SMA AIRCRAFT WAS ISSUED GO AROUND BECAUSE OF NO GEAR; INSTRUCTOR REPORTER DESCRIBED EVENTS THAT LED TO THE EVENT; LISTING A NUMBER OF DISTRACTIONS.

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I WAS PRACTICING LNDGS WITH MY MULTI-ENG STUDENT AT ZZZ ARPT. WE HAD MADE 3 LNDGS PREVIOUSLY BEFORE THE INCIDENT OCCURRED. WHILE ON DOWNWIND TWR HAD CALLED US AND ASKED FOR THE BASES OF THE CLOUDS. THEY HAD CALLED RIGHT IN THE MIDDLE OF OUR DOWNWIND LNDG CHKS; SO WE WERE DISTR. AFTER WE RPTED THE BASES THE ARPT NEEDED TO GO IFR SO WE WERE INSTRUCTED TO LAND. WE HAD BEEN PRACTICING STOP AND GO LNDGS ON RWY 30; AND WE WERE GOING TO PERFORM A FULL STOP ON RWY 35. AGAIN; THIS WAS HAPPENING IN THE DOWNWIND PHASE OF OUR FLT. WHEN TWR CALLED THE FIRST TIME DURING OUR DOWNWIND CHKLIST THE GEAR HORN WAS GOING OFF AND WE WERE ABOUT TO PUT THE GEAR DOWN. I RESPONDED TO TWR WHILE MY STUDENT FLEW AND MENTALLY TUNED OUT THE GEAR HORN. AFTER TWR CALLED FOR THE BASES; THEY CAME RIGHT BACK AND ASKED WHAT RWY WE PREFERRED TO LAND ON. AGAIN; I RESPONDED TO TWR AND TOLD HIM RWY 35. AT THIS POINT WE NEEDED TO START OUR TURN TOWARDS RWY 35 BECAUSE WE WERE READY TO TURN BASE FOR RWY 30; SO WE NEEDED TO CORRECT AND MADE A CONTINUOUS TURN TOWARDS RWY 35 TO GET LINED UP WITH IT. I STILL HAD THE LNDG GEAR WARNING HORN TUNED OUT AT THIS TIME. I WAS FOCUSED ON MY STUDENT'S FLYING AS HE WAS COMING IN HIGH AND FAST; AND WAS NOT CORRECTING FOR A XWIND PROPERLY. I HAD BECOME VERY DISTR AND NEVER NOTICED THAT WE DID NOT HAVE 3 GREEN LIGHTS SHOWING OUR GEAR WAS DOWN. WE HAD NEVER FINISHED OUR BEFORE LNDG CHKLIST. WHILE ON FINAL APCH ABOUT 50 FT OVER THE RWY; TWR INSTRUCTED US TO 'GO AROUND.' MY STUDENT HESITATED AND I IMMEDIATELY PUSHED THE THROTTLES FORWARD AND CONDUCTED THE GAR. AT THAT POINT TWR CAME BACK AND SAID 'IT APPEARS YOUR GEAR IS NOT DOWN' AND AT THAT POINT I LOOKED DOWN AND DID NOT SEE 3 GREEN LIGHTS. I USED THIS AS A LEARNING SITUATION FOR MY STUDENT AND IT PROVED HOW EASILY A PLT CAN BECOME DISTR. WHAT CAUSED THE PROB WAS MULTIPLE DISTRS IN THE TFC PATTERN THAT PULLED MY ATTN AWAY FROM BACKING UP MY STUDENT'S CHKLISTS. WHAT CAN BE DONE TO PREVENT THIS IS ALWAYS CHK; CHK; AND TRIPLE CHK THAT THE GEAR IS ACTUALLY DOWN; NO MATTER WHAT THE SITUATION AND ALWAYS FLY THE ACFT BEFORE RESPONDING TO THE CTL TWR. DO NOT LET YOURSELF BECOME DISTR EVEN WHEN THERE ARE 2 PLTS IN THE ACFT. IF IT HAD NOT BEEN FOR THE CTL TWR INSTRUCTING A GAR; WE WOULD HAVE LANDED GEAR UP. I THANKED THEM. SOME CONTRIBUTING FACTORS TO THE INCIDENT WAS A LOWER TFC PATTERN THAN THE STUDENT HAD NORMALLY BEEN PRACTICING WITH AND THAT THE STUDENT HAD NOT FLOWN IN 2 WKS DUE TO WX. I WAS INSTRUCTING THE STUDENT MORE THAN NORMAL BECAUSE HE COULD NOT THINK AHEAD OF THE ACFT WHICH DISTR MY ATTN EVEN MORE.