Row, row, row your boat...
I grew up with the bare minimum of "life is but a dream", with the occasional schoolyard bonus of throwing one's teacher overboard.
Here, the crocodile second verse is mandatory, but somewhat boggling in the way it's worded. What would happen if one absent-mindedly forgot to scream? It's like a bored tourist with a rote travel itinerary: Rowed boat? Check. Saw crocodile? Check. Screamed? Oh, what a waste, I totally forgot to do that.
The crocodile verse, on less frequent occasions, can also lead to lots of other animal variants. ("gently down the river/if you see a polar bear/don't forget to shiver")
The "tide" version I've heard a couple of times, but always at the same place, in a recording.