GA Flight Instructor with student reported an NMAC with a glider plane near BAE VOR requiring evasive action to avoid a possible collision. Reportedly; TRACON never advised them of glider activity in the area.

Narrative

My student and I were on an instrument flight plan from FLD to ZZZ during the last leg of his 250 NM cross country. We were near the BAE VOR North of UES. We were popping in and out of clouds as the sky condition was about a solid scattered layer or light broken layer with ceilings at roughly ~3500-3800 MSL and tops at ~4500 MSL. We were cruising at 4000 MSL and in IMC. I looked at our MFD and saw traffic at 11 o'clock 5 NM same altitude and converging. I suspected that Approach was going to give us a traffic alert for them so I was ready to look for them as soon as we exited IMC. As we exited the cloud; I looked at 11 o'clock to scan for traffic and could not identify the traffic. I then quickly glanced at my instruments to make sure my student was still on course and altitude. After; I started my scan at 9 o'clock and worked my way around from left to right. Upon reaching the 1 o'clock position; I saw another aircraft heading directly for us approximately 300 feet ahead and at our altitude. All of this occurred in roughly 45-50 seconds after exiting IMC. I immediately took the controls from my student and executed a climbing right hand turn to avoid the traffic. I climbed 500 feet and turned about 45 degrees to the right and avoided the traffic. ATC gave no warning about the traffic or potential aircraft activity in the area. Once clear of the traffic my student and I continued the flight to our destination of ZZZ. On the ground I contacted approach and described the event to them.