Some foods are far more sustaining than others. A lot of the traditional snacky items like crackers hardly even seem to pay rent in the tummy before they're gone. Which is part of the reason why you can eat a box and still feel hungry!
Protein tends to keep us feeling fuller for longer. I always try to load up the boys at lunchtime so they can make it through the afternoon and then activities without wanting to gnaw their own arms ..
If you have a selective eater who loves protein have you tried sending as a lunch option? My boys have a thermos most days so can take hot chicken/pork/beef/fish etc.
Today they have a cold thermos with coleslaw, mini chicken pieces and a boiled egg but generally they would have warmed left-overs.
Will your child eat protein? Cheese, eggs, meat, seafood, beans, lentils, tofu ?