First printed source of the Nursery Rhyme was in 1838 in A. e. Bray’s Traditions of Devonshire (Volume II, pp. 287-288)
Although it was first printed in 1838, the tradition of fortune telling by days of birth is much older. Thomas Nashe recalled stories told to young children in Suffolk in the 1570s, known as fortune-telling rhymes.
What does it mean to be full of grace? Googling it reports that a child of Tuesday will be gracious, agreeable, refined, and polite in manner of behavior. (From The Free Dictionary) idioms.
That sounds wonderful. Could we all try it for today, being it’s Tuesday?