charges $200 setup fee and $30 per service hour. How much for 8 hours?