I think the problem is the teacher moved from one type of "fraction problem" to another kind. The example of drinking 4 bottles of water to only have 2/6 left

I think the problem is the teacher moved from one type of "fraction problem" to another kind. The example of drinking 4 bottles of water to only have 2/6 left of the original pack is doing an integral problem and wrapping up the answer as a fraction. Same deal with the pack of 12 pencils. The students can grasp those problems as e.g. (1+1)/6 rather than (1/6 + 1/6). In other words, there is only one "whole" in the problem. When you're adding the fractions of desks filled with students, the fraction is counter-intuitive because both desks have to have the same number of students for it to make sense. (1/3 of a 5000-student round table is different from a 3-student table). And to say "the units are wrong" is kind of a limited way of explaining this. The units also need to have the table capacity as part of the unit identity (i.e. the units would have to be 3-student-table). That's a pretty sophisticated way of thinking about units. I think that after the pencil/water examples, transitioning from the pencil/water pack examples to a more "pure" fraction example would be better. e.g. one group of students eats 2/3 of a pizza, and another group eats 2/3 of a pizza. Now you can throw away one of the original pizza boxes and put the two remaining 1/3 in a single box which is 2/3 full. Now the "whole" for each fraction is no longer arbitrary (like 6 bottles of water or 12 pencils).