By Steve McIlrath, APA Math Teacher
Recently Mr. Varela from the Machine Shop teamed up with the Advanced Placement (AP) Calculus class, helping bring to life the idea of rotating volumes around a fixed axis. The AP Calculus students just finished a unit on finding volumes of solids using integration techniques. With machining tools located in APA’s very own Manufacturing Technology Center, a piece of solid steel stock was fashioned into a complex shape with one end hollowed out. The Calculus students were presented with the metal solid, a dial caliper, and the density of steel. Their task is to use their knowledge of Calculus to predict the weight of the solid steel object as accurately as possible.
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| Brittany Trotter and Nicole Thorp try to predict the weight of the object. |
The students were allowed to work together as a class to solve the problem, but were not permitted to ask for any help from the instructor. After 2 days of measuring, drawing, curve-fitting, and integrating, they were ready to test their answers on the scales of truth.
In the end, the Calculus students were 67 grams off from the actual weight of 1,840 grams. That’s a 3.6% margin of error – not quite industry standard yet, but certainly a fantastic approximation given the tools with which they had to work. Most importantly though, the project highlighted the polytechnical nature of who we are striving to be as a school. There just aren’t many high schools in the country that are as equipped to expose students to such a rich blend of theoretical and practical rigor as we are at APA.
Filed under: Austin Polytech, Education Tagged: | Austin Polytech, Education
Guest Contributor
Erica Swinney
Dan Swinney
Leonard McKinnis
Ingrid Gonçalves
Bill McMahon
Dear Mr. McIlrath, Just read your article about the volume of revolution of a piece of steel, was referred to it by seeing the name of Dan Swinney in the Chicago Tribune today, 6/05/11; had to immediately send a personal email to Dan Swinney, he worked hard for me as a unionist way back in 1980, when I was a 24-year old machinist, trying hard to make a living, in any case, without boring you too much about me, I’m now an older guy who’s made a living as a machinist for 30 years, who’s just this year finally getting around to learning something about calculus, and most of all would like to somehow help the work of Austin Polytechnical, could you use a volunteer math tutor, or possibly I could donate tools, surely there must be some way I could help; I understand, from the Chicago Tribune article, that CPS requires an “improvement plan,” if in some way a volunteer could help, please let me know, in any case, your article was strongly uplifting to me, the spirit of Jaime Escalante lives on, nice going, sincerest regards, Dan Kelly