In the 18th century, the family was an extended family, where grandparents lived with their children and grandchildren. Families in the 18th century were large, consisting of the father, mother, and grandparents, and averaged five or more children.
Children were important assets because they took care of their parents when they were old. There were no rest homes for people to go to when they grew old. Government social security systems did not exist either. The family was the social security then.
In some countries, children were treated as miniature adults in the 18th century, they even dressed as adults, you can see this in paintings of the times. Children married young or their parents betrothed them by arrangement. Children were apprenticed to the local tradesman to learn a trade or profession. Only upper-class children would go to college or university. The poor did not have schooling as most children do today. Education was not very high on the agenda for the poor, because they were needed to work the family farm or business.
Quite often, the trade engaged in by many children of the time was crime. As large poor families often fell on hard times, young children were left to fend for themselves much of the time. This was especially true in Europe. The street urchins picked pockets of the wealthy, or stole food from the vendors in the marketplace, just to get some food. When caught, these young children were treated as adult offenders where punishment was harsh, even cruel by today's standards. For example in England, pickpockets would be punished by having their fingers or hands cut off. There were no reform schools then.
The richer children had it easier because their needs were met by their family's wealth. These upper-class children had tutors to teach them how to read, write and do basic arithmetic. The boys would be prepared for the university. The girls would also be taught the basics but they would go to finishing schools to learn how to be proper women when they grew up.