Trying to find math inside everything else

The Secret of the Chormagons

(Doesn’t that title sound like it should be a YA fantasy book?)

I shared this Desmos Activity Builder I made on Twitter, but never wrote a post about it. Oops! Let’s do that now.

First, here’s the activity.

This activity is basically adapted from Sam’s Blermions post that I had helped him think about but he did all the hard work of creating questions and sequencing them. I’ve used the blermion lesson in the past and it went well, but that last part lacked the punch I was hoping for, having to work with analog points and compiling them together myself. But then I thought – wait, Desmos AB does overlays that will do this beautifully, if I can just figure out how to get the Computation Layer to do what I want. So I set to it.

The pacing helped pause things to conjecture about what chormagons are – I stopped them at slide 5 so they can make those conjectures. I then advanced the pacing to 6 for the “surprise,” and 7-8 to make further conjectures. Look at some of theirs below.

Even showing them everyone’s, I tended to get conjectures about the shape their points make – a trapezoid, a pentagon, a heptagon, etc. (One person seemed to guess the truth, but that was uncommon.)

Then I showed them the overlay.

I saw at least one jaw literally drop, which totally made my day. We talked about why it might be a circle, and what that means for these shapes, then I introduce the proper terminology “cyclic quadrilaterals.” (I taught this lesson as an interstitial between my Quads unit and my Circles unit.)

Speaking of proper terminology, you may notice I called them Chormagons here, as opposed to Blermions. That’s important – Blermions is very google-able, it leads right to Sam’s post! But Chormagons led them nowhere. (And they were so mad about that!)

Now Chormagons will lead right here. So this is an important tip if you use this DAB: make sure you change the name of the shape!

Two main things I wound up talking about at MfA Summer Think were talking in math class and grades. One thing we talked about in regards to grades is that students (and parents) often flip out when introduced to a new grading system that is different from what they are used to, even if by the end of the semester they come around and say that they are glad it was done that way.

I thought, then, instead of just springing my grading/SBG system on them, that we could reflect on what grading systems really mean and what they should do first, to prime the transition. So I created a grading Talking Points (with help from my Twitter mentions for some statements).

Free-writes

At the MfA Summer Think, I went to a Teacher’s Poetry Circle. It was pretty great. Below are what I wrote during the two free-write times, slightly edited/punched up.

Why do I teach?

To rebel in small ways
To rebel in larger ways
To comprehend a system that was not designed with our best interests at heart

To share knowledge
To forge connections and broaden horizons
To create experiences that linger in hearts and minds

To help others reach their true potential
To help myself reach it, too
To help us all figure out how this world works
To help us all figure out where to go next

Hard

This is hard
but there are harder things.
Changing the world
Dismantling structures that oppress
that
is hard.

But maybe that’s what this is,
just at a smaller scale?
Maybe “hard” is just a matter of scale.
Can we scale up what we do?

Maybe it is impossible –
the square-cube law restricts us all
and our attempts to scale up
collapse
under their own weight.

Sometimes a law must be broken
To do what is right.
Why not this one?
Why not push ourselves to the edge
of the possible?
Will we fail?
Will we fall?

I allow myself to fall
because only by falling can you see
the true heights and depths of where you were and where you can go

From the air, you can see everything.

A Way to Foster Productive Struggle?

My school has been trying to better create conditions for productive struggle in our classes, because a lot of students have taken a very receiving stance. So early in our Area and Volume unit, I decided to use this task from Illustrative Mathematics.

The task is a 7th grade task, and so involved nothing new for my high school geometry students – just area and perimeter/circumference. But the task has a lot of parts, not all of which are obvious from looking at it. So I gave them task, and then I was “less helpful.” In fact, I barely spoke during the lesson, only quietly clarifying things, but reflecting their proximity questions back towards themselves and their other group members.

Almost every group that attempted the task solved the problem on their own. (I followed up with an extension where they designed their own stained class on the coordinate plane and found the price using the same pricing, for those who finished quickly.) I had a group of three girls who don’t usually feel very confident in my class feel like rock stars after figuring the whole thing out themselves.

A few days ago, I saw this tweet:

I thought it really applied here. While the content was still related to what we were learning in high school geometry, the opportunity to solve a complex task with little scaffolding was really helped by using a task from an earlier grade. I recommend it.

One Problem, Eight Ways

I had a pretty good lesson recently that I wanted to share. It was at the end of my quadrilaterals unit, and so we were working on coordinate proofs. I love coordinate proofs because you can get so much information from just a pair of coordinates, which lends itself to lots of different ways of solving the same problem. Add to that how many different ways there are to prove something is a square, and we have the start of something good.

I gave the students the above sheet, starting off with some noticing/wondering about the graphed figure. Then I assigned each table a different method to prove that the quadrilateral is a square. Each group was off to their whiteboards to get started.

