Flight Instructor on training flight with student reported a NMAC with another aircraft in the traffic pattern. The pilot of the other aircraft also reported the event.
Synopsis
Flight Instructor on training flight with student reported a NMAC with another aircraft in the traffic pattern. The pilot of the other aircraft also reported the event.
Narrative
I was the instructor giving my student a lesson on landings in practice for their commercial rating. The ZZZ tower controller asked us to make RIGHT traffic for runway XX. We made right traffic and was then asked if we have Aircraft Y in sight. I said no I don't and the tower controller asked us to look for traffic and extend the right downwind. Aircraft Y said he was on a base leg for XX and the controller asked if we had him in sight; which I replied with yes. I thought I saw him as I saw a white light which I thought was his landing light. The controller explicitly said don't go into the ZZZ1 airspace. We never got a call to turn base so I told my student we need to turn right because we are very close to the ZZZ1 airspace. I heard Aircraft Y say he's on final and landing in one minute so my head and eyes are looking directly 90 degrees to the right at final for XX. I don't see Aircraft Y or anyone else; I then look directly out the windscreen and see the jet right over top of us. I pushed the controls forward and then told my student to just fly westbound. The controller was asking us what our intentions are. I didn't have any intentions because we were in a near miss head one collision course; I was looking for some type of help from the controller. Instead we had received a possible pilot deviation and a phone number to call. I went back to look at the Aircraft Y's track log and our track log. Aircraft Y was extremely wide on his pattern into runway XX and he gave wrong position reports. ZZZ tower is a VFR tower; they have no radar and they rely on pilots position reports and their own eyes. This could be avoided with the tower either giving me a left 360 entry back into the downwind; Aircraft Y flying a normal VFR pattern; or just giving us a short approach. Either way this was avoidable and us receiving the possible pilot deviation was unnecessary.
Second reporter narrative
Training flight at ZZZ. The tower controller told us to make right traffic as Aircraft Y was inbound from the north for the left downwind that he was not talking to yet. We were on a right downwind for runway XX; south of the airport; when the tower controller instructed us to remain clear of the airspace south of the airport as Aircraft Y was reporting he was on final for runway XX. We turned right base to remain outside of the airspace looking for the traffic on final. Aircraft Y was not reporting correct position and was 5 miles west of the airport when they said they were on final. At this point; I had Aircraft Y insight and maintained visual separation and continued the base leg to depart the area to the west and get sequenced back into the left downwind for runway XX. Incident could have been avoided if Aircraft Y flew a tighter; proper traffic pattern; if the tower controller told us to make a left 360 on downwind; or if we continued into the nearby airspace for proper spacing.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.