Try and think of your filter media as paired with the fish, not the tank or filter.
So, if you're moving half the fish, half the media has to move with them; all the fish, all the media, a quarter of the fish, a quarter of the media, etc
So, if you're moving half the fish, half the media has to move with them; all the fish, all the media, a quarter of the fish, a quarter of the media, etc