The song this chapter's title references is a song called “Earthquake, Lightning, Fire, Me”, and seems to be about the singer's domestic woes. Asari's adaptation is a bit more literal.
The song the class sings at the beginning is based on a childrens’ song about animals (Japanese), sung to the tune of “John Brown's Body” (“Battle Hymn of the Republic” and a bunch of other adaptations also use it). A quick translation (not to meter) is something like the following.
Tadpoles are the babies of a frog. They certainly don't come from catfish! And the best proof for that is: After a little while, they put out arms and legs!
Snails are molluscs like slugs. They certainly don't come from their shells! And the best proof for that is: As children or when cooked, they don't have them!
Blades of grass wave in the breeze. They certainly don't come from brooms! And the best proof for that is: Cats don't play with grass!
Octopi are bald, with eight legs. They certainly aren't just old squids! And the best proof for that is: You can't make squid dumplings!
I'm not clear on what Asari's intended fourth line was regarding the lineage of Battra/Batora, and I'm certainly not enough of an expert on historical Godzilla lore to venture my own guess.