I assigned a new project this year: Rollercoaster Project I found it online but forget where to give you credit (sorry). It looked really cool, so I thought I would give it a try.
It is two parts. First, it asks students to answer about 17 questions on rollercoasters and the behaviors of the polynomial. It was pretty straightforward.
The second part asks them to design their own with some specifications like it has to start at 250 feet up, last for a least 4 minutes, have a double root, go underground, have at least one real root, and at least one (two) imaginary roots.
I originally had this due right before Thanksgiving but we had a test then too and kids were focused on that, as they should be. Also, I had only had 2 out of 48 kids come for extra help with questions on it and their questions were showing me their struggles. I thought, uh oh, what had I done. Is this too hard for them? Is this too much for them? So, I decided to extend the deadline to this Thursday. I had students come for extra help today and they were doing it! And, they were sticking with it. They were getting frustrated at points, but they were working together and helping each other find their mistakes.
Oh, and the thing that made this wonderful was desmos.com. The kids love the site. We figured out how to adjust the axes so we could see the rollercoaster they were graphing. They started in factored form. Then, they needed to figure out how to get their y-intercept to be 250. They graphed it. It looked good. It looked like what they intended it to look. However, I wanted it in standard form as well. And, this is where they were running into trouble. They did a lot of work and then entered it into desmos as a different colored line and they weren't the same. Ugh! Some had the graph as x<0, why? how come? Oh, they wrote their factored form as (x+2) etc. So, she needed to change her signs. Others found small sign errors or dropped x's or incorrect multiplication. But, they stuck with it. They persevered and let me tell you....they were excited when they finally saw their green line and their purple line become the same line on desmos! So cool. They could see it worked! And, this was all AFTER school!
It was fun to work with them. However, I am not looking forward to grading 48 projects.