"Common Thread" was actually written by Pat Humphries.
I would also suggest "Sing Along" by Malvina Reynolds, "Moving Mountains" by Arlene Mantle.
Then there's Shel Silverstein's great kids song, which I can't remember the name of:
Agatha Frye, she made a pie, and Christopher John helped bake it
Christopher John, he mowed the lawn, and Agatha Frye helped rake it
Zachary Zug took out the rug, and Jennifer Joy helped shake it
Jennifer Joy, she made a toy, and Zachary Zug helped break it
And some kind of help, is the kind of help, that helping's all about
And some kind of help, is the kind of help...
We all can do without.