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07 January 2015

Adapting an AP Physics 1 question: motion graphs of a student in an elevator

The picture to the right is from the first problem on the 1993 AP Physics B exam.  That problem
asked for calculations and numerically correct graphs of position-, velocity-, and acceleration-time graphs given the force vs. time graph shown.  

When I adapted this problem for my AP Physics 1 class, I took into account two major considerations:

(1) The AP Physics 1 exam is not likely to require twelve(!) sets of kinematics and Newton's Law calculations.  So I need to find and ask about the conceptual essence of the problem.

(2) Short answer questions on the AP Physics 1 exam are only 7 points.  The original AP Physics B problem was graded on a 30(!) point scale*, looking at the results and methodology of each calculation and graph segment separately.  The revised question must be doable in 15 minutes -- that generally means only three lettered parts to the problem -- and scored with "fatter" points.

* The 30-point score was divided in half to get a standard 15-point problem.  This is the only AP Physics B problem in recorded history with such a nonstandard rubric.

The point of this post is not to show you a finished product, ready for the College Board to pick up for a future exam.  Note that I also am not correlating this question to any standards or learning objectives.  No, I'm just trying to respond to the numerous questions I've received about how to write test questions for AP Physics 1, while we don't have much in the way of officially published resources.  This question ain't perfect, but I hope I'm revealing some of my own thought process in writing problems; and then I hope you'll take my thoughts and make them your own.

Here's the revised AP Physics 1 style problem.  The rubric is below, too.  

(a) Describe the motion of the elevator.  In each of the five-second segments, be clear about the direction of motion, and whether the elevator is speeding up or slowing down.  Justify your answer.  [Comment: This question takes a good bit of writing to answer.  But it really rewards students who understand the physical process represented by the original graph.  No one can skate by, or even get partial credit, with just memorized equations.]

(b) On the axes below, sketch a graph of position vs. time for the 20 s shown in in the graph above. 

(c) On the axes below, sketch a graph of velocity vs. time for the 20 s shown in in the graph above.  [Comment:  Parts (b) and (c) are subsets of what the original problem asked, just with no calculational element, nor a justification.  When we do test corrections, I ask for justification with respect to facts about position-time and velocity-time graphs.  But since I asked such a verbally intense part (a), I don't think students would have time to justify these parts as well.]

The rubric I used to grade this problem:

(a)        3 points

1 pt for using N2L to correctly justify that acceleration or net force is upward from 5-10 s, zero from 10-15 s, and downward from 15-20 s

1 pt for describing upward motion the entire time from 5-20 s

1 pt for describing speeding up from 5-10 s, constant speed from 10-15 s, and slowing down from 15-20 s

(b)        2 points
1 pt for curved graphs of any sort from 5-10 s and 15-20 s, coupled with a straight graph of any sort from 10-15 s
1 pt for completely correct graph

(c)        2 points
1 pt for straight segments throughout
1 pt for completely correct graph

Remember, this rubric hasn't been vetted by anyone else; it seemed to work okay when I graded my one class's work one time.  At the real AP Physics 1 exam, we'll be grading three orders of magnitude more student responses than I graded.  I've no doubt that this rubric would have to be amended somewhere, somehow.


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