I gave this problem to my Calculus class while
we were studying Optimization. The first three parts of the problem are understandably
below the students’ level as they only require the basic use of the Pythagoras
theorem. However, the students seemed to enjoy watching Dan’s reveal videos
confirming their solutions that I let them tackle the first three parts as a fun
and “warm up” exercise!
Part three, determining the position
of the Taco Cart so that both Dan and Ben reach it at the same time, allowed me
to introduce the students to Desmos and Wolfram Alpha for the first time. The
students created an algebraic model and used the two tools to confirm their
answers graphically and algebraically.
The Sequel was where it got
interesting. Finding the fastest path to the Taco Cart is certainly a fun
application for the Optimization section of Calculus.
What excited me most was that when I looked
around the room at the students working on their vertical boards, I saw
examples of numeric, graphic, and algebraic methods being used. All with
literally no guidance from me! It was so great to see the students select a
method that they felt most comfortable with.
The groups using the numeric method soon
realized that it wasn’t the most efficient method for determining an exact
solution. At that point, I had all groups share and show their strategies to
the whole class. The students were then asked to solve the problem using all three
methods, first manually and then with the help of Desmos and Wolfram Alpha.
I found this to be a great problem because
it can be tackled by students from all grades from Math 9 to Calculus, since
each part of the problem can be approached numerically, graphically,
algebraically, and through the use of Calculus concepts.
It was also a great problem to do with Vertical Non-Permanent Surfaces as it eased the collaboration process within groups and allowed many opportunities for students to share their strategies with the entire class. It also facilitated discussion with the teacher, because I could immediately see which groups needed help and which groups were doing something unique.
The student groups’ solutions and
reflections on the whole problem can be viewed by clicking on the links below:
I showed my class the following MasterCard commercial, featuring World Hot Dog eating champions Kobayashi and Sonya: commercial.
I then asked the students to formulate and discuss any interesting mathematical questions or ideas emerging from the video that were worth exploring. Given below are two samples that students submitted as a product to present their learning in the form of a Prezi. (The files are in zipped form.)