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In my Adv. Precalculus classes, I use an “anchor problem” of winning the lottery to talk about geometric series. The setup has students getting $50,000 at the end of each year, for 20 years. As we explore the problem, we talk about what happens if you leave the money under the mattress, what happens if you put it in a high yield savings account, and what happens if you put it in the stock market.

However, we have to see if anyone in the class actually wins a million dollars! So I create scratch off tickets for each kid, and they all scratch them off at the same time, and we see who the winner is. It sounds more exciting as I type it than it was in class. Instead of a million dollars, I gave the winner in each class 4 kitkats, a large math-y sticker I designed and got printed, and an exclusive math button I designed and got printed years ago.

One of my favorite things from today is that in one class, a student who won the million dollars immediately took the button and put it on. I told that student how happy that made me!

A second thing that was good today was that another teacher wanted to meet with me for some basic advice on a project they were doing, and then after that short meeting, we got to have lunch together for like 20 minutes. It was one of my best teacher friends and I hadn’t chatted with them forever, and so it was so nice to reconnect. In that meeting, I was saying something good about a student to my friend, and then like 20 minutes later I saw that student in the hallway and said “were your ears ringing because I was singing your praises?” and then they smiled greatly and fistbumped me and I don’t think I’ve fistbumped with a student this whole year and so that was fun.

My last good thing is that we had our final meeting for the Flatland book club. One person couldn’t make it, but someone who couldn’t make the first meeting was able to come to this meeting! We discussed the second part of the novella, and it seemed like everyone enjoyed that part of the book. I started thinking much deeper about some of the religious language in the book than I had done previously. We took a group picture, and we might even get together again to watch the movie!

I’m slowly going crazy with all the work on my plate, and I’m still being crazy productive to deal with it, but I’m also being positive about feeling I can get it done and there is a light at the end of the tunnel.

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Workaholic

Today, I think my good this is that I was a workaholic. I woke up 20 minutes early, did a lot of work with that extra time, I worked throughout all my free periods fairly efficiently, and after our department meeting ended at 5pm, I went home, threw out a couch (!), and then worked for another two hours. In theory this isn’t a “good thing.” But I have so much coming up way in terms of grading (giving tests this week) and parent-conferences (next week), that I needed to get all this done. And althoughh I know what’s ahead of me, it feels great to have a good chunk of stuff out of the way. It’s going to be a brutal two weeks, where I’m probably going to be driving myself crazy working, but I know there’s a light at the end of the tunnel!

Another good thing is that in math club today, a student put together a great set of problems for us to work on based around “the difference of squares.” It had some really nice challenge questions. And I was proud of figuring out this one (I think it was problem 19 on some AMC contest):

You have a two digit number x, and then you reverse the digits and get y. It turns out that x^2-y^2=m^2, where m is an integer. What is the value of x+y+m?

I think that was the problem… in any case, it felt really good when I solved it because I had a key insight that unlocked it for me.

Great Pattern Recognition

Today is our first day back from a 5 day weekend (Fall Break/Thanksgiving Break). It was a lot, coming back, but I did okay and wasn’t dying in any of my classes.

One really great thing that happened in 2 of my 3 precalculus classes… I showed students this geometric series:

They haven’t learned anything about how to add this all together, except by hand. But in two of my three classes, a few groups — in just a few minutes — were able to use pattern recognition to find this sum.

They started with smaller things, and said…

if s=5+10+20, then it’s s=(5+10)+20=15+20

if s=5+10+20+40, then it’s s=(5+10+20)+40=35+40

if s=5+10, then it’s s=(5)+10=5+10

if s+5+10+20+40+80, then it’s s=(5+10+20+40)+80=75+80

So they said it’s the (last number)+(last number-5).

So lovely! They didn’t have a proof (I barely gave them, any time for this, so I wouldn’t expect a proof). And I know this only works nicely because it has a common ratio of 2. But I wanted to give them something nice to start things off.

I definitely did not see that, or expect that approach, when posing the question! Ingenious!

FALL BREAK!

So we have Wednesday, Thursday, and Friday off for Thanksgiving! So there is literally nothing better than the fact that I taught all my classes in the morning, and I don’t have a double-block class today at the end of the day. So I’m done teaching today, and I’m now officially on 5-day vacation mode!

(But also, today in geometry, kids were doing super good thinking and I was so excited to see them reason through some very cool stuff involving rotations. I just looked and I have a blogpost about what I designed for rotations here.)

Tried out something new…

In my geometry class, I tried out something new. It was fun and hands-on, and I enjoyed seeing kids make sense of it. It took longer than I anticipated… I assumed kids would figure things out and then it would be done in 10 minutes. But it took around 10 minutes for a kid to have the key insight, which I allowed to spread around the room. And even with that, it took another 15 minutes. It was a good 15 minutes because kids got to really understand the contours of the problem and how it related to something we had learned previously. (It seemed, initially, unrelated.) I’m being vague because I don’t want to type out what we did — but I hope to blog about it (on my teaching blog) soon.

I had a former student email me last week about coming to Packer and wanting to meeting up. And today was the day, so I got to have coffee and hear about their college life for around a half hour!

