For today's the Do Now, I ask my students to access their prior knowledge and answer questions about transformations on the coordinate plane (see earlier lessons). They are asked to identify the specific transformation that maps a pre-image to a given image. I expect some variation in their recall. Some students' answers will be more general, while others will be specific and precise. When we go over the answers, I question students further about lines of reflection, angles of rotation, scale factor of dilations, etc. to review the concepts we covered in the Fall.
Later in the lesson, students will use compositions of transformations to explain how a pre-image is mapped to an image. As students are working on the Do Now, I pass out laptops, for most of today's work will occur using Geometer's Sketchpad.
At the beginning of the Mini-Lesson, I instruct students to open Geometer's SketchPad 5 and give them a couple of minutes to “play around” and re-familiarize themselves with the program.
After two or three minutes I show the students how to define a coordinate plane and plot points on the plane. We investigate the difference between constructing points using the point tool and plotting points by defining their coordinates using the menu. When students plot a point, the point cannot be moved because its location is defined. Then, I will have students practice plotting different points and connecting them using the segment tool.
Once the students are comfortable with the difference between a plotted point and a constructed point, we will move on to the Main Activity for the lesson.
My plan for today is for my students to work in pairs to complete the activity. Each pair gets one computer. Although I have enough computers for the students to work independently, I find that by pairing them they are able to participate in more mathematical discourse, and, they can effectively assist each other with Sketchpad.
The activity for today provides instructions for students to follow and guiding questions on a worksheet. The questions lead the students to discover the how images differ after a dilation centered at different points on the coordinate plane.
As they work, I circulate and check their sketches. I see if the sketches pass the “drag test.” I drag the vertices and lines of the diagrams to see if they maintain the properties. Points that are constructed, rather than plotted will fail the drag test. I find that my students often draw points that look as if they have certain coordinates instead of graphing points that actually have the necessary coordinates. But, the more often we use Geometer’s Sketchpad, the better students get at using the program.
For the summary, we share out as a whole class. Since the last part of the activity involves students using their own triangles, scale factors, and centers, I call on multiple students to describe their findings. Students recognize that dilations about a center that is not the origin is a translation of a dilation about a center that is the origin. We investigate this concept further in later lessons.
This activity helps students delve deeper into dilations and similarity and allows them to come up with their own conclusions (G.SRT.1, MP3).