| This lesson is intended to be a great
supplement to normal optimization lessons using derivatives
(max and mins)
Break the class into four groups. Assign each group a
link to the following webpages. Instruct the students that you
want them to become familiar with the problem given on the
webpages, and that they'll have to finish up a number of
assignments for this problem. Each group will need to
write a one-page essay about the problem and it's significance
in terms of the mathematics being learned, and what the
students in the class can gain from learning this type of
problem. Also included can be a short description of the
website and what's included. Each group will need to
present their website to the class, and demonstrate the pages
capabilities and explain and solve the problem involved in a
8-10 minute presentation. And each group will need to
write 3 free-response essay questions giving a similar but
significantly different problem that will be given on a quiz
for the entire class. You can explain to the students
that the quiz will be easy, since every person should know how
to do one of the problems perfectly since they are the ones
writing the problem.
Maximum area of a rectangle inscribed in a semi-circle
http://archives.math.utk.edu/visual.calculus/3/applications.1/index.html
Longest ladder that can be carried through a hallway
corner
http://archives.math.utk.edu/visual.calculus/3/applications.2/index.html
Shortest time to move from through a desert to a town
http://archives.math.utk.edu/visual.calculus/3/applications.3/index.html
Shortest ladder that can lean over a fence to a building
http://archives.math.utk.edu/visual.calculus/3/applications.4/index.html
Day One - Have students break into groups and go to the
computer lab. Tell the students today's day is a working
day to get familiar with the website and go over the
mathematics. All mathematical questions and the
distribution of work in the group should be assigned
today. The teacher's responsibility is to make sure the
students stay on task, help them through mathematical
problems, and to answer questions about their project.
Day
Two - This day should be geared as a working day to finish all
three assignments for the presentation. The essay and
quiz questions should be turned in this day, and the
presentation should be planned very well. Given the
teacher's discretion, the presentation and quiz (days three
and four) do not necessarily have to be directly following Day
two if the students need more time working both in and out of
class
Day Three - Presentations. All four groups
should present their website to the class.
Day Four -
Review of optimization and mathematics, quiz from questions
given by students..
Note: expect the students to share their quiz
questions with each other, and the answers. Make sure
you stress that the bulk of points assigned to the quiz will
be for the process and thinking involved, not for the
solution. The students will need to show all their work
and be able to explain the
problem. | 