# WCYDWT: Geometry in Geography

As I was flying home from the 2012 NAIS Annual Conference in Seattle, I looked out airplane’s window and saw these patterns in the farmland below. I’m going to figure out a way to use them in my geometry classes. We just finished learning about areas of polygons and circles, so I’m sure these pictures can spark some interesting questions and investigations.

By the way, WCYDWT stands for “What Can You Do With This”, a teaching technique pioneered and championed by Dan Meyer. There’s a permanent link to his blog at the bottom of my home page.

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# When Are We Ever Gonna Use This?

How many times have math teachers heard that question? I question the assumption underlying it – that math should only be learned if it has “real-life” application. I wonder if my colleagues who teach literature have to deal with that! Of course, math is worth studying in and of itself, just as poetry is.

That said, I do try to make connections between abstract mathematical concepts and things my students encounter in their lives. So, as my precalculus students wrapped up their investigations into parabolas, ellipses, and hyperbolas, we looked at some examples of how they occur in the real world. We took photos of the water coming out of a drinking fountain, the fireplace of our school’s library, and a flashlight’s beam when it is next to a wall. Then, we pasted the photos into Geometer’s Sketchpad, placed a grid over them, and came up with functions that model each conic section. They got very excited as they saw their function plots match the photos so closely. Hmm, maybe there is something to these crazy conics after all….

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# Conic Sections Are Everywhere

My Honors Precalculus students just wrapped up a unit on conics sections: circles, parabolas, ellipses, and hyperbolas. As a final project, I had them find examples of each type, and take pictures of them. They came up with some very creative responses:

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