When I was in kindergarten, back when the dinosaurs roamed, I remember my teacher asking another child in the class what his mother's last name was, and thought that was the silliest question I'd ever heard. Today, such a question is fairly common, due to changes in many families. A child today may have one or two parent/stepparent combinations or other domestic arrangements that were even less common only a couple of decades past. Which might give such a child something in common with their colonial counterparts.
In any society where the mortality rate is higher than usual, it's a part of life that not every individual will live to raise their own children to adulthood. Especially in the early days of the American colonies, any number of factors might cause what we'd call premature death. The weather and climate of a strange land, scarce or unfamiliar food, disease, injury, death in childbirth or other factors could turn a two parent family into a one parent family. Widows or widowers with young children often began the search for a new mate within weeks or in some cases, even days of their previous spouse's death. A Dutch proverb even states "the best time to court a widow is on the way home from the funeral."
For colonial families, this made sense. Beside the companionship of another adult, two extra hands to feed, bathe, and generally wrangle the young ones came in, pardon the pun, handy, and a widowed mother would find life far easier economically with the help of a husband. A widowed father, also, could benefit from having someone to care for the homestead while he worked at providing for the blended family. Before anyone gets an image of a buckskin-clad Brady Bunch, these step families of course faced the same issues blended families face today; grief for the late parent or spouse, adapting to new ways of doing things they'd always done another way, or perhaps moving to a new home and leaving their old one behind. An only child might now be the youngest, or a pair of boys might find themselves overrun by a passel of girls or vice versa. Not so different from today?
There's one exception: the high mortality rate.
Let's say John and Mary came over from England to build a new life and produced bouncing baby Elizabeth. Unfortunately, their first year didn't go well, and John did not survive a hunting accident. Mary marries Thomas, and Elizabeth gets little brother, Luke, though Mary does not survive Luke's birth. Thomas now has two children under five he has to raise, and marries Abigail, a widow slightly older than himself, with daughters Ruth and Jane. Ruth is sixteen and a comely lass, and soon catches the eye of Jacob, a young man with his own small farm. Ruth and Jacob marry, and welcome the birth of son Samuel at the same time Thomas and Abigail have baby Josiah. Things are getting crowded at Thomas and Abigail's home as Abigail is expecting again, they've had to take in her elderly mother, and it's not the best year for farming, so there's a family discussion and Luke will go live with Ruth and Jacob. Plus cousin Ezekiel's wife doesn't exactly believe he somehow found an orphaned Indian child all by itself in the woods, and really, the toddler does have Ezekiel's nose, and there is the matter of Christian charity, as well as the stipend Ezekiel is willing to give whichever family will take in the poor dear.
Phew. That might not be the last adjustment for Elizabeth and her family; subsequent deaths and remarriages anywhere along the above lines could change things yet again, or one or more of the children might leave the family home(s) for indenture or apprenticeship, or even military service for the boys once they are old enough. By the time Elizabeth is ready to start her own family, probably in her late teens to early twenties, she may have acquired a few more branches to the family tree. If her teacher asked the class to draw family trees, Elizabeth might well raise her hand to ask for more paper, and she might not be the only one in her class, either.