The "little box" in front of the goal mouth is the goal area. There is no rule governing the goalkeeper and the goal box except that if the keeper is taking a goal kick, the ball must be placed on or within the lines of the goal box to restart play. (Note that the keeper or any of his teammates may take the goal kick - there is no mandate that the keeper take the goal kick.) Following the taking of the goal kick, the ball is considered not to be in play until it crosses out of the associated penalty area, which is the "big box" inside which the defending goalkeeper my use his hands to play the ball according to the Laws of the Game. It is highly unlikely that these rules are modified in high school soccer. It could be fairly said that the sole purpose of the goal area is to define the area from inside which the ball is to be placed in the taking of a goal kick on that restart of play.
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Although a goalkeeper is counted as a player on the field, special accommodations are given to him/her, including:
The goalkeeper in futsal may use their hands within their own penalty area in order to block, catch, parry, or throw the ball. However, the GK must give up possession of the ball (ideally, to a teammate) within four seconds of touching it (with hands OR feet). Once the goalkeeper has played the ball (including taking a kick-in or delivering a goal clearance), he must not touch the ball again until it has touched an opponent or gone out of play.
That said, if the goalkeeper leaves his area and goes to the opponent's half of the field, he is considered a field player and none of the restrictions (or abilities) listed above are applicable. As soon as the keeper returns to his own half, he is again liable for those rules.
rules for middle school soccer are similer to pro rules. i am not sure about the rules on subsitutions, but as far as i know there are not any other differences