# 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.

# Days 136-140: Closing out Trig

Day 140: Circles Pre-Assessment

Today, the last classes finished the Trig Unit Quiz. To prepare for our next unit (Circles), we had them do a pre-assessment, which included drawing circles. They seem to get the basic ideas, but seem to be hindered by the compasses themselves (which are somewhat cheap and flimsy). Toying with the idea of giving them pre-drawn circles. We’ll see.

Day 139: Class on the Go

In addition to today being the day where some of our classes made up the Trig Individual Quiz, it was also the meeting of our Translation Club (something a few other residents and I started as part of a service project; we help students translate documents from English to their home languages). These meetings happen at lunch, which is the same time some students stayed to take their quizzes. As a result, we packed up and headed to Translation Club. However, some of the trig identities we wrote on the board didn’t make the transition, so I stole some space on another teacher’s blackboard and wrote them down. Make do with what you got…

Day 138: Reflection

For the end of each unit, we ask students to reflect on the work they’ve done for the unit – what went well, what they’d like to improve upon, what pieces of work reflect their best work. We’ve decided that a short reflection worksheet is (so far) our best bet at getting that done.

Day 137: Ah-Jay-Sent

One of the things I’m thinking about is how to increase students’ use of academic language. This unit, many of them struggle with the word “adjacent”, which is something I take for granted. It’s not spelled the way it’s pronounced and it’s pretty complicated for just trying to say “next to”. So we wrote it on the board with a pronunciation key and try to make students say it as much as possible.

Day 136: Inverse Trig Diagram

Today was a quick lesson on Inverse Trig. One of my students asked when you use each of the functions, so I whipped up the following diagram on the spot. In retrospect, I wish I’d said “Ratio of sides” and maybe done something more specific with each of the trig identities. Students also seem to not connect “inverse trig” and “tan -1” (for example) as much as I’d like. For next time, I guess…