Children's Songs in Polish

It is not little but had. And not grandma but a country woman. Miała baba koguta - a country woman had a rooster.

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Polish children's songs

My grandfather used to bounce a baby on his knee while singing (phonetically in English) "shoe pie shoe pie da-na shoe pie shoe pie da-na, weeee!" I tried to look up some possible Polish spellings but couldn't find any thing with good translations:

szupaj dana
Szczupaj dana
siupaj dana
śćupaj dana, etc.

Couldn't find anything good. Any ideas?

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children's songs

Does anyone know the lyrics to a Polish song that start like this: O sloneczko sliczne, O sloneczko mile, Ty masz czarujaco, I ponentna sile

Ty masz czarującą i ponętną siłę.

@Alien
that is the next line...do you know the rest of the song's lyrics?

Alien provided the next line....any one else know the rest?