Discussion:  All Topics in Algebra 
Topic:  Factoring Quadratics 
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Subject:  RE: Factoring Quadratics 
Author:  stek 
Date:  Jan 26 2009 
Thanks for the video and also for the discussion about the value (or lack
thereof) of factoring trinomials when a is not 1.
I like the dropping cannonball example; it's a nice application of quadratics.
(I encourage you to considerrelating the time slider to the horizontal axis. It
might be a bit confusing to students to see two different horizontal elements
representing time, particularly when they have different scales.)
Coincidentally, about a month ago I put together a very similar Sketchpad
example, in response to a student teacher who had her students gather data by
timing a penny that they dropped down a stairwell. Not surprisingly, students
found the experiment difficult: it's hard to get accurate timings from a
handheld stopwatch, and it's also hard to vary the height. I observed to her
that rolling a cart down an inclined plane would have allowed students to
collect more useful quadratic data.
It seemed to me that after students did the freefall experiment (either by
dropping pennies or rolling a cart) they would be pretty interested in a model
that makes it easier to collect data. This was the motivation for my Penny Drop
sketch, which I'll gladly send to anyone who cares to ask for it. At this point
there's nothing but the sketch  no worksheet or activity notes. But at least
you can vary the acceleration (to simulate the penny, a cart on various slopes,
freefall on the moon, etc.) and the initial velocity (in case you want to launch
the penny (or cannonball) upward to begin the motion.
If anyone wants the Sketchpad document, please let me know by sending an email
to stek <at> keypress.com with "Penny Drop" in the subject line.
Scott
Scott Steketee
Sketchpad Projects
 
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