GA Flight Instructor with student reported a NMAC while practicing maneuvers with an aircraft that was not making position reports. The Instructor took over the controls and executed evasive maneuvers to avoid a possible collision.

Narrative

My student and I were doing ground reference maneuvers over the location getting set up for a turn over a point; as he was doing his checklist we made a position reporting call and stated what we were doing; our position and our altitude 2;600 (600-1000 feet AGL for ground reference) we had someone 5 miles north of us doing acrobatics but they called and let us know they weren't going to be going under 4;000 and will stay away from us. I proceeded to ask if they wanted us to move to be convenient for them if they wanted the area for it but they let us know we were fine where we were. My student made a final clearing turn to make sure our area is clear as well as our Garmin 430 for traffic and the only traffic that was seen was the acrobatic aircraft 3;400 above us. No other calls were made for other aircraft positions. As my student got ready to turn left for his point a White and Blue Piper; aircraft was about 300 feet to the left of us coming straight into us and about 100 feet above us (roughly 2;800 feet). They never made a call to report their position; I instantly told my student my controls and turned right and instantly called on the radios to again report my position and that aircraft never called back. Once we were away we ran cruise checklist and headed back in to ZZZ to do landings.