Even after teaching all of grades 7 through 12, I still LOVE teaching 8th-graders the best. (This is my 5th year teaching 8th-graders.) They have just accumulated enough algebra under their belts to be able to do rich explorations, and they are still so naturally curious about the world. They are like math ninjas, always ready to pull out their math skills to apply to the world at a short notice, and never intimidated by the look of a problem.
In the past couple of years, I realized that it's a real shame that we don't do modeling with three variables in middle-school math. It's a shame because it would be such a terrific tie in to the scientific process, to show how in mathematics you can also hold one variable constant while examining the effect of another variable on the output, and vice versa, and then in the end generalize the results into one grand conclusion. (I realized this because, looking at the past IB portfolios, this is a required skill for 11th- and 12th- graders. This was news to me as a person coming from the American curriculum.)
This year, I decided that I will try to remedy this gaping hole in our curriculum by exposing my 8th-graders to a new assignment. Take a look! They will be completing parts of this at home, then bringing it to class for discussions as a group. And then they will take more of it home to do. Eventually, when all kids feel comfortable with the process and the results, they will write it up like a modeling report. (We have already written one lab report this year based on Dan's awesome activity, and they found it very challenging / a great learning experience. In that lab, they had to learn how to define variables, collect data, determine the type of regression, perform regression, interpret results, make mathematical predictions, test their prediction, and then do error analysis. We followed it up with a very rigorous write-up process that included carefully critiqued rough drafts and a day spent on discussing how to create / insert graphs using GeoGebra and how to structure their writeup in a logical sequence.) Since I am a firm believer that kids learn more through writing about their understanding, the gears in my head are already turning to think about this next modeling assignment.
Anyway, I am VERRRRY excited about this three-variable assignment. Since the topic is already abstract, I kept the patterns linear to make it more accessible to all kids. But, I am very hopeful that it could turn out to be an awesome learning experience.
Addendum: For you new readers, this analogy is what I am going to use to kick off the introduction of 3-variable relationships in the real world.