I remember a time when half birthday's were VERY important in my life. But that must have been like 6 or 8 or something. At 4 it is just very confusing. We mostly just ended up calling it her "pretend birthday" because "half" was a concept that we just weren't ready for.
When a student has a birthday they sing a special song where they mix up a cake. When it gets to the part about eggs they get to say the number that they are turning for the number of eggs they need. We talked about it being her pretend 5th birthday and she talked about how there was a 5 on her crown but when the teacher asked her how many eggs she needed she paused then said, "Four and a half."
Oh sure, now she gets it.
Love this beautiful little 4 1/2 year old!