As we headed into Spring Break, it was time for a project in AB Calc. I have been trying to stress curve relationships throughout the year. Early on we talked generics, how to indicate a minimum, maximum, and point of inflection. Then came integrals, absolute minimums, and absolute maximums. When we moved into position, velocity, and accleration, I hit those contexts again and again. By far, this is the biggest thing AB students need, how are the interactions between a function and its derivatives the same regardless of context.
Particle motion was a huge problem last year. I found myself having to do a lot of reteach prior to the AP exam over concepts I thought we had gotten (change in direction, particle at rest in particular). In combination with my new thoughts on FRQ, I'm trying to review as we go and combine ideas as much as possible.
Student's objective in this project was to create a polynomial, restrict it, and discuss a variety of properties. Specifically, the difference between a change in position and total distance traveled, where and how a particle is said to change direction, and how to determine what's required for a speed increase/decrease.
The projects were all fairly similar, but here's a particularly outstanding example:
Giving students ownership of the process had really been the best move for my projects. Because there were so many opportunities for variety, students were able to have great conversations about they were or were not meeting the requirements. They also learned a lot of handy Desmos along the way (shading, integrals, absolute value). Project days are my classroom at its very best. The whole room buzzes and I just get to float around assisting as necessary.
Students did outstanding on the free response questions related to this topic. Well, not like everyone got a 9/9 outstanding, but every student got the concepts and had something to contribute when it came to finding the solutions. I'm hoping to roll our review as we go strategy into rate functions next.