Polynomials Chapter

This chapter did not turn out as well as it could have…we had state testing in the middle of it, and the distractions and days off from class did not help a lot of my students. It’s nothing I can control, so it is what it is. I changed my organization of the chapter in my notebook a little bit, and tried my best to adjust for all of the interruptions.

I start this chapter with a factoring review since this chapter expects the students to be able to factor any factorable polynomial. I found a great flow chart to include in my notebook on a precalculus blog. I used a few more of his ideas later in the chapter! I love finding resources out there, so hopefully someone else will be able to benefit from my posts as well. I also gave students practice problems to complete after their last test.

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The chapter starts with quadratics, a quick review. I’m finding that no matter how much time is spent on these functions, students struggle.  It’s a lot to sort out, when to set it equal to zero, when to look for the vertex, etc.

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Next, we talked about division and the theorems that utilize the operation. And then some vocabulary terms.

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This part of the chapter, students are creating polynomials given some “zeros”. I showed them how to more easily multiply polynomials, or to organize their work a little more using charts. These are honors students, but they appreciated not having to distribute as usual and to try to add up like terms that someone go all over their paper. It’s good that they have as much trouble reading their own work as I do sometimes!

We then go through a few tests that help students to make a challenging polynomial more factorable, and then graph these polynomials. I tried to teach end behaviors using limit notation, to introduce the students to this topic. We will work more with this notation later in the class, it is just meant to be an introduction. During this time, I have students explore the shape of the graphs around the zeros on this  WS_Exploring_Polynomial_Functions_with_repeated_linear_fac.

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At the end of the chapter, I gave students a worksheet I borrowed from Sam Shah. It gets them thinking about polynomials in reverse, writing equations from the graph. They have to pay attention to the end behaviors, zeros, even y-intercepts. equations from graphs ws

My project for this chapter is related to this idea as well…Birthday Polynomial Project. I found the idea for this project on Miss Rudolph’s site. I can’t wait to see what they come up with!

180 – Days 20 and 21

Tangents….it’s just slopes and lines, right?! I’m not sure if my introduction notes the past couple of days have made it any easier…we’ll have to work on it some more the next couple of days, after the discontinuities quiz tomorrow. Why is setting up a difference quotient such a difficult task for some? By the time most get it, we’ll be onto the power rule and everyone will be happy!

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Honors Precalculus is almost ready to graph. We did a short exploration on multiplicity and the effects it has on the graph at the zeros today. This was created by a former colleague of mine, but after today I realized a couple of the questions need minor adjustments. The synthesis questions were the ones most skipped (or weren’t positive were right, so didn’t care to share), but that seems to be the way. Honors Precalculus students are afraid of making mistakes…even though I try to convince them the mistakes help us learn. Maybe a few more leading questions before the synthesizing questions will help with the confidence issues.

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180 – Day 18

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More with Polynomials in Honors Precalculus! By tomorrow, my students should be able to factor any polynomial! How exciting! I couldn’t figure out a better way to do these types of problems with the limited space in my INB, and not wanting to fill it with a bunch of examples, so I had the students work through some examples on a separate sheet of paper. We are definitely going to work through a full polynomial on the LHS tomorrow, so there is a full problem in their notebook for future reference. There are also a lot of examples from the “pieces” leading up to completely factoring a standard form polynomial. If anyone has a better way of putting this big idea into an INB, I would love to hear from you! I am sure that this is a section of my notebook that will get a little tweeting when I teach it again next semester. I’m just not sure how much space to budget for each unit…once I go through this, I’ll probably find I have more room. For now, I’ll preserve space for the really important.

A further look at infinite limits was the topic for Calculus today.

I was also happy with most of the quiz results today! My students scored better on the Algebraic Limits quiz than they have in past years….and I’m going to owe that all to the organization of their INB! I did see many students referring back to it when working in class yesterday! I still am having a tougher time convincing a few of the boys that this is a helpful tool and not an excuse for “scrapbooking” in school (I am not a scrapbooker!).

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