From a Wiki:
A union free school district has absolutely nothing to do with labor unions. According to the NY State Department of Education:
<<A union free school district is a school district generally formed from one or more common school districts to operate a high school program, which common school districts cannot do. First authorized by legislation in 1853, union free school districts are administered by a school board of between three and nine members. The number of members of the board of education of a union free school district may be increased or decreased as set forth in law (???1702, 1703; see 2:4). Currently, not all union free school districts operate a secondary school program, and some have been established solely as special act school districts to serve children who reside in specified childcare institutions (see 1:25).>>
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What is a union free school district