End of 3rd Quarter

Hi everyone.

It’s the end of 3rd quarter, and we’ve got a grading day. Actually half-day. So I thought I should blog since I got the time! No kids! It’s some sort of miracle. I’m fortunate at my school to have a prep period and a department planning period… but during my prep, I can expect to supervise 8 to 10 up-to-no-good-but-so-lovable seniors. Up-to-no-good is definitely putting a positive spin on it. During my plan period, I can expect to supervise two or three accelerated freshmen for whom school comes easy and are mostly bored with it, and two or three sophomores who care, but need me to give them 1-1 tutoring in Geometry.

In short, having some time to myself in my classroom is some sort of miracle. It never happens. Now if only I had something interesting and substantial to blog about.

The kids are the best part of the job though. Forget grading, planning, and prepping. I do what I do because I believe in those little punks. They’re beautiful, lovely, funny, and smart. They deserve the best.

OK, here’s something worth blogging about. I just taught right triangle trigonometry to my Geometry kiddos. I love introducing trig. This year it conveniently followed a similarity unit, so I introduced it with a quick lab measuring sides of triangles and computing SOHCAHTOA ratios. Huh, weird, for any 30 degree angle in a right triangle, the ratio of the opposite side and the hypotenuse is the same. Huh, weird. (Similar triangles, anyone?)

Then we do some boring, but straightforward practice. Then the next class we go on a field trip. I love to advertise this next bit as a field trip, even though we only go down two floors to the Commons.

I start by having them estimate the height of the ceiling in the Commons (we regularly do Estimation180 in Geometry). Then I have them take out their telly-phones and download a free clinometer app. The only issue is the kids who say, “but I don’t have any room on my phone”. Maybe if you deleted some of those dang selfies, kid.

I crappily, but enthusiastically, model what they’re supposed to do. (My teaching career is a work in progress, OK? Year two is better than year one, at least.) I pass out the awesome, giant tape measures that the math department owns. We disperse down to the Commons. Chaos ensues, naturally, but we’re on a field trip in math class, so it’s a good thing. Tape measures are being stretched out, kids are pointing their phones at the ceiling, and most kids are sketching a triangle and writing down some sort of trigonometric equation. It’s my favorite day of the year.

Eventually we return to the classroom. My least-focused kid (one of those with an ADHD star next to his name in Infinite Campus) happily sits down and gets to work solving trig equations. How could he not? I just let him run around the Commons for 10 minutes.

They’re beautiful creatures, ya feel?


8.4 trig lab

8.5 trig invest how high is ceiling (I think this was adapted from something from Tina Cardone @ drawingonmath ??? Not sure. But I definitely stand on the shoulders of giants. Thank you all.)

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Filed under fun, Geometry, grading, trig

Why Do We Memorize the Unit Circle?

Let me preface this blog post by saying I teach a “lower-track” Alg 2/Trig class. (The school tries to spin it as “we have many options for math classes, blah, blah, blah, so that students can be successful”, which is great, but it’s also silly not to call it what it is.) Almost all of my students are seniors, and the average student is going to a 2-year college. Some will go to a 4-year college. They’ve got a lot of potential, but they’re not particularly motivated by academics.

So keep in mind I’m thinking of my students, not a group of juniors in Pre-Calculus who will take Calculus AB next year; however I think the following question applies to those students as well.

Why do we make students memorize the unit circle?

Isn’t it more important to understand what the unit circle is? Memorizing a few selected values didn’t help with conceptual knowledge of the unit circle, and I ultimately felt like I was making them memorize it simply because I could. And then I could give them a quiz. I almost feel dirty about it because instead of making sure they actually know what the unit circle is and why it works, I had them memorize a bunch of numbers.

I love trig and love teaching trig, but I’m not sure memorizing the unit circle is helping any of my students actually learn trig.

Any feedback is appreciated! Thanks!


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Filed under FST / Algebra 2, trig

Happy Thanksgiving Week

Listen to them. Love them. Even if you don’t or can’t.

Some random thoughts from today.

I want to get better at differentiating. I have some meager ideas, but it’s a start.

Let them pick which homework problems to do. Assign some level 1, level 2, and level 3 problems, and they pick x of them to do. Any x that they want.

And be really frank about the levels and what they can expect from working at that level. Be direct about everything.

I need more challenges for the upper end. The kids who are bored.

Tell them the minimum requirements and what grade they can expect by doing that.

Get them hyped about level 2, level 3, and beyond. They want to be challenged.

Constantly remind them of positive behaviors. If you want to be an A student, do this. Or just tell them to pretend to be an A student even if they’re not.

I want to get better at soliciting responses. I want to get better at letting them do the talking.

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Filed under Uncategorized

A Note on Equity

Yesterday one of the guidance counselors sent out an email asking for nominations of a sophomore student to send to a leadership conference. This student was supposed to demonstrate leadership and contribute positively to the school community.

I thought about who to nominate. A student who immediately jumped to the front of my mind was a black male who fits the criteria and is an awesome person in general. He’s kind of quiet though, so I wasn’t sure whether to nominate him or not. I ended up not nominating anyone and decided to let other teachers make the nominations.

Today the guidance counselor sent out the list of nominated students. The black male mentioned above was on the list. I immediately thought, oh, good , I’ll vote for him.

Then I saw another name on the list, a white male, who I have in class this year. I didn’t think of him yesterday, but he is a great leader, and I am so thankful to have his positive influence in my classroom.

So, of course, the typical internal debate ensued. Do I vote for the black kid or the white kid? Does the black kid “need” my vote more? Is this an opportunity that he might not get elsewhere?

