A C172 INSTRUCTOR DEMONSTRATING ADVANCED NAV REPORTS AN NMAC WITH A NON TRANSPONDER EQUIPPED HELICOPTER THAT MISREPORTED ITS POSITION.

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AFTER HAVING BEEN GIVEN OWN NAV AND ALT TO W PRACTICE AREA; CLBED TO 3500 FT MSL AND PROCEEDED TO SOUTHERN PORTION OF PRACTICE AREA DUE TO OBSERVED TFC INFO SYS (TIS) ACTIVITY IN THE NORTHERN PORTION. DEMONSTRATED THE LEAN ASSIST FUNCTION OF THE G1000 SYS. UPON COMPLETED SAW A DARK SHADOW OVERHEAD WHICH MY STUDENT IDENTED AS A HELI; I THOUGHT IT WAS A FLOCK OF BIRDS. NO TIS INFO OR WARNING WAS RECEIVED. TO VERIFY IT WAS A HELI; DID A QUICK L 360 DEGS AND DID OBSERVE THE HELI TFC EBOUND AT OUR ALT. RPTED THE EVENT AND WAS TOLD THERE WAS 'A LIFEGUARD HELI WITH NO XPONDER IN THE AREA WHICH SHOULD PASS UNDERNEATH.' TOLD ATC HE PASSED OVERHEAD AT AROUND 100 FT (ESTIMATED). ATC THEN STATED THE HELI INITIALLY CALLED ZZZ1 INBOUND; WHICH IS TO THE NW OF ZZZ. THEY SAID THEN HE CALLED ZZZ2 INBOUND WHICH IS TO THE SE OF ZZZ AND IN A DIRECT LINE WITH OUR COURSE. NO COMS WITH THE HELI WERE NOTED AFTER THE INCIDENT. IT WAS APPARENT ATC ALLOWED THE INOP-XPONDER HELI IN CLASS C AIRSPACE PRIOR TO HAVING POSITIVE RADAR CONTACT WITH HIM. CONTRIBUTING FACTORS MAY HAVE BEEN THE FACT IT WAS A LIFEGUARD CALL SIGN AND THE HELI PLT MAY HAVE INITIALLY MISIDENTED HIS INBOUND VFR RPTING POINT UPON INITIAL CALL-UP.