Skyhawk 172/Cutlass 172
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 100; Flight Crew Total 530; Flight Crew Type 400
Situational Awareness
Conflict NMAC
Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Human Factors
This was a training flight to a local training area that returned to RDD for pattern practice. After several circuits in the pattern at RDD; my aircraft was on left downwind for RWY 16.  Tower instructed my flight; 'You are number 3 following a Duchess on right base; cleared touch and go; RWY 16.'  I had mistaken a King Air that appeared to have just turned from a right base to final as the Duchess I was instructed to follow. For this approach; I asked the student to remain at Traffic Pattern Altitude (TPA) for the forward slip from TPA to on glideslope indication; to then a normal zero flap landing.When established on final approach; but right of centerline; I saw an aircraft on my left and immediately took control of the aircraft; applied full power for a climbing right turn to the east at 79 knots. While in the climbing right turn (west bound); I heard the Duchess pilot transmit that there was an aircraft near his aircraft on the right. The Tower transmitted that he wasn't aware of another aircraft on final for RWY 16. After several seconds; Tower asked the position of my aircraft and I transmitted that I was in a climbing right turn on a west heading. Tower instructed me turn immediately continue turn and climb on an east heading - I complied with the instructions. Tower asked my intentions; I replied that I would continue my eastbound climb out of class Delta airspace. Tower instructed me to turn north and report leaving class Delta airspace.After leaving class Delta airspace; I reported that I had left class Delta; and tower asked that I report when ready to re-enter class Delta for landing. After a few minutes; I asked [Tower] for a full-stop landing and was issued ATC instructions; which I followed for a successful landing and to parking. While taxiing; [Tower] asked that I call them.  After securing the aircraft on the ramp; I called [Tower] and spoke with the Controller who I had been in contact with at the time of this incident.
C172 instructor pilot reported a NMAC in the pattern at RDD airport.