"He sits on the big stone."
Translation:Er sitzt auf dem großen Stein.
OK, it seems this sentence in English can have two meanings: 1. It's a description of his location; He's already sitting on the stone, which would require Dative form after "auf" and 2. It's describing his action, that he's in the process of placing himself onto the stone, which would call for "Akkusativ" form after "auf." So couldn't one legitimately answer "Er stizt auf den großen Stein." for this exercise as well as "Er sitzt auf dem großen Stein."?
You are right about the Akkusativ after "auf" in this case (the process of placing himself onto the stone). But "sitzen" is always the inactive form of already sitting. To describe the process, you would need the verb "sich setzen". Thus the sentence would be:
"Er setzt sich auf den großen Stein"
auf goes with the dative case when you are describing the location of something, and with the accusative case when you are describing the destination of motion.
Here, you are talking about sitting which is taking place on the stone (there is no movement involved in sitting, and so you are not sitting "onto" the stone but simply "on" it), so you use the dative case.
I have a few different ways I 'cement' nouns: gender, concept and context in memory.
This is one of those examples where using Google translate can help. If one uses GT (Google Translate) your word Fels or Felsen as mizinamo indicates, one can see that GT lists two meanings. One is rock, and the other is cliff. For me this brings to mind a "fall" or the area at the bottom of a cliff where rocks have tumbled from the cliff face. While these are often large, they can be small; but, the point here taken is that they're at or near the bottom of a cliff. I picture sitting on rocks at the bottom of the cliff; which explains the double use of the word.
GT also indicates that the most often form is the meaning Rock (rated: 3), which here along with (Cliff) (rated 2) indicates that while used more often for Rock, the 2nd most often used is Cliff, and so, it's not just any rock; but a Cliff Rock.
Her answer was succinct; but I wanted to give the method I use when examining meanings in German that often works to show the subtleties. If I feel I need more clarity, I use a German-English Dictionary Definition. In this case: https://en.langenscheidt.com/german-english/fels https://en.langenscheidt.com/german-english/felsen
I would also point out, that for me... this is simply a way to further embed the concept, gender, and sentence contexts for various words. I've found even slight diversions like this tend to 'bind' words conceptually and contextually in memory.
However, FWIW GT says "the stone" is Der Stein preferred, and confirmed by the "Community". :-)