## Thursday, June 18, 2009

### Evolving Rational Expressions and Equations Unit

*update* The embedded file is not the original one that was posted. Improvements made 6/19/09.

To recap from comments in previous post, I have this for day 1, reviewing operations on polynomials and monomials.

For Day 1 homework, they will research a way to explain why dividing a number by zero is undefined and be prepared to explain it in class the next day.

For Day 2, we will start by explaining to partners our reasoning for a/0 is undefined. Then a few students will explain it to the class.

Then we get into this... I'm looking for feedback to make it better if you have any. Thanks Dan Greene for the idea and not minding me ripping you off.

Classwork 8 2

Mrs. G said...

I've been lurking on your site for quite a while. I teach middle school in Texas and I totally love the questions at the end of your assignment on the habits of successful college student. I hope you don't mind but I'd sure like to add those (in some fashion) to the end of my assignments - it's never to early to get my socio-economacially disadvanted students to believe they CAN go to college if they choose (and I can help them learn good college habits now). I'm also working on setting up a facebook (opps, another idea I'm borrowing from you...) and I'm trying to decide how I could use twitter...

Thank you for sharing your lessons and ideas!

Kate Nowak said...

Mrs. G, take and use whatever you like from this site. That's what it's here for.

Thanks for unlurking. Nice to meet you. "Pleasure, Ma'am." (That is so you feel comfortable as a Texan.)

Pat B said...

Kate,
Love your blog, and just two quick suggestions about the worksheet... I would throw in something that asks them about the horizontal asymptotes..(I know, not everything in one day, but Waaaayyyy out there, what happens with ANY ratio of linear functions is worth calling to their attention)...
also, You asked about the domain restrictions in the extra problems, but not the zeros (or asymptotes)... can you hear them saying,"Ms. Nowak thinks THIS is the important idea."...
and I'm totally stealing your worksheet idea, thanks

Kate Nowak said...

Thanks, Pat!

I did ask about the zeros, in #6: What about the original graphs f(x) and g(x) determined where the root (x-intercept) of the new graph would be?

Also, this isn't the end-all for graphing in this unit, I'm going to go back to it when we solve rational equations and inequalities.

I made the choice not to get into the horizontal asymptotes. It's not in the Algebra 2 curriculum and I only have 40 minutes for this. Sometimes with period scheduling vs blocks, I have to make decisions about what to leave out!

Dan Greene said...

Looks good! I wonder if you might have them graph the product function as well. That's really cool, to see that multiplying two lines gives a parabola, and dividing two lines gives this totally different shape. They could also think about why there is one x-intercept in common, while the other x-intercept is at the place where the hyperbola goes wacky.

Dan Greene said...

Oh yeah, one more thing. I don't know how good your students are with dividing fractions.. for mine, it was really important to not just talk about why dividing by zero is impossible, but what happens when you divide by smaller and smaller numbers. I had them think that through conceptually, and actually do a series of examples (8/8, 8/4, 8/2, 8/1, 8/.5, 8/.25, etc.) This helped them see why the function would shoot up so quickly when the denominator approaches zero.

Kate Nowak said...

I really like the idea of doing the product function, too. I wonder how the timing will work out. I wish they'd take something out of this curriculum so we didn't have to race through everything.

Instead of leading them through an investigation of dividing by successively smaller values, it's part of their previous night homework to research explanations for why /0 is undefined (on the Internet, most likely.) If you google it the first few links have lots of different ways of looking at it. We'll spend the first several minutes of class sharing the different explanations they found.

Kate Nowak said...

I did some additional work on this today (6/19) and replaced the old file with the new.

Mr. Condescending said...

Kate, sorry to be a pain but I inquired a couple months ago about calculating a hip roof but never followed through. I did post it on my blog today is there any chance you could help with your expertise?? pretty please!

Mimi said...

This is excellent. Thanks for sharing!