A two sentence paragraph is not a good example for this particular question. Not that two sentence paragraphs, or even one line paragraphs, are not perfectly acceptable, but they are poor for illustrating the reasons for changing to the next concept. Perhaps three successive paragraphs would have told us more.
Depending on the importance of adult intervention I feel it could be safely appended to this paragraph, or not. Yes, if it was merely the closure of the scene; not if the scolding and the breaking up (if, for example the opponents need to be physically separated rather than obeying a verbal command) are an important element in their own right.
It does, however, give us a chance to look at sentence structure. Yes, I am aware of the fact this is not a genuine sentence, merely a flung-off sequence of words, so you can't be offended when I point out that the second one is really badly organised. Ignoring the "sunk" instead of "sank" (I did point out that I was a pedant, no?) the structure informs me that the jaw punch staggers not only the person it hits but the approving students, while the gut punch is tacked on the end, not feeling part of the structure at all. Even the first sentence, although there the problem is largely word choice; I suspect they were 'clenching' rather than 'tensing', and jaw and gut punch do not merit the adjective 'bloody'; about the only things that do in playground fights are nosebleeds (and some cuts, generally from falling on the wrong things. All sorts of adjectives like 'brutal' are available.
So, now you're not upset because it wasn't really your writing I criticised, yes?
Nobody has said you should not follow formulaic rules of construction; there are generally reasons those rules have come into existence. What we do suggest is that you attempt to understand the reasons, so you can break the rules (or twist them into unrecognisable forms, which is just as effective) when the story, or the story structure, do not invite them. Real dialogue is rarely grammatically perfect; you have to choose whether to modify it to fit the rules, and maximise information transfer, or transcribe the actual words for added veracity (or, most likely, steer an intermediate path). If anyone else decides for you it is no longer your story, but a collaboration.
If the more formal approach feels right for you, use it; you're not going to write anything worthwhile while you're forcing yourself into informality ("I'll show them! I will use swearwords, and be modern").
Pray excuse me. I rant.