Ahem. Mic check. One. Two. Three. Is anybody out there?

Holy cow—has it really been since 2015 since I blogged??? Oops. Time to dust off the ole wordpress and put some stuff out there.

I just returned from scoring AP Statistics exams and after re-connecting with some dear friends, have felt compelled to try and get back into the online math universe and post some stuff for other people to read. No promises for anything good–just stuff. I am going to *try* and blog once a week. We’ll see how long that lasts. Since we are in the midst of summer (glory, hallelujah) I am working on plans for the upcoming school year. I’ll be teaching AP Stats, Pre-calculus, and a new course called Financial Math. In addition, we are switching from trimesters to a hybrid block/regular schedule so, yay. I think.

Anyway…this post is about entrance cards.

Last year I taught precalculus for the first time and I knew (from talking to the calculus teacher) that one area which historically had been a problem for many students was that they didn’t truly know the values of the exact trig functions. They had been asked to “memorize” the unit circle but we all know what they did. I’m sure they took a couple of days to “build” it, either with paper plates and adding machine tape or with technology of some sort or with some other interesting method designed to help them see the values and understand where they come from. They were then told to memorize those values. The quiz to assess knowledge was probably a blank unit circle and they had to fill it in. Perhaps multiple times, perhaps only once. And BOOM. They “knew” the unit circle. And then class moved on to identities and perhaps referenced a unit circle value once in a while. I did not want my students leaving my class without at least making some attempt at doing it better than that. So…

I started with the fairly traditional “build-the-unit-circle” stuff; adding machine tape, paper plates, and lovely special right triangles to trace. We measured, labeled, discuss, identified patterns, all the good stuff. Then I said, “Now you have to memorize all of this.”  After all the moaning and groaning subsided, I shared a couple of memory tools that I knew or found on Pinterest and set them free to memorize. To help them practice as well as know that I really was serious about this, I decided to orally quiz them every day at the start of class. I created a set of flash cards (available below) and as students came to the door, I held one up. Initially I thought students would stand in line and wait their turn, but it ended up being a big cluster of people and the first person to get the question right got to go in. Everyone else had to wait for the next question. I cannot tell you how beautifully this worked. So much better than I had even imagined. Students knew it was coming. Every day. For almost two weeks. Some of them learned the values quickly, others took more time, but they all knew they needed to know this stuff. For those that were struggling, I was able to work with them one-on-one in the moment. Sometimes they just needed a little encouragement, sometimes we needed to revisit the memory technique they chose to use and see what misconceptions they had.

I did not use all of the flash cards–if you open the file you will see they include all the special angles around the entire unit circle. My goal was for students to know quadrant I and the axis angles, so I stuck with only those. The first few days, I only used cards with degrees/radians and had them practice converting the key angles back and forth. Then I added the trig values. Finally, I created some (sorry–just wrote on index cards) for inverse trig, prepping them to solve equations.

Trig Entrance Cards.Exact Unit Circle Values

Since I experienced such success with this topic, my first thought was, “How can I capitalize on this and use it more often, and in more classes, next year?” I realize this is only good for things that need to be available in “quick recall” format, but I’m thinking there are some skills precalculus kids need to be able to do that with. In stats, I’m thinking about quick vocabulary checks or basic formulas that need to be committed to memory. I know this won’t work for getting at deep understanding, but it gives students motivation to know at least something and I get to interact with each student individually EVERY time I use these. That’s a win in my book.

Here’s my current brain dump…I hope you’ll all add some ideas and suggestions.


Logarithms; Evaluating nth roots; Factoring quadratics and higher order polynomials;

AP Statistics:

Describing data (Shape, center, spread); Classifying data (categorical/quantitative); Estimating the center of a distribution; Which measures should you use for a given set of data (standard deviation and mean OR IQR and median); Interpreting slope, r, r^2, y-intercept; Choosing the right probability setting (and, or, conditional); which inference test; Should you reject/fail to reject the null (from p-value, from a critical value); Have a calculator available to check for basic skills (finding a 5 number summary, creating a histogram, finding mean and standard deviation, etc);

Thanks for reading. Maybe I’ll make it back next week.