C172 INSTRUCTOR AND STUDENT HAD LESS THAN LEGAL SEPARATION WITH AN ACR MD80 IN SCT CLASS E.

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I WAS FLYING A CESSNA 172/U WITH A STUDENT; DEPARTING SMO DOWN THROUGH THE LOS ANGELES SPECIAL FLT RULES AREA (SFRA) TO THE LONG BEACH PRACTICE AREA. MY STUDENT IS A PVT PLT; WHO HAD NOT FLOWN IN 3 YRS (EXCEPT FOR 2 LESSONS IN THE PRECEDING WKS); AND WHO IS UNFAMILIAR WITH THE LOS ANGELES BASIN AIRSPACE. THE GOAL OF THE LESSON WAS TO TEACH THE STUDENT HOW TO TRANSITION THROUGH THE AIRSPACE S FROM SANTA MONICA AND HOW TO GET ON FREQ WITH SOCAL APCH FOR TA'S. WE WERE GOING TO DO A FEW STEEP TURN MANEUVERS FOR PRACTICE AND THEN HEAD BACK THROUGH THE FLT RULES AREA BACK TO SMO. AFTER COMING THROUGH THE SFRA AT 3500 FT; WE CALLED ATC ON THE FREQ OF 127.2; WHICH IS RESERVED FOR ABOVE 3000 FT. AS IT WAS A TRAINING FLT; MY STUDENT WAS MAKING THE RADIO CALLS. WE REQUESTED TA'S FOR PRACTICING. WE WERE TOLD RADAR CONTACT 2 MI NW OF TORRANCE; AND TO FLY SE FOR 5 MI; REMAINING AT OR BELOW 4500 FT. WE FLEW WHAT I THOUGHT WAS MORE THAN 5 MI SE; AND CLBED TO 4300 FT TO PREPARE FOR MANEUVERING. WE WERE PLANNING ON PRACTICING STEEP TURNS AND I DID NOT WANT TO INADVERTENTLY GO ABOVE THE 4500 FT RESTR; SO WE PLANNED TO PRACTICE THEM AT 4300 FT. WE WERE OVER THE INDUSTRIAL PORTION OF THE LONG BEACH HARBOR. I REMEMBER POINTING OUT THE BREAKWATER TO THE STUDENT AS A PLACE THAT GND REF MANEUVERS ARE SOMETIMES PRACTICED. WE DID 2 90 DEG CLRING TURNS AND THEN PROCEEDED TO PRACTICE STEEP TURNS. AS WE WERE MANEUVERING THROUGH A STEEP TURN (35 DEGS TO 45 DEGS) TO THE R; WE RECEIVED A XMISSION FROM ATC INSTRUCTING US TO TURN SE AND CLB AND MAINTAIN 4500 FT. (I INTERPRETED THIS AS A DIFFERENT INSTRUCTION FROM THE FIRST ONE; AS IT WAS TO MAINTAIN 4500 FT. AS WE HAD PREVIOUSLY FINISHED COMPLYING WITH THE ONE DIRECTING US SE FOR 5 MI AND REMAINING AT OR BELOW 4500 FT.) AS WE WERE IN THE MIDDLE OF THE MANEUVER; WE WERE TURNING THROUGH A HEADING OF NW; AND MIGHT HAVE DROPPED A LITTLE BELOW 4300 FT IN THE MANEUVER. WE CONTINUED THE MANEUVER TO THE R; (SO AS TO END UP IN THE DIRECTION OF SE); AND IMMEDIATELY BEGAN A CLB TO 4500 FT. THE BANK ANGLE OF THE STEEP TURN WAS SHALLOWED OUT A LITTLE AT THAT POINT IN ORDER TO EXPEDITE THE CLB. CESSNA 172'S DO NOT TURN VERY FAST. WHILE WE WERE STILL TURNING; I HEARD THE CTLR SAY SOMETHING TO THE OTHER ACFT ABOUT A CESSNA THAT WAS NOT COMPLYING; AND I THOUGHT THAT WAS STRANGE SINCE I BELIEVED WE WERE COMPLYING TO THE BEST OF OUR ACFT'S ABILITIES. THE OTHER ACFT (AN MD80) SAID WE REGISTERED ON THEIR TCASII. AT THAT POINT; WE STABILIZED AT 4500 FT; AND HEADED FURTHER SE AND DECIDED TO GO BACK TO SANTA MONICA. I GOT ON THE FREQ WITH THE CTLR; SINCE THE STUDENT HAD DONE ALL RADIO COMS. I APOLOGIZED AND EXPLAINED THAT WE WERE IN THE MIDDLE OF A MANEUVER WHEN HE GAVE US THE SECOND INSTRUCTION TO TURN SE AND CLB AND MAINTAIN 4500 FT. (I THOUGHT WE JUST DIDN'T TURN FAST ENOUGH RESULTING IN THE NON-COMPLIANCE.) I THEN TOLD HIM OF OUR INTENTIONS TO RETURN TO SANTA MONICA THROUGH THE SFRA; AND HE SAID TO TURN AROUND AND MAINTAIN 4500 FT FOR THE SHORELINE RTE. I CLARIFIED IF HE WANTED US TO TAKE THE SHORELINE RTE; OR IF WE COULD USE THE SFRA AS PREFERRED AND HE CORRECTED HIMSELF AND SAID YES THE SFRA WAS FINE. WE PROCEEDED BACK TOWARDS TORRANCE TO GET SET UP FOR THE FLT RULES AREA AND WERE THEN TOLD TO COPY A NUMBER. WHEN I GOT BACK TO SMO; I CALLED THE SOCAL MGR TO DISCUSS THIS. SHE ASKED AT ONE POINT IF I WAS TOLD THAT THERE WAS AN MD80 THAT JUST DEPARTED LONG BEACH AND WAS RESTR TO 4000 FT. I TOLD HER NO; AND I ASKED MY STUDENT; AND HE AGREED; THAT WAS NEVER SOMETHING THAT WE WERE TOLD ON FREQ. I BELIEVE THE CAUSE OF THE SIT COULD HAVE BEEN A FEW THINGS. 1) IT IS POSSIBLE THAT THE CTLR WAS TALKING ON 2 FREQS; WHICH COULD BE DISTRACTING. 2) GETTING AN INSTRUCTION OF 'TURN SE FOR 5 MI' IS TOO VAGUE FOR SUCH A CRITICALLY BUSY PRACTICE AREA. THE CTLR KNOWING WE WERE GOING TO BE MANEUVERING MIGHT HAVE GIVEN US MORE SPECIFIC INSTRUCTIONS: A BETTER INSTRUCTION MIGHT HAVE BEEN; 'TURN TO A HEADING OF 135 DEGS AND FLY PAST THE BREAKWATER;' OR 'FLY HEADING OF 135 DEGS UNTIL FURTHER INSTRUCTED;' SO THERE IS NO CONFUSION; ESPECIALLY IF THEY ARE LAUNCHING JETS OUT OF A NEARBY ARPT. SOMETHING I WILL DO IN THE FUTURE IS TO DOUBLE-CHK AND CONFIRM WITH ATC AS TO WHETHER OR NOT I'VE GONE FAR ENOUGH. I WILL ALSO PROBABLY NOT GO DOWN TO LONG BEACH TO PRACTICE MUCH; AS IT IS GETTING REALLY TOO BUSY WITH ALL THE LARGE JETS DEPARTING LGB.