Prior to leaving my kiddos alone for two days before their test (I was in a wedding), I spent our last bit of time together "teaching" them how to identify conic sections. Now, I spent a good amount of time planning the pieces to this lesson as I was being doubly observed (my resident educator mentor as well as one of my administrators).
The night before, I assigned a small investigative homework assignment where the kids were given four equations and asked to state which equation was which conic section. The goal was to have them not do this algebraically but of course, they did as they hadn't known any other method.
When the kids entered the room, they were split into groups. In these groups, I had the kids discuss which equation they thought was which conic section. After about 5 minutes of justifying these to one another. The class shared their results and they typically struggled with the hyperbola and circles. With each equation, we discussed qualities that made it a particular conic section all the while, I was recording these observations on the board.
Their next assignment, as a group was to create a flow chart that would help a fellow student determine which conic section they were looking at. Now, as I have previously mentioned, my students weren't quite sure what dominos were so I also had a discussion about what a flow chart was. After creating an appropriate definition, I provided a slightly humorous example that I added some humorous commentary to.....
Some of my kids questioned whether or not we actually went through this process. I also added in my thoughts on the second question, if you are carrying an empty water bottle when you ask the question, what do you think the answer would be..... They had never thought about that before... hilarious.
Anyways, so my kids then created the flowcharts and my favorite part was that nearly none of them were designed the way that I would have created them. And that was okay because it lead into a difficult discussion about the different between "2" and "-2" as being two different coefficients. Many of the students forget that they are two different numbers as they do not regard the sign as part of the coefficient. When this was addressed, I asked the students how they could account for this on their flow chart.
After the flow charts were created, a member from each group lead us through the questions they asked based upon a random equation that I provided to them. This allowed for us to see any mistakes they may have encountered.
Halfway through the day, I realized that the kids needed more practice before getting into the game that I had set up so I added classwork practice and the kids were really excited when they were getting answers correct that they had taught themselves. In fact they were so excited, that during the game, we were a little too loud and had to have quiet time, sad face :( but it was still kind of awesome about how pumped they were!
The final activity that I had the kids do was play the flyswatter game described by a function of time blogger. I had pinned this activity a long time ago and couldn't wait to use it as the lesson itself, was pretty easy and desired something more. For my kids, I gave them much more difficult conics (thus, the reason I added classwork practice) and I don't include rational functions as originally described in the game. I've included my equations below. Be very thorough in your classroom expectations, you have been warned!
The kids LOVED the lesson that day and I could verify that as we had school observers come into my classroom at the end of the lesson (this happens frequently at Metro) while the kids were taking a schoolwide survey, boring. I sadly said to the adults that they had missed all of the excitement when.... One of my students enthusiatically jumped up and explained to them the entire day's lesson. She ran over to me asking for her groups' flow chart so that she could explain it to the observers before telling them about the fly swatter game.
Overall, I LOVED the lesson and got great feedback from my administrator. She offered that I should add a postassessment onto assistments for my own feedback, which I proceeded to create that afternoon for next year :) Oh, and this semesters' algebra 2 class LOVED conics, unlike previous classes. GO CONICS!!!