C172 INSTRUCTOR AND STUDENTS FLEW THROUGH A TFR.

Narrative

WE WERE ON A MOUNTAIN FLYING TRIP WITH A GROUP OF STUDENTS. WE HAD PLANNED A XCOUNTRY THROUGH THE MOUNTAINS. ONE OF MY STUDENTS RECEIVED A WX BRIEFING THAT MORNING COMPLETE WITH NOTAMS. THIS INCLUDED FDC NOTAM WHICH WE UNDERSTOOD TO BE 12 MI N OF ZZZ VOR WITH A 12 NM RADIUS. WE TOOK THE TIME TO MEASURE AND DOUBLECHK THAT AREA ON THE SECTIONAL TO MAKE SURE WE WOULDN'T FLY THROUGH IT. WE WERE ON OUR RTE WHEN WE SAW A FIRE FIGHTING HELI AND A MULTI ENG TURBINE AIRPLANE. THAT WAS WHEN WE REALIZED OUR MISTAKE. WE LANDED AT THE NEAREST ARPT AND TALKED TO THE CREW OF THE HELI WHO INFORMED US OF WHAT HAPPENED AND THE ACTUAL POS OF THE TFR. WE HAD FLOWN RIGHT THROUGH THE CTR OF IT. WE WERE IN THE WRONG PLACE. I REALIZE HOW DANGEROUS AND SERIOUS THIS WAS. WE WERE FORTUNATE THAT THERE WEREN'T MORE PLANES IN THE AREA. IN THE FUTURE. I WILL BE SURE TO DOUBLECHK NOTAMS AND WX FOR THE RTES I AM FLYING AND NOT RELY ON STUDENTS FOR THIS INFO. I WILL ALSO DOUBLECHK THE POS AND STATUS OF TFR'S AND OTHER NOTAMS TO BE SURE I HAVE THE CORRECT INFO.