Last fall I posted some experiences and conversations that took place during our work with transformations. I learned something so simple from my students and this year, I have shared it with my geometry classes again. When looking to rotate about the origin, simply rotation the graph and identify the “new” coordinates.
Sure, we do the typical, here’s a preimage, here’s the new image after rotating. Now, what do you notice happened to the coordinates? What’s the rule? (x, y) -> (-y, x) for 90º and so on… but once again, they get so focused on remembering the rules, then they get the x’s and y’s and the signs all jumbled and its a mess. I wanted to give them something, a visual, they could go back to…
Shortly before fall break, while assessing some student work, I had an idea. It seemed so obvious at the time, yet, I had never thought of it before. Using color-coded axes to demonstrate the rotations about the origin. I chose to make the positive side of each axis a different color than the negative side. We would rotate, then discuss which color was now in place of (x, y) for the first quadrant.
For several students, you could hear their light bulb.
Again, nothing new, but something that gave my students a concrete reference rather than remembering the rules.