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.

180 – Day 60

Test day for Calculus. Implicit Diff, Chain Rule, Related Rates. It is the logical thing to do, test before Thanksgiving Break, but there were a number of students absent. They’ll have to do the make up after break, but I am not sure how well that is going to go for some.

I was a little ambitious in Honors Precalculus. My goal for today was to introduce students to Conics in Polar Form. I first wanted students to determine what cosine and sine did to the graphs of polars with this exploration:

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Students worked well on this, but it took much longer than expected, I think because the holiday weekend was almost here. So we ended up going through these notes a little fast. Again, there were a few absent students, so doing a refresher problem or two after Thanksgiving Break may not be a bad idea. Of course, my goal is exposure to the topic, in case their future math classes use conics and parametrics, they would have at least heard of this.

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180 – Day 58

More with Related Rates:

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These notes are nothing fancy or spectacular, I just like how they fit neatly into the notebook. I wish that some of my students would utilize the color more. I need to do a better job with reminding them to get the highlighters out ahead of time. Some do, and their notes are very usable. Things just stand out more.

In Honors Precalculus, we started a short unit on Polars and Parametrics. Our goal is to expose them to the topics, not necessarily to make them experts at it.

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Color really helps the formulas stand out in these notes. If nothing else, it draws the student’s eyes to the place they would probably look when using their notes later.