I’m heading to Seattle this week for the National Association of Independent Schools’ annual conference, so I am preparing screencasts for all the classes I’ll be absent from. This one is for my geometry students – we just wrapped up areas of polygons and circles, so it’s time to add another dimension! Prisms are the simplest solids to work with, so that’s how I introduce surface area and volume. All the dirty details are included in the screencast below:
Something new I’ve been doing this year is have some music playing in my room as my students enter at the beginning of a class. They have responded most positively to classical music, believe it or not. When we are doing collaborative work, they usually request solo piano music (Carol Rosenberger’s albums are very popular), Mozart, or Bach. Another favorite is Christopher O’Riley’s solo piano transcriptions of Radiohead songs (his rendition of “Let Down” is the track playing above). Having this music in the background definitely sets an atmosphere of high intellectual pursuit, and I believe my students are more productive in class because of it.
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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This screencast is all about polar coordinates. They are merely another way of locating points in a plane. Rectangular coordinates are limited to moving horizontally and vertically from the origin until you reach your point’s location. With polar coordinates, you stand at the pole (the origin), rotate through an angle until you are facing in the right direction, and walk out the specified number of units (the radius).
Why do we need another way of plotting points? Well, rectangular coordinates are very handy, but sometimes a relation’s or function’s equation is far simpler when written in polar form. Take circles: in rectangular form, a circle centered at the origin with a radius of 3 has the equation x^2 + y^2 = 9. The same circle in polar form is r = 3!
