When teaching garage physics, I make sure that each kid uses a multimeter.
Yes, start with the continuity beeper. Perhaps the most handy part of the meter.
Now, pass around a few resistors: 10 ohms, 50 ohms, a hundred, etc. A few are little half-watters, a 5 and 10 watter, maybe a honking 25 or 50 watt resistors. Measure their resistance -- does the meter agree with the resistor's markings? Does the physical size of the resistor say anything about its resistance?
Now set up a battery - what's its voltage? Clip it to a resistor and measure the current. Did Ohm get it right?
For icing on the cake, get the kids to hook a few resistors in series or parallel. Is Kirchoff smiling?
One joyous occasion, I scribbled a complex series/parallel circuit for my 8th graders; one girl thought about it, and went ahead and simplified the circuit - after numerous calculations, determined that the total resistance should be 15.7 ohms. Three other kids took up her challenge. They got a handful of clipleads and built the circuit. After 15 minutes of connecting and arguing, they measured the resistance of the network. To everyone's amazement, the multimeter read 15.7 ohms. One of those classroom experiences that the teacher never forgets...
At the end of the class, each student keeps her multimeter ($10 at Al Lasher's in Berkeley).