The Elevator Problem. Christine Belledin The North Carolina School of Science and Mathematics Teaching Contemporary Mathematics Conference 2014. What is mathematical modeling?. According to the Common Core Standards for High School: Modeling is the process of choosing and using appropriate
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The North Carolina School of Science and Mathematics
Teaching Contemporary Mathematics Conference 2014
According to the Common Core Standards for High School:
Modeling is the process ofchoosing andusing appropriate
Mathematics and statisticsto analyze empiricalsituations, to understand thembetter, and toimprove decisions.
“Never before, in all my math experiences, had I seen a problem as open ended and varying as this one. Working on a problem like this with no obvious answer and many different options was a wholly new experience for me. This problem helped me visualize the role math could and most likely will play in my future.”
In some buildings, all of the elevators can travel to all of the floors, while in others, the elevators are restricted to stopping only on certain floors. Why? What might be the advantage of having elevators that travel only between certain floors?
Suppose a building has 5 floors (1-5) that are occupied. The ground floor (0) is not used for business. Each floor has 60 people working on it. There are three elevators (A, B and C) available to take these employees to their offices in the morning. Everyone arrives at approximately the same time and enters the elevators on the ground floor. Each elevator holds 10 people and takes approximately 25 seconds to fill on the ground floor. The elevators then take 5 seconds between floors and 15 seconds on each floor on which it stops.
Why was question (2) harder to answer than question (1)? What assumptions will you need to make in order to simplify the problem?
“I loved how realistic it was, aside from no one taking the stairs.”
What else did students have to say?
We see the power of collaboration.
“In my pod, I felt like none of us could have solved the problem on our own but we pooled together our knowledge and we found that it was possible to solve it together.”
“It was also a very complex problem, much more complex than I had ever done before. We had to set assumptions to reduce the amount of variables and make the project manageable. Even with the assumptions the problem was daunting. We had to break it down logically instead of just trying to plug it into a memorized equation. This thought process is very common in this class, and while I found it confusing and hard, I end with deeper understanding of how to do the problems.”
“The elevator problem was probably the first time in the class that I felt like I was trying to comprehend something completely beyond my intelligence, but eventually I figured out what we are doing.”
“I absolutely loved the elevator problem because it was so intricate and complex. I also liked that it might actually be helpful one day and have real world application. I liked that in order to find the one of many possible final solutions, you must first solve for one tiny section, how long it takes to get to one floor, and then apply it to the whole process. I think this was also one of my favorite problems because it was a reasoning problem instead of a computation problem. I wish we would do more problems like these more often.”
“I don't know what a profession that focuses on efficiency (workplace or public) is called, but I would love to work out things like this for a living.”
“In most of my other math classes, the concepts were mostly superficial; in the sense that we only learned the basics and processes of a certain idea without working on how it could be used in real life. Of course, this was often nice and easy, bit if I'm looking to work in a STEM field one day, it is crucial to understand the applications of the different things we learn.”
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