CESSNA 172RG INSTRUCTOR PLT TAXIED OFF SIDE OF RWY TO GIVE WAY TO ANOTHER ACFT. WHEN THE RWY WAS CLR; THE INSTRUCTOR STRUCK THE PROP ON THE EDGE OF THE RWY WHILE TRYING TO RETURN TO THE RWY TO BACK TAXI.

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UPON TOUCHDOWN AND ROLLOUT; I TOOK THE CTLS OF THE ACFT WITH NO PROB. REASON WAS THAT WE NEED TO CLR THE RWY ONTO THE GRASS AREA THAT COULD BE USED AS A TXWY. I FELT IT WAS MY RESPONSIBILITY AS INSTRUCTOR IN CASE OF ANY PROBS. THE REASON TO CLR THE RWY WAS SO THAT ANOTHER ACFT (CESSNA 172 WHO CALLED DEPARTING) COULD TAKE OFF WITHOUT THE POSSIBILITY OF US BACK TAXIING TO RESULT IN A RWY INCURSION. AS THE ACFT TOOK OFF AND CLBED OUT; I INITIATED A TAXI BACK ONTO THE RWY. ONCE THE R MAIN WAS ON THE RWY; I GAVE IT ADDITIONAL PWR AND EXTRA R RUDDER TO GET THE NOSEWHEEL ONTO THE RWY. AS THE NOSEWHEEL GOT ONTO THE RWY; IT SEEMED AS IF IT SLIPPED BACK OFF AND IT WAS THEN WHEN IT DUG INTO THE SOFT SOIL/GRASS. THIS CAUSED THE PROP TO STRIKE THE RWY A COUPLE TIMES; CAUSING THE ENG TO SEIZE. I INFORMED MY STUDENT TO MAKE A RADIO CALL TO THE DEPARTING C172 THAT WE WERE STUCK AND SUGGESTED HE LEAVE THE PATTERN. I THEN CHKED THE DAMAGE. THE NOSEWHEEL WAS COMPLETELY INTO THE GND. THERE WAS ALSO A CHUNK OF RWY CUT OUT DUE TO THE PROP STRIKE.