#Teach180 Reboot

And here we are, August again. I spent the weekend at a large gathering of teachers and the talk inevitably turned to “When  do you head back to school?” I answered (usually grumpily), “Monday – though it’s planning days for 2 weeks,” which is somewhere between wishing it were still June and perhaps unfairly using an early August return as a badge of honor and being about as ready to go back as I’ll ever be.

August also coincides with #MTBoSBlaugust. The Mathematics Twitter Blog-o-Sphere – a group of mathematics teachers who share their practice on the internet – is dedicating the month of August to writing a blog a day. It’s spearheaded by DruinOK (Hashtag: that moment when you only know teachers by their Twitter handle). Also gotta shout out Ms. DiMaria, Mrs. Orr, and  STEMinist in the Classroom – 3 colleagues who are also rising to the #MTBoSBlaugust challenge.

One of the prompts asks “What do you hope to get out of #MTBoSBlaugust?” While the obvious answer is a sweet book deal and maybe a Netflix series (“Teacher falls down in 1st period a lot! Loses lunch in desk!”), I’m using #MTBoSBlaugust to reboot #teach180. (Sidenote: A couple of colleagues and I wrote an article about our experiences with #teach180. This post is getting strangely meta)

I struggled with #blog180, which is still how I think of #teach180 (a blog a day versus 140 characters and a picture a day. You can guess how that went). I have grand visions of writing out long complex blogs (many of which remain drafted in my head, though their usefulness has long since ended), only to be thwarted by horrible time management and an inability to adult.

So I’m doing what I think good teachers do. I’m cutting out most of my talking and explaining* (with this blog being the exception, I guess) and letting my audience drive the learning. I’m going to post a picture and a few sentences of background context, if necessary, and then let you, gentle reader, ask the questions. I’m hoping that this simplification will engage readers and be both a bit more realistic and sustainable. The more I hear about mathematics blogging, I hope that a slightly boring (OK, really boring) photo every day will be more of a window in my teaching practice than a finely crafted blog that I’ve secretly been writing and rewriting in my head for the last year.

2016-08-01 08.15.08

*Ha. Don’t count on it.

**Also, you don’t have to say what you notice and/or wonder about this photo. It’s mostly so that an image shows up when I tweet it. I wouldn’t not give you extra points for doing it, though.

Day 60: Patty Paper versus Rubber Bands

2013-11-13 13.38.11Our transformation unit continues. Students spent most of today’s class practicing transformations. At this point, students seem to be stronger at translating than they are with dilating. I’m not sure if it’s because of the tools (patty paper versus rubber bands) or because dilation seems like a bigger change to wrap one’s head around. Flipping was a problematic word, but once I demonstrated (by flipping over a sheet of paper), students caught on pretty quick.

The blue paper is from an activity that Curriculum Partner designed last night on a whim. It gave students a chance to practice more transformations and to talk about naming shapes. I tried it with various amounts of structure and direct instruction. One group imploded when two group members started arguing. I think it sidetracked me more than I would have liked, though I figured out (I think) that one group member felt the other wasn’t pulling their weight while the other group member felt left behind. We’ll see how it goes tomorrow.

Day 57: More Mobiles (Maybe)

Stages of the Mobile Project

Stages of the Mobile Project

More work on the Mobile Project today (recap: students choose an object, identify the shapes, and create a mobile object with an area of 200 cm squared. Sound easy? Yeah, that’s what I thought, too). Students started at all stages of the project today and I’m not sure if we’re closer or further together now. One class feels further behind, two feel like we’re making progress and one…I don’t know.

Today’s picture(s) show various stages of the project. The yellow picture is a drawing of a house that one student (who was absent for a bit and is frequently distracted) drew today. I’m pretty pumped for them.

The yellow person is the stage where the student uses a grid to show that their object (the person) is 200 centimeters squared. Right now the person is 60 centimeters squared. I think they can do it, even though we have extremely short periods tomorrow (40 minutes instead of 65 minutes). This student is also easily distracted and I’m psyched they got this far today.

The green and blue truck is actually a tree-truck created by a pair of pretty spunky students. They’re from yesterday’s Dark Horse Class, which has the most finished objects so far. These kids started out wanting to create cars (We’ll make cars! And motors! ¿Còmo se dice “llantas” en ingles?). After struggling valiantly all of yesterday, they came up to me holding the green rectangle and blue circle at the right five minutes into the period today.

“We made a tree!” they exclaimed.

“Too easy,” I said. “What happened to that carro chèvere you were making?”

