Skyhawk 172/Cutlass 172
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 87.1; Flight Crew Total 441; Flight Crew Type 338
Communication Breakdown
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors
Upon second lap around the pattern on ZZZ; I heard Aircraft Y calling 5 miles away with intend to join pattern behind downwind traffic in sight. That radio call came right came in between my Student Pilot call from crosswind to downwind. And there was another aircraft that was just passing the numbers. I made a second left downwind RWY XX call in case my Student Pilot's position call wasn't heard.I was passing mid-runway point and couldn't see the airplane that was joining pattern. Aircraft Y reported 45 degree entry ; left downwind [Runway] XX behind downwind traffic. After I passed the abeam point; I instructed Student Pilot to not turn base nor descend until ahead traffic passed our wing; in which we had momentarily lost sight as they were doing a very wide pattern. At that moment; Aircraft Y and I were about to collide. Aircraft Y was positioned/ entering traffic on left base instead of downwind; behind us; as they called previously. I took controls from Student Pilot executing an evasive maneuver; steep left turn from base to final; while trying to not collide with aircraft on final that had just passed us. Aircraft Y made a turn to their right. No one was hurt nor lost aircraft control.
Flight Instructor reported an NMAC event during traffic pattern training due to inaccurate communication and pattern entry by the conflict aircraft.