Circuit building challenge -- a last-minute class idea that worked

On Sunday night when I went to bed, I had no clue what to do on Monday in conceptual physics.

The problems were, about a quarter of my students were going to be on a field trip; and everyone has half-expected the headmaster to declare a free day each day since a week ago Wednesday.  I know enough to plan for the spontaneous one-day vacation by padding my lesson plans.  This year, though, the free day never came.  So I was out of material, and I couldn't just push on to a new topic with so many folks gone.

A day like this calls out for "enrichment."  Show a Julius Sumner Miller video.  Read a chapter of Surely You're Joking, Mr. Feynman.  Play "Crayon Physics Deluxe."  In the shower Monday morning, though, I had an even better brainstorm for freshmen in a circuits unit.

We have taught the freshmen how to deal with resistors in series and in parallel.  However, rather than make explicit calculations, we have taught the art of ESTIMATING the voltage across each series resistor, and the equivalent resistance of parallel resistors.  Why not, I thought, use my extra day of class to refine my students' estimation instincts?

On the board, I listed each of the resistor values I have available in my lab, including 130 ohms, 68 ohms, 57 ohms, 47 ohms, 41 ohms, 20 ohms, and 15 ohms.*

*Okay, really these are all KILOohm values.  I can't use 41 ohms with a 14 V battery, because that would dissipate 4 watts with quarter-watt resistors, and then Bob help us all.  But the 9th graders don't have to know that, since we're not measuring current!  I called a 41 kiloohm resistor a "41 ohm" resistor; all is peaceful, and all measurements are correct.

I handed each group of two a sheet that said:

You have a 13.8 V battery.  Build a circuit in which one resistor takes _____ V (+/- 0.3 V) across it.  When you have it correct, draw a diagram of the circuit in the space below.

In the blank I wrote a random number between 1.0 and 12.0.  They were allowed to use any combination of resistors.  At first they tried to make calculational guesses; finally they figured out that the best strategy was to just choose some resistors, try it, and then choose some new resistors.

What a wonderful exercise!  It was modeling at its purest... eventually each group got the intuitive idea of a proportional distribution of voltage across series resistors.

Next, they got a different sheet:

Build a circuit which has an equivalent resistance of _____ ohms (+/- 1 ohm).  When you have it correct, draw a diagram of the circuit in the space below.

This time, the number was between 3 and 100.  I made sure that the answers were never truly trivial, i.e. equal to one of the resistors in the box.  Some groups even figured out -- with minimal if any prompting! -- that they could get a 10 ohm resistor in series with a 20 ohm resistor by using two 20-ohmers together in parallel to get the 10 ohms.  This even though we never once discussed combinations of resistors in both series and parallel.  

This day turned out even nicer when I found out that too many students hadn't completed their quiz corrections from last week.  The ones who were done with corrections got to play with circuits, earning candy and extra credit for each successfully built circuit; the others got to sit in the meeting room finishing corrections before attacking the circuits.