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Improving the "Unit with Room for Improvement"

Last year I wrote a blog post about "The Unit with Room for Improvement."

So, how'd it go this year?

Much better!



I divided the not-so-successful unit into two units, as I decided last year it needed to be. We did polynomial operations, tested, then moved into factoring.

My students rocked polynomial operations! It was one of the most successful tests of the school year.

(As a side note, I taught multiplication without FOIL, hoping to help students understand it better, and I think it worked. I sort of needed the "OI" part when it came to checking their factoring work, but they seemed to even check their work better this year having NOT been taught to FOIL.)

As we got ready to transition into factoring, I was once again staring at the calendar. So few days left, lots of interruptions coming, but factoring AND quadratics left to go. The panic tried to set in.

But I determined to ignore it. I was going to take my time and make sure students understood material as we covered it, even if it killed me.

So I started factoring in class, sort of in an explore-flip-apply style. And I only covered one thing: the simplest case, all positive numbers.

And I started with an activity that revolutionized my students' understanding of factoring.


I took from a couple of different sources, and created these sum-and-product-X's in each of the different factoring possibilities.

The first day I had the first one on the board, handed the students a sheet as they came in, told them there was a pattern, and instructed them to find the pattern and fill in the rest of the X's.

A few students saw it quickly, and a few struggled. I let them think about it individually for a few minutes, and then let them discuss with an elbow partner. Everybody was excited when they finally "saw it," and they filled in the rest of the page.

By the end of the lesson, they were factoring the simplest case like champs.

Their video that night was the next simplest case.

So I took what was normally a one day lesson (and covered completely in one video last year) and made it two days.

And it paid off in spades.

Students quickly got into the mindset of finding pairs of numbers that gave a certain sum and product. Many students used the X's throughout the factoring unit.

I was a little concerned once we got to the more difficult cases - such as a leading coefficient other than 1 - but even the harder cases were easier after the foundation laid in the simpler cases.

Students did well on the factoring test, and I feel much better about their grasp of the material. Now, will they remember it when they get to Algebra 2 in two years? We'll see....

I still used the Punchline pages more than I would have liked. They gave great, self-checking practice, and I could see while they worked that they were understanding the material, but a few students felt they were experiencing "death by Punchline." I will continue to work on that part of the unit next year.

Balancing time in the classroom is a delicate art. Don't go too fast, don't go too slow, get everything covered. But my flipped classroom has continued to teach me that slower is better than faster. Smaller chunks of material is preferable to large boulders. Student understanding is much more desirable than confusion and tears.

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