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1.
Any day that takes place before a strange and sometimes seemingly pointless day off of school, like Columbus Day, or Superintendent Conference Day.

A Bucket Friday can take place on any day of the week. If there is no school on Wednesday, Tuesday is a Bucket Friday (NOT a Bucket Tuesday).

The term originated when a high school student misheard his band director's words "I could get fired" as "Bucket Friday". In the weeks that followed, the term spread throughout the school with no real meaning. Annoyed with the constant yelling of "Bucket Friday!" without any meaning, the band director decided on a definition in hopes that some day before he retires, there will be a section of Hallmark cards for Bucket Friday.
Jack: Man, i hate Mondays.
James: Cheer up, we dont have school tomorrow.
Jack: You mean today is a Bucket Friday??
James: Hell yeah dude!
by Josh K. March 26, 2007
 
2.
the name given to the friday of a three-day weekend.
Happy Bucket Friday, Children.
by Dylan Healy November 06, 2006