A common nursery rhyme goes like this:

Pat a cake, pat a cake, baker's man
Bake me a cake as fast as you can
Pat it and prick it and mark it with B
And put it in the oven for baby and me.

According to Wikipedia, "pat a cake" could be any of "pat-a-cake", "patty-cake", or "pattycake".

My question is: Is "to pat" a verb here and if so, what is its meaning? (In context, it obviously would relate preparing and/or baking a cake, but what is its etymology?)

A common nursery rhyme goes like this:

Pat a cake, pat a cake, baker's man
Bake me a cake as fast as you can
Pat it and prick it and mark it with B
And put it in the oven for baby and me.

According to Wikipedia, "pat a cake" could be any of "pat-a-cake", "patty-cake", or "pattycake".

My question is: Is "to pat" a verb here and if so, what is its meaning?

Marriam-Webster lists three meanings for "to pat" as a transitive verb:

1: to strike lightly with a flat instrument
2: to flatten, smooth, or put into place or shape with light blows
3: to tap or stroke gently with the hand to soothe, caress, or show approval

Meaning 2 would seem to fit best. However unbaked cakes are not put in shape with blows, even light ones. Did the historic meaning of "pat", or perhaps that of "cake", change since?