Exodus 30:13 – 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.
Jerusalem Gemora Shekalim Chapter 2, Halacha 3 – Rabbi Nehemiah said in the name of Rabbi Yochanan ben Zakai “Because they transgressed the ten commandments, that is the reason why everyone needs to give ten gerahs”.
Torah Temimah Colloquial Translation Note #24:
Rabbi Yochanan ben Zakai’s explanation is meant to explain the overall reason for the commandment to give a half a shekel. On the other hand, the prior comments of Rabbi Yehuda and Rabbi Nehemiah were meant only to state why “half” a shekel needed to be given rather than a whole shekel. [Editor’s note: Check out the Torah Temimah’s comment on note 23.] Otherwise, one could ask on their explanations why Levites must also donate half a shekel since the Levites didn’t participate in the transgression of the Golden Calf. Rather, the reason for the giving of the money is so that there would be money to pay for the communal sacrifices each year as the verse states “to atone for their sins” – since that is the function of the sacrifices.
It is important to note that the custom in our day to give half a shekel in charity before the holiday of Purim is hinted at in our verse here. This is in accordance with that which is stated in Gemora Megilah 13b as follows “it was known to God [at the time this commandment was given] that in the future Haman would weigh plans [shkalim] against the Jews. There God preceded His shkalim to Haman’s shkalim.” Also look at the Shulchan Aruch Orach Chaim section 694 and in the Magen Avraham where they express surprise in the Maimonidean Notes that women and children are also obligated to give half a shekel before Purim. They are surprised at this because in the half a shekel mentioned in the Torah they are exempt.
In my opinion the issue is clear: in the Scriptural half a shekel the purpose was the take a census. Since women and children were not counted as part of the census, they were exempt at that time. This is not the case in the requirement to give half a shekel before Purim. This commandment is in remembrance of the miracle of Purim. Since women and children were included in that miracle, they are also obligated in the requirement to give half a shekel before Purim.
Editor’s Note: In this note, the Torah Temimah again emphasizes women’s mitzvah obligations against other authorities stating a lesser level of obligation.