Day 19: The One with the Windows


I keep forgetting (or just denying) that Afternoon Me is the Worst Me (as the cool kids say).

We did a reading guide, which went slowly in some classes, just right in some classes/groups, and was a struggle in others. Now wishing I had been harsher and a bit more vocal with the participation quiz aspect.

Student work (from the afternoon, but still some solid work)

At any rate, I liked the opening. We showed them a bunch of windows and asked them how many there were. Almost every kiddo was talking or writing:

Teacher confession: after 1 class, a colleague pointed out that there were different numbers of small windows in each cluster, so my initial calculation of 900 was far greater than what many students calculated as about 768 windows.

Also, we cleaned almost all of the papers (except notes) out of the math section of our binders. Maybe this is the organized year. (Dinna hold yer breath.)

Day 57: The One With the Area, Perimeter, Surface Area and Volume Group Test

Came back from a sub day (got to attend a meeting with fellow rookie math and science teachers) and went straight into two check-ins and a group quiz.

How was your Monday?

Photo: Area, Perimeter, Surface Area and Volume Group Quiz

Area Group Quiz

After we switched groups (did I mention today was busy?), kiddos pretty much got right to work. At Curriculum Partner’s suggestion, we did an opening about what groupwork looks like, cleaned out folders (sort of) and got to work.

Kiddos got most of the class period to work together and talk through four problems. Problems are written so that kiddos fill in what they know – they get some basic information to get them started, but have to fill in steps or explain or pick and justify an answer, so that everyone has a bit of access, but still has to say what they know.

Individual test tomorrow. So many projects still to grade. We’ll see how it goes.

Day 55: The One With the Grading Question


Grading is the worst. Projects are challenging. We’re at that part of the Packaging Project where groups find the surface area and volume of their package.

This group got off to a solid start. I gave them a less scaffolded version of the Find the Surface Area and Volume page. They called me over at one point and we had a talk about what to do next. We figured out how to find volume

And then one of the kiddos turned this in:

2015-11-09 17.45.46

I remember asking myself, “How do I grade this? They haven’t shown very much of their work. But I know they can find the volume because they told me how to.”

In the end, I think I gave them a C+ for that part of the project. They can do it, but I want them to explain each step. I wish I had made that clearer somehow.

Pythagorean Theorem Student Data

Every few months, I meet with other beginning math and science teachers to discuss teaching and what it looks like for us (though the Knowles Science Teaching Fellowship). Recently, this has meant collecting data on our classrooms, presenting it to two other fellows, then discussing it.

The lesson I discussed was an exploration of the Pythagorean Theorem. Students read a reading guide and used Pythagorean Tangrams to see if the two smaller area squares added up to the bigger area square. (photos below)

Part of our assignment was to think about the Standards for Mathematical Practices, which, admittedly, I didn’t.

A couple of thoughts:

  • Students sometimes got stuck when trying to put together the two smaller squares to make the big square and I’d have to show them a hint or first step.This felt useful in terms of keeping the kiddos moving and not letting them get stuck on anything that was probably not hugely important (though if it wasn’t hugely important…) In general, I think I need to try and push students to struggle with math without giving up before asking for help. It feels like such a fine line between getting them engaged and than letting them be independent.
  • We also established that the students may not have understood the goal of the activity. Do they fully understand what it means when they make the two smaller squares equal the big square? Do they think that putting together the two smaller squares means that this will work for all squares?
  • It’s interesting to see how students explain and justify. One student says “I don’t know how to explain” which is frustrating because they probably could explain, but at least shows that they know they need to explain. It’s also interesting to see how students explain something tricky like “why do we need to write the small 2.” (This maybe feels like a “guess what the teacher is thinking” question)
  • In thinking about standards for mathematical practices, I go back and forth about which ones are “most important” (they’re all important, which makes it difficult for me to try and focus). So I might try and get our department (four people) to pick a math practice to focus on across courses next year. We’ll see.

Photos 1 and 2: Student AStudent A - Page 1

Student A - Page 2

Photos 3 and 4: Student BStudent B - Page 1Student B  - Page 2Photos 5 and 6: Student CStudent C - Page 1Student C  - Page 2

Day 156: The One with the Pythagorean Word Problems

1 full day and 3 half days to go before we’re done with content for the year. #JesusTakeTheWheel

In unrelated news, my favorite thing to do this unit is add “Pythagorean” in front of whatever the lesson is. I’m also duly impressed with how hard the kiddos try to say “Pythagorean”.

Photo: Pythagorean Word Problem

2015-04-28 16.16.15One of the structures that we’ve had success with this year is giving our kiddos (all English Language Learners) a word problem. They read it through, solve the problem, then write about it. Initially, I thought it would be too easy, but I am constantly reminded how many new words there are to learn and seeing the problem in multiple ways (reading, drawing/solving, writing about it) seems to give students more access to it.

