## Sunday, March 25, 2007

### Update and Upcoming

I haven't posted much recently for a few reasons:

1) We administered the CAHSEE (exit exam) last week, which ate up a bunch of class time. Hopefully, our students will do as well this year as in the past. Last year, we had 88% of sophomores pass the math section on their first try.

2) Perplex City. Ok, I have a problem. :)

3) The last 3 lessons in my rational functions unit are BORING. We just practice adding, subtracting, multiplying, and dividing, and solving rational equations. Good mathematics, but I don't have any clever ideas on how to teach it, so it's just me modeling the method and the students practicing. Nothing wrong with that per se, but nothing much to be said about it either. On Tuesday, we'll have a review lesson before the unit test which is on Thursday, and the students will spend most of the class working on Showdown cards created for this unit.

To make up for the recent lows, I have a couple of cool things coming up which I'll preview here and then write more about later (after they've been, you know, actually created).

1) The Financial Literacy project I wrote about earlier is now coming to fruition. I met last week with the College Readiness teacher and we hashed out the outline for the project. It will look something like this:

• Freshmen will earn weekly income by performing their "job" - i.e. doing homework, being ready for class, etc. They can earn "lobobucks" in all their freshmen classes (assuming we can get all the teachers on board!). Each Friday, students will deposit their lobobucks with their college readiness teacher, and on Monday, they will receive an account statement.

• They will also receive a weekly bill for expenses. For example: "rent" = their chair in class, "utilities" = worksheets and materials they are given. They must use their money to pay their bills. We are considering consequences - i.e., if you don't pay rent, you have to sit on the floor...

• To make things more interesting, students will be required to sign up for a credit card. That is where my Algebra 2 class comes in. On Friday, we begin our exponentials and logs unit. I will teach them about interest rates and credit cards, and they will design their own cards and rate plans for the freshmen to sign up. They can use their credit cards to buy extras (though they come at a steep price!) such as free dress, bathroom passes, homework passes, listening to music during tutorial, and a double lunch period. There will be credit limits to prevent out of control spending too.

• To complicate things further, when students get detentions, the interest rate on their credit card will increase!

• Each Friday, my students will get a log of purchases made by the freshmen, and any payments that have been made. They will take into account any rate hikes, and will then generate a new balance and create a bill, which will be presented to the freshman on the following Monday along with their income and expenses.

• The freshmen that are able to stay in budget (or maybe hit some sort of savings goal) will earn a big prize at the end of the unit (like a pizza party and trip to the imax)

• My students, approaching things from the opposite angle, will be competing to see who can get their "clients" most in debt. What better way to understand how things really work?

2) The "STAR Search" Treasure Hunt. (Can you help me with a better name??)

To help energize my students and prepare them for the STAR test in May, I will create a treasure hunt for them, beginning with a puzzle. I ordered some blank, printable jigsaw puzzles from this site, and I will create a picture/clue that will launch students into the hunt. Each day, they will spend the first 15 minutes of class working on released STAR questions in teams. For each question they get right, they will earn a puzzle piece. By the time the test is here, they should have completed most of the puzzle. Once they do, and they figure out the clue (which leads to a teacher), that teacher will give the group their next puzzle, which will lead to the next, and so on. Each puzzle will require the students to review some Algebra 2 concept, and will also incorporate some sort of fun puzzle, and will lead to another staff member. Ultimately, there will be a prize for the group that gets there first.

The front side of each puzzle will have the same picture. The backs, however, will be different, and will be part of a puzzle that the class will need to solve together, with a class reward as the prize. I don't think any of my students read this, but, just in case they do, I won't post any more details here. After the hunt, I'll post up what we did. For now, just send me an email if you want to hear more, or if you have good ideas for puzzles and clues I can use.

## Monday, March 12, 2007

### Next Lesson: The Hidden Dangers of Simplifying

(aka Holey Functions, Batman!)

Quite a few students got the hidden message, and they did it faster than I would have expected. Mostly, it went like this:

Student: "Mr. Greene, I got the answer."
(I look at student's paper and see only a string of numbers.)
Me: "What does it say?"
Student: "What do you mean 'say'? You can't read numbers!"
(I look at student meaningfully. Single or double arched eyebrow, with a slight off-center forward head-tilt. Admit it - you're doing it right now!)
(Student looks at the puzzle again.) "Oh, wait!" (Student excitedly grabs pencil and gets back to work.)

Anyway, we took a quiz at the end of the class, and they did fine, so I hope we are ready to move into simplification in tomorrow's lesson.

For the warm up, students will review finding vertical asymptotes and end behavior functions, and they will do this when given a graph only, or when given a function. (Go Representational Fluency!)

Then, I will have them analyze f(x) = (x^2-x-6)/(x+2). (Sorry, I haven't spent the time to learn LaTex yet...) They will assume there is a vertical asymptote at x = -2, and won't they be surprised when they see the graph on the TI! This will lead in to the discussion of 0/0 and holes in functions, and so forth. We'll do a couple practice problems, where students need to simplify (clearly writing the domain of the simplified form of the function) and graph (clearly indicating any holes). If there is more time left, I have a few practice problems for them to do on their own.

Wish us luck!

## Thursday, March 08, 2007

### Rational Review

Today, I did a lecture on the end behavior of rational functions. We used polynomial division to rewrite the rational function, and then figured out what terms would approach 0, leaving us with a lovely end-behavior function.

Students are starting to get overwhelmed - though they know the differences between x-intercepts, y-intercepts, and vertical asymptotes, when called on to figure them all out for a problem, they tend to mix things up. So I need to stop and take a day for review. So, I present:

Another Perplex City inspired creation for tomorrow's lesson. Enjoy!

## Monday, March 05, 2007

### Next Lesson: Rational Functions

The unit 5 test is over, vacation is over, and I'm ready to get back on track with posting.

In the last lesson, we started the Rational Functions unit (as I described in a previous post). As a warmup, I had students do some division work to explore what happens to a quotient as the divisor approaches zero. They did this visually (i.e. fitting smaller and smaller boxes into a fixed space) and numerically (filling in tables of values).

After they were clear on the effects of dividing by a number approaching 0, I gave them a graph with two linear functions on it, and asked them to work in teams to find the quotient function. They had to look at each value of x, estimate the y-values of the two lines, divide, and then plot a point for the quotient function. It doesn't sound like this would take too long, but I knew from experience that it would take at least a half hour (and it did!). But the division warmup did really help a lot, and my main goal was for them to really understand why a vertical asymptote occurs.

We then moved into some direct instruction where we reviewed the difference between 0/4 and 4/0, I introduced them to hyperbolas (the shape of the graph generated when you divide two linear functions... conic section definitions will have to wait), and we looked at vertical asymptotes and x-intercepts, and where they occur. Students have a lot of trouble with fractions (duh!) and this translates to confusion when trying to deal with rational functions. I hope that continued reminders about what happens when you divide by 0 will help them remember. Finally, I taught them the "as x approaches 2 from the left/right" type notation, with the minus/plus sign as superscript.

We did some example problems, and that was that. I came up with a good way of testing their understanding in the homework: I gave a graph of a hyperbola with two linear functions A and B, and asked them to determine which line was the numerator and which was the denominator.

In tomorrow's lesson, students will continue to practice these ideas, and I will introduce them to Rational Functions as a concept. We will solidify their understanding of x-intercepts, y-intercepts, and vertical asymptotes, and we will discuss the domain of rational functions. I will throw in some factoring, but nothing yet that simplifies (holes will be discussed a few lessons later on).