## Precal files: Conics

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First of all, thanks for all the great comments/tweets/retweets about yesterday’s post. I want to be clear that I love the #MTBoS and I know everyone in it genuinely cares about improving math education everywhere, just we sometimes have a tendency to get a little bit evangelical about our beliefs.

Ok, now back to some boring ol’ Precal files! (See more files and FAQs here) How about some conics, eh?  This chapter really shows that I’m a visual learner/teacher at heart!

First, circles:

(File here) With some homework:

(file here) Then graphing parabolas using the focus and latus rectum (obvious proof that whoever thought up these labels did not think they would be taught in high school).  We started the day by making patty paper parabolas.

(file here) Instead of trying to memorize 1,000 different formulas in order to write an equation, we just draw a picture and find the important stuff from there:

(file here) Let them loose on #8 and see how many will tell you that the focus is at the origin.  (Spoiler alert: all of them).  At some point during this chapter, we also derive the formula for a parabola.  Hint: derive it with the vertex at (0, 0) and then just talk about how we can move it around with (h, k).

Then ellipses:

(File here) I need to update this answer key because instead of memorizing the focal length formula, we now draw the right triangle and label.  Then it’s time for writing equations:

(same file as above)  Homework:

(file here) And last, but not least, hyperbolas!

(file here)  Oooh, and this one is updated to show the right triangles.

The next day is a fun one.  We start off with this desmos file, which is totally mesmerizing (I had to use “p” instead of “e” because turns out desmos thinks e is a number!  Silly desmos, how could a letter be a number?)  We also talk about degenerate conics for about 2 minutes.  Then we talk about decision tree flowcharts and I usually show this one:

And then I tell them that secretly this one from buzzfeed is my favorite and should be dropped from the skies:

Then I tell them that they need to make their own flow chart to determine conic sections given an equation.  Then we go through this powerpoint and check that the flow chart works, making modifications as needed.

(file here) Ok, most of them are more straight-forward than this one, but I gotta challenge them sometimes, right?

Homework:

I also love to spend some time with conic cards during this chapter–if you haven’t tried them, you need to!  I’m planning on using them almost exclusively to teach the chapter next year in Algebra II.  But for now, let’s wrap it up with a study guide!

And a review powerpoint:

Now if you want to get super extra teacher bonus points, may I direct you to Julie’s Rice Krispie Treat conics?