Date: 202106
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: Corporate
Operating under: Part 91
Flight plan: VFR
Mission: Training
Flight phase: Cruise
Airspace: Class D ZZZ
Second aircraft: PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Reporter organization: Personal
Reporter function: Instructor; Pilot Not Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Commercial; Flight Crew Flight Instructor
Human factors: Communication Breakdown
Anomaly: Conflict NMAC; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Flight Crew
When detected: In-flight
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: I was returning from ZZZ1 to ZZZ on a training cross country flight with a pre private student. We used flight following for the duration of the flight. While under the 3000 shelve of the Bravo at 2500 MSL and assigned a heading; Approach pointed out traffic to our 9 o'clock and 500 below. The student made visual contact; reported contact with ATC; and pointed out the traffic to myself and I quickly made visual contact also. I was surprised at how close the aircraft was to us; so I had the student continue flying while I maintained continuous visual contact. Initially I thought they weren't in contact with Approach; as it would be highly unusual to return to ZZZ at 2;000 MSL. We continued inbound to ZZZ with the Student flying and myself maintaining contact with the traffic. The traffic began to drift towards both laterally and vertically with only 300 feet. vertical separation at one point. I began to think the traffic was not in contact with Approach; again unusual; and wondered its intentions while constantly preparing for evasive maneuvers. The student was flying excellently so I opted to let him continue to fly while maintaining SA and visual contact. The traffic then began rocking his wings which the student also noticed; I instructed the student to also rock wings. The traffic then began a sudden and sharp turn to cross underneath us in our blind spot. I was rapidly monitoring below us on both sides of the aircraft; the traffic display on the MFD (G1000) and the student's performance. I opted not to make any evasive actions as I felt our forward speed outpaced the traffic's forward speed and continuing flight straight ahead gave us the safest separation at the moment. Once the aircraft appeared on our 3 o'clock side they made another sharp turn to once again parallel our flight path. Approach instructed us to contact ZZZ Tower as we were rapidly approaching the Class D airspace; normally we are switched much further back. We contacted Tower and the traffic began a turn away from us. I maintained visual contact on my side until the aircraft was far enough away to no longer present a danger. I observed them on the MFD skirting the edge of the Class D airspace likely within 1/4 mile. I asked Tower if they were in contact with the aircraft and they said they were not.




Synopsis: C172 instructor pilot reported encountering another aircraft that was not in communication with the Tower and was required to maintain visual contact on approach.