After teaching three different ways to find the greatest common factor of two numbers (list all of the factors, use prime factorization, simplify fractions), I split the students up into three groups and asked each group to solve the problem a different way.
As they solved it, I took note of which groups finished earlier, which groups made more mistakes, which groups were more confused, etc. We reviewed each of the three solutions on the board and I then asked everyone to write one good thing and one bad thing about each method. I then asked students to share those thoughts and I summarized them on the board next to each solution (see picture).
Not only did creating this pro/con list help students decide which method they preferred, but it also clarified some misconceptions about why each solution works. They also saw some similarities between the three methods (the numbers 5 and 7 keep showing up). Incidentally, most students did not like method #1, but I warned them that, because it is so intuitive, it would be the method they remember the best.
