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.

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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.

Day 149: The One With the Survey (and other stuff)

Curriculum partner was out Friday and we needed our kiddos to fill out a district survey on positive school culture. So, we spent the first part of class signing onto computers and filling out a computerized survey in English, Spanish or Chinese and the rest of class (25 minutes for students, 0 minutes for others) catching up on homework or doing other stuff.

Photo: The Other Stuff Day 149: SurveyIn retrospect, one thought we’ve had this year regarding homework is that it’s good to have it, but it’s also good to build time into the school day to do it. We have an afterschool tutoring program that quite a few kiddos take advantage of, but many of them have to work after school.

This is my long, roundabout way of saying that some kiddos (with a lot of prodding) caught up on homework that needed to be done. Others…doodled a lot.

Other things I observed:

  • lots of kiddos got caught up on questions, even in their home language. I wonder about some of the phrases they used (I had trouble understanding it, so it must not have been an Ecuadorian translator). I think some of the questions were unfamiliar to kiddos and helped push their thinking (I hope).
  • Kiddos did a strong job of not giving up, even though there were lots of questions with academic language.
  • It was also nice to be able to check in with students. I don’t know if it was because they needed less support with the surveys (or if I checked less frequently as I didn’t want to influence their answers), but it felt like I had more time to check in and have needed conversations with students – lots of kiddos needed time to talk to our Wellness center or just talk about their lives or needed more support and I felt like I was somehow able to give this in a way that I’m usually not able to (do to time and such)

New mini-unit starts Monday. Cross your fingers.

Day 148: The One Where We Taught Each Other Fractions

One of the quirky things about working in a school with lots of recent immigrants is that we can never quite be sure what they’ve learned prior to being at our school. State standards? Fantastic. They don’t apply out of the country, though.

One of the gaps that we generally count on is fractions, which are typically taught in middle school in the United States. They come up frequently on the state exit exam and are good to know about in general.

After trying some stuff in homework and review packets, we (my curriculum partner, really) bit the bullet and purchased fraction circles. (“What do we call them?” ask the kiddos. “Tiles?” I suggest. “But we already have tiles,” they respond. I tried to convince them that they were called “pie pieces”, but I think that is asking too much.)

On Friday, Monday and Tuesday, curriculum partner and I split our classes in two. Some students worked on fractions with the pie pieces and some students working on writing steps to solve equations.

Today, students who learned about fractions taught the rest of the class how to use the pie pieces, how to write fractions and how to write and find equivalent fractions.

Photo: Student Worksheet on Making Fractions

2015-04-16 15.46.51This worksheet is from a student where the teacher admittedly struggled at first, but pulled off a pretty strong showing. The student who wrote this is a pretty good artist and despite many ups and downs, was pretty engaged (there were also 6 adult visitors in the room – one for each group and enough to engage our students while pushing their thinking).

I wonder why this student (and others) sometimes shade in non-consecutive pie pieces (see 6/12). I also observe that most of their pie pieces are the same size (except for 2/3), which is not always a given with our students (especially those with Formal Interrupted Education, which I do not think applies to this student).

WCYDWT: 200 Years of Immigration to the US

Math teachers (and I suspect other teachers) love to find interesting images and then ask each other: “What Can You Do With This?” It prompts a lot of good questions and gets people to engage in ways that a drafted, scripted curriculum often can’t. (As an aside, we often prompt our ELL kiddos by asking them “What do you observe?” “What do you wonder?”)

So, I ask you, “What Can You Do With This?”* “What do you observe? What do you wonder?”:

Captura de pantalla 2015-04-15 19.53.14

Useful phrases: “I observe _____.” “I wonder ____.”

I obviously have my own observations and wonderings, which I can share later.

*Images and data from Natalia Bronshtein, who credits them to the Yearbook of Immigration Statistics.

Day 147: The One Where We Write Solving Steps (or Just the Answers)

We are rounding the bend. Two and a half weeks of content left and 2 days (really 1) left in this min-unit on solving steps. Grades for the fifth marking period were also due today, which means that I should be doing something totally not school related (which probably means blogging, watching TV, doing BTSA. Not exercising.)

Previously, curriculum partner and I divided students in half. One of us taught kiddos about fractions. One of us taught the other kiddos about writing the steps to solve equations. Today, everyone was back together for the first time in a few days. Students spent today working on a series of slow release equations – some with decimals and negatives for students who learned to write the solving steps and some with negatives for students who had studied fractions.

Photo 1: The One With the Solving Steps

Student work showing solving steps.Making seating charts is hard. I know some teachers are very firm about not ever letting students change groups. I will sometimes change groups if students advocate for themselves with a good reason (our kiddos also have all of their classes together for the whole day, so personalities can get more explosive as the day goes on).

I’ve been trouble placing one kiddo. But today, he ended up working really well with his new group. They talked and worked and wrote together. His work is shown above.

Photo 2: The One with the Equations and Answers

2015-04-15 16.47.28This year is the second year that we’ve used algebra tiles, so some of our kiddos are getting really good at using them. Today, most students who had only seen them this year continued using them to solve equations. Their groups tended to be more homogenous than usual and it was really exciting to see some students really step up their algebra tile game.

Since we haven’t taught these kiddos how to go from algebra tiles to writing the steps, I just had them write the equation and the answer. This photo is from one kiddo who was left alone (the rest of his group had to help out another class) and sat there for about 30 minutes and plowed through all the problems. Pretty cool.