Tag Archives: Parametric Equations

Entire Lesson Videotaped: Intro to Parametrics

On a whim, I decided to videotape an entire 45 minute lesson in one of my classes. The only thing I had on hand was an iPad (2nd Gen), so the video quality is low, but I’m also kinda banking on that so I don’t have to blur out students’ faces.

Other information possibly of importance:

  1. There are 15 students in this Precalculus class.
  2. This class is the last period of the day. [1]
  3. Yes, that is my principal who strolls in at [29:43], and yes he picks up a student’s guitar and starts playing in the last 10 minutes of class.   (Oh, and it was his birthday.) Don’t you wish you had a principal as cool as mine?

Outline of the Video

[0:00] to [3:46] Waiting for class to start. (I should have edited it out, but this is why the video starts at [3:46].

[3:46] to [5:40] Waiting for student let out of choir to get to my room (they’re late most of the time because our choir teachers let them out late).  Because I have all these students for Chemistry, we discuss a little Chemistry while waiting for everyone else to get here.

[5:40] to [8:36] I show students how they can find all the standards from the class on my website.  We also discuss Inverses of functions and they convince me to give the quiz on Tuesday instead of Monday of next week.

[8:36] to [12:30] 1st Act: I develop a reason for Parametric Equations and we do a really rough experiment of a student walking into the room.

[12:30] to [31:47] 2nd Act: Through questions I build an intuition for Parametric Equations through graphs and the measurement of our “experiment”.

[31:47] to [40:04] 3rd Act: We answer the questions I provided for them at the start of the lesson (although I didn’t vocalize them, and I didn’t have a “hook” for them like your typical good 3 Acts lesson. We look at two ways to use technology to graph this equation and I give them two of these types problems for homework (see the sheet below). I use the TI Calculator because they’ll need to know how to use that for most standardized tests. I use Desmos because it is awesome and easy to use (and way cooler than the TI Calculators).

[40:04] to [50:03] I promised them from the day that I would do the Fibonacci Magic trick.  If you haven’t seen it, here’s a video of it being done, long with an explanation of how to do it (however, I don’t like his explanation of how to multiply a 3-digit number by 11).  If you prefer to read, here’s an good explanation of how to do it.

Supplemental Materials

Since the board is hard to see in the video, here are two pictures of what I put on there.  For the most part, the black is what I had up before class started and green is what I added during class.

Picture of Classroom

Four Representations of a Parametric Equation

Here’s the worksheet I gave for homework.  Notice how I set up the board so all 4 parts match the worksheet.

Please leave feedback on my lesson and on my teaching style: both constructive and destructive comments are welcome, so please let me know what you think!

 

[1] The students recognize their tiredness at this point and frequently complain when I ask them to do a particularly mentally challenging problem or task.  I suppose I am fortunate that they recognize this, though I wish they had a bit more motivation and didn’t use it quite so often as an excuse.  Fortunately these are all good kids who try despite their tiredness, though they have vocalized to me that they wish this class was taught earlier in the day.

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