There are age exceptions for agriculture, where kids as young as 12 are permitted to work as long as they have written permission from their parents.

I assume these exceptions exist because of an historical limited labor pool during critical time periods for farmers, such as harvest. For example detasseling corn is a common summer job for teenagers in the Midwest. https://en.wikipedia.org/wiki/Detasseling

Here are more details on the rules: http://webapps.dol.gov/elaws/whd/flsa/docs/hours.asp