I got to have lunch with our lower school math coach, where I got to catch up with him (which was lovely) but also answer some of his questions about the Park City Math Institute (PCMI), where he’s considering applying to go this summer.

Today, as I was leaving school, I saw a cart filled with library books, but the cart said “FREE FREE FREE!” And there were so many good books, some of which were among my favorites!, and so I grabbed a large stash. And a friend was nearby in their office, so I grabbed them and made them take all of the books I love and had already read. Here are the books I snagged, all of which are new to me (except the Jhumpa Lahiri book which I own, but wanted to give to a friend):

Feel free to let me know in the comments if any of these books are books you’ve enjoyed! I’ll put them higher on my giant “To Be Read” stack of books in my apartment!

Random Acts of Kindness

So yesterday the juniors had their first college night, where they get introduced to the whole process from our amazing college counselors. Because of that, the juniors had a “no homework night.” 

And I teach three junior classes, which I saw all yesterday. AND I BROKE THE RULE. I assigned nightly work. BWAHAHAHAHA. But you know me… I didn’t really break the rule. I asked every kid to do a random act of kindness before our next class.

And then today, I saw two of those classes. So after our warmup question, I asked kids to share what they did. I had my candy jar, and after a kid shared, I threw them a piece of candy. I heard wonderful things, like helping someone who dropped their groceries. to letting their younger kid sister sleep in their room because they were scared of monsters, to finding a way to wake up a friend who was in college and had an important deadline that they were sleeping through, to taking their pets out on extra long walks and get extra cuddles, to helping a sibling with their science homework, to noticing a possible ongoing collision between a stranger and a vehicle and trying to avert it, to …

It took only 5 minutes in each class and was so freaking sweet. 

I didn’t expect everyone to share, but I think the fact that I had candy, and the fact that so many people shared something, eventually everyone did. Honestly I don’t think all students intentionally went out to do a random act of kindness, but I do think many of them reflected on their days and found a moment that worked, and that works just fine for me. 

PS. I taught a long block today (it’s a double period). It’s at the end of the day. And as I walked in, I dramatically said “Draw the cat eyes sharp enough to kill a man.” I had just been listening to Taylor Swift’s new album (the start of the lyrics of “Vigilante Sh*t”). And a student said “This is why.”

Apparently, they had just said they enjoyed coming to math long block because of the energy I bring (something they’d said before… I even think I might have put it on this blog before). But I don’t feel good about my teaching usually — so I’m going to take these wins. 

I didn’t die during my hell day

Today I introduced a puzzle that goes on for a bunch of weeks to my geometry kids. Each time we have a few extra minutes, I give them a piece of information, and they have to figure out the pattern in the puzzle. The details aren’t important, but I was excited by their thinking. I also saw some really great thinking when they were working on “Algebrainiac Attack” puzzles. It was my “hell day” (where I teach all my classes, and one of them in the long block), but even during my geometry class during the long band, I still kept my energy up.

I had two great meetings with kids.

During community time, I went for half the time to one of the clubs I advise (“Crafting for a Cause”) and as usual, we had a fun chill time! And we got a new student to join in (one who I also teach, so double bonus!). 

I have a lot to do — including this weekend — but I think I can actually get it done. Fingers crossed. 

More Fraction Thinking

To think about fractions of sets, we thought about our group of kids.

I teach on a military post and our kids all live on post. It’s a bit odd though because there’s a section of housing that is considered post but is off the physical land of post. Or, at least, off the land that you get to by going through a gate and showing your pass. So we counted all the kids in our room at the time and tallied who went through a gate to get to school and who didn’t. Then I asked them what fraction went through a gate. It took a bit for them to transfer what they understand about area models to this set, but once one kid did, I could see the light bulbs go on.

Counting Around

We just started our unit on fractions in third grade, often a challenging study. Today I had the kids count around by 1s. We got to 20 (a few kids were out of the room for various reasons). So I asked where they thought we’d end if we counted by 2s. Most kids thought it would be 40 but a few thought it would be 22. So we did it and, of course, ended on 40. There was some thinking about that.

Then I asked where they thought we’d end if we counted by halves. Lots of different thoughts on that! There was one kid who was certain it would be 10 and could explain why. We counted, but this time each kid had half a circle and we added them to a chart as we counted so that we could do the visual of our counting.

It was really exciting to hear the kids’ thoughts after our counting when they could see what we’d done and what it meant. They did come to the conclusion that their one classmate is brilliant!

Counting Around

We just started our unit on fractions in third grade, often a challenging study. Today I had the kids count around by 1s. We got to 20 (a few kids were out of the room for various reasons). So I asked where they thought we’d end if we counted by 2s. Most kids thought it would be 40 but a few thought it would be 22. So we did it and, of course, ended on 40. There was some thinking about that.

Then I asked where they thought we’d end if we counted by halves. Lots of different thoughts on that! There was one kid who was certain it would be 10 and could explain why. We counted, but this time each kid had half a circle and we added them to a chart as we counted so that we could do the visual of our counting.

It was really exciting to hear the kids’ thoughts after our counting when they could see what we’d done and what it meant. They did come to the conclusion that their one classmate is brilliant!