Playing music while playing a game

I have been bragging to everyone about all the things my new IPod Touch 6 can do. I've just found something so basic that it can't do, that it just blows my mind. While playing music, I cannot play a game at the same time, even if all sound is turned off in the game. Is it possible, that I cannot do this? If so, it is unbelievable considering everything else it can do. I have researched this and have tried everything people have suggested, to no avail.

Please tell me there is a way to do this.