John and Corey plot brightness of a mini light bulb with a vernier light sensor vs. voltage of a variable power supply. They get a parabola, as they predicted. |

I'm trying to teach my freshmen to predict what a graph looks like. We are well used to using equations like

*V=IR*and*P=V*, identifying the constant value, and drawing arrows to show which quantities increase or decrease. Now I want them to be able to sketch graphs.^{2}/R
With these types of equations, we're only going to get one of about four general graph shapes. Although I don't describe them in words to my class, for you I'd call them a sloped line, a parabola, a hyperbola, or possibly a flat line. You can see these, with my very simplistic description of how to know which one we're looking for, here.

The day after I hand these out, we do an in-class circuits graphing exercise in which students are asked to predict what four different graphs would look like:

* voltage vs. current for constant resistance

* current vs. resistance for constant voltage

* brightness of a bulb vs. resistance at constant voltage

* brightness of a bulb vs. voltage at constant resistance

The beauty is, each of these experiments can be set up very easily in our laboratory. I have "decade boxes" which allow you to dial any resistance you want, from 1 ohm to 100 kilo-ohms.* I have vernier light sensors, which measure brightness in lux.

** careful... on the graphs that DON'T include the light bulb you have to use kilo-ohms rather than ohms so that the power dissipated by the resistance box doesn't exceed a quarter-watt. Twice today a student accidentally turned the resistance box to zero, causing the resistor box to smell bad because it was starting to burn off the insulation.*

In order to make this a relatively quick exercise, I provided a blank and scaled graph on the back page of each handout. (Check the link above to see. You may use these in your class.) The key is, FIRST the students had to predict what the graph should look like; THEN, they had to do the experiment. And sure enough, the graph looked like we expected.

I always tell my students, "don't let the smoke out, we work hard to put that smoke in those resistors/decade boxes/whatever."

ReplyDeleteI'm curious what your students make of the decade boxes. Do you show them how they work? Are they just "black boxes?"

I love the approach of getting your students to try to predict what a graph will look like. For me, I always think of things graphically, even if I'm not encouraged to. I have a strong connection in my head between the word parabola, an actual parabola, and the concept of x^2. What about your students? Which of those three do that have the strongest connection to?

They're just black boxes. Variable resistors, if you will.

ReplyDeleteInteresting question... I've always found that my students label any concave-up increasing graph "exponential," despite all evidence to the contrary. So I avoid labeling these graphs with a word at all. I say "When the arrows go in the same direction..." -- that is, when they can show algebraically that the horizontal and vertical axis variables increase or decrease in tandem -- "...but one of the variables is squared, the graph looks like this" -- and I draw the parabola. By the end of the year my students have the strongest connection, therefore, to the concept of y=x^2.