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.

Calculus INB – Limits

I made a few changes to my INB for the winter/spring semester. I get a chance to modify some things being on 4×4 block scheduling, but didn’t seem to have any time to write about it here! Now that I’m on summer break, let’s see what I can share.

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They aren’t too different from the pages in my first INB for this chapter. I modified the discontinuities pages slightly. This semester I tried to put less information per page, knowing that I had plenty of room in the notebook to spread things out, but there is still quite a bit of information in there. I also have a link to some of the files I used. I hope it works!

Limits INB folder

Starting Calculus Out Right

The past seven days of Calculus have involved putting together their INB with a lot of Algebra Review. Some in the MTBoS have referred to this as “Algebra Bootcamp”. I haven’t done too much differently from the start of the year, here is a post from one of the first few days in September, but have modified a few INB pages and activities with my students. I have also done less algebra here at the beginning. I plan to do some more review as needed prior to a topic when it matches up better. I think it is important to review some Algebraic topics at the beginning of Calculus for many reasons. A lot of my students have not had a math course since the end of last year, or possibly since the middle of last year. Just getting their brain thinking mathematically again helps in introducing the abstract topic of Limits. We will use all of the topics I review throughout the course, and I don’t spend a lot of time on each one. Just enough to spark a memory. Here are a few pictures of my Calculus INB so far.

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I gave a few bonus points if they decided to decorate their covers this time. It was not mandatory because I still made an Author Page mandatory and I thought it was a lot of the same.

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After these pages, and some book practice, we took a quiz. Students did a lot better this term after breaking up the material into two quizzes.

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Hopefully students will have repeated success on the graphing quiz.

So far, we have gotten through the piecewise function notes, but the last picture…we will work on in class before the graphing quiz. On Friday, after completing a few example problems, I had the students work on a card sort activity matching up equations with graphs and domains, and key features. It was a nice relaxing activity to keep the class thinking about math on a Friday afternoon. I do not have a link to this assignment, unfortunately, because I cannot remember where it came from!

Calculus Algebra INB Folder

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

MTBoS Mission #4 – Listen and Learn (and Day 45)

Yesterday, I finally got around to some professional development at Global Math Department. I have watched a Global Math Department conference on Interactive Notebooks over the summer. It was actually my introduction to the MTBoS! From the Global Math Conference, I found links to people’s blogs, links to twitter, a whole new world of online math improvement! I loved the Interactive Notebooks so much, all of my classes are now using them! Through this week’s mission, I found that there was a conference on Foldables! I have developed a love for foldables this year, in case you couldn’t tell by past posts, so I was thrilled to get some new ideas from @jreulbach.

From the conference, I clicked on Julie’s wiki link where I found some templates for new foldables. What a find, because I am starting a new term, and students are always excited to see a new way to present the material. The templates I found used PowerPoint to create the foldables. Why hadn’t I thought of that before?! It is so much easier to get everything to line up the way I want using PowerPoint versus Word! This led to putting together my all new Chain Rule lesson I used today in Calculus. Well, this and a fellow bloggers – Rebecka and Sam.

Sam, through his post, helped me to develop the idea of outer and inner functions (so much easier than all of the letters students usually get lost in!), which helped me to create this introduction paper:

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I then handed out notes to the students, the notes I created after watching the Global Math Conference on foldables.

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We worked on the top flaps (left picture) together, as well as discussed the outer functions and their derivatives. This was all leading to an activity I found via Rebecka. I handed out cards to students in groups of 2 and after a short while, I had the students find the group with the same color writing to compare answers and to help complete the task, in case any of the groups were stuck.

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Students then wrote their group’s information on a table projected to the entire class. From that table, and a few leading questions, students actually formed the chain rule! Actually, in my 3rd hour, I had a student state it pretty close to perfectly: “The derivative of the outer with the inner plugged in times the derivative of the outer”!! YES!! Awesome!!!

Then we discussed it a little more, having students try to explain in to their partner. I wrote on the board: y=f ‘ ( g(x) ) * g ‘ (x) and we discussed this, whether this made sense, and how this was similar to what the student said. Class time was just about up at this point, and I assigned 5 short problems for students to try using what we had discussed today. This will lead into tomorrow, where we will finish my foldable notes.

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I was formulating the lesson since last week, prior to watching the Global Math Department post, but without viewing Julie’s conference, the lesson would not be put together in the same way. I can’t wait to have more time to watch more conferences…I really want to watch the Desmos one. Time is never on my side! Thank you to this fabulous community!