AN INSTRUCTIONAL FLT RECEIVING VFR TFC ADVISORY FROM TRACON ENTERED A TFR THAT WAS ACTIVATED AFTER THE PLTS CHECKED NOTAMS AND WERE AIRBORNE.

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I FLT INSTRUCT AT ZZZ. WE ARE VERY GOOD AT CHECKING NOTAMS. WE HAD NOTAMS ISSUED AT XA42Z. THESE SHOWED THAT THE TFR AT BEALE AFB WERE NOT ACTIVE. DURING CRUISE WE WERE MONITORING NORCAL AND BELIEVED THEY HAD CALLED US FOR TFC TO A JET AIRLINER. WE CALLED NORCAL; GAVE THEM AN IDENT AND ASKED FOR A TFC ADVISORY RELATED TO THAT TFC. THEY COMPLIED. WE DID NOT RECEIVE A SQUAWK; BUT A FEW MINUTES LATER THE CTLR STATED; ACFT THAT RECENTLY CALLED FOR TFC; STEER CLEAR OF BEALE AS THE TFR IS ACTIVE. MY STUDENT'S COURSE LINE FOR HIS CROSS COUNTRY CROSSED ABOUT 1 NM SOUTH OF THE CLASS C AIRSPACE; BUT HE WAS LEFT OF COURSE A LITTLE. I DO NOT BELIEVE SO; BUT WE POSSIBLY ENTERED THE TFR JUST AT THE EDGE AT 5500 FT MSL. THE TFR WENT UP TO 18000 FT FOR UNMANNED ACFT. THE NEW NOTAM HAD BEEN POSTED AT XB04Z; JUST 22 MINUTES AFTER THE NOTAMS WE HAD!!!! OUCH! AS HARD AS WE TRY; SOMETIMES WE STILL GET IN TROUBLE. ARE WE SUPPOSED TO CHECK NOTAMS EVERY 22 MINUTES? FOR NOW; I CALL NORCAL OR FSS AND CONFIRM THE INACTIVE STATUS OF TFR ANY TIME WE ARE CLOSE.