Skyhawk 172/Cutlass 172
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Commercial; Flight Crew Flight Instructor
Flight Crew Last 90 Days 60; Flight Crew Total 530; Flight Crew Type 370
Workload; Communication Breakdown; Time Pressure; Situational Awareness
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Human Factors; Equipment / Tooling; Procedure
We; a C172S G1000; were flying to ZZZ under VFR radar vector with RNAV Y RWYXX for practice approach. While approaching to FAF; right after Approach told us to contact Tower; we found a Piper Cherokee on our 11 o'clock less than 500 feet horizontal above us and descending and approaching to us. We could not see them until last moment because they were above our wing 'blind spot.' Approach never mentioned about this traffic and our G1000 display never displayed its ADS-B location.  After I found the traffic; I took over the control from student who was under the hood and started descent in about 500-700 feet per minute. We reported to Approach after the traffic passed behind us. Approach responded that; it was showing 1;000 feet vertical separation with us so Approach did not mentioned that traffic. Also; that traffic was not talking to Approach; so Approach did not know their intention. After that; we continued the approach and landed at ZZZ.
C172 flight crew reported NMAC on approach.