AP Calculus MPACs

Nothing major to share tonight, but did create some classroom decorations I wanted to put out there. AP Calculus has Math Practices similar to the common core. I made some displays to remind me and my classes (AP and Honors Precalculus) why we do the things we do.

The first is a link to the actual MPAC banners. This second link is to the subtopics banners. These are editable PowerPoint files. I will try to edit this post with PDF files if I think of it later.

Enjoy!

#MTBoSBlogsplosion Round #3

Better late than never, right?! I read the prompt for this week’s Exploring the MathTwitterBlogosphere and thought…who is spying on me? Has the MTBoS found a way to get in my mind?! Next week, I will start teaching Honors Trigonometry for the first time in 2 years. I was looking over my old Interactive Notebook and realized I had only used the INB idea once for honors trigonometry, so some of the pages could use a makeover. Off to Pinterest I go! My colleague and I share a Trigonometry page so I wanted to see what was there.
A few minutes on Pinterest led me to Sarah’s Math = Love site and Shireen’s Math Teacher Mambo blog! Great blogs, if you have never been! They both have fabulous ideas for my beginning Trigonometry unit. The pages I used the first time teaching this course with an INB are not bad, but I like to spice things up with some fresh ideas.

The first unit in trig consists of a lot of angle basics necessary for the rest of trig. First, I saved an idea from the agony and dx/dt‘s page to explore what a radian is. I have done this activity before, or one similar…with string. How boring is string when you can use candy!!!!

Twizzler’s Pull and Peel to be exact. I love using food whenever I can, and don’t know why I didn’t think of that! I will probably do something like Sarah’s pipe cleaner idea when transferring the lesson to their notebooks, candy doesn’t last on paper.

Instead of my boring sketching angles pages, I am going to use the cool page Sarah created. I even get to use a fastener so the angle rotates in the notebook! Oh boy oh boy oh boy!

What drew me to Math=Love’s trig page was her Coterminal Angles Sort. So that will be next in my notebook.

The coolest thing ever in getting students to understand reference triangles and special angles though might be from Math Teacher Mambo, and I am so excited to give it a try and see if my students think as highly of it as I do! I love how colorful this all is…and I especially like doing something that helps with student’s understanding of fractions.

That is as far as my thoughts have gone considering I am not yet done with this semester and have some planning yet to do with my current classes. The MTBoS is so helpful and I love that these teachers have provided links to the handouts. Things I create will too be uploaded here…as the unit goes. It is so tough to choose just one thing to write about as far as the usefulness of this community, I utilize so many great ideas every day and try to make them my own. Please know I appreciate all of your blogs so much for inspiring me. Thank you for sharing your ideas!!

Honors vs Non-Honors

There are many instances in my classes where I tell my students “This is where you earn your honors points.” At our school, students earn an extra half point for taking a class with honors in the title and an extra point for an AP class. This is to reward/encourage students to take the more challenging version of the courses, or just the challenging course if there is no other non-honors counterpart.

This year I taught both Honors Geometry and Geometry (skinny version). The skinny version of Geometry is slightly different from the Block Geometry we have and from the Honors Geometry class. Some of the time, Geometry is Geometry, and there are things we need to do regardless of the class. Sometimes students “earn” their points in Honors, whether it is through tougher problems on assignments and assessments, the speed at which we work on topics or through the level of notes we take together in class. Here is an example of Honors Geometry note for Special Parallelograms…

   

hon geom special parallelograms notes

Pretty basic and right to the point. Students have to spend some time sorting through what makes something a square versus a rectangle versus a rhombus on their own after we talk about what determines each special parallelogram. Then students summarize their thinking by completing a table, checking the quadrilaterals and their properties.

As far as Skinny Geometry goes, a little more time and instruction is necessary for students to completely grasp the concept and we spend more time sorting through the differences together. Here are some pictures from our interactive notebook:

     

     

Then we get into the coordinate proofs:

     

We do additional work in class, including a coordinate proof maze I made up in both classes. we complete them a little differently in each class…both being partner work though. In skinny, time is also spent on the properties with a card sort. We did not have time to play the card sort as a game (spoons or go fish) but that is something I would like to make time for in the future.

Avoiding Worksheets

In my spare time, I love to peruse Pinterest. You can follow me here. I think it’s relaxing…even if I don’t particularly need new activities for the topics I’m teaching at the moment. I may find something useful, or something to store for later. Most of the time I get ideas…not anything I use as is. But there are so many creative teachers out there who give me great ideas for my own class. Today was one of those days I used a lot of what I found on Pinterest, with my own spin.

