To Market to Market is believed to have been around in some form since the late 1500's - early 1600's. It's a knee bouncing rhyme.

To Market, To Market to Buy a Fat Pig - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Intro Image

Notes

Here's a variation:

To Market, To Market to Buy a Plum Cake

To market, to market, to buy a plum cake,
Home again, home again, market is late;
To market, to market, to buy a plum bun,
Home again, home again, market is done.

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Here's another version from The Only True Mother Goose Melodies (Published and Copyrighted in Boston in 1833 by Munroe & Francis ).

To Market, To Market to Buy a Penny Bun

To market, to market, to buy a penny bun,
Home again, home again, market is done.

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Here's the version from The Little Mother Goose (1912), illustrated by Jessie Willcox Smith:

To Market, To Market, A Gallop, A Trot

To market, to market, a gallop, a trot,
To buy some meat to put in the pot;
Five cents a quarter, ten cents a side,
If it hadn't been killed, it must have died.

To Market, To Market to Buy a Fat Pig - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World - Comment After Song Image
To Market, To Market to Buy a Fat Pig - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World 1
To Market, To Market to Buy a Fat Pig - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World 2
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Thanks and Acknowledgements

The first illustration comes from Kate Greenaway's Mother Goose (1881) and the second one is from The Real Mother Goose (1916), illustrated by Blanche Fisher Wright. The 3rd illustration is from The Nursery Rhyme Book, edited by Andrew Lang and illustrated by L. Leslie Brooke (1897). The 4th illustration is from The Little Mother Goose (1912), illustrated by Jessie Willcox Smith.