The Factor Pair Spoons Game is a new game that was inspired by participants in the Professional Development Series that I’m conducting every month this semester at my college. Last month’s topic was ‘Playing Games to Learn Math’ and I asked the participants to come up with a game for a topic that they felt was a difficult topic for students. This game is a variation on what they came up with. The spoons game was one of their suggestions, but they ended up turning it into more of a rummy-style game because they thought that the spoons might become too chaotic for some students in the classroom.
Here is why I believe that the FOIL method for multiplying two binomial expressions should NOT be used:
The underlying premise of the FOIL method is that students must first be able to identify a binomial. However, most instructors do not seem to stress enough that the FOIL method can only be used to multiply two binomials. We can only speculate on the reason for why they might not do this – Maybe they only teach multiplying binomials so they do not need to make any distinction or maybe whey wrongly assume that students will be able to identify a binomial. However, in my opinion, if a student cannot identify a binomial, then they should not even be using the FOIL method.
Either way, what worries me the most is that fact that a student will get to a problem that involves multiplying expressions that are not binomials and will not know what to do. If I would have taught the student the distributive property that can be used in every case, rather than the FOIL method that can only be used in the special case of multiplying two binomials, wouldn’t that have been a better use of class time?
I have also had students who have asked me if they can use the FOIL method to multiply two trinomials and I, of course, tell them that they cannot. But then the student objects because they have just multiplied two trinomials using the FOIL method and want to show me that their answer is correct.
Even in the cases when the student has shown correct work and has arrived at the correct answer, I still have to cringe at the fact that the FOIL method involves the student multiplying four times and multiplying two trinomials involves the student multiplying nine times, but the student still wants to argue about the fact that he can use the FOIL method on every problem. There is a big difference between four multiplications and nine multiplications.
I honestly believe that students would benefit more if we simply dropped the FOIL method and instead taught them the distributive property along with a review of counting properties by asking them to count how many different multiplications must be done before they even begin. It is definitely one way that we could help increase ‘number sense’ in our students.
And ultimately, FOIL is for baked chicken, NOT for multiplying binomials.
This problem came up in my Intermediate Algebra class today and one of my students said that we should call it “Factor Gate” since even though all of the students have correct work, they all ended up with a “different” answer.
A few weeks ago a colleague of mine was in need of an activity for Factoring. He was ahead of his pacing chart and wanted something to fill up some class time with. I referred him towww.ilovemath.org, which has hundreds of free activities to download. Here is a list of a few that I have successfully used the in the classroom: