High School: Geometry
12. 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.
For this standard, students are expected to be able to draw. Okay, so it is a little more complicated than that, but that's essentially the gist of it.
Like aspiring artists everywhere who send for their free art talent test and studiously copy the turtle or pirate, your students will be very intentional and deliberate as they construct lines and angles.
Art students use their charcoal and oil pastels; geometry students will whip out their compasses and straightedges. Art students take suggestions to make their drawings more lifelike; geometry students will rely on properties, postulates, theorems, and corollaries to make their drawings more rigid. Art students know that practice makes progress; geometry students will figure this out soon enough.
The standard itself lists a few examples of both the tools students might be presented with and the tasks they should be able to perform. However, it takes more than fancy tools to make these constructions. Students should keep definitions, properties, and theorems about line segments, rays, angles, and parallel and perpendicular lines safe in their back pockets in order to support their drawings.
Students will benefit from plenty of opportunities to practice each skill. Even more helpful will be different contexts for each one. For example, students might first construct an angle bisector on a single angle, then the angle bisectors for all three angles of a triangle to show that they are concurrent, and finally explore whether the angle bisectors for other polygons are also concurrent.
Once they have mastered using a compass and straightedge for a particular construction, students will benefit from exploring using other tools and methods, such as paper folding or using a mirror, to complete the same task. This will reinforce their understanding of the rules of the shape they're working with.
Even though artists are ultimately free to create whatever art they want, remind your students that they still follow general rules. That way, students can't claim that you're stifling their creativity when you're actually giving them tools to nurture it. They'll be acing those geometry exams (and art talent tests) before they know it.