Monday was our first day back from spring break. We had started looking at right triangles, pythagorean theorem and special right triangles before the break. After a week off, I was sure they had forgotten some of it. I wanted to move on to trigonometry, so I began searching out some ideas for how to present this. I have learned in the past that just trying to teach them the ratios and show them how to use them rarely resulted in good understanding of the ratios or how to determine which one to use when. I wanted to do something that would really drive home that these were related to the acute angles in the triangle and the ratio of specific sides in relation to the angles.
I found a couple of activities that others had done, but was not quite satisfied with the way they were written or convinced that they would really drive home what I was hoping to help students understand. I decided to write something myself expanding on some of the ideas I had seen, and as I worked on it I realized that we needed two days to do this. Monday was a pre-discovery activity, mainly to refresh what they knew already about right triangles and to begin to encourage them to start relating the angles and sides. They worked on this in groups, discussing and writing out their conclusions together. This went well, better than I had expected, and I gave them a problem to work on after finishing it, which I thought they would need to take home and finish. A large portion of the students finished in class and were able to clearly explain what they were thinking and how they found an entry into the problem. I was pleasantly surprised at the work.
Tuesday I had a trigonometry discovery activity for the groups to work on together. Unfortunately, my planning was not quite as organized as I would have hoped. Tuesday’s are our short days, our PLC teams meet for an hour in the morning, so we start school one hour later. This shortens our periods approximately 10 min, which doesn’t seem like much, but this can be crucial for an activity. It definitely was for this one. I tried to get the students started right away, but kids will be kids. Several groups did not make it to the 3rd problem, and I even told them to skip the second, explaining that it was to verify that the results of the first problem would be consistent no matter what type of right triangle they used. I gave them some homework problems to work on identifying trigonometric ratios in several right triangles in both fraction and decimal form, but I felt uneasy about what might happen.
Today I decided that we would go back to the 3rd problem in the discovery and discuss it as a class. It turned out more students that I had anticipated actually did understand what they were seeing, and we went over a couple of the homework problems and the class really did have a vision of how they should be setting up the ratios. We looked at a couple of problems where they had to find the angle measure using the inverse functions and made sure everyone’s calculators were set properly to use the trig functions.
All in all, a good activity and the students are really verbalizing understanding of the functions better than I have ever seen in the past. We will work on application problems tomorrow and friday, which will give me a better idea of how well they are truly understanding this, but I feel better about it right now that usual.