Seventeen-year-old Kenneth May rode his skateboard to school yesterday.

He was one of about 5,000 junior and senior high school students in Montgomery County whose bus service was cut off this fall when the school board decreed that students who live within 1 3/4 miles of their school are no longer eligible to ride. Last year's cutoff was 1 1/2 miles.

May believes that the elimination of busing will have one beneficial effect: "I think teachers will respect our using skateboards now, he said as he stepped on his board and sped down Gainsborough Road to Churchill Senior High School.

Some parents, fearful that their children would be forced to walk along dangerous roadways, attempted last week to have the school board continue to bus their children. Some parents won concessions, but the majority of the affected students still are required to walk.

The Montgomery County cutback in bus service was one of the most controversial aspects of a generally smooth opening of metropolitan area schools.

An estimated 470,000 students began the fall term yesterday in Fairfax, Arlington, Montgomery and Prince George's counties and in the city of Alexandria. Schools open this morning in the District of Columbia.

Another problem yesterday for school officials was the handling of students who were not properly immunized.

Both Maryland and Virginia law make immunization of school children mandatory, but school authorities in the various jurisdictions took different approaches to the problem. Arlington officials yesterday warned the parents of 203 pupils that their children could not attend school until they had been immunized against polio, rubella, diphtheria, whooping cough, and tetanus.

Enforcement of the no-admittance policy was inconsistent throughout the Arlington schools. According to Howard Bouee, the director of community activities for Arlington, some children were sent home and others were put in the school libraries.

"We're trying not to punish the children for something the parents failed to do," Bovee said. "We're not putting any children on the street, but we intend to have everyone immunized shortly."

Bovee said that compared to the 3,000 students who had been immunized by last June, the 203 figure yesterday was "almost insignificant."

A spokeman for the Fairfax County school system said children who have not been vaccinated will not be turned away from classes but their parents will be warned that their children must be immunized.