The Recreation Board shall plan for and guide Council, the mayor and the officials of the city on recreational offerings in the City, and shall consist of five members, who shall each serve for a term of three years or until their successors are appointed. The Board of Education of the Brooklyn City School District shall be requested to appoint one of its members to the Recreation Board and Council shall appoint one of its members to the Recreation Board. The mayor shall appoint three members, which appointments shall be approved by Council. A vacancy occurring during the term of any member of the Recreation Board shall be filled for the unexpired term in the manner authorized for an original appointment.