Adam's father, Heber, was enslaved by the Reverend William Pratt of Easton, Massachusetts, who might have purchased him in Charleston, South Carolina. In 1722, Pratt's widow freed Heber and provided him with 10 acres of land. On some records Heber's surname appears as “Pratt,” but he probably changed it to “Honestman” (also seen as “Honesty”) sometime after he became free. On June 26, 1733, or 1735, Heber married Susanna Cordner of Bridgewater, Massachusetts. The couple had at least one child, Adam, born on September 23,1738, in Easton. In 1737, Heber purchased from a Josiah Pratt “one sixty-third part of one right” to land in newly established Huntstown (now Ashfield), a tiny community in what was then the wilds of Western Massachusetts. He did not move there immediately. He sold his Easton land to Josiah Pratt in 1740, and by 1743, the family was living in Huntstown.