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.

Download:

Les réponses données encouragent les étudiants à essayer plus.

Distance and Midpoint Formula Row Game

On our third day of summer Geometry, students are starting to open up a little more. We reviewed a little more of planes, lines, intersections, and parallel/skew by using the room as a space again. I think that really helps some of the students who aren’t able to visualize it on their paper. We then got into the Segment and Angle Addition Postulates. We reviewed with some Kuta worksheets. I wish I had a better way to show this to a very mixed class. Most students were able to see right away what parts needed to be added and set equal to the whole segment or angle, but some I think were intimidated by the algebra. I tried to see if they could substitute an algebraic expression with a single letter or picture (so they could see that they need to put        🙂 + ❤ = m<ABC    and then substitute in the expressions that were given) but those students just consistently wanted to add whatever was with a variable up to get whatever was given with just a number. I’m thinking next time I could actually have protractors and rulers and have them cut out angles and measure and put them together, seeing which parts need to be added and then move to the algebraic problems afterward.

We also got to the distance and midpoint formulas. For the most part, this was review for students, but it was a good reminder of order of operations and how square roots work. I loved using this row game that I found on Elissa Miller’s blog (again – she might as well be teaching my class because I will be using so many of her activities – thanks Elissa!). Elissa had this for just the midpoint formula, but then I made a second copy for the distance formula. I loved hearing kids really work to justify their responses or help their partner correct their work when they were comparing. It was just enough practice for them before we moved on and got them talking about the math and engaged.

I’m grappling with the idea of doing a “180” blog for the summer. It really would only be 29 days, but I can get a feel for if I like this type of blogging and if it’s useful for me. We’ll see if I can last all six weeks.

J’utilise les activités des autres blogs presque chaque jour et je vois pourquoi le #MTBoS est vraiment magnifique!