#myfavfriday

What a long week…every Friday I feel it. There were some great moments this week though.

On Tuesday, the 9th graders in my Honors Geometry were at an assembly. Just enough kids that would make it a pain to move on with the remaining 8th graders (they come up from the 3 middle schools to take the course a year early). I was at first struggling with the thought of what to do…and then MTBOS! Of course we would spend some time with WODB and counting dots! This group of kids got into it! They were all geeking out over it, not worrying about others thinking they weren’t cool. Love that these kids have a place to enjoy math!

In AP, we were working with the definition of the derivative. Since it’s BC, chances of them seeing this on their test are low. They do need to recognize the functions and the difference between average and instantaneous rate of change. On Facebook someone posted a picture of an activity that looked intriguing to me as an opener. Rather than rewriting the cards every year, I typed the expressions on “cards” and I plan to laminate them when I get a chance. It turned out to be an ok activity 2nd hour…but so much better 3rd as usual after an hour of experience!!

Cards

Yesterday, as part of my basic derivatives lesson we worked on this Desmos activity to “discover” the derivative of sine and cosine. The kids found it very useful to remember how those derivatives happen!

Sine Cosine

I forget where I found the links but I know it was in the #mtbos.

And to top the week off…Math with Bad Drawings came in the mail today! I had a stack of papers to check, but not sure I’m going to get to them now!!

Calculus INB – Extreme Values

This chapter is more uses for the derivatives, and how we can graph without being dependent on the graphing calculator. It seems to be an obsolete topic nowadays, but I think it offers a lot of thinking opportunities for students. They have to organize a lot of information for themselves, what each derivative tells them about the graph, how to apply the intervals and turn them into graphs. Even with the graphing calculators and apps and computer programs, it is definitely necessary. The other part of this unit I find important is the use of the theorems. These theorems really force the students to think about the hypotheses and whether they’re applicable to each problem. I think it is one of the first times since geometry that students really have to consider the hypotheses and what they are telling them. By calculus, students are definitely more mature math students, so it is nice to come back to this. Special shout out to Math=Love for the vocabulary sheets! They have been working out awesomely this semester, usually as an introduction to the chapter. I have to find a way to get my students to do this more independently next year.

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Dropbox files

Calculus INB – More Derivatives

It seems like Derivatives go on forever in this class. As I’ve mentioned before, it’s non-AP, so there is more time to spend on topics that AP goes over more quickly because we do not have to be at a certain place for the AP test at the end of the semester. Plus, these students need more time processing the Algebra involved. I always tell my students they should ace the college algebra placement test by the end of this class because we actually use all of the algebra they have learned since 9th grade, or whenever they took algebra!

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A couple of the pages were hand-written and you can see the scanned pages here: File-25-06-2014-09-47-45

I also talked about related rates applications in this chapter, but my notes were not different from the notes I posted in my post from first semester. There are several related rates posts…this is just one link.

Dropbox files.

Calculus INB – Derivatives

I really tried to focus on the use of color, especially at the beginning of this chapter, graphs of derivatives and the power rule. There were some students who continued this on throughout the quizzes and tests we took over the material. This helped those students a lot, I think. My students are mostly seniors though, and they were a little on the lazier side this semester, or they never really used this learning technique before, so were not as open to trying this.

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I also had a few pages that I scanned in since they were hand-written pages and not handouts: File-25-06-2014-09-23-35

My INB files for this chapter can be found here.

Optimization and Integration

After getting back to business from the holiday break and many snow/cold days, my students were ready to be done with Calculus (block schedule means classes are only a semester, then all new classes). Administration decided to push back exams a week to allow for enough time to go through the curriculum. I was ok with it either way, but it gave us a chance to get through some optimization problems in calculus, as well as introduce Integration. Coming back to school on a Thursday, a week after we were supposed to return from break, I was very happy that I had planned for some activities for the students to do. Last year I found the following introduction to optimization activities online (sorry, I cannot remember where!). They are nice because they work students through doing them by creating objects, doing the algebra and finally calculating with calculus. It gives the students a visual to think about later.

Introduction to Optimization

We then spent a few days working on example problems and worksheets. Here are my INB pages:

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I particularly enjoyed the notes on the pink paper. They actually created shapes that were being described in the problems.

The extra few days of the term allowed for me to introduce the integral, or the anti-derivative. We just went through the basics, what it is, how to use the power rule. Two days does not allow for a lengthy, in-depth conversation about it. Some years we have more time spent on integrals, other years we don’t even get to them.

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First Derivative, so what?!

In a previous post (found here), I talked about using some things from other bloggers relating the derivatives and their graphs. In that post, I forgot to mention the work we did dissecting the first derivative’s graph. At first, my students weren’t so sure, but by the end, it seemed to help them put all the theorems we learned throughout the chapter in order for them, and helped them make more sense, for some 😉

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given f’ determine f (PDF of the worksheet above)

Here are a couple of more worksheets my students worked on. Most of these problems come from old calc books, but I thought they were great problems for my students to better show understanding:

Understanding_Derivatives Applying the Tests

180 – ??? Calculus Edition

Ok, so December always kicks my butt. Between work, conferences, Christmas parties, shopping, decorating, kid’s activities, and the list goes on and on, some things were bound to get put on the back-burner, and apparently this blog was one of those things. It’s really too bad though, we have been doing some great things in my classes! I’ll try to catch you up on some of them…in this post, Calculus.

Last week we worked on the Mean Value Theorem and its consequences.

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Students were doing well with the hypotheses of the Mean Value Theorem, but applying it was surprisingly challenging for some. It’s always the notation that gets to some students. I’m pretty straightforward with them though. This is not new notation, even in this course, and they are seniors who will be taking college placement tests soon. It’s expected that they know function notation and how to apply it. Prior to notes about the tests, and points of inflection, I introduced this vocabulary term with an activity I read on Bowman’s Blog. I then used a worksheet I found on Sam Shah’s blog reinforcing the vocabulary and trying to get my students to relate the first derivative to increasing and decreasing intervals and the second derivative to concavity.

Friday, we did a wrap up activity (which I don’t have here at home right now, I will have to post it later) and completed a graph example from function to finish.

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