PA28 INSTRUCTOR PILOT REPORTS NEAR MISS WITH ANOTHER LIGHT ACFT AFTER A FEW MOMENTS OF INATTENTION DURING TRAINING.

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WE WERE ON THE END OF A XCOUNTRY TRAINING FLT. WE HAD JUST PRACTICED THE DIVERSION TECHNIQUE AND I WAS GIVING INSTRUCTION TO MY STUDENT. WE HAD BOTH BEEN KEEPING A GOOD EYE OUT FOR TFC THAT DAY BECAUSE IT WAS A GREAT WX DAY FOR FLYING AND WAS THE FIRST GOOD DAY IN A FEW DAYS AND KNEW THAT THERE WOULD PROBABLY BE A FAIR AMOUNT OF TFC AROUND. WE BOTH LOOKED DOWN IN THE COCKPIT FOR WHAT SEEMED LIKE JUST A MIN AND THEN LOOKED UP TO SEE AN ACFT SLIGHTLY HIGHER THAN WE WERE AND JUST OFF TO OUR R PASSING IN FRONT OF OUR ACFT. I QUICKLY TOOK THE CTLS AND STARTED AN IMMEDIATE DSCNT. I AM NOT SURE IF THE OTHER ACFT EVER DID SEE US AS HE NEVER SEEMED TO TAKE ANY ACTION. I KNOW THE RULES SAY THAT ACFT ON THE R HAVE THE RIGHT-OF-WAY AND I DO KNOW AND UNDERSTAND THAT. THIS WAS JUST A TIMING ERROR ON MY PART WHEN I DECIDED TO LOOK IN THE COCKPIT FOR JUST A MIN. ON FUTURE FLTS SPENDING AS MUCH TIME OUTSIDE AS POSSIBLE IS A MUCH BETTER IDEA; AND DO THE BEST ONE CAN DO WITH BALANCING WORK INSIDE THE COCKPIT WITH WORK OUTSIDE AS WELL. ANOTHER POSSIBLE SOLUTION IS TO USE ATC AND GET ADVISORIES WHEN POSSIBLE. I SHOULD HAVE DONE THAT.