Just heard my first this year, so off to report it. See https://ykalaska.wordpress.com/2007/04/27/frogs/
[my mother used to read Bartholomew the Beaver to me (all the time I guess) which has this still delightful refrain in it.
Ruth Dixon [a.k.a., Ruth Marjorie Barrows], Bartholomew the Beaver, 1952. Elf Books (Rand-McNally)]