Flight Instructor reported a NMAC with an ultralight aircraft while on final approach.

Narrative

On a return flight from the ZZZ1 airport for traffic pattern work; we entered the pattern for 18 at 1I9 on the 45. Aircraft Z was inbound from the northwest and announced its intentions to enter midfield behind us. Radio reports were made by both aircraft on each leg of the pattern. Once my student had rolled out on final and was making his final landing checks; I tried to acquire Aircraft Z visually and found them on the downwind behind us. As I brought my scan back towards the runway; I noticed movement out of the left corner of my eye.At around 300 ft. AGL; I visually acquired an ultralight at around the same altitude heading opposite direction from us away from the runway; what felt as around 4 seconds from collision. It appeared as though it was on a close-in left downwind; which was odd as the pattern is published as right in the on the sectional charts and AF/D. Both we and the ultralight pilot appeared to spot each other at the same time; I took over controls from my student and broke right away from the ultralight as he did the same. We then executed a go-around. We learned from Aircraft Z behind us that the ultralight proceeded to cut him off and land in front of him as well.