Cessna Aircraft Undifferentiated or Other Model
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 50; Flight Crew Total 700; Flight Crew Type 250
Situational Awareness
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Human Factors; Procedure
Student and I were performing right-hand traffic patterns for Runway 03 at MHK. ATC instructed us to follow a [light twin] on our way to land. Visual contact was maintained with the [light twin] until they did a full stop and departed the runway. As my student was turning base to final; we noticed an aircraft that ATC had not warned us about approximately 200-300 ft. away from us. I took control of the aircraft in order to perform evasive action. My first priority was to get away from the aircraft; then to re-enter the downwind when it was safe to do so. Specifically; the power was advanced to full; the aircraft was positioned in a way to climb away from the conflict aircraft; and flaps were retracted per the published go-around procedure.According to ATC transmissions; the conflict aircraft (I believe it was a low-wing complex aircraft) was performing a practice instrument approach and was supposed to report when they were passing the FAF; which they apparently did not. I am unsure if the conflict aircraft ever saw us.As far as I am aware; my student (Pilot Flying) and I (Pilot Monitoring) were in good physical and mental shape at the time of the incident; and I first noticed the conflict aircraft as I was visually scanning the final approach corridor as we were preparing to turn final. Initially; my student could not see the conflict aircraft due to blind spots inherent with the model of the aircraft.
Cessna Flight Instructor reported an NMAC with another light aircraft on approach to MHK airport.