The Law of Sines | Algebra 2

Last Friday, Kyle Barriger came by the lab with an idea. In his Algebra II classes, the students are learning about the law of sines. (And truth be told, I had to ask him to be my math teacher for a moment and remind me what the law of sines is!) While students generally have no problems visualizing when the law results in no solutions, understanding why there can be ambiguous cases where there are two solutions seems to be much more difficult.

So Kyle thought maybe we can build some sort of contraption to physically show this concept. After some quick planning and sketching on the whiteboard tables, we got to work building such a contraption.

There were a few design requirements we had to keep in mind:
- a way to set a fixed angle of a certain degree
- a fixed length for one side of the triangle
- variable length for the pivoting side of the triangle
- a way for the pivoting side to actually pivot

A few cardboard prototypes later, we were ready to print out our contraption in wood and assemble it using a few screws and nuts. To fulfill requirement #3, we made various lengths for the pivoting side that can be swapped in and out. We even scavenged some strong magnets from old name tags so the whole thing can be stuck on a whiteboard!

During our initial meeting, we had also discussed the idea of having the students build their own contraptions to explain this law. So in today's class, after Kyle used our wooden version to review the law of sines, the students got to work building their own models with everything from pipe cleaners to string to popsicle sticks.

Although many groups weren't able to fully finish their "explanation contraptions," we enjoyed watching how this hands-on activity got them moving and talking and even witnessed some "ah-ha” moments! Now if that isn't a lovely result for such a quick and simple project, I don't know what is.