Last week, I mentioned my plans to help my students understand the ratio element in right triangle trig.
It worked! I didn’t let anyone call out the answer; the kids had to discuss it in their groups first. As I walked round the room, I could hear them tussling with the question. In some cases, one or two of the students figured it out and explained it to everyone else; in others, the group “got” it while talking about it.
I gave them triangles with clearly distinguished cosine and sine ratios, and could start to see it click. Then I drew a 30-60-90 and 45-45-90 triangles, asking them which had a tangent of 1. Half the class figured out it was the isosceles right.
Seriously, it’s sinking in. All of the students in both classes were successfully solving for unknown sides by the time we tabled trig to focus on the state tests.
Now, the next big checkpoint: will they all be able to move between solving using trig ratios vs. the Pythagorean theorem vs. special rights. Here’s hoping.