Because they are precious. Rashi wishes to explain why the Torah writes all of these details. He answers that “Because they are precious … [Hashem counts them all the time].” He means to say that even without these details one would have to explain why the Torah writes “Take a head count of the entire congregation” (v. 2), given that He had already counted them in Parshas Ki Siso. Therefore one must say that these details are mentioned “Because they are precious.”

To know the number of those who remained. It is written [regarding the golden calf] “From the people approximately three thousand men fell” (Shemos 32:28), so by counting the fallen, [Hashem] knew the [number of the] remainder. Thus Rashi explains: When they fell because of the calf He counted the dead to know how many remained alive.

And on the first of Iyar He counted them. Re’m writes: This count occurred once the Divine Presence had rested among them. Do not ask why [Hashem] did not count them in Nissan when the Divine Presence first rested. He answers that that on the first of Nissan the Divine Presence rested and so when He counted them on the first of Iyar, it was as if He counted them in Nissan. It appears to me that Rashi’s intent here so that you should not ask how he knows that Hashem counted them three times. Perhaps [you may think that] He only counted them twice! This would seem to be the case because the total mentioned here and the one mentioned in Parshas Ki Siso are one and the same. Accordingly, Rashi explains that on the first of Nissan the Mishkon was set up, and on the first of Iyar [Hashem] counted them. Because if this count was the one mentioned previously, why is it written there (Shemos 38:27) that they made sockets for the Mishkon from the silver that they brought as an atonement for the count of their souls, while here it is written that “on the first of Iyar He counted them.” Surely the Mishkon had already been erected on the first of Nissan. Rather, this must have been a different count. You might ask: Why did the Torah not count them immediately after the setting up of the Mishkon, since immediately afterwards the Divine Presence came to rest. The answer is, as we say concerning oaths, (Bava Basra 8a): If one prohibits oneself from benefiting from the residents of a town, he is permitted to benefit from people who have not lived there for thirty days because they are not considered established there. Similarly, Hashem did not count them until the Divine Presence had been established for thirty days.

The number of each tribe. But not each and every family — because the Torah does not mention a count of families in the subsequent verses, only a count of the tribes (Gur Aryeh). You might ask: Then why did it write “according to their families”? The answer is that through the families they knew the count of the tribes, as the Torah writes (v. 18), “and they were registered by family ancestry” implying that they were not known by the name of their tribe. Therefore, one must say that it was by their families that Moshe and Aharon knew which tribe they were from.

Maintained in his father’s tribe. Meaning that if his father was from one tribe and his mother was from another tribe, he would be maintained in his father’s tribe. However, it does not refer to [a case where] his father was from one family and his mother was from another family, even if they were from the same tribe, as would be understood from the plain meaning of the verse. Because what difference would there be if the father was from the Chanochite family and the mother was from the Paluite family, and consequently they were included among the Chanochites? Since both were from the tribe of Reuven, there would be no difference whether he is established in the family of the father or the mother.

Through the shekolim. Rashi wishes to answer why they were counted. Surely a plague comes when one counts them [directly]. Therefore he explains that it was done “through the shekolim.”

Below the age of twenty. You might ask: From where does Rashi know this? Perhaps even those younger than twenty were eligible for the army. And accordingly, the Torah would be understood as saying that you shall count those from twenty years old and above who are eligible for the army. However, if they are twenty years old but are not eligible, such as the old or sick, or are eligible but are not twenty years old — do not count them. The answer is that if this were so the Torah should have stated “from twenty years and above who are eligible for the army,” why then does the Torah state “all those eligible for the army.” Thus, it is certain that the verse must be explained as Rashi says. Similarly, when Rashi writes in Parshas Ki Siso (Shemos 30:14) that below the age of twenty no one is eligible for the army, this is derived from here (Re’m). See also Parshas Ki Siso.

