Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line
INTERPRETATION OF OBJECTIVE - G.CO.D.12
Not much to interpret here.... learn the basic constructions. I guess it is important to note that they can be done in a variety of ways (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
(1) The student will be able to use geometric concepts to establish a rationale for the steps/procedures used in performing a construction.
(2) The student will be able to use a compass and straightedge to create the following constructions.
(a) copy a given line segment.
(b) copy a given angle.
(c) bisect a line segment.
(d) bisect an angle.
(e) construct a line perpendicular to a given line through a point on that line.
(f) construct a line perpendicular to a given line through a point not on that line.
(g) construct the perpendicular bisector of a line segment.
(h) construct a line parallel to a given line through a point not on the line.
(i) construct geometric figures using a variety of tools and methods
THE BIG IDEA
Geometric constructions help students connect the theory of definitions to a practical physical medium. Constructions support students by reaffirming definitions as they apply them to make the desired relationship. Constructions are a powerful way to test out conjectures and search for new concepts. Throughout the course constructions will be used to support or reveal the concepts needed for application.
TRAPS & PITFALLS
A major issue with constructions is having the tools and how do you handle homework. If you start with them at the beginning of the year as I do, not all students have bought a compass yet and so asking them to do work outside the classroom is difficult. One way to deal with that would be to have them describe steps in doing a particular construction or watching a video about how to do it and then giving a summary of what they learned.
I also think that students need extra practice with notation. I would have them notate all the constructions that they create. Not just labeling the diagram with dashes, arcs, right angle symbols, etc... but also list beside the diagram congruent statements or equality statements.
Students need to know the basic geometric terms and their definitions. These terms and their definitions will give students a place to start, so if they are attempting to construct a perpendicular bisector, they need to know what perpendicular means and what bisector means.
Constructions will occur all throughout the course. We continue to connect theory to practical through constructions. As the year progresses constructions become more complex building on previous constructions.
MY REFLECTIONS (over line l)
I teach constructions right away. I find it a great start to the year - they definitely know that they are in geometry class. The beauty of starting the year with constructions is that right away we are introducing definitions, notation, and the essential relationships of midpoint, perpendicular, and parallel. Also by starting them right away it provides the opportunity to continue to integrate them throughout the course. We need them with translations, we need them with quadrilaterals, we need them with circles... they can and should show up all year long as a way to connect the abstract theory to a practical/physical format. It was constructions that always made geometry special for me when I was taking it as a High School student.