Does the Fourth Amendment offer lesser protection to children than it does to adults?Public school children can be subjected to searches upon...

I agree with the observations made in the previous answer,
but it does not state the real reason for why children have less protection than adults
in the school setting.  The reason for this is not the fact that schools are a public
setting.  Instead, it is because schools have a mission to educate children and to keep
them safe while they are being educated.  Schools are given more latitude to search
students because of this mission.  As the link below
says,

Issues
involving safety to all students may justify searches of students' personal property
while on school
premises.

Outside of a school
setting, children do not have fewer rights to be free from searches and seizures.  In
school, however, they do have less in the way of 4th Amendment protections than either
they or adults would have out on the street.