So they enlisted their friends to create a truck (’cause Complex Instruction). This was in the midst of kids running around with glue guns, a giant box of foam, a pencil sharpening accident and a referral.

“We made a truck!” they exclaimed about 20 minutes later (their friends watched, too).

“Too big,”I said. “It has to be 200 centimeters.”

They’re now in the process of measuring it and cutting it down to size. They’re less than thrilled with me, but they’ll survive. This a case of me not being not as clear with expectations as I’d hoped and an amazing case of students persevering and revising work,

Day 56: The First Mobiles


First MobilesFast forward a bit: we’re now at the end of the area unit, working on the Mobile Project. Students draw themed objects, then find the area and cut them out of foam. Much harder than it looks. Today, we’re about mid-way through the project, meaning that the kiddos are at drastically different parts and beginning to struggle. I felt like I was all over the place trying to help everyone, without making effective use of group structure. I’m also wishing we (I) had dedicated more time to scaffolding and just to the lesson in general. (Did I also mention that we have 4 short weeks to finish the last unit of the semester? Starting Tuesday?)

I never know which of my classes will surprise me. It was a struggle throughout the day. Then, all of a sudden, my last class (the one that was furthest behind) pulled out of nowhere; five students finished their portion of the mobile. Kind of a nice reminder that the kiddos will always surprise you. There’s still some tweaking and reflecting to do, but I had to take a photo as evidence. I wish I had a photo that showed the math (calculations, drawings, etc), but for now, this’ll do.


Day 41: Elevators and Negative Numbers

Weird day today – the 10th graders all took the PSAT (whole ‘nother post) so I had my 9th graders, plus the 9th graders from the other team. And also took half a day off to go to professional development.

We wanted to use what time we had wisely (with a sub facilitating at least half the classes), so my curriculum partner and I cooked up a lesson on negative numbers based on this worksheet from Illuminations. I got to see the first two classes, which happen to be my tougher classes.

Lots of students struggled with “up” being positive and “down” being negative. At one point, I made tables point up and say “up is plus” and “down is negative”, which I now wish I had made everyone do.

This photo of Jaime’s* work is pretty representative of some of the errors I saw – kiddos were able to connect the different numbers, but not always in the way I wanted them (and to be fair, I don’t know how culturally relevant elevators are to most of them):

Elevator misconceptionsI’d rate today a 3, but I don’t know how fair it is to give such a weird day a rating.

Here’s a shot of the board and my pockets and other work:

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*not his real name.

Day 40: Triangle Area Equations

Triangle Area Equations

This photo is of two ways of finding a formula to calculate the area of a triangle and how I marked up the diagram to help students think through it. In retrospect, I wish I’d held the camera more steadily when taking this photo. I also wish I’d done more thinking on this beforehand (aside from the grading and other work I did this weekend. Uy.)

I’d rate today a 2 (in my ideal world, I rank every day on a 0-5 scale and then see how the ups and downs play out throughout the year). Today’s lesson was rough. Curriculum partner and I spent quite a bit of Friday afternoon planning, but I think the idea was still too abstract for our kiddos. First period was struggle bus (though they fought valiantly). I think they had trouble wrapping their heads around why we were multiplying (to get the area of the rectangles) and then dividing (because the area of the triangle is half the area of the rectangle). Possibly too abstract, possibly casualties of the 3-day weekend.

I did have a talk with a student after school, who I’m trying to get to reflect on his behavior and he mentioned that he can do basic area things (count the squares in a gridded rectangle and even multiply base and height when they are numbers) but variables are still a jump for him.

And a collage of today’s photos:

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(the behavior contract in the middle frame is from the same student)

Day 21: Structuring Growth Exercises

One period in, curricular partner (the teacher I plan with) and I realized that the lesson we planned for today (“growth by shrinking” with negative numbers and decimals) was too ambitious. Kiddos seemed OK with negative numbers, but struggled with place value. We decided to review/practice growth by adding and growth by multiplying (which is what we had just finished learning on Thursday). The idea is to start with a number, then grow four times, either by adding or multiplying the same number.

I wonder how much the structure of the activity/graphic organizers confuses our kiddos.  There were stairs that were supposed to help students organize the starting number, ending number, and steps in between. Most students understood the addition and multiplication bits, but I think they were confused about where to put which numbers and operations. Photo below is 2 student work samples. One shows a bit of confusion about how to use the steps, one shows some pretty good multiplication. I would have loved both kiddos to show more problems in general, but you take what you can get. 


Also featured: Things in My Pocket at the End of the Day:

Things in My Pocket - Monday, September 16th

Left school at 6:30. Pretty bad considering I thought I could get out at 4:30.

