Q:

What was the origin of the nursery rhyme "Don't care was made to care"?

Many a child who has expressed indifference has had the following verse spoken to them:

Don’t care was made to care,
  Don’t care was hung:
  Don’t care was put in a pot
  And boiled till he was done.

What is its origin?

A:

Looks like the author is unknown; but its origins appear to be mid-1800s London’s East End. The full rhyme is as follow: 

Don’t care didn’t care,
  Don’t care was wild:
  Don’t care stole plum and pear
  Like any beggar’s child.
Don’t care was made to care,
  Don’t care was hung:
  Don’t care was put in a pot
  And boiled till he was done.

Don't care didn't care (idea)

