Lesson Plan: Representing Proportional Relationships

Lesson Summary

In this lesson, students will explore different ways to represent proportional relationships using tables, graphs, and equations. They will analyze proportional relationships in real-world contexts and learn how to determine the constant of proportionality. The lesson emphasizes how proportional relationships appear as linear functions that pass through the origin when graphed.

Students will practice:

• Using tables to identify proportional relationships.
• Graphing proportional relationships and understanding their characteristics.
• Writing equations in the form $y = kx$, where $k$ is the constant of proportionality.
• Interpreting real-world problems involving proportions.

Key Vocabulary

• Proportional Relationship: A relationship between two quantities where the ratio remains constant.
• Constant of Proportionality: The fixed number $k$ in the equation $y = kx$, which represents the ratio of $y$ to $x$.
• Unit Rate: A rate in which the denominator is 1, such as $\frac{60}{1}$ miles per hour.
• Linear Relationship: A relationship where the graph forms a straight line.
• Graph of a Proportional Relationship: A straight line passing through the origin (0,0) with a slope equal to the constant of proportionality.

Real-World Applications

This lesson applies proportional relationships to real-world situations such as:

• Buying fruit by the pound and determining the total cost.
• Calculating travel distance at a constant speed.
• Understanding unit pricing and rates in financial transactions.

Subscribers to Media4Math can download these lessons in PDF format for easy classroom use.