Depends which half the child is there for and what you need to provide. Example a child coming for the afternoon and napping or playing alone till hometime and given one snack is different than a child coming for the morning and having snack, using craft supplies, participating in activities like baking. Also if lunch is included it counts differently as does whether child comes to you or you have to go get them at school or take them to school.
I would probably charge more than half. Also as the child gets older they will eat more even at snack. Cut your day in half and add $5.