# Engaging students: Graphing parabolas

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Tiffany Wilhoit. Her topic, from Algebra: graphing parabolas.

How did people’s conception of this topic change over time?

The parabola has been around for a long time! Menaechmus (380 BC-320 BC) was likely the first person to have found the parabola. Therefore, the parabola has been around since the ancient Greek times. However, it wasn’t until around a century later that Apollonius gave the parabola its name. Pappus (290-350) is the mathematician who discovered the focus and directrix of the parabola, and their given relation. One of the most famous mathematicians to contribute to the study of parabolas was Galileo. He determined that objects falling due to gravity fall in parabolic pathways, since gravity has a constant acceleration. Later, in the 17th century, many mathematicians studied properties of the parabola. Gregory and Newton discovered that parabolas cause rays of light to meet at a focus. While Newton opted out of using parabolic mirrors for his first telescope, most modern reflecting telescopes use them. Mathematicians have been studying parabolas for thousands of years, and have discovered many interesting properties of the parabola.

How could you as a teacher create an activity or project that involves your topic?

A fun activity to set up for your students will include several boxes and balls, for a smaller set up, you can use solo cups and ping pong balls. Divide the class into groups, and give each group a set of boxes and balls. First, have the students set up a tower(s) with the boxes. The students will now attempt to knock the boxes down using the balls. The students can map out the parabolic curve showing the path they want to take. By changing the distance from the student throwing the ball and the boxes, the students will be able to see how the curve changes. If students have the tendency to throw the ball straight instead of in the shape of a parabola, have a member of the group stand between the thrower and the boxes. This will force the ball to be thrown over the student’s head, resulting in the parabolic curve. The students can also see what happens to the curve depending on where the student stands between the thrower and boxes. In order for the students to make a positive parabolic curve, have them throw the ball underhanded. This activity will engage the students by getting them involved and active, plus they will have some fun too! (To start off with, you can show the video from part E1, since the students are playing a real life version of Angry Birds!)

How can technology be used to effectively engage students with this topic?

A great video to show students before studying parabolas can be found on YouTube:

The video uses the popular game Angry Birds to introduce parabolic graphs. First, the video shows the bird flying a parabolic path, but the bird misses the pig. The video goes on to explain why the pig can’t be hit. It does a good job of explaining what a parabola is, why the first parabolic curve would not allow the bird to hit the pig, and how to change the curve to line up the path of the bird to the pig. This video would be interesting to the students, because a majority of the class (if not all) will know the game, and most have played the game! The video goes even further by encouraging students to look for parabolas in their lives. It even gives other examples such as arches and basketball. This will get the students thinking about parabolas outside of the classroom. (This video would be perfect to show before the students try their own version of Angry Birds discussed in part A2)

Resources:

Parabolaonline.tripod.com/history.html

http://www-history.mcs.st-and.ac.uk/Curves/Parabola.html