John Gill Commentary Numbers 17:3

"And thou shalt write Aaron`s name upon the rod of Levi; for there shall be one rod for each head of their fathers` houses." — Numbers 17:3 (ASV)

And you shall 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 ^F5; 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.

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FOOTNOTES:

• F5: Antiqu. l. 4. c. 4. sect. 2.