My students do well with reflecting across x-axis or y-axis. Though they struggle literally flipping a transparency or patty paper across the line y=x. During whole class discussions today, someone stated “just read what it says in the equation.” OK. “Y becomes the x. And read it the other direction, starting with x. X becomes the y.” True. Simple.
Now, its rotation’s turn.
While using whiteboards to assess our FAL from Friday, it was obvious a handful were having trouble remembering “the rules” they had developed in their pair work. They stated as long as they had the transparency, they could physically perform the transformation. But wondered what they could do without those tools. One student suggested, ‘I just rotate my paper/graph as it says.’ Another chimed in, ‘that’s what I do too.’ Well, duh. An example – the point (1, 4) rotated 90 degrees clockwise about the origin, would simply be one quarter turn to the right; resulting in (4, -1). Rotate another 90 degrees for a 180 degree total results in (-1, -4).
So, as a class, we practice their strategy. Genius. Why can’t I think of the simple things? So glad I finally figured out how to listen to my students – their way is so much better than mine.
Another strategy was to draw a line segment from the point through the origin to find the image rotated 180 degrees. To find the 90 or 270, simply take your scrap paper and use a corner edge from the origin and draw a line perpendicular to the 180 line segment. Students went on to suggest they used “slope” to place the image.
This is a sample of what they suggested. Rotations around the origin.*
I like this last strategy, because it will also work when rotating around a given point. Rotation around a given point.* Another suggested that drawing a segment from the point through the given point of rotation…is kind of like the point of rotation is actually the midpoint of the image and pre-image.
I’m happy with the fact that they’re looking for a way that makes sense of the transformations. They’re considering different strategies and our discussions often lead to whether it will work or not.
*created with screen recordings on Promethean ActivBoard – not sure if they will play otherwise.