Flight Instructor with trainee reported a loss of oil pressure and engine failure resulting in an off-airport landing.

Narrative

While on an instructor flight; engine failure was imminent. On this flight; I had a student maneuvering about 20 NM east of ZZZ at 1500 ft; the plane's oil pressure was indicating 0 and oil temperature was increasing rapidly. Once I noticed; I took control of the aircraft and reduced throttle to 1600RPM while pitching for a best glide speed of 63 knots. I ran the mixture rich and told my student to enter the nearest airport; ZZZ; into the GPS unit. After only flying a few minutes; the oil temperature was now in the red and we were too far from any airport; I decided to land in a nearby field. I made an initial call on ZZZ's CTAF; then switched to 121.5 to make another announcement.Moments later; an airline pilot came on frequency to tell me that ATC had identified our aircraft and would send help as soon as they could. I was descending at this time to the field I had designated; noticing the engine was running very rough at this point. I initiated the engine shut down checklist as I assured the landing was going to be made. Just before touchdown; I dumped flaps and shut the master and ignition switches off. My student and I evacuated the aircraft immediately.Although I landed an aircraft in a field; there was no property damage nor personal injury at all. It also seemed the aircraft was relatively in good shape. It would appear there was an oil leak as there was liquid dripping on to the nose gear at a heavy rate. EIS (Engine Indication System) indicated normal levels on taxi and run-up so the oil leak must have occurred at some point in flight. Monitoring the EIS was pivotal; but training emergency procedures saved us. I would take more steps to streamlining the communication process more so as to accelerate a response time. Info like how many people on board and a more precise location call out may have helped out more. I would also emphasize to check engine instruments much more often than typical. I will increase my instrument scan to occur more frequently during flight.