# Day 25: Finishing Trig

Today was the end of our tiny trig unit. Students worked on using trig to find areas of regular polygons that they hadn’t been able to find before (nonagons, pentagons, etc.) and did a group activity that I call a Roundtable. There are up to four members of each group and all start with a very similar problem. The first step is very simple and after everyone is done, they all pass their papers clockwise in the group. The next step will have something to do with what the person did before them, so they have to not only check the work from before, which could lead to great discussions, but they also have to continue with the problem. You will find two versions in the file below – one for a pentagon and one for an octagon. To challenge some groups that finished quickly, I asked them to check their answer using the similarity ratio before I check their final answers. They seemed to like being able to check themselves and I heard awesome discussions.

I am also attaching a picture of some students’ work on angle of elevation/depression problems that they did on the board. I introduce these with statements like “Guys, these are all gonna be word problems *listen to groans* but word problems are the best ones to show your creativity! We’re leaning a ladder against a house here – look at how nice my dream house is! *takes a little too much time to draw a nice house with a ladder leaning on it in front of class*” Now most of my students actually draw out what they’re seeing. It might waste some time but I feel it gets a little more investment out of the ones who would normally shut down to a word problem.

They also did a row game last class that I forgot to include. Basic trig stuff, but once again I think the students like being able to check their own answers and that’s what the row game gives you. Download below.

Les réponses données encouragent les étudiants à essayer plus.

# Day 23-24: Similarity Day 2 + Trig

Busy day yesterday and wasn’t able to post – I’ll combine yesterday with today:

We finished the similarity unit by talking about perimeter, area, and volume ratios. I started class with an investigation on area and perimeter of similar rectangles. The sheet is downloadable below. I first started with some students giving guesses for how the ratio of perimeters and areas changed with the similarity ratio and If students finished early, I asked extension questions like, “Will this work for all rectangles? Will this work for all shapes? How is the volume ratio affected?”  I liked that students were able to confirm or disprove their guess by this investigation.

Then, after looking at similar solids we reviewed the similarity unit. I used another trail activity for this. I actually made this when I student taught for an honors geometry class. I still use it because, even though the questions might be more challenging than what’s going to be on the test, the students don’t know that and they still try their best to get through the trail. They all were able to complete it (some with some guidance) in about 45 minutes to an hour instead of the 30 minutes that I had given in student teaching. I still think it’s a great way to review, practice, and challenge the students. It is downloadable below.

The class ended with a test.

Today, we started with an introduction to trigonometry. I feel like it’s really hard to just give an introduction, though. I got into the ratios and how these are really functions instead of multiplying by a “sin” or something like that. It’s hard to understand the inverse trig functions without having a firm grasp on the fact that these are functions, but then some of my students have never heard of a function before. I don’t remember running into this issue before but it definitely took a little longer to introduce it than normal. I had groups in the class trying to answer some questions about trig properties – Can sine ever be greater than 1? Can cosine ever be greater than 1? Can tangent ever be greater than 1? Can any of the trig functions be less than 0? What about the inverse trig functions? Some students just started by trying to plug in a ton of numbers in their calculator. Eventually, groups realized that they really had to look at the ratios.

When we got into angle of elevation I was so excited to try Kate Nowak’s “Measuring a Really Tall Thing” activity. I had the meter/yard sticks and the students had a member of each group with a clinometer app (the iPhone actually has it automatically in it within the compass app so most of my students were able to get it). I then took them outside and they got to measuring. I only had six meter/yard sticks so I had groups of 2 and 3 and about half the groups were able to do it correctly within half an hour. They then had to help the other groups figure out what was going on. I blame this on not giving enough time for the kids to really figure out what they were doing and also test how the clinometer works.  I was so excited that I just kind of said “go”. Next time, I actually should have them mess around with the clinometer maybe even before we leave the classroom. Overall, I think they saw how this could be applied to find the height of something very tall and were excited to be applying what they learned to something outside (even in the 90 degrees). It was fun and the students were excited, and next time it will be much better because I’ll know how to introduce it better. I really wish I had taken pictures…

Je suis trop occupée maintenant. C’est difficile quelquefois d’écrire le blog.