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If one wants to count the people, he does so by having them each give a half-shekel coin. If it is done improperly, it could cause a plague (ibid. 12-13). There are different opinions among the commentaries as to whether this is a halacha or a life-protecting idea (see Abarbanel ad loc.). It is also a question whether the practice of giving a half-shekel is always the way to go as part of a count, or whether this was a special method employed at the time when they were also accumulating materials for the building of the Mishkan (see ibid. and Ramban ad loc.).
Everyone of the age to be counted was to give a half-shekel as a "teruma laHashem" (donation to Hashem) (ibid. 14). It mentions "teruma laHashem" another two times in these p’sukim, which prompted Rashi to say that there were three donations at that time (see also Megilla 29b, which comes to the same conclusion). One was for the adanim (the bases) of the Mishkan; one was for other uses in the construction of the Mishkan; one, which was given after the Mishkan was complete, at the time of yet another counting, was used for public korbanot. That which the Torah says that people must give no more and no less than a half-shekel each (ibid. 15) is in regard to the third donation.
What is also notable about the third donation is that while the first ones were related to one-time events (counting and/or construction of the Mishkan), the one for public sacrifices is a mitzva from the Torah to do every year (Sefer Hachinuch, mitzva 105), as long as the Beit Hamikdash is functioning (Rambam, Shekalim 1:8) (even by those outside Israel). It is in commemoration of that mitzva, which we are not able to fulfill (at the time these words are being written), that we read in shul this week the Parashat Shekalim. At the time the mitzva existed, the word to do so was spread on the 1st of Adar (ibid. 9).
Why is a half-shekel the currency of choice for all of these various purposes? Rav Hirsch explains beautifully. On the one hand, the donation is to be the donation of the individual. On the other hand, each individual is to realize that his contribution is only a part; it is not complete on its own. We can add that while it begins as an individual donation, it does not remain so, as they are gathered together and jointly become the donation of the whole congregation. They were put in shofar-shaped receptacles (Rambam, Shekalim 2:1), and from that point on they were jointly the korbanot of everyone together. It was never that one group of people sponsored (with or without a plaque) the korban on one day and others did so on another day. The halves formed wholes in the most complete manner.

P'ninat Mishpat P'ninat Mishpat: Complaints about Contractor’s Work – part II
(based on ruling 83037.1 of the Eretz Hemdah-Gazit Rabbinical Courts)
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