Small Aircraft
Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Commercial
Confusion; Distraction; Situational Awareness; Training / Qualification; Communication Breakdown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Staffing; Human Factors; Environment - Non Weather Related
I was training a student in the local ZZZ area (ZZZ). After completing training maneuvers [XX] miles east of ZZZ we returned to ZZZ for touch and go landings. After the 2nd landing we climbed to [an] upwind leg. The Tower Controller was talking to me and another aircraft in the pattern. He gave an instruction to the other aircraft which was doing another touch and go. I heard the Controller say extend upwind he will call the crosswind turn. At the time I made a quick comment correcting my student on his climb speed. I believed the Controller was talking to the other aircraft. I proceeded to make a normal left crosswind turn and continue a normal traffic pattern. As I was on downwind the Controller advised me I should have been on crosswind. I apologized and informed him I didn't realize that instruction was for us. ZZZ has been working with minimum staffing due the pandemic. A single Controller handles three positions Clearance Delivery; Ground Control; and Tower. With this in mind I would've chosen to do touch and go landings at an airport with less traffic. I will be sure to be cautious about this fact until air traffic and controller staffing goes back to normal.
Instructor pilot reported thinking Tower instructions for them were for another aircraft resulting in a heading deviation. Reporter cited Tower staffing issues due the COVID-19 pandemic as a contributing factor.