Day 55: One of these things is not like the others.
As an opener/introduction to periodic functions for my precalculus class, I asked the above question. We are starting trig equations, but I wanted to develop the idea of periodic functions and their characteristics first and then build on it for the sinusoidal functions tomorrow. It was interesting to hear what the students attended to (are those lines vertical, are they all on the same axis, is continuity important?) and what attributes slipped their attention (the idea of repeated patterns…darn, I thought they would see it in the graphs). I wonder if I gave them too many choices? The one I didn’t expect was that E is not continuous whereas the others are…should have seen it, duh! Either I need another discontinuous periodic function or remove this one from the choices…what would you do? We will debrief the question in our block period tomorrow in addition to adding in the meaning of the words: amplitude, period, axis, frequency as they attach to a real-world situation. In the past, I have used this approach and students were very comfortable with the vocabulary when we then applied it to sinusoids. How do you introduce new vocabulary?