Teaching Geometry - Right Triangle Trigonometry #VNPS

I am figuring out three things about teaching Geometry:
1.) Geometry is when they really are introduced to a lot of things for the first time.  Therefore, it is great for discovery type lessons.  Versus when I have been teaching Algebra 2 and I am saying, you have already learned this, let's make it more challenging.
2.) Discovering at the boards with VNPS is exhausting.  I am doing 3 lessons a day at the board with classes of 28 kids all at the board.  Then, sometimes, add my Alg 1 and 2 classes at the board.
3.) Learning is messy and productive struggle is uncomfortable for both the kids and the teacher.  I want to jump in and help, but I can see them building their understanding one piece at a time and I don't jump in and save them.  I let them build.

Lesson in point - yesterday's lesson about Right Triangle Trig.  The lesson was ambitious and I knew that going in.  I was supposed to teach them all 6 trig functions, including how to solve for the ratio or the angle on the calculator plus introduce angles of elevation and depression.

I did my best to really stress that the trig functions are just side ratios.  They were able to stumble through my board problems.  I did introduce SOHCAHTOA as a when of remembering them.  I introduced the three reciprocals.  I got to one problem introducing angle of elevation and they were able to do it.  I did not get to angle of depression.

Here is the powerpoint lesson: Right Triangle Trig Lesson

Here are the board problems: Right Tri Trig Board

Here is some student work:

I read somewhere online to start them off relating trig to a ramp.  I asked them to draw the ground and a ramp that had a slope of 3/4.  This is what I got:


So, I asked them to erase it and label the horizontal and vertical instead:



We learned about theta and from theta we labeled opposite, adjacent, and hypotenuse.  I told them the 3/4 was a tangent ratio.  I asked them to come up with 5 more combinations of side ratios using opp, adj, and hyp. Then, we named them:



I left each lesson not feeling done.  They left feeling confused.

The thought came to me that I fed them all a huge Thanksgiving dinner and then I kicked them out without giving them time to digest.

They tried the homework.  I went over it today.  I went over each problem.  They were starting to see the connections for each side ratio.  Some of the word problems were challenging because they were overlapping triangles.

I did discover one student's misunderstanding.  She thought COSECANT was another acronym and couldn't figure out what it stood for.  She kept asked what it was. I kept saying it was the reciprocal of Sine.  Then, she finally said, but what does it stand for.  I think I corrected her.

Next lesson...practice.