If you've been reading my blog lately, you probably can tell that I'm a conic section convert. I'm a conic section hater turned a conic section lover. Confession time. Before this school year, I didn't really know why they were called conic sections. Maybe you're thinking, "Duh, Sarah! It tells you in the name!" Or, maybe you're like me and you never made the connection. Conic means "of or pertaining to a cone." Every single conic section can be formed from a cone. How did I not see that before? I guess I never really questioned why they were called conic sections when I studied them in high school.
This isn't the first obvious connection I've failed to make. A couple of weeks ago, I was in my car, driving to visit my parents. One of the roads that I grew up around in Broken Arrow is known as "County Line Road." Well, technically, it's 193rd E Ave, but everybody just calls it "County Line." As I was driving down an entirely different road, I had an epiphany. It's called County Line Road because it follows the county line between Wagoner County and Tulsa County. How in the world did it take me 24 years of my life to figure this out? It should have been obvious. I was so excited about the realization that I had to call my mom and tell her about my discovery. Instead of laughing or making fun of me for taking so long to realize this, she commented, "Well, I guess you've had more important things to think about than the names of roads." Thanks, Mom! But, I still think I probably should have realized this sooner than I did. Apparently, my sister had realized this because she was less than impressed with my recent discovery. Her reaction was more along the lines of: "How in the world did you not know that?!?" It happens, okay?
Since I didn't want my students to be like me and go throughout high school, four years of college to get a math degree, and a year of teaching without realizing exactly what conic sections were, I designed this foldable to put in their interactive notebooks.
I stole some pictures from online that show how each conic section is created by taking the cross section of a cone. And, I put these on the outside flaps of the foldable.
On the inside, I decided to steal an idea I had seen online. Take paper cones (think snow cones), cut them to form the conic section, dip them in paint, and stamp the conic section. I was going to have students work together in groups of 4. Each student would be responsible for cutting one conic section. All the students would stamp the cut cone in the correct section inside their foldable to form the conic section.
Other people have done it. I read about it from Miss Ruldolph. And, I originally saw the idea on Walking In Mathland. Seriously, you need to follow these links and then come back here to read about my adventures. I promise. It'll make a lot more sense if you do!
The day before I wanted to do this in class, I decided I needed to go to Wal-Mart and buy some paper cones. Did I mention this was back in late January? Either I was looking at the wrong place in the store OR it's a seasonal item. All I know, is I couldn't find the paper cones at two different Wal-Marts. Of course, in retrospect, maybe I should have looked in the sporting goods section where they sell water jugs and the like.
It's okay, I thought, paper cones are just made out of paper. So, I printed off some cone templates on card stock, cut them out, and glued together several cones. So far, so good, or so I thought. Then, I went to cut them. I figured I would start with the circle because it looked to be the easiest. I squeezed the cone shut, made a straight cut, and opened the cone back up to find that I had most definitely NOT made a circle. I tried again. And, again, I ended up with something that was not a circle. I tried cutting an ellipse. It didn't work any better. The parabola came out looking like a hybrid between a quadratic function and an absolute value function. And, let's not even talk about the hyperbola.
Obviously, it can be done because I've seen it on other blogs. But, I couldn't figure out how to cut the cones so they actually formed the conic sections. Needless to say, I ended up scrapping this idea and just jumping into the formulas for various conic sections. If anyone has some advice for how to actually cut the cones, I'd gladly take it. I feel like I must be overlooking something obvious. I think my problem is that I'm squeezing the cone shut before I cut it. But, I'm not sure how to cut the cone without squeezing it shut first. Help!
But, I thought I would go ahead and post the foldable I created in case it would be of use to anybody else. I planned on having my students stamp conic sections on the inside. But, I guess you could have your students write formulas or work out examples.
You can download the file and my other conic section files here.