## Alg II Files: Rationals

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My second-to-last post for my Algebra II files! (See more files and FAQs here)You can tell by how long I’ve procrastinated that I’m not really a fan of what I do for this chapter. Each year seems to get a little bit better, but I would never classify put it in the “win” column. In other words, feel free to take any of this and make it awesome. Then let me use it. 🙂

The first few sections don’t have note taker makers, because the problems need space to be neat and tidy:

Some notes on my notes: At the very top, it’s hard to see, but we start off talking about how we reduce 12/15. We don’t subtract 10 from each and say it’s 2/5! We talk about invisible ones.  This year, I want to focus on the fact that in the expressions, I can substitute any value for x and you will get the same value in the beginning expression and in the final expression. Magic!

Also, I talk about restrictions as “warning the villagers.” What if someone came along and put 5 into x/(x-5)? THE WORLD WOULD ERUPT INTO FLAMES.  And sure, I know *you* wouldn’t do that, but what if some innocent villager came in off the street and started putting numbers in? We need to warn them! This year, I also want to pull in the graph and talk about how the original has a hole at 5, so in order to be equivalent, the reduced one also needs a hole, which we make by excluding 5 from the domain. (I *just* realized this fact in the last few weeks.)

Some homework:

Then…can you hear the jaws music….

Then some practice with every operation as either a worksheet

or as a step-by-step powerpoint (great for whiteboard practice)

Let’s solve some now!

I’m not *in love* with just crossing those denominators out, but haven’t figured out anything better yet.

Some practice:

(file here) And a study guide for these three sections:

(file here)

Some inverse graphing:

(file here). Hint: make a t-chart by listing pairs that will equal k. Super easy!

Inverse/Direct/Compound variation:

Powerpoint to go along with NTM:

(file here)  Yes, I’d like to do a lot more with this, but this chapter is always rushed since it’s the last one before we have to start trig at the end of the year.

Homework:

Then it’s time for graphing rational functions. I like what I do, but I think I want to streamline the process a bit–we don’t have to do all of these by hand!- and bring in some of Sam’s stuff.

We spend the first day talking about end behavior and points of discontinuity:

(file here) Why, of course there’s a powerpoint!

Then the next day we review the first two steps, then jump into graphing them. This goes a lot better than just throwing everything at them in the first problem!

And yes, another powerpoint:

(File here) There’s even a powerpoint to check the homework that’s at the bottom of the NTM-file here!

Then it’s finally time for the study guide (note: this does repeat problems from the first study guide!)