FIU Modeling Workshop – Day 3

We started today by finishing our whiteboard discussion for our constant velocity lab (buggy lab).  As mentioned the previous post, Jon and Chris recommended to not worry about which variable was on a given axis (just make sure they had thought it through and had a reason).  However, they said as the whiteboard session is winding down, begin to force the discussion (with Socratic questions) to which graph ($d$ vs $t$ or $t$ vs $d$) gives more meaningful information (answer: $d$ vs $t$ since the slope is speed/velocity).  They also mentioned to direct the students to think about position and time interval rather than distance and elapsed time, as the former will help with the distinction of speed and velocity (which haven’t been resolved as yet), and the concept of acceleration.

They also reminded us, that at this point in the year, the students “know” LoggerPro and scientific techniques learned in the first unit.  The supposedly know what slope means (but in reality they know how to calculate it, not what it means).

One important line of questioning to pose to the students is, “What does the slope of the $x$ vs $t$ graph represent?”

Slope is defined in algebra classes as the change in $y$ divided by the change in $x$.

$\large m= \frac{\Delta y}{\Delta x}$

Since the $y$-axis of a $x$ vs $t$ graph represents position, a change in position relative to a change in time, the slope represents the average speed over the elapsed time

$\large \overline{v}= \frac{\Delta x}{\Delta t}$
Since $\Delta x$ is a distance, it would have units $\textit m$.  $\Delta t$ is an elapsed time, so it would have units $\textit s$. Thus the slope of the x vs t graph should have units $\textit m/s$, which is consistent with the units for speed.  {Thanks Global Physics Department for introducing me to LaTex!}
Next on the agenda was using LoggerPro to create a $v$ vs $t$ graph for our data.  After which, we used the integral function to find the area under the “curve.”  Again, we discussed the meaning of this area.  From math, we know:
$area=(base)(height)$
Since the base is time, $t$, and the height is velocity/speed, $v$, we can show that the area is displacement/distance.  In looking at my notes, one thing that I’ll get clarification on, is when due we, the teacher, distinguish between speed/velocity and distance/displacement during this process.  Have we gotten to that point, and I forgot to note it, or are we not to that stage in the cycle.
Next on the agenda, we were asked to work on Unit II worksheets One & Two.  Each group was again  asked to present one part of this assignment on a whiteboard.  A few comments to note:
1. Jon mention that before beginning these experiments, he has the lab groups perform a vernier experiment using motion detectors and labquest mini interfaces to match their motion to given position vs time and velocity vs time graphs. (I mentioned that I do the same activity as a competition between lab groups, which I find gets the kids very excited.  I’ll probably write about my “Physics Olympics” at some point in the near future.)
2. On wkst 1, question 2a, ask the group “How do you know they are the same?”  Meaning, get them to discover how the could determine the scales were the same given the limited information.
3. On wkst 1, question 2d, ask the group “Can two of your members enact the motion depicted in the graph?”
4. On wkst 2, question 6&7, use Socratic questioning to lead students to drawing dashed vertical lines at the points of discontinuity.  Someone asked about including open and closed dots to show where the object was at the point of discontinuity.  Chris answered that we don’t know, nor do you need to get into that level of sophistication.

We ended the day by discussing the last tool in the modeling arsenal, Motion Maps:

The above examples show two different maps (the first above the red line, the second is below).  Some key features of the map are: the position vector, which shows the origin (X) and the direction of positive motion; the dot (which I couldn’t get to work as a small dot); the arrow on the dot, which represents the velocity of the object at that location and time.

That’s where we ended today.