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.

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.

 

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 27

So, I skipped over the Intermediate Value Theorem in the limits chapter because I never quite saw the necessity of it. I mean, I get why they put it in the continuity chapter, continuity is in the hypothesis. I then noticed they reference the calculus version of the IVT in my book in the upcoming Derivatives chapter, so I thought I should make mention of it. I came across a small break down of the theorem on f(t) over the weekend. I assigned the first side of the worksheet for their after-test assignment. We discussed it today in class, and then flipped the page over…revealing that one could be impossible. It was a semi-non-threatening way to start the theorem, though these students are still overly concerned about making mistakes. This was the most interesting IVT day I’ve had.

Honors Precalculus’ big topic was Inverses. Ooooh! I did make a foldable for the INB though…

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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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180 – Day 10

We made it to double-digits! Honors Precalculus was once again on the graphing kick…working more with piecewise functions, which we started on Friday. I used notes I found on Sam Shah’s site, and they worked great! Today we reviewed a bit of piecewise, and applied the transformations with (a, b). When you put everything in one problem…it really gets the student’s brain churning!

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We then moved onto Operations on Functions, the last topic for this function chapter. I made a foldable to use for their notes. We got part-way through it in my block today. This too is review, but I’m really stressing the domains with students because there is less of an emphasis on that in Honors Advanced Algebra.

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180 – Day 9

On Friday, my calculus students were reviewing their Algebra review…so nothing too exciting there. 

In Honors Precalculus, students started class by working on some transformations…work we began on Thursday. This was pretty much a review for these students, though the odd-shaped graphs still give the kids trouble. No matter what I do with them, there are still kids dumb-founded when graphing the functions that don’t look like the families of functions. The stretch is really what challenges them. We’ll keep working at it though! I know this group can get it.Image