Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Not one of the best units for my students this year. It was basically where we started the year (which in hindsight might need to be modified). Translations were easy enough. Students could easily see that when a shape is moved that the basic shape remains the same, but the location changes.
Dilations, rotations and reflections, however, were not as easy. The first problem I came across was that students had difficulty picturing that a 1x1 square that doubled in size (becoming a larger square) didn't have an area of 2. Even after drawing many examples in their notebooks, I still had students who struggled with seeing this.
Next, I noticed students confusing how a polygon would look when rotated. A triangle with an acute angle pointing in one direction in the original image should end up with its acute angle facing another direction, but this wasn't the case with many of the students. Reflections were confusing as well.
I am thinking that I will start off next year looking at shapes (capital "T" comes to mind) and go through the transformations (without dilation) before even introducing the idea of graphing this shape. (which explains why I keep asking everyone where the district die-cut press has gone) I figure if the students can keep picturing what happened to the "T" it might give them a visual cue to when there is a problem with their doing these transformations on a graph.
I also will be stressing the graphing aspect of this more next year. The way this has been done has been with the graphing being an after-thought more than a goal. I think seeing the changes and coming up with ways of describing these changes (either by verbal or symbolic description) adds necessary depth to the topic.