Working with triangle dilations

Today we moved back to work with Triangle Dilations. This work starts with students constructing dilations. Students grabbed their compasses and started working right away. Having worked through constructing dilations last class really helped. There were no questions and students were able to work through the initial constructions.

Listing proportions were a bit more troublesome. I had to clarify what was being asked. I decided to have students focus on the relationship of segments, for example, AB = 2A''B'', etc. Students could understand relationships expressed this way and it tied into the idea of scale factor. I'll wait until we go through responses to get into how to take these relationships and re-express them as proportions. I also am waiting to discuss their findings on the proportion relationships until next class.

The review of angle relationships was interesting. Students recognized that we had worked with these relationships but quite a few struggled with naming one or the other of the relationship names. I thought it was good review to keep the vocabulary up front with the class.

The next section on creating the described dilation seemed to be going well with the class. As I walked around, there really wasn't any questions about this section and the drawings appeared to be correct. Most of the class was either working on this section or just completing this section when class ended.

I asked students to complete the remainder of the questions as homework. I also told them that they should use a ruler to complete any remaining constructions.

The class worked throughout the entire period. I was encouraged by the work I saw produced and the small amount of support that the students needed to complete the tasks.

Next class we'll discuss responses to the questions. I want to flesh out the side relationships that exist between the pre-image and image in a dilation. I also want to get students to think about the side relationships in terms of a proportional relation.