I do the same as play and learn, my 1/2 day rate is 10 less than the full day rate. My b/a school rate is only 15 for both and it's 10 if only before or after care is needed, I have a cap on after school care at 10 of 2.5 hrs, if you need more than that you pay the $15.
I used to do more of an hourly rate but it got too confusing so now I stick to my b/a school rate, 1/2 day and full day. I used to take my highest rate figure out over a 9 hr day what it was per hour and round up to the closest .5 and charge that. So right now I charge $35/9 is 3.88 so I would round it up to maybe 4, but since it's so close I'd probably go to 4.50.
HTH