Grey+Lancaster

My name is Grey Lancaster and I am a senior at Clemson University majoring in Mathematics Teaching.

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Real World Math




 * The Flat Earth**

An Exploratory Lesson

Grades: 8-12

Spherical Geometry (Non-Euclidean)

This lesson uses Google Earth to explore geometric relations of a sphere. It examines postulates and theorems that are accepted in Euclidean Geometry and compares them to there equivalent relations on a sphere. Many times this previously held ideas don't hold in which case students form new ones for the new geometry.

What I like about this lesson is it gives a very hands on approach to a topic that would be very foreign to students. Many students do not even realize a different type of geometry exists and it is often hard for them to explore other types simply on paper. Google Earth gives them a good way to see spherical geometry and see where spherical geometry could actually be a better type of geometry to use. The biggest weakness I see in this lesson is that it may require a little more guidance from the teacher than just the Google file gives students because this is such a new topic for them. I think I would intro non-Euclidean geometry in my classroom first and then show them this, not let this be their first exposure.

Initially I was very excited about the ease of creating objects in sketch up, however I felt like it was very limited for math applications because it was difficult to measure abstract objects like cones and such. My goal was to create a cone so that I could show how different conic equations were formed and sketch up didn't enable me to do that. Maybe I'm a little biased against it because the particular problem I wanted to do wasn't possible. The question I finally ended up making was having a cylinder and a cone drawn, and then having my students find the volumes of each, and finally compare the ratio of the volumes which should come out to be 1/3.
 * Motivational Math Slides**
 * Google Sketch Up**