Normally I skip right over constructions in geometry because I've just never found them to be that important.
I hope that I am teaching more authentically, in a way that involves doing math like (what I think) a mathematician does. I also hope that I am teaching more with kids in mind, in a way that realizes different students think differently and can be successful at different parts of math.
So, I'm doing them.
I found step-by-step demos of tons of constructions over at Math Open Reference. They have printable step-by-step instructions that go along with them but I took a different approach.
As a class, we watched the demo and did one step at a time. Then we tried to do another drawing from memory. We stopped and wrote out own directions (hey hey another writing across the curriculum moment!) and then completed two more drawings.
Here's what the demo for perpendicular bisector looks like.
I used this method for several constructions and I was pretty happy with the results.
I also like the alternative circle method for drawing an equilateral triangle. Definitely doable without a demo. Especially since I didn't find one.
Demo: Centroid/Median and Altitude/Orthocenter