S.D. Codified Laws § 13-8-4
If at an election held pursuant to § 13-8-3 an increase in the number of board members is authorized, the school board must designate the number of vacancies and the number of years, not to exceed three years, or four years if authorized pursuant to § 13-8-2, in each vacancy, so that all succeeding regular elections have, insofar as practicable, the same number of vacancies to be filled.
The procedure for decreasing the number of board members is the same as for increasing the number of board members, and the board shall designate the vacancies and terms not to exceed three years, or four years if authorized pursuant to § 13-8-2; provided, that each school board member is entitled to complete the term of office to which the member was elected.
SDCL 13-8-4