PA28 INSTRUCTOR PLT WHILE GIVING ENG OUT INSTRUCTION ENCOUNTERS ANOTHER ACFT ON FINAL AND TAKES EVASIVE ACTION.

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WHILE ON A SIMULATED ENG FAILURE TO A STRAIGHT-IN LNDG AT RWY 2L1; I CALLED LARIMORE TFC 5 MI OUT AND ANNOUNCED MY POS (5 MI W; 3500 FT DSNDING) AND INTENTIONS. PA28 ANNOUNCED THEY WERE ALSO AT LARIMORE; OVER THE FIELD AT 2400 FT GOING TO BE ENTERING A L DOWNWIND FOR RWY 12. 2L1 RWY 12 IS A R-HAND PATTERN; SO I VERIFIED THIS WITH THE OTHER ACFT THAT THEY WERE IN FACT ON A L DOWNWIND FOR RWY 12. PA28 CONFIRMED THEY WERE OVERFLYING THE FIELD AND ENTERING A L DOWNWIND FOR RWY 12. MY STUDENT AND I BEGAN SCANNING THE AREA WHERE THE TFC RPTED IN ORDER TO FIND IT. I ANNOUNCED MY POS AGAIN AT 2.5 MI W OF THE FIELD AT 2500 FT; AS WELL AS INTENTIONS TO LAND STRAIGHT-IN RWY 12. AT THIS TIME; PA28 SAID; 'WE HAVE LARIMORE TFC IN SIGHT;' AND PASSED ROUGHLY 100 YARDS OFF MY R WING. THIS PLACED THEM ON A HIGH; EXTENDED R DOWNWIND FOR RWY 12. THE LNDG TOOK PLACE WITHOUT INCIDENT. CONTRIBUTING TO THIS WAS THAT MY STUDENT AND I CONCENTRATED OUR SCAN ON THE AREA OF THE L DOWNWIND WHERE THE TFC RPTED ITSELF; AND OMITTED THE REST OF THE SKY. WE WOULD PROBABLY HAVE SEEN THE TFC EARLIER HAD WE CONTINUED TO SCAN THE REST OF THE SKY. ALSO; AT THE ANNOUNCEMENT THERE WAS TFC AT LARIMORE; AND NOT HAVING THEM IN SIGHT; I SHOULD'VE BROKEN OFF THE SIMULATED ENG FAILURE AND ENTERED THE PATTERN IN A STANDARD DIRECTION; RATHER THAN THE STRAIGHT-IN WE WERE ATTEMPTING. HAD I DONE THIS; THE CONFLICT MAY NOT HAVE TAKEN PLACE. I WOULD NOTE; HOWEVER; THAT PROPER POS RPTING IS ESSENTIAL WHILE IN THE TFC PATTERN. BASED ON THE RPTS OF PA28'S POS; I FIGURED WE WOULD BE INTO THE ARPT BEFORE HE EXITED HIS DOWNWIND; WHICH IS WHY I CONTINUED THE APCH. HOWEVER; DUE TO HIM IMPROPERLY RPTING HIS POS; THIS INCIDENT OCCURRED.