In Honors Precalculus, we worked on a Maze Review for Polynomials. This activity was intended as an in class review, to get students familiar with the skills they still need to fine-tune when they go home to study. This is an example of a time where it is better to pay a fellow teacher on Teachers Pay Teachers for an activity then try to recreate the wheel. The activity was perfect for what I wanted my students to do in class.

I was particularly proud of the MathLib I did in Calculus though. We are beginning our chapter on Derivatives and the power rule, but I know that half the trouble (or more) that students have with this rule is their understanding of exponent properties. Sometimes they haven’t even thought of this since Algebra One. So we did a quick graphic organizer on the Exponent Properties and tried a few tougher examples together. Then students paired up to tackle the MathLib. I got the idea from Pinterest, using All Things Algebra‘s Similar Triangles MathLib in my Honors Geometry class last semester. The students enjoyed it, and I like that these types of activities give students a chance to practice the math and know if what they chose is correct almost immediately. They serve the purpose of a worksheet, without the bore of a worksheet. Plus, working on it in class gives students the opportunity to ask questions of each other and me. Here is a shot of one of my slides…and I’ve linked my dropbox file here.

I used some fonts I found on Pinterest, mostly Kimberly Geswein fonts. The students had fun with the nonsensical MadLib and were able to fix any mistakes they might have made by the end of class because all I had to do was check the answers they chose:

If there was anything wrong…they went back and tried again, something students do not do too often on a typical worksheet.

My final Pinterest inspiration for today was in Geometry. We are working on our Area unit, and in need of breaks from the typical area problems in the book. We spent Thursday and Friday talking about the basic area formulas (parallelograms, trapezoids…) and today we took some time to start their banner problems. We only had time to do 4 of the problems, but it was a good start since we haven’t spent too much time in this unit yet. 

I got the idea from Scaffolded Math and Science. She has a ton of great ideas on her site, including her own area banner activity. The problems on hers would not have completely been right for my group of students, so I created my own. I appreciate the inspirations, they really get my mind working.

 

A Few Changes

I have taught Honors Precalculus for years…though I try to switch some things up, mostly to keep things fresh for me. This semester I thought that the first chapter needed a couple changes, since the things at the end tended to be the things students missed (if anything) on the test. Rather than doing the Piecewise Functions graph right after the Parent Functions (as the book does) I thought to teach Operations on Functions with Domain and then go back to graphing after. It gives the students some extra time to work with composition of functions, and it also spreads graphing out, leaving time for students to process that. I think it was a good choice. Students did well on their test, even on the composition questions, something that in the past they may have gotten wrong because not enough days were spent thinking about the topic and how to work with the domain. Here are some pictures from my Interactive Notebook on these topics.

I also changed some of the notes from past years…with more emphasis on composition of functions.

New Notebooks

Yesterday, we started a new semester, meaning all new classes (except for one). I started off my new classes the same way I have for the past few years…with my Interactive Notebooks! I really believe in starting these on the first day. It sets a tone from the start that this is what we do here, and there is no arguing. The best way I have found to do this is to hand out composition notebooks from the start (then students owe me one in return). And the beginning of the notebook is all about the class. I have taken a lot of ideas from some great notebook blogs, especially Everybody is a Genius as far as the start of the notebook is concerned.

Even though I don’t start my courses with content on the first day, the notebook is still an integral part of the day. I have also noticed that the word is out on my class. Students are starting to expect my “scrapbook” (as some refer to it) when they see I’m their teacher. And the fun in my math department is, a few more teachers are using Interactive Notebooks in their classes to help keep their students organized and to give them a tool for studying!

I need to remind students each day next week the purpose of their notebook…to be used! I started using them to help students with their assignments, but a lot of times they get put away once the assignment or any class work is started. This semester, I hope to do a better job of encouraging my classes to have the notebook out and open while working on math problems…to utilize the notes they take! What a novel idea!

-Lucy

Calculus INB – Optimization and Integration

Seniors leave early due to graduation every year in May. With the seniors, we made it through Optimization…and then spent some time on a project optimizing boxes and cans. Maybe I’ll have some time later to post about that. With three juniors, we finished up the year learning about differentials, linearization and integration. The topics don’t necessarily lend themselves to being a unit…but hey, it’s the end of the year!

Optimization was pretty much done like I did first semester, so I won’t bore you too much with those details. Integration was done in a similar fashion as that post too, though I had some time to use rectangular approximation to introduce the topic, which I did not have time for first semester due to the crazy amount of snow days we had.

Newton’s Method: File-25-06-2014-10-39-20 A neat topic to spend a short amount of time on, relating how these numbers were approximated before the advent of graphing calculators and computers. It’s really amazing how close these approximations were so long ago!

Optimization Files

Differentials Files

Integration Files

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.

File-25-06-2014-10-11-33

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!

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.

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.