In a Roman family the father would run the family including the mother, children, sons and their wives, and slaves in the house. The father could be mean or caring, depending on the father’s personality. Also the father organizes the marriages, and if there is no father then the eldest son or close relative will take the task.
Now if you were growing up in Rome you serve the state. Boys will have to serve the army or the government, while girls have to marry and give birth to babies who will serve the state.
Like in Greece the father could choose to either keep the child or leave it to die. When the child is 8 or 9 years old they will be given a Bula which is a charm to ward off evil spirits.
If the child is poor he will work instead of going to school, but if their parent can afford the school the child will start school learning reading, writing, and arithmetic, when he is 7 years old, until they are 11 years old when school ends. More wealthier children will continue school which are only for boys.
Girls will have to start planning for marriage. Girls get marry in the age 12-14. Boys became adult when they are 14 years old or when they finished their basic education program. When they become adults a ceremony is held, that is when he will throw away his childhood clothes and the Bula, and given an adult toga and be registered as a citizen.