C172RG INSTRUCTOR PLT AND STUDENT DID NOT DO THE BEFORE LNDG CHKLIST. THEY LANDED GEAR UP AFTER THEY FORGOT TO LOWER THE LNDG GEAR.

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COMMERCIAL PLT/CFII AND PVT/INST RATED STUDENT RETURNING FROM LCL AREA. I WANTED TO RETURN TO ZZZ1; WHICH IS THE ACFT'S HOME BASE. ASOS RPTED 10 SM VISIBILITY; BUT TWR RPTED 2 1/2 SM IN HVY RAIN/TSTM. I SUGGESTED TO THE STUDENT THAT WE PROCEED TO ZZZ FOR TOUCH AND GOES. ZZZ RPTED 10 SM AND BROKEN CLOUDS AT APPROX 2000 FT. TSTMS AND RAIN SHOWERS SURROUNDED THE ARPT. WE MADE A STRAIGHT IN APCH TO RWY 9R. AFTER SEVERAL TOUCH AND GOES; TWR TOLD US TO MAKE L TFC FOR THE SAME RWY (FROM PREVIOUS L TFC). THE STUDENT THOUGHT THE TWR HAD ORDERED A RWY CHANGE. I CORRECTED HIM; AND HE TURNED DOWNWIND. IN THE CONFUSION; THE STUDENT FORGOT TO PUT THE GEAR DOWN WHEN TURNING DOWNWIND. I FORGOT TO VERIFY THAT THE GEAR WAS DOWN. I TOLD THE STUDENT TO EXECUTE A 180 DEG PWR OFF ACCURACY LNDG; SHORTENING THE DOWNWIND; BASE; AND FINAL LEGS; WHERE THE BEFORE LNDG CHKLISTS WOULD BE VERIFIED; THE ACFT CONTACTED THE GND TAIL FIRST AND SLID TO A STOP ON ITS BELLY. IN RETROSPECT; SEVERAL FACTORS LED TO THE INCIDENT. THE CHANGE IN PLAN; DIFFERENT ARPT; AND DIFFERENT TFC PATTERN THAN NORMAL; ALL LED TO THE INCIDENT. THE STUDENT WAS PREOCCUPIED WITH LNDG THE ACFT ACCURATELY; AND THE INSTRUCTOR WAS PREOCCUPIED WITH RADIO CALLS; WX; AND THE WX AT THE HOME ARPT. IN THE FUTURE; I WILL NOT GET COMPLACENT ABOUT THE CHKLIST AND WILL ALWAYS KEEP DISTRS FROM DISRUPTING THE FLT. SUPPLEMENTAL INFO FROM ACN 595103: DURING A TRAINING FLT IN A C172RG I FAILED TO PUT THE GEAR DOWN FOR MY 4TH LNDG. THIS OCCURRED ON RWY 9R AT ZZZ. AFTER MUCH THOUGHT ABOUT WHY THIS HAPPENED I HAVE COME TO THE CONCLUSION THAT THERE WERE SEVERAL CONTRIBUTING FACTORS OR 'LINKS IN THE CHAIN' LEADING TO THIS INCIDENT. 1) MY PTT (PUSH TO TALK) BUTTON WENT INOPERABLE AFTER DEPARTING ZZZ1 AND ENTERING THE TRAINING AREA. MY INSTRUCTOR HANDLED THE RADIO CALLS AS NECESSARY. THIS IS NOT UNUSUAL DURING A TRAINING FLT. I BELIEVE I WAS NOT AS INTENSELY FOCUSED ON THE RADIO XMISSIONS AS A RESULT. WHEN REMAINING IN THE TFC PATTERN I TYPICALLY PUT THE GEAR DOWN JUST AFTER TURNING DOWNWIND. ON THIS CIRCUIT DURING CLBOUT THE TWR CHANGED THE TFC PATTERN FROM R TO L. THERE WAS HVY RAIN TO THE S GETTING CLOSE TO THE TFC PATTERN. NOT BEING FOCUSED ON THE RADIO CALLS I