As a student back in the 9th grade, I remember my first encounter with this thing called F-O-I-L. We were learning how to multiply two binomials using this method. I seriously thought it was a joke and that my algebra teacher was playing a trick on us. I recall looking around at my peers in class, hoping someone would ask the first question, or better yet, burst out laughing like I was wanting to do. I did catch on. It was just a set of procedures. I could follow directions. The problem came when I needed to reverse this procedure and factor a trinomial to get back to the two binomials that were multiplied. I was ready to throw in the towel. I couldn’t make sense of the procedures. Actually, I wouldn’t even say it was a procedure per se, but rather a lot of steps to run steps to see which set of numbers did the trick. Apparently, I didn’t have the patience for trial and error. This was certainly a turning point for me as a student. I remember at asking “Why” for the first time in my math education experience.
This brings me up to my first year teaching. I was very excited to get to teach algebra and I certainly felt prepared to do so with my wonderful experience as a student teacher. I remembered prepping for the lesson on factoring trinomials. My students had mastered multiplying two binomials as we recited, “First, outer, inner, last”, aloud in class. The first example, of course, didn’t go so smoothly. Lots of wrinkled foreheads! It was most telling by the fact that the fifth example received the same reaction as the first. I had hit a brick wall. I didn’t know any other way to teach factoring trinomials. Unfortunately I, as well as my students, suffered through several years of me teaching the trial and error method of factoring, or reverse FOIL as some refer to it as, before I found the easiest way to teach this concept. I did not come up with this way of teaching. In fact, since learning this method, I have found it in current textbooks. I first experienced this through a workshop at the 2009 South Carolina Council of Teachers of Mathematics conference in Columbia, South Carolina. Unfortunately, I do not recall the name of the presenter who facilitated this workshop.
To set the wheels in motion for this easier factoring method, I begin with NOT teaching the FOIL method for multiplying two binomials. Instead I have students apply the distributive property twice, pulling each term of the first binomial through the second binomial. I take this opportunity to utilize the different pen tools of my Tablet PC when teaching this method. You can do the same by using different color chalk, whiteboard markers, or smartboard markers to get the same effect.
I have included an instructional sheet that is quite comprehensive and explains this method of factoring. I not only provide worked out examples, but also guiding questions and tips in teaching factoring trinomials to students. I’m very proud of this piece and will certainly work it in to the book I’m currently writing. I look forward to your feedback on this method of factoring as well as on the explanation I have included in the attached document.
Instructional Piece FactoringTrinomialstheEasyWay
Word Document Version Factoring Trinomials the Easy Way