I went back and forth for quite awhile, and then started scanning other names on the list. Suddenly it occurred to me that perhaps I was having the wrong debate. I was so stuck on racial equity, but what about gender equity? How come I immediately focused on two males for a leadership conference?

I am regularly in disbelief (and sometimes in shock) about the lack of women in leadership positions, yet here I was debating between two male students to send to a leadership conference. Although I immediately considered racial inequity, I almost didn’t even acknowledge gender inequity. Weird. This made me wonder if I am somehow influenced by societal norms about men assuming leadership positions.

Once I came to this realization, I completely changed tactics. I recognized many female students on the list and quickly settled on one who I think is, and will continue to be, a great leader and positive role model.

She happens to be white, but I’m completely satisfied with my choice.


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Filed under conversations, culture

Take Aways from Green Lake

Yesterday I had the good fortune of attending the Wisconsin Math Council Conference for the first time, and it was a lovely experience.

I went with my colleague who is also a first year teacher, and we ended up in some really great sessions.

My favorite session was definitely Get Up and Move, which was exactly how it sounds. I learned some great new strategies for getting kids out of their seats and moving, including Bucket Sort, Musical Math, Relay Race, and Clue. I think my kids sit too much, and I want to get better at doing fewer, chunked activities rather than long work times, so doing a practice activity where they’re out of their seats and moving sounds like a win-win.

I also went to Jo Boaler’s keynote. I’ve been following Boaler’s work for awhile now, so I didn’t really learn anything new, but her presentation was so lovely and her message so true. I can’t agree with her more, and I hope to see a major shift in mathematics education soon that encompasses her ideas on mindset, mistakes, and success in the math classroom.

One session that I wish would have existed is lesson planning or unit planning. I feel like maybe I should have learned that in teacher school, but whatever. I want to get better at planning.

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Filed under collaboration, conversations, Uncategorized

Fun with Expected Value

I just taught expected value in FST and really enjoyed it. The two main tasks I used were: The Carnival Candy Game and Dan Meyer’s Money Duck.

The Carnival Candy Game

You’re at a carnival and you get to pick one piece of candy from a bag. The color candy you draw determines how much money you win. I used starbursts, and I set it up like so:

starburst data as jpg

The students didn’t win money; rather they won that many starbursts. (I had a different bag of starbursts for prize winnings because I made sure that the candy drawn was replaced each time to keep the probabilities the same for everyone.)

This was enjoyable because naturally all the kids wanted to pick the purple one. Not surprisingly, most picked pink, yellow, or red, but I have 45 FST students (two classes), and the 44th student did pick the purple one.

Then I asked them to calculate the expected value for their prize winnings when playing this game.

Then I said, suppose it costs $5 to play this game. What does that mean for the player? What does it mean for the carnival game host?

Money Duck

Love the Money Duck. The students were very engaged by the idea of the money duck. I basically followed Dan Anderson’s lesson plan for this one. Like Dan’s students, and as I commented on his post, my students also wanted to determine the possible/impossible distributions based on what they saw in the video instead of in theory. I slightly fixed that in my second class by stopping the video after the first $1 money duck, explaining that the video was made up, and stressing that we were interested in what is possible, not necessarily what the company actually does.

Like Dan, I had my students come up with company names, probabilities, and price. They then had to compute expected value and their profit. I also compiled the data in a spreadsheet, but didn’t really do anything with it, unfortunately. If I did it again I would like to have the students do some more sharing and comparing between groups.

money duck groups jpg

I definitely recommend both tasks.

And then things got even better. Today was the grand opening of a new Cabela’s nearby my school, so several of my male seniors told me how they all skipped class this morning (well, some of them probably had open campus 1st period… I hope) to get in line at the new store because the first 500 customers received a gift card up to $500. One of them said, “But Ms. Cummins, they didn’t tell us how many were for $500″. It turned out that they all got $10 gift cards except for one who got a $25. It was perfect. I told them I was going to write a test question about that.


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Filed under FST / Algebra 2, fun, probability

Second semester

I’ve been enjoying second semester so far.

In geometry, we just finished up the unit on triangle congruence. I felt like it was kind of rushed, but progress was definitely made. We revisited proofs after a brief introduction back in October, and I enjoyed seeing kids reasoning again.

One practice that I used several times was having small groups write out proofs on the whiteboards and then sharing them with the rest of the class. I asked each person to contribute one thing to the board (the diagram, marking the diagram, writing the congruence statements, using cpctc, etc) which was a good way to make sure no one was dead weight. One thing I’d want to improve is what the kids in the. audience are doing while the other groups share. Too many were tuned out and I felt like I was the only one listening and asking questions. However I think everyone was listening when one student ended up saying FU is congruent to FU.

I’m now teaching stats in FST. The curriculum is… lacking to say the least. I feel like stats could be so cool, but these crappy worksheets with blurry images are pretty uninspiring. My mentor said she’d help me come up with some cool stats projects, so I have to remember to follow through on that.

Speaking of curriculum, during the last inservice, the math department met and had a pretty kickass discussion on equity in our curriculum. Nothing concrete came out of it, but it was refreshing to hear everyone’s ideas, and I was glad to learn that I’m not the only one who thinks much of our curriculum is really out-dated, non-rigorous, and inequitable. I really do feel like I’m teaching something that was written in the late 80s or early 90s. I can’t relate to it all, and I sympathsize with my students when they can’t either.

So there’s much work to be done, but so far second semester has been shaping up nicely. It’s frickin cold out and we won’t have any vacation until spring break, but I’ve been enjoying every day so what more could I ask for? I’ve been feeling pretty lucky lately.

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Filed under collaboration, Geometry, group work, productive struggle