Planning for Serendipity
Ever come across a device, particularly one that appears to be obsolete, and end up creating an interesting lesson with it? That "lucky accident" happened to me recently when I found a light meter that probably was used when photographers had to set their camera's shutter speed and aperture rather than rely on electronics embedded within their cameras.
After a brief "I wonder what this does" I realized the small box I held measured light intensity. I was unfamiliar with the units but noticed a needle swing to higher and lower numbers when I pointed it toward or away from a light. A few mental clicks later I realized I could use the device to test something I had been told was true but had no data to substantiate myself how light intensity changes with distance from the source. The following table (from a TI-83+ calculator) lists the data from roughly measuring how far the receiving end of the meter was away from a light source (distance, in L1) and the reading on the meter (brightness, in L2).
Figure 1
Data table within the graphing calculator.
Adjust the graphing WINDOW to show all the data and go into STATPLOT to activate Plot1. We see the familiar "falls off as the inverse square" plot, as predicted by my dusty physics books.
Figure 2 Suggested window dimensions for the given data. |
Figure
3
Turning
the plot
ON within STATPLOT |
Figure
4
Scatter plot of the data. |
Figure 5
Equation drawn over data.
For me, it was satisfying to gather data that matched an inverse square. The surprise was realizing there had to be a coefficient from which the real-world data had meaning. I learned a great deal by first trying several numbers then working backward from the data points. I solved the equation for the coefficient, meaning it should equal the distance2 * brightness. The first two data yielded 560000, which provided a visually acceptable model. Knowing the actual units of the device would provide even more meaning, which I will leave to my students to explore!
My next step will be to turn the device over to my Math I students to perform a more carefully executed exploration. They will take more care with the length measurements and record from many more distances. I also have in mind a few other explorations my kids will undertake, one will be to see how closely the wattage of a light bulb is related to the amount of light it gives.
Like me, hopefully you will encounter a device your students can use to create models of some of the basic equation forms they are studying. You can find a wide variety of basic instruments at yard sales, swap meets, online auctions (e.g. eBay.com), and thrift stores (e.g. Value Village). Tell the vendor you are a teacher, show them any school-related identification you have, and ask if you can have a discount on the device--it often works for me! Get an interesting tool (or toy, if you will) and try to see what learning situation you can make of it.
Please send me your ideas, lesson plans, and student results to post on the WSMC Website in our new Teacher Exchange area--we can all learn from each other and I look forward to hearing from you.
Richard
T.
Edgerton, Ph.D.
Seattle
Public
Schools