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 Discussion: All Topics Topic: Runners Activity: Some Observations Related Item: http://mathforum.org/mathtools/tool/13171/

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 Subject: RE: Runners Activity: Some Observations Author: Craig Date: Jun 28 2006
Perpendicular lines on a graph are pretty much for aesthetics only, and a nice
tie-in to geometry.  However, in the context of a distance versus time graph,
perpendicularity is practically meaningless.

I especially like that the graph does NOT have the same scale on both axes, for
several reasons:
1.  The UNITS are different on both axes, so the area of a unit grid square is
feet-seconds, rather than something like square feet (which you might expect
to be square in some instances).
2.  Graphs of real data almost never have the same scales on both axes, and
introducing different scales early on in the students' graphing experience could
eliminate a common learning obstacle later on, when students seem to "default"
to graphs with equal scaling on both axes.
3.  Although the applet doesn't require students to set up their own graphs, it
is important for students to spend a little time thinking about what each axis
represents, and deciding on an appropriate scaling for each axis at the outset
is very important.  In fact, I think this single observation (about a
rectangular, rather than square, grid) merits some serious discussion in the
classroom!