I love Trigonometry, but I don’t love teaching the basics. A few weeks ago, this article came across my social media feed, and it got me thinking about my upcoming Trig unit. I followed most of the suggestions in here. We’re a week in, and I still haven’t introduced SOHCAHTOA. Many of them remember it, and they are getting the hang of the ratios first.
I spent one period on labeling, and found a Kahoot to practice just the labeling from the angle of reference. The next day I was out for a soccer tournament, so I left an investigation for them to complete on their own. It was from our textbook, and showed an image of a 30-60-90 triangle with lines marking several sizes of similar triangles. Students needed to measure the sides and then find various ratios. (A colleague told me he has students measure several triangles and find all the ratios of the sides they can, even though we skip the secant, coseceant, and cotangent ratios in our curriculum.)
When I returned, I asked the students what they discovered, and they had noticed that the sides were the same. I then introduced a unit circle triangle and we filled in the same chart from the investigation. We then labeled the sides as adjacent, opposite, and hypotenuse and then found the ratios from 60 degrees. Then it was a simple step to introduce the special names of sine, cosine, and tangent.
I’ll introduce the idea of the unit circle in another week, but they have the foundation for finding the basic ratios from this lesson set up. We also did another page showing the 45-45-90 triangle.
The rest of the lesson was spent on drawing triangles and setting up the ratios that we could see. The next day I showed them how to use the calculator to find the sides and how to use the inverse functions to find the angles. You can see the rest of the notes by downloading this pdf: 20170425 trig ratios.
We’ve added more and more each day, including some problem solving. (We went outside and used clinometers to help measure the heights of the buildings) Today I just introduced bearings, and then will do 3D trig ratios before moving on to the sine and cosine rules. I haven’t decided at what point I will introduce SOHCAHTOA as a way to remember the ratios, but it’ll be before a test. It’s a memory tool that I still use to make sure I don’t use the wrong ratios, but introducing it too soon turns it into a trick rather than a way to help remember the understanding that has been developed.
I am starting to bring more Depth of Knowledge into my lessons, but haven’t been able to find many DOK2 level tasks for trigonometry. I check Open Middle often to see if there are new problems, but I guess I need to make up some and submit them!