PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Flight Crew Commercial
Situational Awareness
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors
While practicing landings at X04 we took off of Runway 15 and made a radio call on the CTAF that we would be making right traffic to stay in the pattern. We started our takeoff roll and immediately after we were rolling down the runway another aircraft (it was a light sport aircraft I had heard numerous times as I've taken students to X04) called that they were taking off as well behind us. We continued on the upwind up to 700 feet before we turned right crosswind; we made a radio call stating we were turning right crosswind and then downwind; making proper radio calls each time. The aircraft behind us did not make radio calls and turned crosswind early right towards us. We were not able to see him due to the low wing of the Archer but the G1000 alerted us to the traffic and we started an immediate climb. When I glanced at the PFD it had the other aircraft as -02 and climbing; I estimate the other aircraft was within 200' of us and had I not initiated the immediate climb when alerted by the G1000 that this event would've most likely resulted in a collision. The other aircraft did not make any other radio calls as they exited the pattern to the west. We continued landing practice at X04.I would suggest understanding the blindspots of the aircraft your are operating. I feel I was not fully used to the blind spots in the Archer and this played a factor as the other aircraft was high wing aircraft so this was the perfect recipe for potential disaster. Also I would suggest monitoring the traffic on the G1000 for better situational awareness when operating in the traffic pattern at an uncontrolled airfields.
PA-28 Instructor Pilot reported an NMAC in the pattern at X04.