Flight Instructor with student reported a NMAC while maneuvering in a practice area. Flight Instructor took evasive action to avoid a collision.

Narrative

During a routine training flight in an Aircraft X with a private pilot student and myself; a Flight Instructor; a near mid-air collision (NMAC) situation occurred. The following details the chain of events; human performance considerations; contributing factors; discovery; corrective actions; and additional post-flight findings:Departing from BTL airspace; we leveled off at 3000 feet before ascending to 5500 feet MSL after exiting the lateral boundaries of the class D airspace. Moderate turbulence and wind speeds prompted our climb to 5500 feet MSL during the southbound departure. Upon entering our designated practice area; we made an entry call on the radio; announcing our altitude of 5500 feet MSL to alert other aircraft in the vicinity. I instructed the student to initiate a left climbing turn to a northerly heading to avoid cloud development and turbulence in the southeast. As the student began the turn; they spotted nearby traffic to the southeast (traffic heading westbound and our approx. heading of 150); and the SkyWatch system alerted us to the presence of the same altitude traffic. Although I hadn't initially sighted the traffic; I assumed control from the student and expedited the turn and climb away from the other aircraft. We continued our climb to 6500 feet MSL to maintain separation; with the other aircraft observed in a steep-banked left turn away from us.The decision to initiate a left climbing turn to avoid turbulence and cloud development was appropriate given the weather conditions. However; incomplete situational awareness led to potential conflict with nearby traffic.Moderate turbulence and wind speeds increased workload and distracted attention from scanning for traffic. Lack of visual confirmation of nearby traffic highlighted a lapse in situational awareness.Assuming control from the student and rapidly expediting the turn and climb away from the traffic demonstrated decisive action in mitigating the risk of a mid-air collision.Weather conditions prompted a decision to maneuver away from turbulence and cloud development; leading to potential conflict with nearby traffic. The other aircraft's failure to initiate communication to ease separation heightened the potential for a conflict.The presence of nearby traffic was initially spotted by the student pilot; and the SkyWatch system alerted us to the same altitude traffic. Visual confirmation of the other aircraft was made by the student pilot before I took control and expedited the turn and climb away from the potential conflict.Enhanced emphasis on situational awareness and scanning techniques will be incorporated into future flight training sessions to mitigate the risk of similar incidents. Review of procedures for communication and evasive action in the event of traffic conflicts will be conducted to ensure appropriate responses in similar situations. Continued reinforcement of the importance of effective communication and vigilance during flight operations will be emphasized to prevent future near mid-air collisions.Upon post-flight review; it was determined that the NMAC distance was approximately 6000-7000 feet horizontally and 50-100 feet vertically. While this distance may not strictly qualify as an NMAC; the evasive action taken was deemed necessary considering the potential hazards involved had there been any further delay in action.