This mistake seems to say something significant about the way this student sees fractions, but I’m not able to piece it all together. Maybe you can?

• Factor = fraction?
You get to the bottom of the tree, and then you cancel out the common factors and make a fraction with what’s left. In the last one, only one branch made it to the bottom of the factor tree, so it’s the only one that you can use to make a fraction with.

• It seems to me this student may be confusing reducing to factors with simplifying a fraction. However, Denise’s thought that the confusion is simply between factors and fractions is also logical. I’m fascinated by the fact that the student did all the work correctly but clearly didn’t understand the objective. Did the student understand what was happening in their factor tree? This would be an amazing conversation.

• LSquared

I’ve been teaching a few sixth graders to use factor trees to both simplify and multiply fractions and to find least common denominators. It’s tricky because for a while they get the two processes mixed up, and I need to repeat that to simplify by cancelling you have to have one factor on top and one on the bottom (not two on the bottom).

• Owen Thomas

the student sees fractions as *meaningless*.