# Activities

• • • ##### Subject Area

• Math: Calculus: Applications of the Derivative
• Math: Calculus: Antiderivatives and Slope Fields

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200

## Hot Tub

#### Activity Overview

This activity is an application of integration. Students first use the calculator to determine specific numeric results to enable them to understand the dynamics of the problem.

#### Before the Activity

Students then use the symbolic capacity of their calculator and derivatives to find the maximum volume. This activity emphasizes using the integral of a rate of change to give the accumulated change. The definite integral of the rate of change of a quantity is interpreted as the change of the quantity.
See the attached Activity PDF file(s) for detailed instructions for this activity.

#### During the Activity

Follow the procedures outlined in the activity.
Students will:

• Be able to use the calculator to determine specific numeric results in the context of the problem.
• Be able to use the symbolic capacity of their calculator and derivatives to find the maximum volume.
• Be able to use the integral of a rate of change to give the accumulated change.
• Recognize that the definite integral of the rate of change of a quantity is interpreted as the change of the quantity.
• #### After the Activity

• Review student results:
• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary