Small Aircraft; High Wing; 1 Eng; Fixed Gear
Flight Crew Commercial; Flight Crew Flight Instructor
Flight Crew Last 90 Days 120; Flight Crew Total 525; Flight Crew Type 500
Situational Awareness; Training / Qualification; Communication Breakdown; Distraction; Human-Machine Interface
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors; Procedure
On a long base to final due to multi engine aircraft in front of us. Student was turning final and I just happened to glance at my iPad connected with ADS-B sentry (aircraft only equipped with ADS-B out).  I saw traffic turning at us at 200 feet above.  I believe he was on a right base.  I thought it might be a weird ghost reading; but checked to make sure. I reduced power angled right.  While checking I saw just above and slightly above and slightly in front an aircraft in front of us.  We called our final and he asked where we were that he didn't see us. We informed him that we were right behind him. Aircraft on extend downwind informed that we were about a 1/4 mile apart on final. The other aircraft broke off to the right and exited traffic pattern. I had full controls from my student at reduced power setting. We stayed on final and departed the traffic pattern on upwind without landing;  just a low approach so we could breath for a second. I believe the only thing that we could have done is to amend our base call to have said ' extended base' I'm not sure why traffic was on a right base for that runway. Possibly because there was a lot of traffic and they didn't want to try to find a spot between the 4 other planes in the left traffic pattern?  I believe without ADS-B in that I purchased on my own that it would have been a lot closer.
A flight instructor providing instruction on base leg at a LMO non-towered airport reported a near miss with another aircraft in the pattern.