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How do you teach your students to simplify (x+3)(x+4)? I used to tell them to use "FOIL," mainly because that's the way I learned it and that's the way the other teachers all taught it. The problem I have with FOIL is when they get to problems involving trinomials. If they've memorized the word FOIL, they have no idea what to do if there are extra terms.
Instead of using FOIL, I've found it works much better to start with simpler problems like (x)(x+4) - this way when you get to (x+3)(x+4), most students correctly suggest that you just need to distribute twice. First distribute the x, then distribute the 3. Why have them memorize FOIL when you could just show them that they're just distributing twice? I've found that my students have a much better understanding of the concept and will be able to tackle harder problems that have more terms.
I know there are other teachers still using FOIL, so I do tell them about it at some point, but most agree with me on the need for it.
I use a grid: each term of the first polynomial along the top, and each term of the second along the side. For example, (3x^2+6x+5)(x+2) would generate a 3x2 grid with 6 empty spaces.
ReplyDeleteFill in the spaces like any multiplication table and add it all up! Voila! No arbitrary orders to memorize or anything - any old way will work. Plus, it helps with division later: http://larkolicio.us/blog/?p=95
nctm has a cool thing at http://illuminations.nctm.org/LessonDetail.aspx?id=L798