A C172; WITH STUDENT AND INSTRUCTOR ABOARD; HAD NMAC WITH C182 NEAR MACON COUNTY ARPT; NC.

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I AND A STUDENT PLT HAD TAXIED OUT TO RWY 7 AT MACON COUNTY; NC; ARPT. AS MY STUDENT FINISHED THE RUN-UP ON OUR C172; A C182 TAXIED UP BEHIND US FOR A PRESUMED RUN-UP. MY STUDENT MADE THE APPROPRIATE RADIO CALL; WE LOOKED; TAXIED OUT AND TOOK OFF; TURNING S DOWN THE VALLEY THAT GOES N/S BELOW THE TOWN OF FRANKLIN. AS WE LEVELED OFF AT 5000 FT MSL; I ANNOUNCED TO 'MACON COUNTY TFC' OUR POS RELATIVE TO TOWN AND THAT WE WOULD BE PERFORMING MANEUVERS IN THE AREA AT APPROX 5000 FT. THERE WAS NO RESPONSE ON THE RADIO. MY STUDENT AND I HEADED S DOWN THE VALLEY; AND ABOUT 8 MI S OF FRANKLIN; TURNED N UP THE VALLEY; AT WHICH TIME I MADE ANOTHER ANNOUNCEMENT CONCERNING OUR ALT (5000 FT) AND INTENTIONS. NO RESPONSE WAS HEARD. AS WE APCHED THE TOWN OF FRANKLIN; AT 5000 FT AND ABOUT 2 MI SE; I HEARD THE C182 ANNOUNCE HIS TKOF AT MACON COUNTY ARPT. THIS WAS APPROX 20 MINS AFTER MY STUDENT AND I HAD TAKEN OFF. THIS SEEMED STRANGE TO ME; BUT I CONTINUED THE INSTRUCTION WITH MY STUDENT. I ANNOUNCED THAT WE WERE (THEN) SE OF THE TOWN AT 4700 FT PERFORMING MANEUVERS. ABOUT 2 MINS LATER; WE HAD JUST FINISHED AN APCH TO LNDG STALL WHEN MY STUDENT AND I BOTH SAW THE C182 SLIGHTLY TO OUR L; NOSE UP APPROX 12 DEGS; BANKING INCREASINGLY TO THE L. THEY WERE BANKING TO THEIR R; ABOUT 6 FT ABOVE OUR PLANE; 50 FT AHEAD AND CLOSING RAPIDLY. THEY MISSED; BUT NOT BY MUCH. I ONLY HAD TIME TO TURN OUR ACFT TO OUR R AS THEY PASSED UP AND TO OUR L. MY STUDENT WAS SHAKEN; BUT I CONTINUED THE INSTRUCTION; KEEPING THINGS CALM AND ASSURING HIM THAT 'A MISS IS AS GOOD AS A MI.' I CALLED MACON COUNTY'S UNICOM FOR A RADIO CHK A COUPLE OF MINS LATER; AND WAS TOLD BY THE LCL OPERATOR WE WERE 'LOUD AND CLR.' AS MY STUDENT WAS SPEAKING AFTER THE RADIO CONFIRMATION; I HEARD A RADIO CALL FROM THE C182; RPTING HIMSELF S. I DID NOT CATCH ALL OF THE RADIO CALL; SO I DO NOT KNOW IF THE C182 WAS MENTIONING THE NEAR MISS OR NOT. MY STUDENT AND I RETURNED TO THE ARPT AND DID SEVERAL TKOFS AND LNDGS WITHOUT INCIDENT; OR MENTION OF THE EVENT UNTIL AFTER THE FLT. MY EVALUATION OF MY PERFORMANCE IS THAT I COULD HAVE BEEN MORE ALERT; DONE MANEUVERS IN ANOTHER AREA; OR DIRECTLY ASKED THE C182'S PLT HIS LOCATION. I BELIEVE I ACTED PROPERLY IN MAKING SEVERAL RADIO CALLS WITH POS AND ALT; AND CONTINUING THE LESSON TO REDUCE THE IMMEDIATE ALARM OF MY STUDENT.