Unit One – Limits, AP Calc

I made it through a year of AP! Well, pretty much. My students were successful, but time to change up a few things for next year.

I started to go through my INB to see what kind of changes could better help my students. Also, I’m considering how I could incorporate other activities to reinforce what I’m teaching. This is how my unit starts:

I typed up a table of contents for them to show the Learning Objectives from the AP curriculum. I’ll take a picture of the next couple of pages, but I’m changing them up a bit.

Here is a link to the modified file for limits graphically and numerically. The delta-epsilon definition is not something I spend a lot of time on but I do talk about with my class. I’m putting that on its own page this year.

Last year I used a lot of the notes I already had from regular Calculus.

I’m changing it up a bit…making it more about content than a cute note sheet.

And properties.

Next, continuity. I found some good notes on Teachers Pay Teachers.

Onto Intermediate Value Theorem. This is important, but not too big of a challenge for my group as we talk about it in Precalculus.

This google site has been helpful to me in organizing my thoughts after a year.

Limits at Infinity wrap the chapter up.

This year, I’m hoping to give my students more opportunities to see AP questions (or AP-like). I want not knowing how to start right away to become no big deal by May. That’s tough for these kids because they’re so used to knowing, or feeling like they should know!

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

A Week’s Worth of Limits

Holiday break, 6 snow/cold days in a row and moving exams back a week gave me 5 days to introduce my honors precalculus students to Limits. Most will be moving on to AP Calculus next year, while a few will take regular calculus the second half of this year or next. Let me just say that teaching limits to a group of honors students is a much different experience than teaching the same topic to my calculus group. It just takes less explaining, less discussion. Here are my INB pages from the week before last. A lot of these pages may look familiar if you have looked through my calculus materials. I made a few adjustments on them, and think I will continue to make a couple of adjustments before talking limits with Calculus next semester.

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180 – Day 28

I’ve had an empty left hand side page in my INB for Calculus for over a week! Ahhh! Today, no more! Last week I posted on tangents and slopes, the limit of the difference quotient notes, but never could figure out something to put on the left of that page. My new textbook starts off the derivatives chapter right where the limits chapter left off…with the alternative form of the limit of the difference quotient. So I went back to that page, and we worked our way though this alternative form, illustrating how we are doing the same thing.

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180 – Day 25

Today was a day full of reviewing…tomorrow tests, all day long. That will be bad tomorrow night! I like to at least get the scores to my students the next day, but not so sure if that will be possible with all of the grading I’ll have to do!

Calculus had a Limits Scavenger Hunt to do. I originally got the idea from Mrs. Cook. I noticed that a few of the problems were more basic than I needed after 3 weeks on a limits chapter, they would think the test tomorrow is going to be easier than it is. So I made a few modifications, which you can find here if you would like. Third hour took the task much more seriously than first hour. They really worked hard to be sure to get the correct solutions. Maybe first hour doesn’t feel as though they need to work at reviewing for the test, or didn’t enjoy the task as much. I guess we will see tomorrow on the test!

Honors precalculus was reviewing today too. We completed the LHS of their Polynomial Graphs INB page.

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Just a summative problem, but it had been a long weekend. I walked around to see the student’s results, and most looked pretty good. I then talked over the page with the few students who had a mistake here or there.

 

180 – Day 23

Practice, practice, practice. Calculus parents asked for more practice at conferences the other night, and more practice is what the students got. We still have no textbook, but that does not matter much to me. I have plenty of resources, and would have to use them to get my students the help they need. My calculus class is not AP, and I ant to expose them to all of the calculus I can before they go onto college math. There are difficult questions right away in the textbooks, so I always put together pieces of other books to give the students the level of practice they need. So we worked on a smattering of limits problems, and the students put their answers on the board.

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Tomorrow is a half day for teacher PD, so extra time for homework, before the test on Tuesday. Excited for my review activity on Monday…stay tuned!

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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