I loved doing the rational functions activities with my Precalc kids!
1. The laser lab was FANTASTIC. I have to say that in El Salvador, it's not easy finding laser pointers. Even though my school has awesome resources and even a full-time driver to whom I can make requests to run school-related errands for me during the day, he was only able to find two $16 punteros laser (muy costosos!!). In the end, I had to run around and borrow make-shift laser pointers that were originally part of some fancy schmancy USB powerpoint clicker device. The science teachers were awesome and let me borrow 4 of their fancy clickers, plus our awesome head librarian had two in her presentation technology collection, plus I had my two very-expensive $16 pointers. Made just enough for a class set! Yay.
But, all of the hassle was super worth it, because in the end, the kids collected beautiful data that fell neatly into a rational function pattern, and we discussed the conceptual linking between where the domain breaks, the amount of vertical shift, and our laser setup. (The domain, which represents the laser source's horizontal distance away from the wall, is x > 30 or so, because the activity instructions indicate that the mirror needs to be placed horizontally 25cm away from the wall, and realistically it's hard to stand/place the laser source right on top of the mirror when you're doing the laser measurements, since the mirror rests on top of a platform made of textbooks, that juts out another few centimeters horizontally. The range of the function, which represents the height of the reflected laser beam on the wall, is y > 15 or so, because the activity instructions indicate that the mirror platform be about 10cm high. Our kids estimated that the lowest point the reflected laser beam could reach on the wall is just above that, or ~15cm. This gave them the partial equation y = a/(x-30) + 15, and all they had to still do was to plug in a point to solve for a.)
It was super!
2. And then today, I ran another lab with my Precalc kiddies on resistors. (See below.) Previously, I had used Megan Golding's resistors questions as intro to solving for equivalent resistances. We did that intro on Friday. Today, for the actual lab portion, my kids first took color-coded resistors and used ohmmeters to find out the resistances across each individual resistor. (Since not all resistors that are color-coded the same actually have the exact same resistances AND since the class needed to share a small stack of resistors, I made the kids grab two of each color to find their average resistance to use in the calculations/predictions. That way, it didn't matter much later on if they grabbed another resistor of that color; its resistance value would be roughly the same as the average resistance they had found earlier.)
I then gave them some series and parallel situations, and they had to make a prediction for the equivalent resistance, and then use the ohmmeter to verify their prediction. It was super cool; the math on paper really came alive for them! They got to see their calculation results match what was popping up in their ohmmeters.
Another cool (but tricky) part of the lab was teaching kids to read ohmmeters. I'm not sure if all ohmmeters do this, but the ones I had borrowed from the physics teachers have a dial of different settings. Depending on the resistance value, you have to change the position of the dial to measure a different maximum resistance, and the result actually takes on different decimal places / different units. After about 10 to 15 minutes, kids were starting to get the hang of reading the different settings for the correct units, but in the beginning it was quite a bit tricky! (The physics teacher was really pleased when I told him this afterwards; he said it's good practice for the kids to read/interpret the outputs from a machine such as an ohmmeter.)