Flight Instructor on training flight with student reported NMAC with Blackhawk helicopter.

Narrative

Conducting touch and go practice Runway XX at ZZZ in a Cessna. Winds were 240 at 10-20 kts. VMC. We were cleared to land while in the left downwind. A UH-60; was on the surface to the north of the runway in an area they call the 'East Side'. They often operate on the surface there and will conduct departures from that location with tower clearance. While we were turning left base; the Blackhawk requested a VFR departure to the south. Tower told them to hold position for landing traffic (us). As we turned final; the tower cleared them to depart with the restriction that they remain north of the centerline (which would have deconflicted them from us) and that there was Cessna traffic on final. The pilot of the Blackhawk read back the 'cleared for takeoff' portion of the clearance but not the remain north restriction portion. She proceeded to depart directly across final as we were approaching the runway. I took the controls from my student; initiated an immediate go around; and began turning right to miss behind the Blackhawk. Tower said something that was blocked and the Blackhawk began making an erratic maneuver directly on the centerline/final. We climbed above them and they continued south; and reported their apologies over the radio. It was very close. We finished out lesson uneventfully after that. It was pretty obvious from the Blackhawk pilot's tone that she did not have situational awareness about the other traffic in the pattern.