"Clap Your Hands Together" - found in the Kodály in the Kindergarten/First Grade/Second Grade Classroom series.
The game "Cut the Cake" is mentioned in Lois Choksy's The Kodály Method I, however no notation is given.
The game is described and notation is given in Choksy's 120 Singing Games and Dances; however, no source is described. The text is folk heritage, but the melody was written by Lorna MacPhee, who worked at James Howe Elementary in 1971.
I found the text of "Here I Brew and Here I Bake" in a book titled Games and Songs of American Children by William Wells Newell and published in 1884.
The game appears to date back to England - it is mentioned in an 1886 autobiography called Ben Brierley's Works: Tales and Sketches of Lacashire Life - he mentions the game in a list of games played around Christmas time.
I attempted to find a description of the game "Bull in the Ring," but I was unsuccessful - I found it in lists, (on this "The Playground Book" - a book about Cincinnati Public schools in 1917) but not as a described game.