Trick for Teaching Basic Trig

During my middle-school teaching days I noticed that often kids would arrive in my 8th-grade class with a half knowledge of sine, cosine, tangent. There were two major problems they often had in solving for unknown sides in a right triangle using trig:

1. They couldn't visually distinguish opposite side vs. adjacent side. Many middle-schoolers I taught had a poor consistency (if any) with recognizing what "opposite" and "adjacent" meant in a diagram; it was just too abstract for them, even though I tried to explain how to look for the sides "across" the triangle, etc.

2. They couldn't figure out whether to use sine, cosine, or tangent in a given situation.

The first problem I solved successfully a few years ago, when I came up with an idea to start teaching kids to reach their hand out and to actually put their hand over the acute angle that is given in the problem. The "opposite" side (from the perspective of the given angle) is the ONLY side that their hand is not touching, since "opposite" implies "far away"; on the contrary, the "adjacent" side is the side (besides the hypotenuse) that their hand IS touching.


Trust me, if you're seeing the same problem in your classes, TRY THIS. It works like a charm. I taught sine, cosine, tangent from scratch today to my 9th-graders, and not a single person had trouble recognizing opposite / adjacent sides. (Granted, they were honors kids, but again, I've tried this with my regular 8th-graders in the Bronx. It had worked like a charm then, too!)

Issue #2 just takes a little bit of practice, but this year I found that I made a nice transition into this by having allowed a couple of days of pure similar-triangles proportions practice. Right from the start, kids really grasped the concept that in order to solve for x, you need a proportion that involved x as an only unknown, so it was super easy for us to transition to speaking about putting together x and the other known side inside the same trig ratio / proportion.

So, surprisingly, I taught all of basic trigonometry to my honors classes in one 75-minute period. (Inverse trig not included.) Seriously, those guys had never ever heard of SOH-CAH-TOA before today. Neat, eh? We'll see next week whether I can translate this success to my regular classes!!