Summertime Blues

I am going to interrupt this blog's usual programming for a few moments of whining and complaining.

Then I will get over it.

So . . . I have been on summer break for more than a week already. Yay me!

But really. When the last bell rang on Friday the 17th of May, there was no skipping down the hallway. I did not hear the hallelujah chorus as I walked out the door. There were no celebratory cartwheels in the parking lot.

I am stressed out and overwhelmed . . . ABOUT NEXT YEAR!!!

I don't know why. . .

My summer list has only three things:

1.  Change everything.

2.  Rewrite curriculum from scratch.

3. Plan two new preps, for a total of five.

Ugh.

Have you ever had that back-to-school nightmare where you have a room full of students looking at you and you have no lesson plans? I had that dream. In May. . . a good three months from the start of the school year.

I will figure it out. I will find balance and I will enjoy summer with my family. I will also be productive. I will find the joy in the profession that I love. I will rise to the challenge and I will plan my little heart out. But right now, just for a little while, I kind of want to not be a teacher.

Best Last Days

In college, one of my professors told a room full of future teachers that our second-hardest day of school would be our first day . . . because we don't know our students. The hardest day? Our last . . . because we do know our students.

I realized that for all the time I spend agonizing over the perfect first day, I rarely put much thought into the perfect ending. I usually write my seniors a letter, but mostly I just pass out a final exam and wave good-bye and good luck as they sprint out of the building. I decided to be more thoughtful and intentional about the ending this year.

For calculus, I allowed some extra days throughout the semester for the students to research and create mathematical art. I was very excited about this, as I am a wanna-be artist myself.

On the next-to-last day, we set up an art gallery and invited the faculty to come view our finished products. Some of the students did the minimum, but a few of them created some beautiful pieces. 

"Can I keep that, please?", begs Mrs. Gruen shamelessly.

I cannot wait to hang these origami archimedean solids by my window!

The students all brought toppings and we had a taco bar lunch together between showings.

On the very last day I asked students to write letters to next year's calculus students. The letters were adorable, and insightful. I can't wait to share them with next year's class.

For physics (all the same students plus one extra), I scheduled the final exam so that we would have one day left afterwards.

I had a brief college advice session, sharing words of wisdom from someone who has been there (even though it was a long time ago). I talked about studying, advocating for yourself, communicating with teachers, and keeping your student loan total as small as possible. That stuff has to be paid back, people! If you sacrifice now by driving a reasonable car, working a part time job to pay the rent, and eating ramen instead of ordering so much pizza . . . . your future self will thank you. I promise.

And then there were presents!

For the girls, I made these necklaces featuring their college logo. I had a little help from Pinterest.

The boys got these clip boards with their college logo painted on the back. It is unusual to have them all going to the same school, but it happens to be my alma mater, so yay!

And finally, because it seemed like a very sophisticated thing to do, I brought glasses from home for a sparkling grape juice toast to their futures. There may have been a few tears.

My calculus and physics classes are usually small groups of all seniors. We become a little family during our year together. I start to feel like their Mom (or maybe a cool Aunt, because I like to pretend I am not old enough to be their mother). I teach them, cheer for them, advise them, and even get frustrated with them. But I still love them. And I will miss them.

Best wishes, class of 2013. You are going to love what comes next!

Plethora of Practice Possibilities

I wanted to help my students practice evaluating different trig ratios for special angles, so I made two sets of cards:

Set #1 is a set of answer cards. I made them out of craft foam so they would be sturdy and also look different from Set #2 which is just a set of small flashcards (problem on the front, answer on the back).

At the time, I had an idea about how I was going to use these . . . but then a bunch of other ideas came to mind. I am probably going to be changing the way that I teach this particular topic for next time (more focus on the conceptual understanding, less on the "trig hand"), but surely these scenarios could be adapted for other topics? Hence, I thought I would share:

Everything went in a bag, one for each table.

Modified flyswatter game:  The flyswatter game is oodles of fun. I thought it would be perfect for trig ratio practice. It was not. Students felt pressure to answer immediately, so they ended up slapping a random answer which was rarely correct. I also wanted to have more than two students answering any given question. For the modified version, students spread the answer cards out on their desk and point to the correct one as I ask questions.

Matching work mat: This is just a card with a bunch of problems, all with unique answers. Students can place their answer cards and move them around until they're all in the right place.

Flashcards:  Students quiz each other at their tables. The flash cards are also perfect for a Kagan Quiz, Quiz, Trade. Gotta love the photo-bombers in the back.

Group Quiz:  The answer cards are spread out on the table, and students have cards with four problems where each person at the table is responsible for a different one. Students can flip over a problem card at their table, and each person reaches for their corresponding answer card. I would choose problems that have similar answers, so that there is a chance of students reaching for the same answer card and being forced to talk it out.

Matching Flashcards to Answers: Students spread the answer cards out on the table and turn all the flashcards face up. They match the flashcards to the answers. The beautiful thing here is that it is super easy to self-check. Students just have to turn over the flashcards to see if they are right.

There's probably more . . . I also thought about the potential for making different sets for each table and then rotating them for multiple days of practice. But at the moment, I can't think of a topic that would require that much practice.

Trig Hand

This is not new. You can read about it here, here, here, and here, just to name a few. 

As of a few months ago, it was new to me. How did I miss this?! I found it when I was searching for unit circle resources, and I thought it was pretty cool. . . Evaluate trig ratios for special angles, quick-and-dirty. I taught my students to use it. That went well.

Here's the summary, followed by the brain dump:

Use your left hand, palm facing you.



Fold over the finger that corresponds to a reference angle. For 45 degrees, there are 2 fingers below and 2 fingers above the bent finger. For 30 degrees, there is one lower finger and three uppers. And so on. Also, I have freakishly small hands. We'll talk about that later.



Then use these three rules:



Other thoughts, in the order they came out of my head:

The trig hand works for angles in other quadrants if you identify the reference angle and know whether the sign should be positive or negative.

It also works if you count the thumb as 90 degrees (four lower fingers and zero upper fingers) and the pinky as 0 degrees (zero lower fingers and four upper fingers), but doesn't extend to the other quadrantal angles. This go-round, I taught these angles separately and used the hand for all four quadrants.

Wait a minute . . . What if the pinky represents the x-axis and the thumb represents the y-axis? Now doesn't the rule also apply to 180 & 270? You would have to add the negative, but we already did that for the other quadrants. Hmmmm.

For finding reference angles my students observed this pattern:
45, 135, 225, and 315 all have 45 degree reference angles and all end in 5.
60, 120, 240, and 300 all have 60 degree reference angles and are all divisible by 60.
30, 150, 210, and 330 all have 30 degree reference angles and are all divisible by JUST 30.
Similar patterns can be found using radians.

My biggest concern, as we all know, is that memorized tricks don't stick. I spent a lot of time on conceptual understanding before I introduced this but still . . .

For next time, I am thinking this is a better fit for my Calculus class. In Algebra 2, students need to understand the why. In calc, we would expect that the understanding is already there. Meanwhile, it would be really convenient to have a quick-and-dirty way to find these values when they pop up.

Finally, someone in almost every class pointed out that, "Mrs. Gruen, I think you have the world's smallest pinky".

Squirrel!



Two nickels. They might be right.