DA40 flight instructor on a training flight with student reported an NMAC in the traffic pattern of a non-towered airport.

Narrative

Pattern operations with student pilot; aligned on the left downwind of Runway XX at ZZZ; making standard calls. Heard on the radio Aircraft X call they were setting up for Runway XX on a 45 degree angle for the downwind. Using my ADS-B in equipment onboard; I could see Aircraft X was lined up on the right upwind of Runway XX going against traffic with multiple other aircraft in the area. After I gained sight of the aircraft; it appeared to be on a collision course with my aircraft; I initially started a turn to the right as standard but it appeared Aircraft X was turning to his left slightly; our internal equipment announced traffic at same altitude; I then changed course and began a bank to my left to avoid the conflict. After becoming clear of the traffic; joined back on a standard downwind for landing on Runway XX. I think the other pilot may have been unaware of his position in consideration with airport and how to safely enter the pattern; Aircraft X made a 180 degree turn to join the left downwind for XX in the process. On the radio it seemed Aircraft X was unaware that multiple DA40 instruction planes were in the area practicing landings. I did not make any calls on the frequency to question their intentions as I was focused on the safety of myself and my student during this situation.I believe that the internal ADS-B in equipment installed and the announcing of potential traffic collisions is directly associated with helping avoid a possible deadly situation as well as the see and avoid concept for VFR pilots. Not knowing what equipment is installed in other persons aircraft; having ADS-B in has become invaluable to the safety of all flight operations and I encourage everyone to have access to this equipment.