The Need for Speed

At some point in a student’s algebra career they need to lose the doctrinaire algorithms and start to feel the need for speed.  Since my college algebra class seemed to accept the change depicted in this figure, I decided to teach them the fast way to work proportion problems.  I wrote letters on small blocks of cardboard, placed them as in this picture,

Movable Variables for a Proportion Demonstration

and started moving them around without violating the equality.  I felt an odd sense of pleasurable relief in the room.  I think if students have worked enough algebra problems, they have a natural need to skip steps and I had just validated this  need and confirmed the pattern that they had intuited.  The class probably has more kinesthetic thinkers than usual so that my demonstration of moving numbers around appealed to them.  Here is part of a handout that I gave them.

Proportions - Any CrissCross is OK

Two notes:  First the idea of moving numbers and changing their signs, also works with exponents when simplifying exponential expressions.  Secondly, I don’t think Tom Cruise in the referenced movie clip from  Top Gun had a “need for speed.”  He actually was “achin’ for acceleration.”  At the elevations of most dogfights the visual clues of speed are not existent.  That’s why the writers scripted low level chases.  Tom really had the need for tight turns and sudden changes in velocity.


About jrh794

I am a sixty-five year old math instructor at Southern Oregon University. I taught at the College of the Siskiyous in Weed California for twenty-six years. Prior to that I worked as a computer programmer, carpenter and in various other jobs. I graduated from Rice University in 1967 and have a MS in Operations Research from Stanford. In the past I have hand-built a stone house and taken long solo bicycle tours. Now I ride my mountain bike and play golf for recreation.
This entry was posted in Curriculum, Pedagogy, Rants, Uncategorized. Bookmark the permalink.

1 Response to The Need for Speed

  1. Nick Chura says:

    I do like the switch-sign-and-move-to-the-other-side shortcut. While adding the opposite is correct, how many times must we combat the tendency to simplify an expression by adding the opposite to both “sides”.

    Incidentally, I always saw in this clip Maverick using danger to medicate himself against the depression of being outshined by the Ice Man. He truly was an adrenaline junky.

    Lastly, I learned that you can append #t=0m8s to your link to go right to that spot:

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