>That is, if you teach the students to "type" all those fractions (e.g., 1/3 of this blue table, etc.), Sure. You can certainly ad hoc extend the analogy to br

>That is, if you teach the students to "type" all those fractions (e.g., 1/3 of this blue table, etc.), Sure. You can certainly ad hoc extend the analogy to bring it in line with the mathematical rules. But at this point, you do hit a higher level of complexity. Your simple analogy is gone and you're slogging through the weeds. That was my point. Analogies are flawed. The teacher started with a very simple rule that worked well and communicated the ideas under certain constraints and then those rules were extended in a logical but incorrect manner by a fourth-grader ... and now the complexity that was hidden in the abstraction is leaking out. Your explanation is more confusing to me and wouldn't be grasped by the vast majority of fourth-graders. At some point, simply stating that fractions have different rules is the most simple (and correct) explanation.