This worksheet is designed to replace a lecture on finding the maximum volume of an open-top rectangular box. It includes a 1 cm X 1 cm grid so that each group can create one box, and we can compare the volumes of each box. Once students see a very short, flat box, compared to a very tall, narrow box, they quickly see that the optimal boxes are somewhere in between.
Make sure you run off the two pages separately, so the worksheet and the grid are separate.
The rest of the worksheet "holds their hands" through the process, and by the end of class, they have a good idea about which box is best.
This is the first in a three-part series.
I start out class with a 15-minute "mini-lesson," giving my students some basic examples of what today's lesson will be about. Once the mini-lesson is over, I have them get to work within their groups on this worksheet, and I circulate to make sure they are getting the purpose of the questions.
Students are expected to show their work on a separate sheet of paper.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.
Keywords: calculus, optimization, maximum volume, Jonnard