Flight instructor with student reported while practicing maneuvers; they had an NMAC with a helicopter that was not making position reports.

Narrative

On Day 0 at about XA:12 UTC (XA:12hrs); my student and I were doing maneuvers (S-turns) in the south practice area using a road as a ground reference. Prior to doing maneuvers several radio calls were made on ZZZ Tower/CTAF XXX.X notifying any traffic of our location and altitude. We attempted to do one S-turn and at the time it appeared that we were the only aircraft in the area. Half way through the S-turn my student wanted to set up again and try it all over from the beginning. We proceeded to fly east of the road and turned around heading west. Another position report was given on CTAF with no response. As we proceeded west and approached the road. My student began his 1st S-turn to the right. At this time; I looked on our flight radar and observed an aircraft to the right of us. I looked out and immediately saw a helicopter that appeared to be hovering in place at the same altitude approx. 300-500 yards away. I immediately took over flight controls from my student and steepened our bank to avoid the area. As I steepened our bank the helicopter quickly began to move forward toward our location and within approximately 50 ft from our location the helicopter quickly turned right narrowly missing us. I again went on CTAF to give our location hoping the operator of the helicopter would transmit something but we did not hear any radio transmissions. The helicopter then appeared to quickly travel north leaving the south practice area. After the near miss; I instructed my student to immediately head back to ZZZ1 for a full stop. The other aircraft was possibly a military helicopter. Possible call sign Aircraft Y and registration XX-XXXXX.Contributing factors: no position reports given by the helicopter and was not scanning the area for traffic. Also when going forward and toward our location the pilots attention must have been directed elsewhere. I believe this situation would have been completely avoidable if radio calls were made or listened too. Also if the pilot had entered the area to have been scanning for other traffic since we were already there prior to their arrival. I'm very thankful nothing happened and we were able to avoid a very serious/fatal situation. In the future I hope the other pilot would be more aware of the area he/she is flying in and would make the necessary radio calls.