6. Battery Operated Cars

It is very interesting that small battery operated toy cars (not fancy “remote control” things; just one or two AA battery cars) run at remarkably constant velocities. So, students can determine a car’s velocity (different cars will have different speeds) by running it over, say an 8 or 10 meter length, and timing it. Of course, you need plenty of easily obtainable stopwatches for this activity. In fact, today, there are enough computers and iPhones to handle this aspect. Once each car’s speed is known (some are very fast, others quite slow; you want a good variety), there are many different experiments that can be performed.

The following is probably the best: On “Go!” the students will start Car A at some 8 or so meters from the intersection of perpendicular “roads.” The question they must resolve is: At the same time, from how far from the intersection (along the perpendicular road) must they also start Car B in order for the two cars to collide at the intersection? This is a favorite MathLab activity because, needless to say, the students (generally 7th or 8th graders) will go wild when the cars actually do collide, demonstrating that mathematics works! [Colleagues throughout the school will ask what you’re doing that is causing so much fun.]

Many experiments can be performed using these battery operated cars. One extreme one is that even a linear “inequality” can be modeled. Here’s how. Tape, say, a 30 cm strip of paper to the back of a slow car (i.e., give the car a 30 cm tail). Give the slow car a head start, on a faster car, of a prescribed distance. Now run them in the same direction. The question for the students is, over what time interval (or, you can also do, “over what stretch of road?”) will the faster car be “within” the slower car (meaning that the front of the faster car is between the end of the slower car’s “tail” and the front of the slower car).

It is very important that teachers rehearse (both without and with the students) these experiments thoroughly before attempting the “verifying” performances. Almost none of these cars will run straight for very long. Therefore, a student will have to run along side the car with, say, a meter stick, to poke it every occasionally in order to keep it on track. Moreover, a student operating a stop watch will botch the job (or the stopwatch will fail) way too often. Therefore, it is important to have multiple students with stop watches (or cell phones) for each experiment. This way, if a couple of students have to drop out, there are still some working time keepers.

In any of the experiments involving battery operated cars:

Q. There is an obvious real world question. In the first example, how far from the intersection should car B be started? In the second example, over what period would the faster car be “within” the slower?

R. Each of these experiments is solvable by simple algebra. Velocities are, of course, originally determined by the formula rate = distance/time.

V. For each experiment, the empirical verification occurs at the moment of performance. Remember, the students know only each car’s velocity. The answer to all questions are determined entirely by the mathematics. It is only after the student answers are submitted that the actual experiment is run. That is the moment at which the results are verified.

Collaborative School Activities for the Teaching and Learning of Mathematics