The screaming egg of a good bungee
None of these projects are my creation and as much as I would love to give due credit for this one, I really can’t remember where I got this from! It has also been adapted and tweaked a lot before getting to what it is now. I have attached the handout to Box.net on the right. One copy is what I give to my Algebra 1A students but since the goals for my former Calc students were a bit different, I modified it and attached that one as well.
Student’s goal: After gathering data on the stretch of the bungee chord for every rubber band added for up to 100 cm, they must use their linear model to predict how many rubber bands will be needed to bungee the egg off the top of the bleacher of 200 inches. The goal is to bungee the egg as close to the ground without having it hit the ground.
Teacher’s goal: For my Algebra 1 class, it is to be able to use a linear equation/model to solve/predict a solution. Not only does the slope of the line show up in how much stretch per rubber band, but the y-intercept shows up in the length of the egg in the harness w/ zero rubber bands.
For my former Calculus students, however, more than just coming up with the linear equation, I really wanted them to be able to formulate what information they needed to gather and be able to come up with a strategy of finding out how many rubber bands they needed for the bleachers while working within their constraint of 100 cm.
Materials needed: Raw eggs (bungee participant), plastic eggs that can be filled (test dummies), candy (test dummy innards), scale to weigh ounces, non-ziplock plastic bags (harness), rubber bands (bungee chord), short tape measure (I used Ikea paper rulers)
Overview of project:
- Weigh out test dummy to equal the weight of the real egg
- Gather how much egg stretches with each rubber band added
- Plot points of rubber bands vs stretch distance
- Come up with a linear equation (by hand for Alg 1, using regression line for Calc)
- Use equation to predict number of rubber bands for bleachers
They usually come out short because they get scared and take off too many. Encourage them to stick to their numbers. The stretch in all the drops also makes their data show the drop to be longer than with the fresh set of rubber bands. *Buy of bag of all the SAME sized rubber bands.* I tried to vary it to see what this class would do with it and it turned out varying too much.
I’ve done this before with my Algebra classes, but this time, I had a whole new goal, which completely changed what I was expecting. For one, I required a write-up of the lab with tons of explanations because I was more interested in the process than the actual equation and result. With this new goal in mind for my Calculus students, I found a very interesting discovery-
My students don’t understand what scientific “error” is. I asked them to explain where there might have been some error while gathering data in this project, as in, explain where they might have lost some accuracy in gathering data and coming up with their math model (like from all their approximated measurements). They, however, kept saying things like “we used 38 rubber bands when we should have used about 20 more.” When I tried to explain what error really meant, they still didn’t get it in the re-write of their write-up. This is so interesting to me because I believe they’re thinking about “error” as they have seen it in their previous years of math, the wrong answer. They kept trying to explain away how many rubber bands would have given them the correct jump instead.
After discussing this with a friend, I think maybe this type of error analysis, as they see in science, is exactly the type of “error” my students should be thinking about in math too. For example, if they get a wrong answer, instead of calling that finality the “error,” the focus of the actual error should be where that error was made back in the process of things.
**New goal for my classes** Have a few regular routines where I give them full credit for explaining where the “error” was made in the process of the math. Maybe I can even coin it to say something like, “the theoretical outcome is 3. One student’s actual outcome came out to be 4. Where could there have been some error?” It’s very scientific this way, no?
I had forgotten how much my students needed structure on explaining mathematical process. They need at least two re-writes before they start to understand what is expected of them. I really wish I could have them journal so much more frequently than I actually do in our two month terms.
I love this thing for my classes. So far, not only did it give me a better Calculus Camp video this year, it makes projects so much more fun. The snapshot above was taken off a Flip recording. We determined how low the eggs fell by video recording it and then analyzing the video frame by frame. In the next project, the M&M Catapults, we use the Flip as a timer. It’s much more accurate than stopwatches this way.
Our very first bungee
One sweet landing