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Discussion: Understanding Distance, Speed, and Time Relationships Using Simulation Software tool
Topic: Runners Activity: Some Observations
Related Item: http://mathforum.org/mathtools/tool/13171/


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Subject:   RE: Runners Activity: Some Observations
Author: SteveW
Date: Jun 28 2006
So, this suggests another problem or two that some students might be ready for.
Suppose the ratio of the vertical unit size to the horiztontal unit size is 6:4.
(It appears to be a little more than that but close enough for now).

How would we calculate the step sizes that would get the lines as close to
perpendicular (visually) as possible in this context? This could be good for
thinking about ratios and slopes.

It's nice that in this particular situation you can play with the applet to get
a value through trial and error and have that guide or check your calculations.


The more general modeling question might be something like: if I have two lines
with slopes of opposite sign, what happens to the angle they form as I change
the ratio of the vertical unit size to the horiztonal unit size.

Your noticing and the wondering it generates is something worth cultivating in
our students and modeling for them.

-- steve

On Jun 26 2006, Chris T. wrote:
>4.  The distance between 0 and 10 on the
> time scale is not the same as the distance between 0 and 10 on the
> position scale.  This means that while it is easy to make parallel
> lines, it is extremely difficult to make perpendicular lines.
> Chris

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