In my Calculus class today I used a Ranking Task to help get at my student’s understanding of Instantaneous Velocity. Students were presented the following graphs of *x*(*t*), which was described as a position on the *x*-axis (in feet) at time *t* (in seconds)

I asked them to rank a couple of things from greatest to least. Most importantly I asked:

What is the ranking from greatest to least of the Instantaneous Velocities of the objects at *t* = 2?

This was an important question in my class not because it was so marvelously crafted, but because it brought out some major misconceptions that my students were holding onto. Specifically, about half of the students thought the Instantaneous Velocity could be found by looking at the “y-value” of the graph.

Yesterday I had no idea that this misconception was floating around in my class, but because I was lucky enough to ask the right question today I was able to address an important issue.

File: Ranking Task-AV and IV

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