I created this year a unit on rational expressions and rational functions for some mixed precalc classes. We will end up with 10-11 days, some of them review.

I am proud of the idea. The execution? It will need much refinement. I liked the third worksheet especially (4 and 5, below) but it needs expansion, clarification, etc. The first two worksheets are probably fine as they are, but they are fairly standard stuff.

The first quiz is gimme. I taught most of these kids to factor 3 years ago, and did it again last year. The second was something new. Only about a quarter attempted the bonuses, but most of those were successful.

I think the third quiz is a wonderful idea, but it needs work. It was very open-ended, so the seniors who are ready to check out probably could come up with something, and the juniors who are scared of AP could write much more. But how to grade it?

1. Reducing, multiplying (worksheet:  PC2 Rational Expr Reduce demo  )

2. Adding and subtracting, review polynomial division, converting  mixed expressions to rational expressions and back (worksheet: PC2 Adding Fractions demo  )

3. Partial Fraction Decomposition (handout borrowed from a text the school uses for another course)

4. Graphing functions of the form $f(x) = k + \frac{a}{x-h}$ – the effects of k, a, and h (worksheet PC2 graphing a over x demo ) This worksheet is for day 5 as well

5. More graphing functions of the form $f(x) = k + \frac{a}{x-h}$ and slightly more complicated forms, eg  $f(x) = mx + k + \frac{a}{x-h}$. Emphasis on asymptotes. Linear behavior of rational functions. Worksheet from 4 and 5 probably needs to be stretched with more guided examples, and over more than 2 lessons. My kids tolerated it, but it was tough.

6. Handgraphing rational functions  Gelfand chapter 5 Functions and Graphs (there is a reason I had the school buy fifty of these suckers. I just didn’t really know the reason back four or so years ago when I pushed it through)

7. More handgraphing Gelfand chapter 7

8. Emphasis on end behavior – I borrowed someone else’s worksheet, didn’t work so well as it really wasn’t written for the purpose I tried to put it to.

9 and 10 will be for review and completion. Also for retaking quizzes that did not show knowledge of the subject. (this is not my general practice, but reflects the reality that these are days D minus 3, 2 and 1 before the AP exams.)

Quizzes:

 Quiz 12: Adding or subtracting rational expressions (two challenging questions, factoring required) PC2 Quiz 12 demo Quiz 13: Decomposing a rational expression using the method of partial fractions (one question, plus bonuses) PC2 Quiz 13 demo Quiz 14: Graphing rational expressions. Two questions: read the graph, write the equation, and given the graph and the equation, explain the relationship between the algebra and the form. PC2 Quiz 14 demo