Even though most 9-13 year olds may not fully comprehend the consequences of their actions, don't think that they can't make up their mind about running something or not or that they will just willy-nilly run any drop.  Kids that have acheived that level of paddling ability do have the capability to make reasoned judgements about how they feel about running a particular drop.  In addition, their parent or mentor will be providing back up advice as well.  My son started paddling at 10 and by 13 was very comfortable in up to Class IV to IV+ rapids and ran some easy Class V (e.g., Charlie's Choice through National on the UY), but if there was something he didn't feel quite up to on a given day (e.g., Ohiopyle Falls), he had no problem saying no.

BobN