Narrative:

I was towards the end of a training flight with a student. We had been in the practice area performing the typical pre-solo training maneuvers. We decided to come back to the airport to practice some touch and goes. We were on our 5th touch and go; and had just announced our intentions of a full stop terminate. We turned right crosswind for runway 17R to follow our sequence traffic at ZZZ. We leveled our wings; looked for traffic; and began our turn to downwind. Upon leveling the wings; my student said 'woah!' and pointed to an aircraft approximately 100 feet off our right wing at the same altitude; on a converging course. I took evasive action and pushed the yoke forward as hard as I could. The bonanza appeared to have no idea we were there. The aircraft passed above us at no more than 10 feet; nearly hitting the top of our aircraft.I made a radio call to tower to let them know of what had just happened. The controller came back and asked the bonanza 'what happened to you following the archer?' the bonanza pilot responded with 'I lost sight of them.' tower told the bonanza pilot that he needed to let them know if he lost visuals on an aircraft. We terminated the flight without further incident.after departing the airport; I called [the] tower to inquire of what had happened. I talked to the controller who instructed the bonanza to follow us in the pattern. It appears that the controller then focused his attention on the arriving aircraft. He did not catch the bonanza turning early. The bonanza seemed to have lost our position and rather than announcing that to tower; he decided to just turn. I believe he had no visual reference to our aircraft in the pattern; causing a near miss.I believe that my action of taking control from my student and immediately beginning a rapid descent is the only thing that resulted in a safe outcome of this situation. If no action would have been taken; we would have collided mid-air; resulting in a very serious accident. The decision of the bonanza pilot to turn without seeing his traffic to follow caused the situation.

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Original NASA ASRS Text

Title: PA28 flight instructor reported a near midair collision on downwind leg for landing.

Narrative: I was towards the end of a training flight with a student. We had been in the practice area performing the typical pre-solo training maneuvers. We decided to come back to the airport to practice some touch and goes. We were on our 5th touch and go; and had just announced our intentions of a full stop terminate. We turned right crosswind for Runway 17R to follow our sequence traffic at ZZZ. We leveled our wings; looked for traffic; and began our turn to downwind. Upon leveling the wings; my student said 'WOAH!' and pointed to an aircraft approximately 100 feet off our right wing at the same altitude; on a converging course. I took evasive action and pushed the yoke forward as hard as I could. The Bonanza appeared to have no idea we were there. The aircraft passed above us at no more than 10 feet; nearly hitting the top of our aircraft.I made a radio call to Tower to let them know of what had just happened. The Controller came back and asked the Bonanza 'What happened to you following the Archer?' The Bonanza pilot responded with 'I lost sight of them.' Tower told the Bonanza pilot that he needed to let them know if he lost visuals on an aircraft. We terminated the flight without further incident.After departing the airport; I called [the] Tower to inquire of what had happened. I talked to the Controller who instructed the Bonanza to follow us in the pattern. It appears that the Controller then focused his attention on the arriving aircraft. He did not catch the Bonanza turning early. The Bonanza seemed to have lost our position and rather than announcing that to Tower; he decided to just turn. I believe he had no visual reference to our aircraft in the pattern; causing a near miss.I believe that my action of taking control from my student and immediately beginning a rapid descent is the only thing that resulted in a safe outcome of this situation. If no action would have been taken; we would have collided mid-air; resulting in a very serious accident. The decision of the Bonanza pilot to turn without seeing his traffic to follow caused the situation.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.