The census in the wilderness illustrates the family structure and relationship of the nation of Israel. All the children of Israel were one large family. The hierarchical family relationships reveal the Bible's patriarchal worldview. The breakdown of the nation into tribe, clan and household demonstrates the strong central position of fathers.
The entire nation looked back to one common father. They were the descendents of Jacob. That's why they were called "children of Israel." (Israel is another name for Jacob.)
Each Israelite could trace his line of descent through one of the twelve sons of Jacob. That line of descent formed his or her tribal identity. Those who were descended from a common father were referred to as a tribe. The twelve sons of Jacob were fathers over the tribes. The tribes of Israel were further broken down into large extended families. The Hebrew word for "family" is mishpachah (משפחה). However, when used in the tribal sense, it does not refer to a nuclear family household; it refers to the large extended family of a common forefather within a tribe. A better English word is "clan." A clan is like a sub-tribe—a tribe within a tribe.
Every clan was composed of many households. The Hebrew word for "household" is beit av (בית אב), a term that literally translates as "house of a father." The father's household was composed of himself, his wife (or wives), children and grandchildren.
The common denominator in all these family rankings is the central position of a father. In the biblical world, fatherhood was the essential ingredient for family and identity. Isn't that chauvinistic? Not from the perspective of the biblical woman. She regarded her father and husband as her prestige and her identity. They were the affirmation of her femininity. They provided her protection, sustenance and dignity. It's a different way of thinking from what we have today.
The patriarchal worldview explains why Paul was so eager to establish spiritual paternity for the Gentile believers. To be reckoned as part of the nation, the Gentile believers needed to come under the household of Israel's fathers. In Paul's theology, Gentile believers are adopted into the family of Israel.
Jew and Gentile alike, we all share in the person of Messiah and are fellow heirs, citizens in the Israel of God—the Kingdom of Messiah. We have all been brought near by the same atonement and given the same Torah.
Still, a Gentile believer might wonder which tribe of Israel he is to be identified with. Since the Gentile disciple's participation in Israel is only by means of faith in Yeshua the son of David, the Gentile's tribal affinity is naturally with David's tribe: the tribe of Judah.