In this first lesson on related rates, students will learn how to compute change in measurements such as the change in the height of a cone given its dimensions and its change in volume.

Concepts included in this lesson are:

· What is a related rate.

· Related rates of common objects such as circles, cubes and spheres.

· Related rates where a ratio relating two measurements is substituted into a formula. (i.e. substituting base for height in determining the area of a triangle given a ratio between the two.)

· A related rates anchor chart is included.

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The no prep lesson and worksheet are easy for students to follow and complete. You can print this lesson and use it as an in-class activity or download the digital learning choice for distance learning students. Even if you have a hybrid class, both types of students can access this lesson. This can also be used for students who were absent when the instructor taught this lesson. Since many of the questions are like previous AP exam questions, this makes a great review.

AP Standards:

CHA-3.A.1 The derivative of a function can be interpreted as the instantaneous rate of change with respect to its independent variable.

CHA-3.A.2 The derivative can be used to express information about rates of change in applied contexts.

CHA-3.D.1 The chain rule is the basis for differentiating variables in a related rates problem with respect to the same independent variable.

CHA-3.D.2 Other differentiation rules, such as the product rule and the quotient rule, may also be necessary to differentiate all variables with respect to the same independent variable.

CHA-3.E.1 The derivative can be used to solve related rates problems; that is, finding a rate at which one quantity is changing by relating it to other quantities whose rates of change are known.

An alternative way to use this lesson is as a review for the AP Exam. Students complete the worksheet, but if they have difficulty, they may refer to the lesson at that point.

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Other products on Derivatives:

· More Differentiation Techniques: Warm-ups

· Lesson on Position, Velocity, and Acceleration

· Lesson on the Chain Rule