Paddycake has taught Kate to clap. Her Yia-yia plays paddycake with her over and over. Usually if you begin the song she will join in, although she always throws it in the pan before you actually get there.
By the way, which way do you play paddycake? Because I did some research, since my mother-in-law does it slightly different. I have always sung "Paddycake, paddycake, baker's man. Bake me a cake as fast as you can. Roll it up, roll it up, throw it in the pan!" Yia-yia leaves out the second line. But upon my Google-ing, I learned that the actual words are this:
"Paddycake, Paddycake, baker’s man,
Bake me a cake as fast as you can;
Roll it, pat it, mark it with a B,
Put it in the oven for baby and me."
I've never heard that version.
Anyway, Kate has started throwing it in the pan, which is too cute for words. She holds her hands over her head and grabs two of her fingers on her right hand with her left hand. Sometimes she does the throw it in the pan before the paddycaking. We just need to work on the rolling it up and she'll have the whole song down.