It was really great to see each group discussing the problem so intently, and it reminded me how easy it is to facilitate discussion when up at the vertical whiteboards. Afterwards, the students went around in a gallery walk to compare their proofs to the other methods. They analyzed how they were similar, how they were different, and thought about which method they might prefer in the future. (Some comments included things like preferring method 2 because it only involved slopes, even though it involves more lines.)

The whole lesson went so smoothly and had tons of intra- and inter-group discussion. Need to use the structure again.

Whole Class Test

I teach an SAT Math Prep this year, which has been an interesting challenge. We basically started off with lessons on all the different content in the exam, then had a long section on tactics (which can be framed as test-taking tactics but I noticed are often just tactics for solving problems in general, which was nice). But we reached the end of those, and the (in-school) SAT is a month away. The obvious thing to do is to just keep doing practice exams, but that can get a bit boring, for both me and the students. Plus, the class that meets Tues/Thurs hasn’t had very many graded assessments this marking period, so I needed to give them something.

I had decided that grading them on correctness in a practice SAT is not appropriate. I had told them this before, and they knew their grades on their assignments were more for things like how they applied the tactic we were learning. But last class they walked in and I gave them a Part 3 exam (the non-calculator part) and told them it would be graded – but there would be a plot twist. For right now, just take it individually, except this half of the room should start from the back and go forward. Oh, and you get 5 fewer minutes than normal.

While they were working, I went around on my whiteboards and put up the numbers 1 through 20 well spread out, and an ABCD for 1-15. (I wish I had taken pictures!) This started to get them suspicious. When time was up, I told them my grading scheme: it was out of 5 pts, and they lost a point for every question they got wrong. So if you got 15 right, that’s a 0. But! They had the remaining 20 minutes of class to work together and figure out what the right answers should be. And if anyone got less than 15, the whole class lost a point – forcing them all to work together. (With limits, of course – they won’t be penalized for that kid who went to the bathroom for 15 minutes during this, for example.)

A suggestion I made to them was to go around and make votes for their answer for each question. A clear consensus might mean that that is the right answer. However! Don’t be afraid to put your answer down even if everyone else’s is different. I’ve seen questions where only one person got it right. I told them they need to convince each other of what the right answer is.

Let me tell you, I heard so many great conversations as they and I went around the room. Because it’s the SAT, no one gets them all right, so everyone is being pushed to make a convincing argument that their answer is right. Students who weren’t sure got explanations from others. It was delightful!

About halfway, I noticed a clear consensus for about 15 of the 20 questions, but the middle 5 were really quite split. So I lead the class in sharing out their reasoning for some of those questions – never saying what the right answer was, but again letting them convince each other.

It was a nice collaborative effort – I highly recommend it.

Vietnamese Age and the SAT

Dwight Eisenhower was born on October 14, 1890, and died on March 28, 1969. What was his age, in years, at the time of his death?

(A) 77
(B) 78
(C) 79
(D) 80

When my boyfriend went to his grandmother’s funeral, he found himself confused about exactly how old she was. Was she 93 or 94? He heard different people say different things. Eventually he figured it out. In Vietnam (and apparently in other places in East Asia), when you are born, you are 1. The next year, you are 2. And this ticks over at the beginning of the solar year, not on your birthday. So I, born on December 22, would, 374 days after my birth, have been considered to be 3 years old using this reckoning. (It might be more accurate to say that I’m in my 3rd year – being alive during 1985, 1986, and 1987 at that point.)

Earlier this week, in my SAT Problem Solving class, we encountered the problem at the top of this post. The correct answer, according to the book, is (B) 78. But according to the Vietnamese reckoning, he’d be 80, and the answer would be (D).

Before my boyfriend went to that funeral, I wouldn’t have even looked at this question twice. I had never heard of another way of determining age. And I’m willing to bet the people who wrote this question haven’t, either.

It’s a small example of the way tests can be biased, and how having more diverse voices in the process could help avoid this kind of mistake.

TMC17 Speaker Proposals

We are starting to gear up for TMC17, which will be at Holy Innocents’ Episcopal School  in Atlanta, GA (map is here) from July 27-30, 2017. We are looking forward to a great event! Part of what makes TMC special is the wonderful presentations we have from math teachers who are facing the same challenges that we all are.

To get an idea of what the community is interested in hearing about and/or learning about we set up a Google Doc (http://bit.ly/TMC17-1). It’s a GDoc for people to list their interests and someone who might be good to present that topic. The form is still open for editing, so if you have an idea of what you’d like to see someone else present as you’re writing your own proposal, feel free to add it!

