3 You shall write Aaron's name on the rod of Levi; for there shall be one rod for each head of their fathers' houses.
*Minor differences ignored. Grouped by changes, with first version listed as example.
Thou shalt write Aaron's name upon the rod of Levi - The Levites had taken part in the late outbreak. It was therefore necessary to vindicate the supremacy of the house of Aaron over them; and accordingly his name was written on the rod of Levi, although being the son of Kohath, the second son of Levi (Exodus 6:16 ff), he would not be the natural head of the tribe.
And thou shalt write Aaron's name upon the rod of Levi,.... Or upon the rod that was for the tribe of Levi; the name of "Aaron" was to be written, not the word "Levi", or a "Levite", as Josephus (e); for that would not have decided the controversy about the priesthood, which chiefly lay between the Levites and the family of Aaron, who were of the same tribe:
for one rod shall be for the head of the house of their fathers; one rod for the head or prince of every tribe, every prince representing his own tribe he was the head of, and the rod the prince; and though the tribe of Levi was divided into two families, the family of the priests, and the family of the Levites; yet, as Jarchi observes, they were but one tribe, and so one rod for them, as for the other tribes.
(e) Antiqu. l. 4. c. 4. sect. 2.
Aaron's name - Rather than Levi's, for that would have left the controversy undecided between Aaron and the other Levites, whereas this would justify the appropriation of the priesthood to Aaron's family. One rod - There shall be in this, as there is in all the other tribes, only one rod, and that for the head of their tribe, who is Aaron in this tribe: whereas it might have been expected that there should have been two rods, one for Aaron, and another for his competitors of the same tribe. But Aaron's name was sufficient to determine both the tribe, and that branch or family of the tribe, to whom this dignity should be affixed.
*More commentary available at chapter level.