I started this lesson with some theatrics. I asked them to simplify the fraction shown in the picture, and of course they all wanted to cancel the terms (as expected). I let them do it, and then changed the pretty pink heart into the fiery eruption you see here. I told them that those red slashes are like daggers through a math teacher's heart. I also told them that, when they go to college, I never ever want them to make the mistake of canceling out terms. Cancel factors, not terms! We spent a lot of time talking about the difference between factors and terms, and why this rule is true. We talked about why you can't add 5 and 5x, but you can cancel the 5's in 5/5x. I think this was time well spent, because this canceling problem is a persistent weed. From there, we practiced factoring and canceling. Pretty straightforward. In the following lesson, we multiplied and reduced products of polynomial fractions. There really were no new skills to learn, so after modeling one problem, I had them do independent practice work.

And now, I am caught up on postings!

Lesson 11 (Reducing Polynomial Fractions) doc / keynote / quicktime

Lesson 12 (Multiplying Polynomial Fractions) doc

A beautiful combinatorics argument

11 hours ago

## 4 comments:

I'm glad I looked through my reader before finishing my lesson plans for tomorrow. One student is will be beginning to divide polynomials. I'm definitely using your heart attack slide.

Thanks again for sharing!

You're welcome. I am actually going to be teaching polynomial long division at the end of this week (right after all the CAHSEE fun). I put together a lesson on it for my intersession prep class (but haven't modified it yet for the whole class). I just put it in my box under unit 5, lesson 14 if you want to take a look. The animations in the keynote took forEVER!

Oooh. The animations take a long time to play, building them really must have taken forever and then some.

I love it! Thank you so much for sharing. I'm in my first year of teaching math, and I've never taken any education classes, so I'm hungry for whatever ideas I can find (tho' I often feel as if I have no time to implement them).

Anyway, I've been surprised at how deeply ingrained the urge is among my honors Algebra 1 students to cancel terms rather than factors. When I was a student, I always clung to my teachers' oft-repeated slogans. I think I'll adopt "Cancel factors, not terms!" as a slogan of my own (supplemented, of course, with a discussion of why that's the slogan to follow).

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