When I started my teaching career, I taught the constructions that were required on the state exams by providing my students with an overview of the conventional steps. I soon learned my approach was completely ineffective. No matter how I varied my instructions, many students perceived constructions as little more than "pictures" that needed to be memorized.
In my fourth year of teaching, I completely abandoned my traditional method. On the first day of the constructions unit, I have students take out their compasses and given them one goal and a few rules:
The Goal: Use only the compass and ruler to make a diagram full of circles and line segments, according to the rules:
- You may start with two points.
- Every circle must be centered on an existing point or intersection and must pass through an existing point or intersection.
- Every segment must pass through at least two existing intersections or points.
- BONUS: See if you can identify any cool patterns or relationships!
While students work, I only walk around to check that students follow the rules. Of course, they quickly identify perpendicular lines, equilateral triangles, parallel lines and more. Using this approach, I never have to teach procedures. If students need to know how to construct perpendicular lines, I ask "do you remember how you figured it out?" and if thy say "no" I say, "I guess you will have to figure it out all over again. Don't forget to follow the rules."
Below, I will add a few of my own assignments. I will update this page periodically, play check back or, if you have any requests or questions, leave a comment!