What Makes You So Special?

Discovering Special Cases of Polynomials in Ms. Wilson's Algebra I Class...

"This lesson was implemented the day after my students learned how to FOIL binomials. Students already had an understanding and mastery of exponent property rules, as well as adding and subtracting polynomials. The day after FOIL, I told students that we were simply going to “practice more multiplication of binomials” so that they really get it. What they didn’t know at the time was that all of the binomials they were multiplying would create perfect square trinomials and a difference of two squares. Students were given 15 problems to FOIL (all special cases) like the ones shown below:

I chose to sit students in groups of 4 for this activity and encouraged them to collaborate and help one another.  As the FOIL’ing began, the lightbulbs started to turn on. I could hear conversations evolving about patterns they were seeing involving additive inverses and things “dropping out”. One student announced to his group, “guys, if the signs are different the x’s always cancel out!” Many groups stopped FOIL’ing altogether and went on to apply the patterns they’d discovered for the remaining problems. Some needed guidance (more so with perfect square trinomials), so I asked them some leading questions that allowed them to own the discovery of these patterns and algebraic rules. The magic that happens in a classroom when you hear that, “ohhh!” – that’s the sweet spot." 

 When have you experienced one of those "aha" moments in your class?

(Catherine Wilson teaches Algebra I at Westbrook Intermediate School in Clear Creek Independent School District)