Instructor Pilot reported a prop ground strike while instructing a Student Pilot. The Instructor was late to take control of the aircraft and a prop strike occurred.

Narrative

Student pilot and I were conducting a flight for takeoff and landing practice; performing touch-and-gos on Runway XX at ZZZ. At the end of our 12th lap of the pattern; totaling about 1.2 hobbs of time since engine start; we had a prop strike on landing at XB23z. Day VMC prevailed; and the METAR at XA53z reported winds 340/09. That was accurate based on looking at the windsock. During the preceding 20 minutes; Tower gave the winds verbally: XB06z reported winds 340 10g16; XB08z reported 320 11g16. The wind sock did not indicate any gusts when observing on the upwind and downwind legs of the pattern; but the winds at TPA were showing as 280 at 10 kts. on the G1000 display. During the 12th lap of the pattern; the Student had a stable descent from TPA on the downwind; turned base at approximately the correct point; stable descent on base. Turning final the Student was slightly fast; so I instructed him to add power for about 5-10 seconds because our indicated airspeed was slowing. I also instructed him to input some left aileron and right rudder; to counteract the left crosswind we were feeling and the G1000 was indicating. As the Student neared the runway on final; we were stabilized at 65 kts. or so. In the round-out and flare; the Student neutralized his crosswind control inputs and the plane started drifting right of centerline. The Student landed slightly hard; bounced; and input left rudder to steer the aircraft back onto centerline. Due to excess left rudder input; the plane landed from the bounce turned to the left; while still travelling down the runway. We then started to skid; and I took the controls to attempt to straighten the aircraft out. The aircraft's left main then lifted due to the momentum of the aircraft; and the aircraft rotated on the nosewheel and right main; striking the prop on the runway. I immediately told Tower that we needed to go to the ramp; and I taxied the aircraft to the ramp without further incident. The SPECI METAR report at XB47z reported winds 340 at 10g16; and Company arriving at XC03z reported windshear - gain of 20 kts. at 100 ft. AGL on final. This Student Pilot had about 8 hours of takeoff/landing practice; 6.5 with me as the Instructor. His skills were improving; but not rapidly; so when his landings on the incident day were better than before; I relaxed slightly. He made several go-around decisions when his approaches were unstabilized; either due to wind gusts or excessive speed. This led to me 'letting my guard down' - so every lap of the pattern I wasn't hovering as close on the controls as normal. I also was not covering the rudder pedals as much with my feet; letting the Student control the rudder with more freedom before the pedal hit my foot in either direction. I also specifically delayed the flight from an [earlier] start to minimize any fatigue either pilot was feeling. In addition; an evaluation flight that was scheduled for the day after was delayed a day; to remove pressure from the Student.