# Day 135: The One With Two Reference Angles

One week to go before spring break. But who’s counting? Certainly not me. Certainly not the kiddos.

More Right Triangle Trig this week as we barrel towards our unit exam and spring break. We’re back into a routine of doing problems in class, which feels a little less crazy than trying to go outside to measure the school.

Photo: The Challenge Problem With Two Reference AnglesDon’t let the wording fool you; this was a problem that everyone did. Kiddos seemed to struggle with it and the idea that there can be 2 reference angles. They also struggled quite a bit with how the ratio changes with the angle. Most kiddos figured out that the sine of one angle was the same as the cosine of the other angle in the triangle, but often couldn’t explain why or point to the corresponding angles in the diagram.

That being said, most students did eventually find the distance of the ramp. In one of many questionable teacher moves, I ended up giving the 2nd challenge (an inverse sine problem, which students seem to find easier) first, which gave students a little bit of confidence.

Related but Unrelated

Graded the rest of the picture projects this weekend. Nearly ended in me being a babbling mess amidst other math teachers. And yes, these are the projects from, uh, a month ago. Students seemed to recognize them when they got them back, which is good.

I am now about to grade as many homeworks as I can in hopes of getting printed progress reports to students tomorrow. I want them to be aware of grades, but am also worrying that we are pushing them to thinking about grades instead of knowledge. Sigh.

# Day 134: The One Where We Estimate the Height of the School, Again

Out on Thursday for a planning day. Sub day went OK – most kiddos worked and one of the ones who was not fantastic the last time was much better.

That meant that Friday’s lesson was extra crammed (the other class got 2 days to do it, so we went a little faster in order to keep up). Whereas the other class spent one day measuring the angle between the ground and the sightline to the top of the school with an inclinometer and then one day writing about their results, we did both in one day. Which was quick but doable.

Photo: Estimating the Height of the SchoolOne of the phrases that I hear teachers at my school use a lot is “What do our students understand? What are they capable of?” It’s interesting to see where this goes with right triangle trigonometry. Finding the opposite side and the adjacent side seemed easy enough. But now there’s a lot of other little details: solving ratios, identifying hypotenuses, figuring out how the opposite and adjacent sides change as the reference angles change.

For many kiddos, identifying the current ratio (sine, cosine, tangent) and setting up the equation feels successful. This student work shows students who (with a lot of help) were able to identify the opposite and adjacent sides and set up the tangent ratio. It was late and we were out of time, so we didn’t actually solve the ratio. But I like that the students were able to show what they know.

# Day 126: The One Where If You Fall Really Far, You Will Die

We’ve been experimenting with word problems as integrated math and English Language Development. Students read the problem, solve the problem and then do a write-up of the problem. It takes about a period to do 2-4 problems (for similarity, some groups finished one; most groups got to 3 for right triangle trigonometry). This might be different for mainstream classrooms, but I’d be curious. In contrast to activities like stations or explanation quizzes which encourage students to practice a range of problems, word problems feel like they allow students to dive deeper into problems.

It’s also curious to watch students mistake “the ground” in a word problem for “the line in the air”. I’m not sure if that’s a case of mis-translation or not reading the directions or something else.

Photo: If You Fall Really Far, You Will Die

Gotta shout out Curriculum Partner on this one, since they wrote the word problems. Teaching 9th and 10th grade recently arrived English Language Learners is interesting. They often spend the first bit of time being confused – there’s a lot of English and the cognitive demands of high school in the US feel like they’re probably a bit higher than some of their prior schooling. But at some point during the year, they start to speak more English, they start to ask more questions, they start to write more things down.

This kiddo has recently become more active. I suspect it’s in part because we’re using scientific calculators (the non-fancy graphing ones for you following along at home) and this kiddo likes using them and feels successful at using them. At any rate, this kiddo was able to find the tangent of the reference angle (39.8) and label the unknown height of the tree as x. I think they also know that the shadow (the adjacent side of the triangle) was 60 feet, though their label is a bit misplaced.

Related, but unrelated: I completed my first Educational History Inventory. Don’t get too excited; it’s just a series of questions about how long a student has attended school for prior to arriving at our school. The vast majority of our students, especially those who arrive without documentation, do not bring transcripts or school records, so it’s hard for us to know if they’ve missed school in the past (something we call Interrupted Formal Education). To be fair, when I asked one student about their transcript, they said “well, my principal got shot, so…”. And I certainly wouldn’t count my transcript as the most important thing to bring with me from my home country.

At any rate, I’m actually finding that quite a few students who I suspected had Interrupted Formal Education have been in school continuously, which is leading me to think more about the transition to United States high schools and how we accelerate the growth in English process.

# Day 125: The One with the Tangent/Inverse Tangent Stations

Why, hello there.

We’re midway through a unit on right triangle trigonometry. There were some struggles in the beginning, mostly with the procedural process of solving ratios and estimating scale factors (tricky for kiddos with interrupted formal education), but it feels like things are back on track.

Photo: Tangent and Inverse Tangent Stations

Having learned about tangents and inverse tangents last week (the latter on a Friday, where many kiddos were absent on a field trip), we decided to have the kiddos work through a series of stations. They had to draw pictures, write the parts they knew (reference angle, adjacent side, opposite side, etc) and then solve for the missing side or angle. Still running into issues with solving ratios, but we’re making progress.

I’m also helped by an instructional coach who wisely reminded me to make expectations clear and reminded me that if I’m in a mood, my students are probably going to be in a mood. I know this (ostensibly) but it’s always nice to be reminded.

Related but unrelated:

• Daylight Savings Time could not get here fast enough. I know John Oliver and most of Facebook disagrees with me (past me disagrees with me, even), but it does wonders for my mental state to get home and go for a run while it’s still light out.
• By coincidence, I have 3 sub days in the next 3 weeks before spring break. Which is simultaneously great and…terrifying.
• Giving a unit quiz and a unit project means…a lot of grading. Which, I knew. But still…