We’ve started the course by thinking about expressions, both arithmetical ones and algebraic ones. We’ve turned things like “twice nine” and “three less than four more than x” into symbols. And we’ve started to talk about what I like to call algebraic “moves”—ways to change what an expression looks like, but that keeps its value the same. (Like how we can change x+x into 2x.)
Each of our core high school courses have subtitles, and students choose between these different course versions. This class—the more “traditional” of the Algebra 1 courses—is subtitled “Techniques and Applications”. I think of algebraic “moves” as techniques; so what are the applications? Well, the above is the first example I’ve shared. We had already come up with a variety of more-and-less interesting arithmetical expressions for 6—like 1+2+3 and 4197-4191 and 12/2. In a seeming non-sequitur, I had everyone pick a number at their whim and proceeded to call out a sequence of operations for them to apply to it. At the end, I had them compare their results with a neighbor, and soon word buzzed around the room that everyone had gotten the same thing! Then we wrote out the subject of today’s photo: one very bizarre to write the number 6.
We’ll justify this result soon. Also, I’m pretty jazzed up to help my students create some arithmetical parlor tricks of their own!