This conference is by teachers, for teachers. That means we need you to present. Yes, you! In the past everyone who submitted on time was accepted, however, this year we cannot guarantee that everyone who submits a proposal will be accepted. We do know that we need 10-12 morning sessions (these sessions are held 3 consecutive mornings for 2 hours each morning) and 12 sessions at each afternoon slot (12 half hour sessions that will be on Thursday, July 27 and 48 one hour sessions that will be either Thursday, July 27, Friday, July 28, or Saturday, July 29). That means we are looking for somewhere around 70 sessions for TMC17.

What can you share that you do in your classroom that others can learn from? Presentations can be anything from a strategy you use to how you organize your entire curriculum. Anything someone has ever asked you about is something worth sharing. And that thing that no one has asked about but you wish they would? That’s worth sharing too. Once you’ve decided on a topic, come up with a title and description and submit the form. The description you submit now is the one that will go into the program, so make sure it is clear and enticing. Please make sure that people can tell the difference between your session and one that may be similar. For example, is your session an Intro to Desmos session or one for power users? This helps us build a better schedule and helps you pick the sessions that will be most helpful to you!

If you have an idea for something short (between 5 and 15 minutes) to share, plan on doing a My Favorite. Those will be submitted at a later date.

The deadline for submitting your TMC Speaker Proposal is January 16, 2017 at 11:59 pm Eastern time. This is a firm deadline since we will reserve spots for all presenters before we begin to open registration on February 1st.

Team TMC17 – Lisa Henry, Lead Organizer, Mary Bourassa, Tina Cardone, James Cleveland, Daniel Forrester, Megan Hayes-Golding, Cortni Muir, Jami Packer, Sam Shah, and Glenn Waddell

Name That Solution

I was reviewing solving equations for my SAT Math class. It’s a tricky thing to do because “equations” includes linear, systems, quadratic, and exponential equations. A lot of different skills to go over in a short amount of time.

After working through the requisite problems, I wanted a little more practice, so I came up with a game that they could play, based on the Bid-a-Note sections of the old “Name That Tune” game shows. I called it Name That Solution. Gameplay goes like this:

• Start over with a simple equation, like “x = 2.”
• Each turn, a team can change the equation in one way to make it more complex. (For example, make it “x + 3 = 2” or “5x = 2”.) Only one operation and one term can be added at most per turn. The team finished by saying “I can name the solution of that equation.”
• On a team’s turn, they may challenge the other team to, in fact, actually solve it. (“Go ahead! Prove it!”) If the challenged team can, in fact, solve the equation, they earn a point. If not, the challenging team gets a point.
• First team to 5 points wins.

They played on whiteboards so they can change the equations quickly. The students quickly learned to not overextend themselves when making the equations harder, lest they find themselves challenged. So it leads to a nice exercise of constantly mentally making sure you know the steps to solve something before you take your turn, getting a lot of practice.

At the end of one of the classes, I did a big class-wide version, half the class versus the other half. But they wound up being very conservative, with neither team challenging the other and only take moves they knew they could solve. Which I guess was the point.

That final round.

Day in the Life: October 5th, 2016

This is part of the Day in the Life Project.

5 1/2 AM – alarm goes off

5 11/12 – I actually get out of bed and start getting ready. I always get home late from trivia on Tuesdays, so Wednesday mornings are the toughest. On top of that is this being the first day of the school week thanks to Rosh Hashanah, and it was a struggle.

6 11/20 – Out the door. Even though I got my bike fixed yesterday, I’m not taking it today because I’m carrying my laptop, all my student work, and the five packs of markers I bought online. I head to the subway.

7 1/20 – That took much longer than it should have. If I had gotten on the first local train, it would have beaten the express I waited for. But the express did wind up beating the second and third local that passed through, so I guess it was right to wait.

Because I’m teaching Mathalicious’s Sweet Tooth in Calculus today, I spent the subway right reviewing the assignment and lesson guide. (Since I taught it last year, it was more of a review than a deep dive.) While I read it, I decided that I needed to add some supplemental questions to more explicitly tie it to what we’ve been doing with area functions and Riemann sums. So that’s on the agenda.

I got off the train, loaded up a podcast (Within the Wires), and started walking to school.

7 7/12 – I arrive at school (after also stopping to get breakfast). As soon as I get in a guidance counselor pops in and asks me to find a room in the school for the attendance meeting they’re having today. I run up to my classroom and grab my SAT book to prep for my problem solving class, then settle into my office to get some things done.

8 – Official start of school day

8 7/15 – I’ve written up the supplemental sheet for Sweet Tooth, adjusted my lesson plan, and decided what we were doing in SAT Problem Solving. I also had to print a schedule for a student who didn’t have one at the request of a different guidance counselor. Now to get some printing and copying done.