Day 20: Too Fat, Mister

Today’s activity was on linear and exponential growth. Students had to scale a model of a human by addition and scale another model by multiplication, with the idea that there are situations when linear growth is a better model and situations where exponential growth is a better model.

The red copy is the “growth by adding” version from a student (who was then exiled to a lone table for goofing off, sigh), the black copy is my hastily drawn version of the same from when one class didn’t quite get as far as I would have liked before the debrief.

Funny how the debrief has to happen anyway.


Interesting that many students instinctively thought they were doing something wrong when their model “turned out funny”. Also curious to see how easily students doubt themselves and how hard it can be for them to defy convention.

(Note: typing from my phone in hopes that I can get these up faster at the end of the day)


Never mind that the school year ended almost two months ago. Never mind that the summer program I worked for ended yesterday (edit: a week ago. Sigh.).

Here are the last few photos of the 2012-2013 school year. Most have little to do with math and more with closing down the year.

(edit the second: I am unable to make the images align nicely with the text. Apologies for the formatting but I am 1 parts frustrated and 3 parts trying to make my flight, so this will have to do for now!)

Day 172: Using diamonds and rectangles to review factoring polynomials. My supervisor and I sometimes talk about how effective this is. It is (like many things) not how I learned to factor (which I used to do mostly by trial and error) but I do think it helps students look at the procedure a little more systematically. I don’t know how clearly that came across in my explanation. Unfortunately, I erased the work before taking a photo.

Diamonds and Rectangles

Day 173: Using generic rectangles to factor polynomials. This time, I left the work in.

Generic Rectangle for Factoring Polynomials

Day 174: Different teachers at our school use different programs to create exams (and graphics for said exams). As a result, I had to redraw a trapezoid for the final. I can’t tell whether this is an example of me trying to be precise or me being OCD. A friend has suggested that I use Geogebra. I think I really just want a free copy of Geometer’s Sketchpad.

Trapezoid for Final Exam

Day 175: Final days, yo. This is a written reminder, both for the students and for myself, that this really is their last chance to turn in all the things. Surprisingly, some of them do not turn in everything. I’m still trying to figure out if this is forgetfulness or something else.

Last Days

Day 176: During quizzes and exams, we’ll generally leave some of the important formulas on the board. At first, I was a bit puzzled by this – we didn’t do this when I was growing up (and yes, 18-year old me can’t believe I just said that). But it’s helped me think about what things are important for students to memorize (not everything) and to see that, even with the formula, that doesn’t mean that students will remember concepts or know how to apply them.

Notes for the Final

Day 177: Last real day with students. My primary class took its final today. We still do some things with objectives and expectations, but hopefully they’re ready to go at this point. In retrospect, students seemed to do better on their unit quizzes. I wonder if that’s a sign of forgetting (which is interesting, since we gave them several days to prepare/study specific things for the final).

Day 178: Finals Expectations

Day 178: Students do say the funniest things. We have them do a quick evaluation of the course at the end of the year. I’m posting a few of them (technically without permission and focusing on the funny rather than the mathematical). Overall, students felt supported, though I need to work on discipline and classroom management (especially with a few tough cookies). I was pleasantly surprised by what they said they learned from this class.

Student Evaluations

Day 179: Grades due today. Students generally don’t attend class. A few showed up to grab work and clean out their binders. We recycled the rest of the work.

Day 179: Binders

Day 180: Clean slate. At this point, I’m so use to coming in, writing objectives and expectations and then figuring out how to communicate math (whether it be by speaking or on the board). It’s weird to see the board empty.

Day 180: Empty Boards


The Evil Math Dictator


Day 172: Last Day of Homework

Today, I assigned the last piece of homework for this year (we begin finals review next week and students can review their packets at home at their discretion). Makes it feel like the year is winding down. I also wish we had assigned a bit more homework this quarter – we got a late start for the unit we’re on now and I feel like more practice might have been helpful. Side note: I also referred to myself as “the evil math dictator” today. I’m pretty sure this has to do with assigning homework.


Day 171: Diamonds and Rectangles

As you may see in the photo from above, we’re learning how to use generic rectangles and diamonds to help students organize their thinking around multiplying and factoring polynomials. I never actually used these strategies in high school, so it’s interesting to teach myself and to see which strategies take (students don’t seem to buy the generic rectangles for multiplying as most of them were taught to FOIL, but they seemed to have used the diamonds quite a bit for factoring). (Side note: this photo is actually from Day 172, but the content holds. Also, I started to erase the work before I took the photo)