GA flight instructor reported a near midair collision while maneuvering near a practice area.

Attributes
ACN	1597233
Time
Date	201811
Place
Locale Reference	ZZZ.Airport
State Reference	US
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	DA40 Diamond Star
Operating Under FAR Part	Part 91
Flight Phase	Cruise
Route In Use	None
Flight Plan	VFR
Aircraft 2
Make Model Name	Any Unknown or Unlisted Aircraft Manufacturer
Operating Under FAR Part	Part 91
Person 1
Function	Instructor Pilot Flying
Qualification	Flight Crew Commercial Flight Crew Multiengine Flight Crew Instrument Flight Crew Flight Instructor
Experience	Flight Crew Last 90 Days 150 Flight Crew Total 675 Flight Crew Type 300
Events
Anomaly	Conflict NMAC
Miss Distance	Vertical 200

Narrative:

I was with a student [who] made the initial call of what we were; where we were; and altitude. Did not hear the other aircraft but saw him in the distance and on TCAS. He then popped off of our TCAS and about two minutes later they popped up directly in front of us with about 400 feet and closing in. I took controls from my student and veered the plane to the right. On TCAS he appeared to be climbing and I pulled back and got us up about 300-400 feet. I then made a call and said traffic at 6500 we were right above you. The pilot then stated we had a near midair collision and then descended down. My student and I finished our lesson and went back to ZZZ.

Original NASA ASRS Text

Title: GA flight instructor reported a NMAC while maneuvering near a practice area.

Narrative: I was with a student [who] made the initial call of what we were; where we were; and altitude. Did not hear the other aircraft but saw him in the distance and on TCAS. He then popped off of our TCAS and about two minutes later they popped up directly in front of us with about 400 feet and closing in. I took controls from my student and veered the plane to the right. On TCAS he appeared to be climbing and I pulled back and got us up about 300-400 feet. I then made a call and said traffic at 6500 we were right above you. The pilot then stated we had a NMAC and then descended down. My student and I finished our lesson and went back to ZZZ.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.