8 4/5 – That was surprisingly painless, considering it’s the equivalent of Monday morning. Maybe it’s because I went at the end of 1st period instead of the beginning of 2nd, when there’s a line. Now the morning announcements are going on, which make me very grateful I don’t teach 2nd period (and, thankfully, it is in my power to make sure I never do).

9 23/60 – I stapled all my feedback slips to the assignments I graded over the weekend and looked into some of the IEP Compliance issues that need to be corrected soon, as well as a few other miscellaneous programming tasks I had to do. Now I’m just last minute prepping myself for class.

12 1/2 – Well, that was a mess. SAT was fine, but Calculus – I tried to do too much. Sweet Tooth was a really great lesson last year, but it was much later in the year after the students had had more time to grapple with the ideas. But because of the holidays and the fact that I may have jury duty next week, I was feeling pressed for time, and so I tried to squeeze the lesson that should have been a follow-up to Sweet Tooth into the same period. And now I’ll need to take another period (or at least another half) working through those ideas anyway. During 4th period my AP came in for a formative observation (not rated), and I’ll be meeting with her tomorrow for feedback. Not the best first lesson to see.

I’m also having a hard time adjusting to not being in my classroom all the time. I spend most of my day in my office and carry all my stuff to the classroom when it’s time. So I feel like I’m spending so much class time doing things like setting up my computer, putting all the papers in the right spot, etc. Most days the SMART board markers don’t work, which was always something I could check before class started but now I can’t, and if they don’t work, I just have to roll with it. It’s a little stressful.

After class ended I went out to Trader Joe’s to grab some lunch, which I am eating now – though my lunch period ends in 5 minutes.

13 2/5 – I’ve spent all of 7th period trying to figure out exactly what needs to be changed and what doesn’t for compliance purposes. Usually the students are getting all the services they need, but the documentation doesn’t match up, so it’s a lot of getting all those ducks in a row. And the systems for doing it are, of course, not all neatly aligned and in one place.

14 4/15 – Just had to do some schedule changes with one of the guidance counselors and chatted with the AP of Special Education about next steps for the compliance process. Then I futzed around on the Internet for a bit because I’m running low on brain capacity. I was intending on staying late today to do work, but I’m not sure I have it in me, thanks to my lack of sleep last night.

14 1/3 – Official end of the school day.

14 4/5 – I made copies of the assignment that I’m going to do either tomorrow or Friday – I’m not sure yet. I had originally planned it for today, and thus made it yesterday, but decided yesterday to move in back in favor of Sweet Tooth. Based on how today went, I’m not sure I want to move forward to it – but I might also want to, as it might let me clarify some things in a new way rather than sitting on the same ideas in the same way.

Either way, I’m heading home now.

17 – Made it home. I took the long way around, playing Pokemon Go and getting a lot more walking in, and stopping for a snack at the taco cart. (I had wanted to go to the Chinese bakery, but ran across the taco cart first.) Now I’m checking up on e-mails that I got in the past 2 hours, and then I’ll probably watch some TV.

19 1/2 – Or wind up falling asleep. I guess I really needed that nap.

20 1/2 – I made a smoothie for dinner and now am working on my Interim Assessment – sorta like midterms that my school gives but we need to submit several weeks ahead of time. It’s a weird thing to me and I still don’t understand how/why it’s different from a normal test – especially for a course that is not taught by more than one teacher, such as my Calculus classes.

21 1/2 – I’m giving up the ghost on this one – I’ll work on it more in the morning. Luckily I’ll have time then since I’m already planned and copied for tomorrow. Now it’s time for maybe a little Ace Attorney 6, then bed.

Reflection

1. Teachers make a lot of decisions throughout the day. Sometimes we make so many it feels overwhelming. When you think about today, what is a decision/teacher move you made that you are proud of? What is one you are worried wasn’t ideal?Well, the decisions I made planning Sweet Tooth are documented above. My good decision today was probably in eating right, haha.
2. Every person’s life is full of highs and lows. Share with us some of what that is like for a teacher. What are you looking forward to? What has been a challenge for you lately?I’m looking forward to settling into a routine. It’s started to come about – programming is starting to peter off (for now), but we have a lot of holidays disrupting the flow.
3. We are reminded constantly of how relational teaching is. As teachers we work to build relationships with our coworkers and students. Describe a relational moment you had with someone recently.I went to a trivia night with some of my coworkers (they brought me in as a ringer). I got to know some of them better – one of my APs tried to purposely make two of us friends because we have a lot of interests in common.
4. Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What have you been doing to work toward your goal? How do you feel you are doing?My Friday Letters, of course, have been helpful, but I’ve also tried to be more actively there. Some students invited me to see their volleyball game and I actually went, which was nice.
5. What else happened this month that you would like to share?I caught a lot of Pokémon? September is always a work-heavy month, so not a lot outside of it.