PA28 Flight Instructor reported low winged converging traffic on downwind entry resulted in evasive action and an NMAC.

Narrative

This was a near midair collision in the traffic pattern on downwind.There were two aircraft in the pattern flying touch and go landings. My Student (left seat) had turned from crosswind to downwind about 30 seconds before the event. Approaching midfield; I looked left and saw an aircraft 5 wingspans away; on the left-aft side on a 45 degree bearing line with about 20 feet of step up. I'm describing this using formation terms because that's what it looked liked.I made a radio call; on Tower/CTAF frequency to the effect of... 'Tower there are two aircraft on downwind in close proximity.' I took the controls; but I didn't take any evasive action because the other aircraft was not closing distance nor changing bearing. On hearing my radio call the other aircraft did a hard left turn and asked for Tower permission for a left 360 for spacing. Although they phrased this as a request; they; appropriately; started the hard left turn before keying the mic.Tower clarified that my aircraft was number one for the runway. The pilot of the other aircraft made an apologetic comment on the radio that they had started their downwind turn inappropriately.Some thoughts.By the time I saw the other aircraft they were in a stable position; but there's no doubt that seconds prior; that aircraft was wing-up with their belly towards our aircraft. Both aircraft were low-wing; so at the time of the greatest hazard; the aggressor aircraft was blind and could not have taken an appropriate evasive maneuver. The other aircraft pilot called me after the flight. We had a good debrief. They were professional and interested in learning from the event. Although the other aircraft in this NMAC had the most opportunity to prevent the situation; there are things I could have done to avoid lining up the holes in the layers of safety. these are.My student was very disciplined about clearing; and confirming with me; before turning in the pattern. In hindsight; I realize we need to clear further aft of the wingtip in order to avoid this specific situation. Both on the crosswind to downwind turn and also base to final. In other words; clear with the mindset that aircraft behind us can cut us off. I had an ipad on my kneeboard; but the volume was turned down so I don't know if it gave me a traffic alert. Also note; the ipad generates many nuisance traffic alerts in the pattern. Traffic on the runway is often shown as a conflict to traffic on downwind. regardless; from now on; I will fly with the volume up.Reflecting on a few years of flying. I focus my SA on aircraft ahead of me in the pattern and I try to devote appropriate mental energy to making it so my aircraft doesn't interfere with them. I don't devote the same energy to aircraft behind me. I will brief this to my students and make sure they all learn from this lesson. My radio call had the desired effect; but in the future; I'll use more urgency.