In full day K the kids get to have 2 snacks (a lunch) and they get 3 recesses due to their age. They need to burn more energy. My DD was in 1/2 day K, so she got 1 snack and 1 recess.
1st - 6th grade get 1 snack provided for by parents for morning or afternoon, depedending on when their lunch is. What is allowed is decided by each teacher. The K teacher only allowed dry foods or whole fruit. If your kid brought in not approved snacks, they wouldn't be allowed to eat it and the teacher always had some choices of animal crackers or pretzels.
The 1st and 2nd grade teachers allowed most things, except nut products. If the child didn't have a snack then the teacher provided saltines.