SMA X HAD NMAC WITH ACFT Y IN TFC PATTERN. SEE AND AVOID CONCEPT.

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TWR INSTRUCTED X (MY STUDENT & I) TO RPT A 2 MI L 45 DEGS FOR RWY 3L. I HAD THE STUDENT (UNDER THE HOOD AT THE TIME) TURN TO A HDG THAT WOULD ESTABLISH US ON A 45 DEG ENTRY FOR MIDFIELD. THIS PLACED US FURTHER S THAN WE WOULD HAVE BEEN IF THE 45 DEGS WAS ALIGNED WITH THE MIDPOINT OF THE ASSIGNED RWY (3L). AFTER SPEAKING TO TWR; THEY INDICATED THAT THIS CAUSED THEM TO NOT SEE X WHERE THEY 'EXPECTED' X TO BE. AT 2 MI; THEY TOLD ME TO FOLLOW TFC; BUT I DON'T REMEMBER ITS POS AT THE TIME BUT I ASSUMED IT WAS ON THE PATTERN. I SCANNED OUTSIDE AND RPTED TFC NOT IN SIGHT. THE TWR GAVE NO FURTHER INSTRUCTIONS SO I CONFORMED AND ENTERED THE DOWNWIND FOR RWY 3L. I CONTINUED; SINCE I ASSUMED THEY WOULD SEPARATE ME FROM THAT OTHER ACFT. I NEVER DID SEE THE OTHER ACFT THROUGHOUT THE INCIDENT. ONCE ESTABLISHED ON DOWNWIND I CONTINUED LOOKING FOR THE TFC AHEAD OF ME (I AGAIN ASSUMED IT WAS AHEAD - NOT BEHIND). IT WAS THEN THAT TWR CONTACTED THE OTHER ACFT ABOUT MY POS SAYING X WAS 'AHEAD AND TO YOUR R.' THEN THE PLT INDICATED I WAS RIGHT ABOVE THEM AND TWR ADVISED ME OF THIS. I ONLY SAW THEIR SHADOW AND STARTED TO TURN BUT TWR THEN SAID TFC WAS NO FACTOR SINCE Y TURNED BASE FOR RWY 3L. I WAS INSTRUCTED TO EXTEND DOWNWIND FOR RWY 3R. AFTER SPEAKING WITH THE OTHER PLT; HE INDICATED THAT HE THOUGHT THE TWR HAD X INSIGHT AND WOULD SEPARATE US. I ASSUMED THE SAME THING. ANOTHER FACTOR; BESIDES TWR'S INSTRUCTIONS OR LACK THEREOF; WAS THAT I WAS BEHIND THE AIRPLANE AND MY STUDENT; BEING AN INEXPERIENCED CFII WITH ONLY 5 HRS DUAL GIVEN; IT WAS POOR JUDGEMENT TO LEAVE THE STUDENT UNDER THE HOOD FOR SO LONG. I ACTUALLY FORGOT THAT HE WAS UNDER THE HOOD; BUT I WAS LOOKING/SCANNING OUTSIDE THE AIRPLANE THE ENTIRE TIME. AT NO TIME DID I FEEL WE WERE IN VIOLATION OF ANY FAR'S. IN RETROSPECT; I SHOULD HAVE HAD THE STUDENT FLY VISUALLY AND SO WOULD HAVE REDUCED MY WORKLOAD. BUT WHY DID TWR ALLOW ME TO CONTINUE AND ENTER THE PATTERN WHEN I DID NOT HAVE TFC IN SIGHT AND I THINK THE OTHER TFC AND TWR DID NOT HAVE ME IN SIGHT EITHER?