What does "pat" in "pat a cake" mean?

Question

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?

Answer 1

The origin is that people without household ovens used long ago to take their cakes to the local baker to be cooked, along with the cakes of other people. The cakes were marked (patted) by the baker to show the ownership when they all came out of the oven.

wikipedia
Nursery rhyme:
Pat-a-cake, pat-a-cake, baker's man
Bake me a cake as fast as you can
Roll it, pat it, and mark it with a B
Throw it in the oven for Baby and me

Marking pastry or baked goods with an identifiable mark may stem from a time when households without an oven of their own could take their items to a local baker or bake house, paying to have their items finished for a small fee. Marking the pastry would have been a way to ensure the return of the proper item.

This poorly rhyming Wikipedia entry for the nursery rhyme is corrupted from a more reliable (according to my own memory and that of several commentators on my original answer) version as quoted here:

Nursery Rhymes
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!

Merriam Webster
pat; patted; patting transitive verb to strike lightly with a flat instrument

Hence, an unbaked cake or dough would be patted with an instrument (not strictly flat in the contemporary M-W sense, but we are speaking of an old usage that goes back a long time ago to the days when many houses had no ovens, and the instrument would have made a simple pattern (such as a letter) that made a mark. The patting would have produced a mark in the unbaked item that would have been preserved through the baking process

In the example of the nursery rhyme, the cake is to be marked with "B" for “Baby”

Comments have stimulated me to add to my answer. I have left the wikipedia quotation merely to point out to other readers that it is not quite right. As regards the technicalities of cake, loaf, pastry, rolling, patting, pricking and other constituent aspects, I think we have to remember that a nursery rhyme even when first composed is bound to be a simplification of usages that have then changed over the decades or centuries. The basic point is that a pat with or without an implement will leave a mark that is retained or amplified by the baking and will serve as an identification when the item comes out of the oven.

Answer 2

OED:

patty-cake, n.

Forms: see patty n.¹ and cake n. and adj².; also 1900s– paddy-cake (U.S. regional (New Jersey)).

Etymons: patty n., cake n. and adj.; pat-a-cake n.

Etymology: Partly < patty n. + cake n. and adj., and partly alteration of pat-a-cake n.

1. Chiefly U.S. A small pie or pastry; a patty (patty n. 1). In quot. 1788 used in the rhyme which usually accompanies the game of pat-a-cake:

1788 ‘Nurse Lovechild’ Tommy Thumb's Song Bk. 23 Patty Cake, Patty Cake, Baker's Man; That I will Master, As fast as I can. Pricket, and Pricket, and mark it with a T; And there will be enough For Tommy and thee.

2. U.S. = pat-a-cake n. Also figurative. Cf. earlier patty- cake v.

1889 Harper's Mag. June 119 He played patty-cake steadily with Porley, looking at the others out of the corner of his eye.

¹ patty, n.

Etymology: < French pâté (see pâté n.3) with substitution of -y suffix

1. A small pie or pasty. Now chiefly Caribbean. Recorded earliest in pattypan n.

1660 R. May Accomplisht Cook x. 224 Bake these quinces raw..either in tart, patty-pan, dish, or in cold butter paste.

1710 P. Lamb Royal Cookery 75 Your Mushroom Patty..is proper for second Course.

² cake, n. and adj.

Etymology: Apparently < early Scandinavian (compare Old Icelandic kaka , Old Swedish kaka .

A. n. I. With reference to food.

1.a. A mass or portion of bread, usually with a rounded, flattened shape, and often baked hard on both sides as a result of being turned during the baking process.

For use as a second element in English regional and Irish English compounds such as barm cake, breadcake, soda cake, stotty cake, etc., see the first element.

c1225 (▸?c1200) Hali Meiðhad (Bodl.) (1940) l. 559 Hire cake bearnen o þe stan.

Edit to summarise:

patty, n.

Origin: Perhaps of multiple origins. A borrowing from French. Perhaps also partly formed within English, by derivation. Etymons: French pâté ; pat n.1, -y suffix.

Etymology: < French pâté with substitution of -y suffix (Used to form pet names and familiar diminutives) for the ending.

U.S. = pat-a-cake n. Cf. earlier patty-cake

Thus, paté > patty > pat-a