A little more than a week after the federal government gave a green light to Pfizer’s COVID-19 vaccine for kids age 5-11, Massachusetts health officials say thousands of local children have already gotten their first dose. Approximately 25,300, or 5%, of the state’s estimated 515,000 eligible kids had received one shot as of Nov. 10, according to the Massachusetts Department of Public Health.Hampshire County has the highest rate of uptake among this newly eligible age group, with 13%.Pfizer’s kid-size shots contain a third of the vaccine dose that was previously authorized to vaccinate millions of people 12 and older. The 5- to 11-year-olds will receive two shots, three weeks apart, the same schedule as everyone else — but a smaller amount in each shot, using a smaller needle.About 28 million children nationwide are eligible for shots and the White House said Wednesday that 900,000 kids had already received their first dose. “We’re off to a very strong start,” said White House COVID-19 coordinator Jeff Zients, during a briefing with reporters Wednesday.More than 2 million COVID-19 cases have been reported in U.S. children ages 5 to 11 since the pandemic started, including 66 deaths over the past year, according to Centers for Disease Control and Prevention data.Zients said the effort to vaccinate younger kids is still ramping up, with new clinics coming online. Government officials expect the number of children who are vaccinated to keep rising in the days and weeks ahead, he said.”We are just getting started,” he said. Final clearance for the shots was granted by federal regulators on Nov. 2, with the first doses to kids beginning in some locations the following day. The Associated Press contributed to this report.