Flight Instructor reported a NMAC while under flight following with ATC.

Narrative

Around XA:30am there was a close pass between two visually separated aircraft. Approach had informed me of traffic 11:00 3 miles headed west while I was headed east. This traffic was type and altitude unknown and was not communicating with anyone. I had an altitude restriction of 3500 ft. to comply with and was on a discovery flight with a prospective student. We proceeded to turn north; which in afterthought; should have been avoided. After turning to this heading; we were told the traffic was 9:00; but that was for our previous heading. The other aircraft was now more 12:00 0'clock and below us; by about 450 ft. Being in a low wing it is harder to see traffic below and this aircraft that was believed to be a Piper Cub; a high wing most likely had a hard time seeing us. After passing us; the Cub proceeded to climb out to around 3500 ft.; which we reported for the other traffic he was heading towards with the TRACON. If the other aircraft in question had a mode C transponder; all this could have been avoided. As the PIC (Pilot in Command) I could have also asked for vectors away from the traffic to ensure flight safety.