Measuring Angles (Plus a Little Dancing)

Geometry A is working through a unit on definitions and introduction to proof, with a good dose of reviewing key ideas that may or may not have been learned in middle school math. Our topic today was recognizing: vertical angles, linear pairs, corresponding, alternate interior, alternate exterior, and same-side interior and how to use that information to start building proof.

I put up a set of lines and a transversal and had student call out angles that fit the above terms. Then I had them all choose a set of taped lines that were spread around the room. We went through each location again, trying to find as may pairs that fit said relationship. After students were comfortable with each, I hooked up “Dance, Dance, Transversal.” I have no idea who I first saw the idea for “Dance Dance Transversal” from or I’d give credit, but there are lots out in the inter-webs of math land, so if you want more, Google returns many hits. We played a few rounds to warm up. Basically, I had a PowerPoint set up to cycle through the terms (I limited it to vertical, AIA, AEA, and corresponding) and students had to jump to the correct location. We had music going and in later rounds, judges. We crowned the class champion and I let them know they’d have to dance on the unit exam.

Then, each student was tasked with getting a protractor and measuring the eight angles formed by the transversal. I had purposefully used both parallel and non-parallel set ups (About 2 parallel for every non-parallel). After measuring, they walked around and had to write down at least two notices and two wonders. (Examples “I noticed all the vertical angles were the same.” “I won
der why some gro
ups have only two different angle measurements and others 4.”   “I noticed an error, or what I think must be an error in set B.”   “I’m wondering if my tape was messed up, because it doesn’t look the same as most of them.”)

We were running short on time, so we shared out a few of the Noticings and Wonderings as a class and we’ll pick back up there tomorrow. The plan is to agree upon, prove, and then practice with the key ideas.