Objective

By the end of this lesson, you will be able to understand the concept of derivatives and how they are used in calculus.

Materials and Prep

• Paper
• Pencil
• Calculator (optional)

No prior knowledge is required, but it would be helpful to have a basic understanding of algebra and functions.

Activities

1. Start by discussing the concept of change and rates of change. Use real-life examples such as speed, growth of plants, or temperature change to illustrate the need for understanding rates of change.

2. Introduce the concept of derivatives by explaining that it represents the rate of change of a function at a particular point. Show how to find the derivative of simple functions using basic rules.

3. Practice finding derivatives of various functions. Start with simple linear and quadratic functions and gradually move to more complex functions.

Seventh Grade Talking Points

• "Derivatives help us understand how things change over time. For example, if we know the position of a car at different times, we can use derivatives to find its speed at a specific moment."
• "When we find the derivative of a function, we are finding the slope of the function at a specific point. It tells us how fast the function is changing at that point."
• "Just like learning multiplication helps us solve more complex math problems, understanding derivatives will help us solve more complex problems in calculus and real-life situations."