To lessen the intimidation factor of constructions, I ask students to warm up for the lesson by having them write their name using a compass and straightedge, which are sometimes challenging for students to use. I tell them:
Afterward, I project student volunteers' work using the document camera and ask them to share out their strategies for using the tools (MP5). Often times, my students share the following:
All of these ideas are helpful for performing constructions! We are on our way.
Understanding the power of constructions requires students to appreciate the important role that sketching, drawing, and construction can all play in modeling and problem solving. To get things rolling, I explain the differences between sketching, drawing, and constructing to students. I emphasize that constructions are valuable because they give us a hands-on way to precisely explain different kinds of geometric ideas. I tell them that constructions are a basis for proof since, for example, understanding how to construct a midpoint reveals deep understanding of what a midpoint truly is. I present these ideas persuasively, and, I encourage my students to take notes about the difference between a construction, a drawing, and a sketch.
Constructions can pose lots of challenges to my students, particularly if they try to memorize a series of steps instead of try to make sense of how to use their constructions tools to show a geometry concept. Throughout the unit, I ask my students to list the factors needed to really show they have performed a construction. For example, in the case of copying segments, questions like, “How would you duplicate a segment if you couldn’t measure it?" and "What would you need to make sure of?” encourage students to think for themselves about the importance of keeping their compass setting the same without me explicitly having to teach this to them. When students deeply understand for themselves, they can transfer these ideas to other constructions.
I call on a student to volunteer to come up to the document camera and to explain how he/she performs the construction, explaining the why behind everything he/she does and how these steps guarantee that the segment is a copy of the given one.
I repeat a similar process for having students copy an angle, asking questions like, “How would you duplicate an angle if you couldn’t measure it?" and "What would you need to make sure of?" Again, I want students to come up with the idea that they need a way to keep/maintain some kind of distance from each side of the angle. To debrief, I call on a student volunteer to perform the construction and to explain why the steps he/she took ensures that the angle must be a copy of the given one.
I want students to explain the constructions to themselves, which is why I choose these two video clip for copying a segment and copying an angle to play for my students. I play each video without sound, asking students to write down the play-by-play commentary for what the teacher is doing and why. I have students check their own explanations by playing each video once more with sound.
COPYING A SEGMENT:
COPYING AN ANGLE: