Date: 201809
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Weather elements / visibility: Haze / Smoke; 10
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: FBO
Operating under: Part 121
Flight plan: VFR
Mission: Training
Flight phase: Initial Approach
Airspace: Class D ZZZ
ATC / advisory: Tower ZZZ
Reporter organization: FBO
Reporter function: Instructor
Reporter qualification: Flight Crew Flight Instructor; Flight Crew Commercial
Human factors: Training / Qualification; Situational Awareness; Confusion; Communication Breakdown
Anomaly: Conflict NMAC; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Took Evasive Action
Contributing factors: Airspace Structure; Procedure; Environment - Non Weather Related
Primary problem: Environment - Non Weather Related

Narrative: When I done my training flight with student in the air; we [were coming] back to [the] airport from east of airport. When we done our training flight; usually we cancel radar service at TRACON; and contact Tower and report position and request intention. But a lot of traffic acting at that time in same practice area so TRACON want to me stay with them while avoid all traffics.Near 3 miles east of airport; TRACON approved frequency change to Tower and we reported for our position and requested touch and go for landing practice. But it was so close [to the] airport.We initial contact; my mind was pretty busy due to distance of airport and a lot of traffic acting in pattern area. After I know Tower told me by phone; Controller told me 'report establish right downwind runway XX' but I misunderstood and read back 'report establish right base runway XX'.When I established right base; I call Tower and 'establish right base runway 31' but Tower said 'you're not insight; say your position' and at that time we are at turning point right base to final. So I said 'We are over at cow farm (one of reporting point at short final runway XX)' And we checked traffic clear at that time before turn but we obviously not traffic see. But Tower said 1 aircraft on final. After I knew they practice forward slip practice. Cessna have high wing and altitude was high for practice That's why we could not find that. I turned to final leg and I heard they doing 360 turn; so I did go-around.It was dangerous situation of me and other aircraft and finally I know I made mistake and how I will do next time as below.Lately and not proper my position to tower. Report my when acting a lots of traffic at same practice area and if TRACON not approved change to frequency to Tower; I will staying at TRACON frequency with circling over the enough distance from airport. after when reduce traffic; I will request to TRACON for cancel radar service after contact Tower and report my enough and exactly where I am after than I will enter to Traffic pattern for land. Because ZZZ Tower don't have radar. So if someone do as like me it will happening again.I miscommunicated and misunderstood with controller. I will more attention when I communicate with controller and verify and confirm when I feel something wrong.Failed 'See and avoid'. VFR is basically fly by see and avoid. But I failed that when I approached to final. I will very be carefully make sure 'clear area'.Unfamiliar area. I am new instructor at that area so unfamiliar environment near airport. After this happened I flew 2 time with other instructor for familiar flight near [the] airport and learned/reviewed all reporting point. So now I know every reporting point for don't make confuse Tower.I got this really bad and dangerous experience after that I am flying more carefully. Will not make a same situation anymore. It was stupid.




Synopsis: C172 Instructor reported that they encountered a near miss because they were unfamiliar with the airport and misunderstood the Tower when to report.