Merely a Half
It is a straightforward commandment: every Jew should give half a shekel coin for a census and atonement. Yet, the Torah gets very detailed in describing the coin:
This they shall give, everyone who goes through the counting: half a shekel according to the holy shekel. Twenty gerahs equal one shekel; half of [such] a shekel shall be an offering to the Lord. (Exodus 30:13)
Instead of saying that a half coin is the equivalent weight of ten Gerah, why does the Torah have to spell out the math for us: “Twenty gerahs equal one shekel; half of [such] a shekel”?
The Half Shekel is the opening commandment of an eventful and dramatic portion, including how the Jews created and served the golden calf, Moses shattering the tablets, G-d’s forgiveness, and giving the second tablets. The Half Shekel at the beginning of the portion is the antidote and the correction for the sin, and therefore, although, in general, we are commanded to offer to G-d only from what is complete and unblemished, in this case, the emphasis is that we offer specifically a half.
The essence of the sin of idolatry is not the denial of G-d but rather the belief that there is duality. The mistaken notion that while G-d is the creator, he is too sublime to be within the creation; creation itself is therfore controlled by the various forces of nature. The essence of idolatry is the belief that there is a space, an energy, a force that is independent of G-d.
The half Shekel reminds the Jew that he is not an independent person. His personality, the Sefirot {attributes} of his soul alluded to by the ten Gerah, are merely half of a greater whole of twenty Gerah. The ten Sefirot of the soul reflect the ten Divine Sefirot, and are only complete when connected to their Divine source.
By giving the half Shekel the Jew declares not only that he is prepared to give his ten attributes to G-d but that he recognizes that his entire being is dependent on, connected to, and a reflection of, his Divine source.
Adapted from the teachings of the Rebbe, Lekutei Sichos 3, Ki Tisa