I remember these also. In my early years in school (mostly in Virginia) it was something often seen done the playground. For reasons unknown, it was an activity done almost exclusively by girls. While there were some rhymes that were accompanied by simple clapping, there were many others that involved two girls, standing face-to-face, palms forward, clapping and slapping each other's hands alternately in a patterned rhythm. The rhymes were substantially similar to those used for jump rope. The fun of it mostly stemmed from repeating the rhyme and clapping pattern faster and faster.

I am sure both of my daughters learned to do this in the lower grades of their schools; but they are 19 and 24 now. I don't know if it is still being done.