Day 60: Trig Graphs in Under 15 Minutes!
I want my precalculus students to be able to quickly AND accurately graph sinusoidal functions, regardless of the mode, the form or the apparent complexity of the equation. After all, there are really only up to 5 transformations that can happen to a sinusoidal function: reflection, vertical and/or horizontal dilation, and vertical and/or horizontal translation. And I want them to be able to clearly and accurately identify the transformed quadrantal points by their coordinates. Here one of my students chose to color-code the parts of the graph. The other shows how to determine the horizontal coordinates. Both of these are done using Notability on the iPad and submitted to Schoology, a learning management system (LMS) our district uses.
I continue to use Foerster’s approach to graphing sinusoidal functions (sometimes referred to as the window method) as I find students have the most success AND understanding. As part of the development, I want students to create a point-rule and a verbal description of the transformations on the parent function that result in the final graph. But the practice can be boring and potentially fraught with errors in thinking if students begin graphing in isolation. So I use complex instruction via a group poster to solidify the process before my students practice on their own. I have a set of 6 colored, various sided dice in a green-topped container. Student roll the dice and it determines the equation. Then they have lots of other things to do once they get the equation.
This year’s students were even more ready to complete these graphs. I think we did a little more sense-making prior to actually starting to graph and this made it easier for them. I also used the Online Stopwatch to help them monitor their time.
I even had one of my students, who proclaimed early in the year that I had students do way TOO MANY posters, say that he now likes doing posters because they help him understand the ideas better. Glory be, he made my day!!
What mini-triumphs have you experienced lately?