In December of 2014, Sony released the movie The Interview online after threats to theaters cancelled the debut in theaters. As originally reported in Wall Street Journal, the sales figures reported in January contained an interesting math problem appropriate for algebra students.
The following January, Sony reported sales of $31 million from the sales and rentals of The Interview. They sold the movies online for $15 and rented through various sites for $6. If there were 4.3 million transactions, how many of the transaction were sales of the movie and how many of the transactions were rentals?
Over the last 9 weeks I have been posting writing on a variety of subjects. These writings are part of Yavapai College’s 9x9x25 Challenge. What is the Challenge? As the father of the Challenge, Todd Conway, writes:
The Challenge is about writing as a reflective practice in teaching. The Challenge is about sharing your experiences as an educator, discovering new ideas about teaching and learning, creating a deeper sense of community between faculty at Yavapai College. The Challenge is also about learning what the internet is capable of and how it can be used in academic environments.
A blog is the natural vehicle for writing. It is a simple content management system that is easy to use. Whether you use a WordPress.com, blogster.com, blogspot.com, or other blogging platform, it is easy to post text, music, pictures, video or practically any other type of content.
Back around 1980, I got my first computer. As I recall, it had the brand name Sinclair and it was connected to a little black and white TV we had in the basement. It had a minimal amount of memory, but I could save programs to a cassette tape connected to the IO port. That computer found its way to a landfill in Alaska a long time ago. It amazes me that almost every one of my students (as well as myself) carries a small computer in their pocket that is hundreds of times more powerful than that old Sinclair. Not only is it more powerful, but my smartphone fits in the palm of my hand. It also amazes me at the growing number of uses a smartphone has in the classroom.
Most of the student teams in my face-to-face classes utilize in person meetings along with collaborations through comments. My online students do not usually meet in person so online comments and email (and some phone calls) are their primary means of collaboration.
Historically, maximization problems have been a problem for calculus students. Not so much in finding critical points from functions and classifying them, but finding the objective function to begin with. Students rely on basic examples to mimic. We wonder why they can’t carry out more complicated examples. They are able to model simple physical situations after much practice, but flounder when faced with slightly more complicated problems because they don’t understand the complication well.
As the maximization and minimization problems become more complicated, using a table to organize examples of what is being modeled becomes more and more useful. Let’s look at another examples of how this might work.
Problem A rectangular tank with a square base, an open top, and a volume of 8788 ft3 is to be constructed of sheet metal. Find the dimensions of the tank that has the minimum surface area.