This rhyme can be found in A History of Nursery Rhymes (1899) by Percy B. Green. Green wrote that it's… "a verse repeated when playing at skimming shells or stones on the water of a pond or lake."

A Duck, A Drake, A Barley Cake - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Intro Image

Notes

*A drake is a male duck.

Here's the version from The Real Mother Goose (1916):

A duck and a drake,
And a halfpenny cake,
With a penny to pay the old baker.
A hop and a scotch
Is another notch,
Slitherum, slatherum, take her.

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Thanks and Acknowledgements

The illustration is from The Real Mother Goose (1916), illustrated by Blanche Fisher Wright.

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