Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Applications of Integral, Antiderivatives and Definite Integrals
• Math: Calculus: Applications of the Derivative

9-12

60 Minutes

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

## Moving Rectangular Objects Around Corners

#### Activity Overview

Many calculus books ask something like, "Ignoring its width and height, find the longest rod that can be moved around a 90 degree corner where 2 halls meet, if the hall is 5 feet wide on one side and 7 feet wide on the other." (See "before the activity")

#### Before the Activity

This problem helps if you're moving very, very long pieces of uncooked spaghetti and it gives good insight into moving long pieces of ½ inch diameter pipe. But what if you have to move a desk or a sofa? You certainly can't ignore their widths. There is a more general solution that has more meaning to more real problems if you do not ignore the width. See Fig. 1 in the attached PDF file.

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:

• Use the graphing calculator to find the solution to a complex optimization problem.
• #### After the Activity

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