May 31, 9:04 p.m. EDT - The Blue Moon. The second full Moon occurring within a calendar month is usually bestowed this title. Although the name suggests that to have two Full Moons in a single month is a rather rare occurrence (happening "just once in a . . . "), it actually occurs once about every three years on average. June 30, 9:49 a.m. EDT - The Full Strawberry Moon. Known to every Algonquin tribe. Europeans called it the Rose Moon.