A C172 Instructor reported a NMAC after departing AUO and making position reports on UNICOM which were not acknowledged.

Narrative

On return flight from a cross country between Auburn airport and our destination; student and instructor were departing Auburn airspace. We maintained runway heading till TPA; then announced intentions for departure toward northwest; direct our destination. Student was navigating via pilotage and Instructor was checking chart momentarily. Both were continuously listening for radio reports as well as scanning for local traffic. Near midair collision approximately 15 NM to the northwest of Auburn (AUO) at 2;900. We had given several position reports stating intentions departure heading; and only heard one vague 'to the north' position reported from what is assumed to be the other aircraft. Instructor looked up and saw another aircraft was approaching head on. Other aircraft (small single engine; model unknown) took evasive action and made a diving turn to the right. Contributing factors to the incident were vague position reporting from other aircraft in the area; and momentary pause in scanning to reference a chart. Corrective actions will be an increased level of situational awareness as well as increased position reporting on student and instructor future flights.