If you can get hold of "The Singing Game" by Peter and Iona Opie (ISBN 0-19-284019-3) there is an account of these clapping games. They write at one point "Boys sometimes clap fiercely in pairs, to keep warm, or 'to drive the other chap back' and this they call 'Hand Drive'. Girls clap hands to rhymes, which time the hand-beats, and their aim is to go on as long as possible without making a mistake. This kind of clapping has been going on for more than 150 years." These sentences are based on observations in around 1975. Elsewhere in the book there is the comment "the games are now under the haphazard guardianship of girls of about seven to nine." Based on when my daughter played these (she is now seventeen), that 7-to-9 range is still more or less right.