A few weeks ago, I had something haven’t had all year: extra time! We had finished up our unit on the Pythagorean theorem and had 3 days before the end of the quarter. Instead of starting something new, I thought I would try to extend our learning with those 3 days when a student in class made this observation: “The Pythagorean theorem only works though if you know two of the sides. What happens if you only know one?” I answered him by saying, “Look at your calculator. You see the buttons ‘sin, cos, tan?’ If I give you one side and an angle, you can find everything else you want to know about the triangle.” It was this conversation that persuaded me to teach trig with the 3 extra days I had.
I started the first day using Geometer’s Sketchpad to show students that the ratios of the sides of a 30-60-90 will always be the same, no matter how I dilate or translate the triangle. I showed them what each of these ratios were called and then we took off. Some students were confused at first and I assigned them the role of finding my third side with Pythagorean theorem, once someone in their group had two sides of the triangle. We did this for two days and then used inverse trig functions to find angles on the third day.
Once fourth quarter started, we began a new unit over volume of prisms and didn’t use trig at all that week. We took an interim assessment after a week on volume and I wanted to see how many students actually learned trig. But, since trigonometry isn’t one of the 8th grade CCSS, I didn’t want it to adversely affect the grades of those who didn’t understand it. So I made it an extra credit question on our quiz, asking students to find two sides of a right triangle, given an angle and a side. I ended up with 26 out of 96 students getting the question correct after a week of not doing anything with trig. I was pretty happy with this and thought that, even though 70 out of the 96 didn’t know how to do it, but about 28% of my students were allowed to learn and master a concept beyond what was expected of them. I would love to have extra time to do this every unit and maybe will next year, once I’m more familiar with Common Core. Overall, I was very happy with everyone’s participation during class, even if they didn’t understand the trig. I challenge you to try doing something that you feel is too difficult for your class as well, the results may surprise you.