C172 Flight Instructor with student reported an NMAC on base leg with another flight school aircraft.
Synopsis
C172 Flight Instructor with student reported an NMAC on base leg with another flight school aircraft.
Narrative
My instructor and I were on the downwind leg at ZZZ and were told cleared touch and go by the tower. With not being told of any traffic to follow; we saw one additional aircraft on final both on our ADS-B and visually; but no others on either. We began our base turn and it became known after there was another aircraft that had extended the downwind and that was who we should had been following. This aircraft did not show up on either our ADS-B or visually; so we were unaware this aircraft existed also due to not being told of any traffic to follow or what sequence number for landing we were by the tower. Approximately 200 feet above this aircraft on short final we were told to go around; which we missed; and then immediately were told to go around again by the tower; which we did. This aircraft only became visible to us after we were going around. Had we seen this aircraft; we never would had begun our base turn; but we didn't and were confronted with this scenario. After being told to go around; we immediately did to ensure our safety as well as the safety of the aircraft below us.
Second reporter narrative
My student and I were on downwind for XXL at ZZZ and had been cleared touch and go without any specific traffic to follow. We proceeded to follow the last traffic ahead of us that was on final showing on ADSB and followed them visually to turn our base. We did not see any additional traffic ahead of us visually or on final. Tower cleared us to land XXL while we were in the base leg; again without any specific traffic to follow or sequence to follow like 'cleared to land number 3' after I requested to make this one a full stop taxi back. We still did not have any additional traffic on final on ADSB but heard from tower that there was another company traffic ahead of us and they told us to go around. We proceeded to turn to go around and offset to the left of the runway and acquired the traffic visually. There was another plane that did not show up on ADSB; another plane and neither me nor my student saw them on final unfortunately. After the go around there was no further incident. I have learned from this that we need to not rely quite as much on ADSB traffic and look even harder for any other possible traffic that may be on final as we are turning our base. I will teach my students to double and triple check final even if there are no targets on ADSB in that direction. I reached out to tower to report this to them as well via their phone number.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.