Skyhawk 172/Cutlass 172
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument
Flight Crew Last 90 Days 90; Flight Crew Total 350; Flight Crew Type 200
Communication Breakdown; Situational Awareness; Time Pressure
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors
My student and I were doing pattern work at ZZZ and there was Aircraft Y waiting to take off who was also staying in the pattern. We did a touch n go and Aircraft Y took off almost right away after we took off. We flew a left hand pattern and Aircraft Y was right behind us. We did another touch n go and Aircraft Y had to go around because he did not give us proper spacing for him to land behind us. He did not announce that he was going around until we were already on the upwind. At about 500 ft. AGL as we got ready to turn left cross wind; I saw Aircraft Y within 500 ft. of us horizontally. I took the controls from my student and started a left turn away from him and got us on the downwind. We were going to do one more landing then depart. As we got abeam the numbers; and started our descent; about to turn base I hear Aircraft Y call out that he was turning left base and I saw him cut us off. I decided to climb out and depart the airport after he did that. I think that the contributing factors were Aircraft Y not having situational awareness of what was going on around him even though we were making all the appropriate radio calls.
Instructing Pilot reported a NMAC with another small aircraft during traffic pattern work with student.