It’s also interesting to see how students react to word problems over time. Today, we were pressed for time, so we spent more time solving the problems than writing about them. And I think I’m OK with that. This particular student translated some of the words into English, which is a good strategy.

Many teachers talk about “pseudo-context” and how making up a word problem doesn’t necessarily engage students further. I think I agree with this, but for students learning English, word problems fulfill a need to learn new words that might not exist for other students. (This is not a measure of success, but many of our standardized tests, which ultimately do count for our students, are filled with words. I’ve seen so many students who can do the math work be stumped by words like “garden” and “astronaut”) Kiddos got stuck on words like “owner” and “porch”. Incidentally, many students translated “porch” as “espacio libre” (free space).

Outside of Class

Building on the “teachers do more than teach” narrative:

In addition to prepping for tomorrow (which the curriculum partners largely did), I spent a bit of time after school trying to get ready for a Student Support Team meeting (which are called when there are students that need extra support for whatever reason). Multiple phone calls, etc. As a result, I may or may not have been late to another meeting (oops) where teachers from schools across the city to talk about implementing Complex Instruction at our schools. Pretty cool to hear what other people are doing.

Came home, tried to go for a run, took a nap instead. Close.

Day 151: The One Where We Pronounce Pythagorean

Spent today doing a reading guide on the Pythagorean Theorem. Reading guides are a structure at our school where students read together. In most classes, they learn and practice common reading strategies like visualizing, making predictions and inferences, etc. In math, they do these things as well though we often walk them through math problems as we go.

I’ve felt very up and down about reading guides this year. For me, they are usually linked to a participation quiz where I narrate (and give points) for the positive behaviors students do (today it was: work in the middle, point to what you’re talking about, connect the area of the square to the side of the square). Up until recently, I’ve felt that I wasn’t able to intervene if students needed help (an ongoing struggle on my part), though I’m beginning to get a better sense of when to stand back and when to quickly step in. (I think. Knock on wood.)

Photo One: The Reading Guide and Tangramsreading about the Pythagorean TheoremThe part of me that signs all my emails “The Worst” (ie “Sorry I haven’t email back #ImTheWorst” or “Sorry I totally Second Year Teacher’ed you when I flaked out on Friday #ImTheWorst”) will also confess to not having read the Common Core progressions in-depth* (though make no mistake, I’m fond of them). So I’m excited that we actually talked a bit about how to show that the sum of the area of the squares of the legs is equal to the square of the hypotenuse (we did not at all describe it in those words). We had students cut out tangrams of the two small squares and try to put them together over the big square. Most students were able to accomplish this, with a hint or two. (In the end, a bit of struggling seemed important, though it also felt useful to show students the result if they hadn’t discovered it) Incidentally, the two constructed squares in this photo were made by two friends in different classes (One student built the pattern in the morning, which I showed to the student I have in the afternoon when they started to struggle. They seemed impressed).

Photo 2: Pythagorean PronunciationPythagorean PronunciationCurriculum partner and I occasionally talk about words that are hard to pronounce. Trigonometry (which we never even taught – we just left it at sine, cosine and tangent) would have been tough, parallelogram is tough, Pythagorean Theorem (let alone “theorem”) is tough. That being said, kiddos have been super down to try, including this student who took notes when I wasn’t looking.

Also, what has two thumbs and is rockin’ out in the kitchen to Billy Joel? Certainly not this guy…

*Just kidding, the ones for middle school geometry, where Pythagorean Theorem should be haven’t been written yet. Told you I hadn’t read them in depth yet.

Day 150: The One with Triangles and Squares

New week, new unit. Pythagorean Theorem is usually taught in middle school, but (again), it’s not a given that our students have learned it, so here we are. It also builds nicely on what we did with right triangle trigonometry.

I should probably change seats today, but I feel like it takes the kiddos a bit to warm up, so I’m leaving them in the same seats for now.

Which probably means we won’t change seats again.

Because there are two weeks of content left to go.

Photo 1: The Recording SheetTriangles and squares activityThe idea behind today’s activity is that students use squares to make right triangles. Our first set of squares was too small and students build several right triangles that looked correct (4-5-6-nope), but weren’t. We spent 2nd period making the squares bigger and removing some of the confusing ones. One class tried to cut up the squares into smaller squares, but otherwise, this helped.

This photo is from a group that worked steadily throughout the whole period. Most kiddos made the connection between the area of the hypotenuse square (as we’re calling it) and the sum of the area of squares 1 and 2.

Photo 2: Explaining Complex Area

Day 150 - Complex AreaWith both of these photos (and most of the photos I post here), I wish I could actually capture the groupwork that is happening. Kiddos who finished the triangles and squares activity worked on a practice area worksheet. We haven’t touched much on complex area, so these kiddos had to struggle their way through it (which is difficult and good at the same time). One of the high status students really struggled with this problem and a student, who would be considered a low status math student, saw how to adjust the height of the rectangle and tried to explain it. So cool to see. This photo doesn’t really do it justice.