The trig students gushed unforeseen excitement about seeing me derive the Law of Sines today. They loved it! My plain old plan for it had been this:
- Go through derivation clearly but quickly so students see a connection between SOHCAHTOA and sinA/a=sinB/b=sinC/c
- Demonstrate using the LoS to solve a triangle
- Have students practice solving a triangle using LoS (make sure they do the practice problem)
Little did I know that step one would be so energizing and fascinating to them! Although I told them they would not have to reproduce the derivation, students who normally forget the proper function of notebook paper were furiously copying down the steps, asking questions (“In the area equations, what represents the height?” “What’s the pattern of the letters in the different equations?” “Why is it that way?”), and answering other students’ questions.
My favorite moment was when I asked the class, “Does everyone understand how I went from this to this?” A pedagogically poor question, it has traditionally been answered by silence, a dull or uncertain “Yeah,” or even a perturbed “We get it.” Today in my class it was answered by, “Yeah, you broke off that part and everything cancelled out except the a on the bottom.” The language is not terribly specific or mathematical, but it’s far more so than any of the traditional replies.
I wonder whether all derivations would strike these students as forcefully, or whether this one was especially suited to the task. Either way, I slapped a sticky note down on my lesson plan to remind myself to hit it out of the park again next year.