When you count them, there shall be with you. One might ask: From where does Rashi know this? Perhaps they should be with you for other matters, but not when you count them. Furthermore, from where does he know that the Torah refers to the leaders of the tribes, perhaps it refers to other people? The answer is: Since it is later written “these are the ones called from the congregation, the leaders of their fathers’ tribes” (v. 16), one can infer that they were the leaders of the tribes. Furthermore, it is written “Moshe and Aharon took these men … and they gathered together the entire congregation” (vs. 17-18) from there one may infer that they did the counting along with Moshe.

To everything of importance. Rashi wishes to explain: Was their importance [only] that they called to the entire the congregation? Thus Rashi explains they were “invited to everything” meaning they were invited to deliberate and decide matters affecting the congregation.

Those twelve leaders. Rashi wished to explain: The Torah should have stated “Moshe and Aharon took them,” and since it previously listed the leaders of the congregation we would automatically know that they were the leaders already mentioned. However, it is clear that because it is written “these men” I might now say that it refers to others, not the leaders of the tribes. Therefore, Rashi explains that it does indeed refer to the twelve leaders. Furthermore, if one were to say that they were others, Rashi explains that [this cannot be because] they were “designated to him here by their names,” and it was the leaders who were designated here by name. The phrase “to him” was added because without it, it would not be known to whom they were designated. One might ask: From where does Rashi know to explain so, perhaps they were indeed others? The answer is: It is written האנשים האלה (those [specific] men) with a hei (implying the definite article) rather than אנשים אלה. If one asks: Then why does it not simply say they “took them,” as the Minchas Yehudah asks? The answer appears to be: The Torah initially said “the head of the fathers’ house” (v.4) while now it says “the leaders of their fathers’ tribes” (v.16). Thus, one might think that the heads of the fathers’ houses were not the leaders of the tribes, only of their families. And when here the Torah writes “the ones called from the congregation, leaders of their fathers’ tribes” it refers to the leaders themselves — but those listed above were indeed others. Consequently the Torah here would have said “the ones called from the congregation” only to inform us that they are the ones called “to any matter of importance.” For this reason the Torah states “these [specific] men” to teach that they were the very same leaders listed above. Maharshal writes that Rashi is answering the question: Why did the Torah write “who were designated by name,” when it would be sufficient to write “these men”? Therefore he explains that they were designated to him here by name, as a matter of importance, that they were worthy of their greatness and leadership. This is in contrast to the spies who were referred to by name in disgrace, due to what would befall them in the end, as is taught in Midrash Rabbah.

Genealogical documents and witnesses. Rashi was obliged to explain so because the word ויתילדו is from the reflexive התפעל construct. Thus, according to its simple meaning as a term of giving birth, it would imply that they caused themselves to give birth. Therefore Rashi explains that they themselves brought their genealogical documents.

Verified the status of their birth. The word חזקת (status) is a term of honor. Rashi explains so in Parshas Behar (Vayikro 25:41) where “he returns to his fathers’ possession” alludes to his fathers’ status, a term of honor.

Counted separately. Meaning that they would not be counted from the age of twenty, but from the age of one month. Since the Levites were the legion of the King, the Levites’ children who had passed the stage when a baby may be categorized as stillborn, were considered as important as those who go forth into the army of Israel.

Another interpretation; … foresaw. According to the first reason, one could ask why it is written אך (however), because the word אך always comes to exclude something. Therefore Rashi explained here that exclusion was from the decree that those aged over twenty should die in the desert. One might ask: Rashi should have said that they did not err during the episode of the spies, whereas the decree of death in the desert was due to this. The answer is: Even the Levites erred in the episode of the spies, and it was only with the golden calf that they did not err. Therefore, they were not punished [for the episode of the spies] given that even the rest of Yisroel were only punished because of these two sins together. Rashi proves this in Parshas Shlach Lecha (Bamidbar 14:33), where the Torah writes “bear your sins” rather than “bear your sin.” Consequently, it is certain that two sins of the golden calf and of the spies were the cause. [You might question:] Rashi explains later in Parshas Devarim (Devarim 1:23) that the Levites were not with them at the sending of the spies, or even at the decision to do so, as we will explain later. The answer is: Initially at the sending they were not with them, even for the decision, however when the spies returned and made an evil report about the land —when the entire congregation raised their voices and wept — the tribe of Levi was included in that weeping. They too said “why would Hashem bring us … to fall by the sword, our women and children to be taken captive.” With this, one may also answer the question that is widely asked: Even if they were counted from the age of twenty, if the Levites did not sin they would not have been included in the decree — because “it is not the serpent that causes death rather it is sin.” Thus we can certainly see that the Levites sinned during the episode of the spies and because of this they were not counted.

