The Itsy Bitsy Pyro

Tonight, as I prepare TK for bed:

TK: I want to sing a song.
Me: Which one?
TK: The Fire Song.
Me: I don't know that one. How does it go?
TK: It goes like this: The itsy bitsy fire--
Me: Do you mean "the itsy bitsy spider?"
TK: NO! It's the itsy bitsy fire!
The itsy bitsy fire
went up the water 'pout
down came the rain and
washed the fire out
out came the sun and
dried up all the rain
and the itsy bitsy fire
went up the 'pout again.

I sure never heard it that way when I was a kid.