I learned a different version in Girl scouts. Makes me think of the telephone game, with all the little changes.

A snake fell out of a window,
A second story window,
And left his eyelash on the sill, on the sill.
Don't lose your head,
There's a flying baby mustache.
A man's best friend is his mother,
You're a genius, I'm another.
Distance make the heart grow fonder,
Peroxide makes the hair grow blonder,
Yule-tide comes but once a year,
My Father shot a tree, BANG!