On a Monday after Winter break I came back to my 8th grade algebra with the topic of multiplying binomials. We had spent about two weeks on the topic before break. Most of the time was devoted to creating specific rectangles using Algebra Tiles, but also we moved onto to the use of "generic rectangles", which in our CPM course, are simple graphic organizers to multiply polynomials.
Before re-visiting the topic, though, I wanted to know when such a skill is actually used. I conducted a quick Google search: why multiply binomials. The only results I got were "how to multiply binomials". So I posted my query on Twitter. Gary Davis (@republicofmath) took up my question and started to write about it based on an email I sent him with my initial thoughts. Later, I read what he wrote and responded.
Several great things happened for me. First, I got to think deeply about a topic with someone who knows so much about it. Secondly, I got to bounce my ideas off of his expertise. Finally, we collaborated on a blog post. The collaboration via Twitter and blogs was fantastic. Thanks, Gary.
This is the blog post: