isanybodythere
Parent's final request is a clear reference to Coq [3]. I yield, mumbling something about lions and claws.
[1] https://en.m.wiktionary.org/wiki/grampus
This taste-based taxonomy is reminiscent of Ishmael's taxonomy of whales in Melville's Moby Dick [2].
It is known, and can indeed be readily proved by inspection, that everything tastes like chicken [3]. I thus propose a taste-based taxonomy of edible organisms, aiming at restoring the former prominent role of Gallus gallus [4].
[1] https://en.m.wiktionary.org/wiki/long_pig
[2] https://en.m.wikipedia.org/wiki/Cetology_of_Moby-Dick
If you add up a sixth of a six-pack and a sixth of another six-pack you get a sixth of two six-packs -- two twelveths.
The student's misunderstanding comes from being taught fraction addition in terms of items in a collection -- which only holds if you keep to the same set (what you called scale).
This is a common choice -- "students already know how to add integers, so let's start from there", but as it did in this case, it doesn't always work as intended.
This is a great example of taking an analogy so far that the student didn't learn anything new at all. Everyone feels happy -- teacher's teaching, student's learning -- until you test what your knowledge on outside the domain of the analogy.
Fraction and integer addition are one and the same, yes -- but from the point of view of fractions, wherefrom integer addition is a special case. It remains challenging to teach and understand from the point of view of the integers, which is where the student stands.