This might have been a nursery or jump rope rhyme but see if you can figure out the region of the country and the why-for of the phrase.
It applies to homes built primarily in New England. There were also some built in PA as I recall.
If memory serves, the small house was built, then the connected barn, then the connected big house.
The “Cape Cod” home which is still very popular in New England is an example of this style.
There is a book by this title about vernacular architecture.
This site describes the architecture in passing.
It probably has no bearing on this topic, but I vaguely recall that “small house” or “little house” was a euphemism for “outhouse,” which is itself a euphemism.
Okay, then. The book is Big House, Little House, Back House, Barn: The Connected Farm Buildings of New England by Hubka, Thomas C., published 1984 (still in print), cover price $24.95
Well, of course, it would be you who would check for books and know I had reversed part of the series! Dang!
Yes, I have the book, grew up in New England and often wondered why all farms in the USA were not set up along these handsome lines.
Back house = out house!
Now the tricky part, bibliophage, did you figure out why?
According to Franklin County Maineguide, it’s from an old New England Nursery Rhyme (which I haven’t found yet).
So I guess this is different from the rhyme “milk, milk, lemonade; around the corner fudge is made.”
The story goes that New England farmland was not suited for one crop but needed several crops and activities to make them economical. So the big house was the home of the family and possibly hired men, little house was an extention of the big house and some of the secondary activities of the farm might take place here. Back house was the out house and the barn was the barn. All four were built in a way that enable the farmer, family and workers to go between the four without going outside.