I remember a number already mentioned. . . “Erie Canal,” “Drill Ye Tarriers,” “I’ve Been to Harlem,” “How Old Is She, Billy Boy?” Probably a lot more if I think about it.
In addition:
Our third grade state history book had this little ditty Carve Dat Possum about eating possum.
Born to Be Free, in which I asked about in 2003. I bumped it in 2012, and got responses until 2017.
In addition, I was in school during our state’s Tricentennial, and this page has a list of songs that were included in an album pressed for that celebration.
Once a year we would watch a film strip of patriotic/military songs that we would sing along to.