More childrens songs

There are two songs I have heard two different versions - of course they are very common children's songs so you may recognize one or the other of the versions as the one you grew up with.

Patty Cake (yes!) - Esme really likes this now so here are the two versions I've heard.
'Patty Cake - Patty Cake, Baker's Man
Bake me a cake as fast as you can,
Roll it up Roll it up, put it in the pan,
Patty Cake - Patty Cake, Baker's Man'

Patty Cake - Patty Cake, Baker's Man
Bake me a cake as fast as you can,
Roll it, and pat it, and mark it with a 'B',
and put it in the oven for Baby and me (squeal and hug baby)

My mom told me the second version and Mark's mom told him the first one. Esme likes both of them.

One, Two, Buckle my shoe
Three, Four Out the Door
Five, Six, Pick up Sticks
Seven, Eight, Lay them Straight
Nine, Ten, Do it Again (do it a-gain...)

And the other version
One, Two, Buckle my shoe
Three, Four, Out the Door,
Five, Six, Pick Up Sticks,
Seven, Eight, Shut the Gate,
Nine, Ten, A Big Fat Hen!