#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!!

Polar Graphing Activities

Happy #mtbosblaugust once again!! I was thinking about some of the activities I did in Honors Precalculus and AP Calc last year to reinforce some new or tough ideas, thinking about what worked and what to use again this year. I’ll briefly try to describe something I learned last summer at an APSI from Dr. Joe Brandell, our AP Calc guru!

Graphing polars is a topic discussed in my honors Precalculus class since we now have a majority students who move onto AP Calculus BC. I do everything from plotting points by hand, plotting on graphing calculators and on Desmos. All seem abstract to my students but they are fun to play with, especially with sliders on Desmos. I don’t want to even think of a time before Desmos existed!

Back to the activity from Dr. Joe. He introduced our group to human polar graphing!! You will need a long rope and a lot of space, oh, and a class of students! Depending on how new or quick students are at computing the radius from given theta, you may want to give them an equation or two to create a table. Pick a point to be the pole (origin in polar) and how far out a radius of 1 or 2, etc. will be.

The first student will hold onto the end of the rope and find their first point in the polar space you created. Then the next volunteer will hold onto the rope at the point of the second coordinate, etc. Eventually, a circle or a cardioid or a rose…will be in the space with kids as the coordinates and the rope as the curve! Human Polar Graph!!

Another polar graphing activity that I do thanks to Infinite Sums can be found here. Now, his goes on and on and I strive to do that with my group! We started small this year.

It was very fun, and who doesn’t love to create with sidewalk chalk?! This is a great activity to get the students to practice plotting points and graphs. It usually shows up at a nice time of year where we need to get out of the class.

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!

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!

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.

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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:

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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. Screen Shot 2016-03-07 at 7.06.13 PM.png

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.

 

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.

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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.

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Dropbox files