This Fun with Music skit is from the second season on ABC (1956-57). The first half is an original number, called Problem (Such as This), by Sidney Miller and Larry Orenstein. The girls and boys skirmish over the use of the gymnasium, with Darlene, Doreen, Sharon, Margene, and Cheryl going toe for toe as it were with Bobby, Lonnie, Larry, Jay-Jay, and Dennis.
The second half is an unusual solo instrumental by Eileen Diamond. Eileen, an accomplished ballerina as well as a pianist, plays Beethoven's Für Elise alone in the gymnasium. The melancholy mood is dissipated when Cubby and the other kids return, amidst a typical Disney ending and an obviously flubbed cue.