MISUNDERSTOOD AND THOUGHT WE WERE TO MAKE L TFC AT RWY 9L ON THE N SIDE OF THE ARPT AND FAR FROM THE RAIN. I MADE A L XWIND TURN AND CLBED TO PATTERN ALT HEADING FOR RWY 9L. MY INSTRUCTOR CAUGHT MY MISTAKE. SIMULTANEOUSLY TURNING L DOWNWIND AND DISCUSSING MY MISTAKE AND CORRECTION I WAS DISTR FROM PUTTING THE GEAR DOWN AT THE TIME I NORMALLY WOULD HAVE. 2) ON THE DOWNWIND LEG THE TWR CALLED US #3 FOR THE RWY. TWO OTHER TRAINING ACFT HAD ENTERED THE PATTERN SINCE OUR ARR. I SAW ONE ACFT ON THE RWY ABOUT MIDFIELD AND ANOTHER ON FINAL. I WAS LOOKING FOR A SECOND ACFT IN THE AIR. I DID NOT REALIZE THE TWR HAD COUNTED THE ACFT ON THE RWY AS #1. THIS CAUSED FURTHER DISCUSSION WITH MY INSTRUCTOR AND A DISTR BECAUSE I WAS LOOKING FOR AN ACFT IN THE AIR THAT WASN'T THERE. 3) APPROX ABEAM THE NUMBERS I WAS CLRED TO LAND #3 BEHIND THE TFC. ALMOST IMMEDIATELY THE ACFT ON SHORT FINAL WAS TOLD TO GO AROUND AND I WAS CLRED TO LAND #1. I WAS STILL CONCENTRATING ON THE TFC SIT; OBSERVING THE GAR; CHKING THE RAIN JUST S OF THE RWY; AND NOW CHANGING MY INTENTIONS FROM EXTENDING MY DOWNWIND TO TURNING FINAL NOW. ANOTHER SMALL DISTR FOR ME. 4) THIS LNDG WAS INTENDED TO BE A SHORT APCH; PWR OFF ACCURACY LNDG. I HAD KEPT PWR UP PAST ABEAM THE NUMBERS BECAUSE I INITIALLY NEEDED TO EXTEND DOWNWIND FOR TFC. AS WE WENT FROM #3 TO CLRED TO LAND #1 SHORT APCH I REDUCED PWR TURNED FOR THE RWY AND I THINK I ASKED MY INSTRUCTOR WHAT HE WANTED ME TO USE FOR AN ACCURACY TOUCHDOWN POINT. I WAS TO LAND ON THE 9 OF RWY 9R. I NOW CONCENTRATED ON AN AIMING POINT TO MAKE AN ACCURATE LNDG; USING FLAPS AS NECESSARY; AND FLYING THE AIRPLANE. THIS MUST HAVE BEEN THE SOLE OCCUPATION OF MY THOUGHT PROCESSES BECAUSE I DID NOT HEAR OR IT DID NOT REGISTER WITH ME THAT THE GEAR WARNING HORN WAS SOUNDING. I ONLY SEEMED TO HEAR IT AFTER THE GEAR UP LNDG. I HAD NO IDEA THAT THE GEAR WAS STILL UP AND WAS SHOCKED BY THE LNDG. ONLY A FRACTION OF A SECOND BEFORE LNDG DID I SUBCONSCIOUSLY THINK THAT I HAD THE NOSE QUITE HIGH AND STILL HAD NOT TOUCHED DOWN. THERE ARE A LOT OF OBVIOUS CONCLUSIONS TO BE DRAWN FROM THIS INCIDENT. I DON'T BELIEVE ANY OF THESE FACTORS BY THEMSELVES WOULD HAVE LED TO THE INCIDENT; BUT TAKEN TOGETHER THEY HAD A CUMULATIVE EFFECT. I DO WONDER IF THE GEAR WARNING SOUND WAS DIFFERENT; SOMETHING ALARMING; SHRILL; OR EXTREMELY LOUD; WOULD IT HAVE BROKEN THROUGH TO MY CONSCIOUSNESS? I AM NOT SURE IT WOULD HAVE.