Authority. One might ask: Why does Rashi explain that this word is to be understood as the Targum translates (with the word מני — “appoint”), was it merely so that one would not say that הפקד (appoint) is a term of counting? What answer is this, given that the Targum also renders terms of counting with the word מני? The answer is: Wherever the Targum uses the word מני for an appointment to authority, the nun is punctuated with a dagesh (מנּי), and here is also punctuated so. Thus we may infer that it refers to an appointment to authority. However, when the nun of the word מני is not punctuated, it refers to counting. Another answer is that Rashi explains that the word is to be understood as the Targum translates, because the word הפקד is also a term of remembrance, as in “Hashem פקד (remembered) Sarah” (Bereishis 21:1) and sometimes it is a term of omission as with “and not one of us is missing” (Bamidbar 31:49). Therefore Rashi explains that it is to be understood as the Targum translates, to exclude those two explanations (remembrance and omission) of the word. One is unable to say that it is a term of counting; therefore he explains that it is to be understood as in the phrase “let the king appoint officials.”

As Targum translates, “they shall dismantle.” Meaning that they dismantle the parts of the Mishkon, separating them from the place where they are attached and leaving each piece on its own. However, they did not take it down from a high place to a low place, as might be understood from the term “take down.”

When they were going to depart. Rashi is answering the question: Why is it written ובנסוע המשכן (lit. when the Mishkon moved), did the Mishkon move? — Surely the people would move it! Furthermore he answers the question: Did they not dismantle it before the journey? Yet the verse implies that they would dismantle during the time of the journey. Therefore Rashi explains: “When they were going to depart” meaning that the departure is referring to the people. He added that they would “carry it…” so that you would not say that only the taking down was an obligation of the Levites, but not the carrying. Even though there is no mention here of their carrying it, it is inferred in a later passage, as explained in Parshas Naso (Bamidbar 4:25, 31).

To [perform] this service of theirs. This is the dismantling and the assembly. Rashi wishes to answer the question: Scripture had already warned several times that one who comes close to perform the service of the altar or who enters the sanctuary would die. Therefore he explains that “to [perform] this service” refers to the dismantling and assembly of the Mishkon. It does not refer to approaching the altar.

By the hand of heaven. One might ask: From where does Rashi know this, surely any death penalty mentioned by the Torah that is not detailed, normally refers to strangulation. The answer is: Rashi himself explains this shortly (v. 53) where he writes that “so that there will not be anger…” refers to death at the hand of heaven, as one finds in the section dealing with Korach, “for the anger had emerged” (Bamidbar 17:11) which refers to death at the hand of heaven. See also above in Parshas Emor (Vayikro 22:9).

There will be anger. There are those who ask: In all of the Torah inferences are mentioned, and from one side of the inference you may infer the other [so what is Rashi adding]? The answer is: Rashi elaborates here so that you do not err and say that when the Torah writes “so that there will not be anger” it refers to that which was juxtaposed to it “Bnei Yisroel shall camp … and the Levites shall camp…” (v. 52-53). Therefore, Rashi explains “if you fulfill my commandments … and if you do not fulfill my commandments…” which refers to the service of the Mishkon — it’s dismantling, loading and assembly, “as we find in the episode of Korach.”

As we find. Rashi says this because of his explanation above where he said that they would die at the hand of heaven. So that one should not question his source, he mentions the incident with Korach.