I think every teacher I know that teaches algebra uses the FOIL method for multiplying binomials. Well, I TOTALLY disagree with the FOIL method. I hope, hope, hope to encourage some discourse on this subject. “Why do you buck all of the math teachers?” you may ask. Well, it’s like this. I am very much of the mindset that you should teach students in the manner that this is not going to be their last math class. Why teach them one way just because there is a cute song or activity or because this way is easier. In the grand scheme of things, multiplying binomials are not the only polynomial multiplication they’ll ever do. I teach students that they must multiply each term in the first polynomial by each term of the second polynomial. If you do the “happy face” or FOIL method, you are limiting it to two binomials. Explaining that you take the first term of the first polynomial and multiply it to each term in the second polynomial and then do that with each subsequent term in the first means that students won’t have to question what to do when they aren’t working with two simple binomials later on. Feel free to comment if you feel differently. I would love to have discussions on this.