During today's lesson I ask the students to continue with their work on the Summative Review (Summative Review Handout). As they work I circulate around the room, assessing student progress and providing leading questions when necessary.
At this point, I pull the class together and we discuss their results on the Summative Review. When we arrive at Question 4, the transformations question, I ask students to write the different compositions of transformations that they arrived at on the board. We take the time to examine and try out the variations, and I try to drive home to them the fact that all of their compositions include a dilation – because of the link between dilations and similar figures.
Question 5 is pretty straightforward and I discuss briefly the “real life” uses of similar triangles to determine the dimensions of objects or landforms that are unable to be measured.
With Question 6, I lead the discussion toward similar two and three-dimensional figures. If two rectangles are similar, what is the ratio of their areas? By giving examples, the students can come to the conclusion that the ratio of the areas of similar figures will equal the ratio of similitude squared. When we look at their results for part c in question 6, the students will see that the ratio of the volumes will be the ratio of similitude cubed. While we have not yet covered volume in this course, this question sets the stage for this unit in the future.
I remind the class that the unit summative assessment will be given during the next class meeting. As final preparation, we discuss the importance of labeling diagrams. I emphasize the importance of explicitly identifying a ratio and recording it as part of the work on a problem. I touch briefly on the importance of assessing one's own answers by asking the question, “Does this answer make sense?”
Finally, I remind the students that I am available for extra help after school, should they have any last minute questions.