Teddy Bear

This song can be sung as an action or bean bag song with young children and is a great challenge to sing as a rope-turning game.
Source: Trinka, Jill.  The Little Black Bull and Other Folk Songs, Singing Games, and Play Parties. Folk Music Works. 1996. pp. 46-47

Bluebells, Cockleshells

This is a good song to pair with early jump-rope skills if you have a big enough space to turn the rope so the player can run under it.  It's also good for preparing and presenting low so.
Source: Brumfield, Susan.  Hot Peas and Barley-O: Children's Songs and Games From England