This is a traditional American call and response song. I first came across it when some year 5 children were singing it with great gusto at local a primary school.
The first (un-named) child, or maybe the teacher, sings the words in CAPITAL LETTERS
The second child (in this case “Jack”) sings the words in lower case, calling a third child (Mary)
Everyone sings the “with a rickety tickety tick” lines.
Now, “Jack” sings the words in CAPITALS, but sings “HEY MARY”
“Mary” sings the words in lower case, calling yet another child
Everyone sings the “with a rickety tickety tick” lines.
It’s a lot easier to do than explain!