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

 Post a new topic to the tool: Understanding Distance, Speed, and Time Relationships Using Simulation Software discussion

 Subject: RE: Runners Activity: Some Observations Author: SteveW Date: Jun 29 2006
When I wrote that the ratio of the vertical unit size to the horizontal unit
size was 6:4, I meant that 6 vertical units is approximately equal to 4
horizontal units. Which, yes,  can be reduced to 3v approx equals 2h. Sorry for
any confusion with that.

-- steve

On Jun 28 2006, SteveW wrote:
> 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