Light aircraft instructor pilot reported an NMAC with another light aircraft on final approach at MAN airport.

Narrative

I was working with a CFI student in the pattern at Nampa (MAN). On the third lap in the pattern (having made all appropriate calls for each leg of the pattern) I (using see and avoid and Foreflight and a Sentry for additional situational awareness) recognized another aircraft attempting to enter the pattern on a collision course with our aircraft from the right. I immediately initiated an evasive turn to the left (toward the runway) to avoid the aircraft and made a radio call to that effect. After achieving sufficient separation i returned to the downwind leg behind the other aircraft (Aircraft Y). My student and I decided to extend the downwind leg to provide additional spacing and continued the flight back to base (ZZZ). I heard no radio calls whatsoever from the other aircraft until after i made my evasive maneuver and radio call. That pilot then did make calls from that point on. This was witnessed by another CFI in the pattern as well. Aircraft Y was not following the recommended procedure (45 degree entry to the downwind) or making appropriate calls.