Alg II Files: Rationals

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:

Rational Functions from megcraig.orgRational Functions from megcraig.org 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:

Rational Functions from megcraig.org(file here)

Then…can you hear the jaws music….

Adding and subtracting!

Rational Functions from megcraig.org Rational Functions from megcraig.org

Then some practice with every operation as either a worksheet

Rational Functions from megcraig.org(file here)

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

Rational Functions from megcraig.org(file here)

Let’s solve some now!

8_3 8_3 pg 2I’m not *in love* with just crossing those denominators out, but haven’t figured out anything better yet.

Some practice:

8_3 HW

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

8_3 SG(file here)

Some inverse graphing:

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

Inverse/Direct/Compound variation:

Rational Functions from megcraig.org(file here)

Powerpoint to go along with NTM:

Rational Functions from megcraig.org

Rational Functions from megcraig.org(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:

Rational Functions from megcraig.org(file here)

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:

Rational Functions from megcraig.org(file here) Why, of course there’s a powerpoint!

Rational Functions from megcraig.org Rational Functions from megcraig.org(file here)

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!

Rational Functions from megcraig.org(file here)

And yes, another powerpoint:

Rational Functions from megcraig.org Rational Functions from megcraig.org

(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!)

Rational Functions from megcraig.org(file here)

So what are some of YOUR magical ways of staying rational while teaching rationals?!? Leave a comment or tweet me your secrets!

One comment on “Alg II Files: Rationals

  1. Yeah, I agree with you: don’t just have them cross the denominator out on the one side and multiply it onto the the other side. Until they “get the why of it” I’d suggest having them write the recip. of the denominator you want outtathere on both sides of the equation and consider the n and the d as a form of 1, the identity element on the side you want gone. So many students at this age only know plug and chug rather than the why and it hurts most of them down the line.

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