Skyhawk 172/Cutlass 172
Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 45; Flight Crew Total 415; Flight Crew Type 362
Communication Breakdown; Situational Awareness; Training / Qualification; Confusion
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors; Procedure; Aircraft
My student and I were coming in to land at the ZZZ Airport on the 45 degree to the left downwind; Runway XX. At the 4 mile point we heard a takeoff call of another aircraft. Their call was as such: 'Aircraft Y; taking off Runway XX' [and] nothing else. We never saw them takeoff or depart but the next radio call we heard from them was them calling turning left downwind Runway XX. At this point we were also turning left downwind so I quickly looked to our left and they were turning into us and we're [now] on a collision course. I assumed flight controls from my student; took evasive action and turned a very wide downwind; let them go ahead; and we both landed unharmed.I feel [that] what could help diminish situations like this; other than us paying more attention to aircraft taking off when coming in on a 45 to the downwind; would be to standardize radio communications at pilot controlled airports and really try to enforce their use in training and everyday operations. If Aircraft Y had specified that they were staying in the traffic pattern; my student and I would have been on heightened alert for aircraft turning from crosswind to downwind into us.
Flight Instructor reported an NMAC event with another aircraft turning to downwind at an uncontrolled airport.