My son who is 5 is the same way. For us it mostly has to do with the age of the other kid(s). He is very mature with 6-10 year olds and fits in well. When he plays with kids his own age he gets all wild and silly and has trouble controlling himself. I'm pretty sure he just thinks he's allowed to act like that because the other kids do. I try to put him in situations where he learns good behaviors and talk to him before a situation where I know he will have a hard time and tell him just because some kids act a certain way doesn't mean it's ok for him to do it. He has plenty of time to run and be a crazy kid when he is not in a lesson and I know he is very capable of acting mature so I encourage that in learning situations. I it was me I'd probably let them run crazy before the lesson and then explain that lessons are a time for being calm and paying attention. This is a skill which I think is important for my kid because I know learning makes him happy and this will help him as he gets further along in school and life. Good luck =].
