For the last week and half of school, my non-AP Calculus class is embarking on a free choice final project. The only requirements are that they must use some sort of Calculus, they must use a real artifact (data, a picture, a video, history etc), they must incorporate technology, and they must find a way to present it to their peers.I have been so excited to see their creative streaks and see some of them get really excited about this, especially because I am impressed that they are still energized two weeks away from their graduation.
Here are some of my favorite ideas. Note that some are not very sophisticated, but are interesting nonetheless and I have been supportive regardless, as I want to see them really carry out something that they feel is their own. I will report back on these after a week and a half when they are done.
- COMPETITIVE EATING RATES: A few students want to eat as many chicken wings as they can, but as they go, time when they finish each one. Then they are going to calculate the rate at which they are eating wings at a few points during the eating. Their prediction is that the more wings they eat, the slower they will eat them. I am hoping they will try to fit some sort of exponential function to the data (that might tell them their limit). They are going to compare their rates to that of an actual professional eater.
- ATTENDANCE TO THE HAJJ: The Hajj is the annual pilgrimage to Mecca that Muslims embark on once in their lifetime (or sometimes more). One student wants to look at aerial photographs of the Hajj to determine the area that the pilgrims fill up and compare the relative areas from different years to the relative levels of attendance. Then, she also wants to make functions for an old man, a young man and a woman doing the hajj that will give their position at any time given the size of the crowd in a given year.
- THE SPREAD OF SENIORITIS: A couple of students are collecting data from their friends about their GPA throughout the year to see how real senioritis is. Then, they are going to use the idea of differentials to expand on the data and predict students’ GPAs in future terms (college?) given their current slide.
- DESIGNING A GREENHOUSE: One girl wants to make a model of a curved-roof greenhouse and then use Calculus to find the amount of glass used and the volume. She also wants to do some sort of optimization exploration to see if the shape has to do with using the least amount of glass for the most sun exposure.
- CELEBRITY LAND AREA: One student is using Google Earth to find the area of various celebrity plots of land. Then he is going to compare the Google method to numerical methods (like Riemann sums and trapezoidal sums) and he is going to try to determine how Google’s mechanism for finding area works.
- INFECTION: A student has a game on her iPad where a disease is being spread around the world. I can’t remember if the object is to infect the world or to save it. Either way she is going to pick a few regions and track the spread of the disease through those regions to see if the curves are logistic, and to see how the curves of regions close to each other relate to each other.
- DERIVATIVE/ANTIDERIVATIVE CHECKERS: Two students are going to design a checkers board to practice derivatives and antiderivatives. The checkers will have derivatives on one side and antiderivatives on the other. When you jump a piece, you have to solve a derivative or antiderivative before you can capture the piece.
- GATSBY’S OPTIMAL PARTY: One student is going to design a prompt from Gatsby himself asking Calculus students to optimize his guest’s happiness at a party. I don’t know the details, but the sense I get is she is going to give Gatsby a limited budget and things that he could purchase for his party – I’m excited to see how this one turns out!
And there are lots of other great ideas too! I liked the ones above because they took one of my ideas for a prompt and totally made it their own, or just came up with something totally random that they wanted to do. I’m excited to hear how these turn out. I had a million other ideas too… here is the packet of ideas that I gave them to get them thinking.