The worn tan slippers of master tap dancer Sandman Sims flashed across the gym floor at Ellington High.

Clickityickityclick . . . clackityackityclack . . . clickityclackityClick!

"Now you do it," he told the 27 senior dance students lined up before him. Taps and sneakers and ballet shoes slapped the floor. They weren't getting it, so he took them through the simple figure one by one, tap by tap. In a few minutes they had it, and he led them in a snake dance around the gym.

CLICKITYICKITYCLICK CLACKITYACKITYCLACK . . .

Sims, Chuck Green and Bunny Briggs were in town yesterday to do a special show at the Smithsonian. Every move they made was put on videotape, because the Smithsonian knows they are national treasures. Their program, built around George Nierenberg's much-honored short film, "No Maps on My Taps," has been touring the country and soon will head for Europe.

They are something of a legend, these three. Green has been dancing 55 of his 61 years, Briggs started at 2 -- he's 58 now -- and Sims, whose age is, as he always says, "a matter of opinion," first danced on Los Angeles street corners but really got into it when he was a boxer.

"I used to do some fancy steps when I was standing in the rosin box," he said, "and the people liked that better than my fighting."

He worked up an act with a board lightly sprinkled with sand, producing, a cool, slippery sound, and it was this sandman act (his original name was Howard) that kept him going all through the lean years when tap dancing virtually disappeared from the scene. For a time the black pride movement looked down its nose at the Stepin Fetchit image for black hoofers in the white entertainment world.

"We went underground, man," Sims muttered. "In Harlem. Did a lot of gigs, club dates, anything you could get. The sand act kept me alive."

Now that tap dancing is the rage again, Sims and his friends seem mildly amused at their new fame. In Harlem they never had to be rediscovered. They would dance on a sidewalk if there was no place else. (The film in fact shows them slapping around on a sidewalk, getting their steps ready for the show.)

Sims carries a bagful of tap shoes with him, each pair wrapped in flannel. Some are 30 years old, and the leather is creased and faded. "The thinner the taps, the better. I have some that are paper thin."

He broke a lace with great deliberation and threaded a new one, pulling it tight as carefully as a violinist tuning his A-string. Sometimes his feet are size 7, sometimes as large as 8, depending on how much he's been dancing. There are calluses on the tops of his toes.

"We're not strictly tappers," he said. "We're hoofers. We dance with the whole foot, not just the heel and toe. It's not just counting the taps, it's more than that. If you count to four, I be to 12, ' be to 32. It's not counting, it's what you hear and feel. It's supposed to be easy and simple and beautiful. All you need is your shoes and a floor and smart feet."

The three friends watched the students warm up. Ellington hasn't taught tap for the last three years, and the movements were definitely balletic."Look at that," said Briggs, "that's ballet. The way they stand. We'll put a stop to that." He chuckled.

Each man took a turn teaching, serious and businesslike. The laconic Green, who hardly says a word offstage, blossomed before the audience and danced a step in excruciating slow motion, his body in perfect balance, perfect control. It was Green, called the Bach of Tap, the successor to great dancer John Bubbles, who gave the show its name.

"maps are full of roads and signs and detours," he once said. "They limit you and steer you. But when I tap I can get lost dancing. I don't have no maps then."

In their dancing competitions they constantly seek new figures, new rhythms, but as Sims said, "We don't invent steps, you don't have to; they come to you. The greatest essence is time. Everything runs by time. Your heart beats in time. It just comes to you."

The program "American Tap Masters" is the first event in the Smithsonian's American Dance Experience series this year, to continue through the winter with workshops, seminars and films.

The men were tired. They came in by train from New York, and they'd been on the move all day. Someone suggested they steal a little rest before the evening show.

"Nah," said Sandman Sims, "I'll be all right, Soon as I get may tap shoes on, I'll be okay."