One who saves coins for his Shekel and discovers that he has designated more than he needs for the Shekel:

(Beis Shamai):The surplus is Nedavah.

(Beis Hillel): The surplus is Chulin.

If he specifically indicated that from these coins he will bring the Shekel, then all agree that the surplus is Chulin.

If the designation was "these will be for my Chatas" then all agree that the balance becomes Nedavah.

Again, if it was from these, then the balance is Chulin.

Question (R. Shimon): What is the difference between Shekalim and Chatas?

Answer: Shekalim has a set limit, whereas Chatas does not.

(R. Yehudah): Shekalim also has no limit.

Upon their return from Bavel B'nei Yisrael used Darkonim as the Shekel.

Subsequently they went back to Sela'im.

Subsequently they went to Tiv'in.

They wanted to give Dinarim (half-Tiv'in but less than the value of a half-Shekel).

They did not accept this (reduced value).

(R. Shimon): Still, everyone gave an equal amount (unlike by Chatas which may vary from person to person).

(R. Yosi): The dispute in the Mishnah is over a collection of Perutos (and he has lost track of how many he has).

If, however, he took a sum of money and designated it, the balance is certainly Nedavah.

(R. Chiya and R. Bibi): If he took a sum, the balance is Chulin.

(R. Chiya): Our Mishnah supports R. Bibi (since the distinction made by R. Shimon can only be seen according to R. Bibi).

Question: What will R. Yosi do with this indication.

Answer: The distinction made by R. Shimon is found only within Beis Hillel when the person collected Perutos.

Question: But the Mishnah later teaches that the balance is Chulin (when will this be so)!?

Answer: The same answer as (f).

One who designated money but is exempt from giving a shekel, such funds are clearly Chulin.

Question: If he designated two and later found out that he only owes one half-Shekel (what becomes of the second)?

Answer: We may infer the answer from the same case regarding Chatas where the Beraisa teaches that the second Chatas ends up being Nedavah.

The Halachah here will follow the Din by "these coins are for my Shekalim."

As we learned in our Mishnah, as the currency changed, they would give the half of that currency, but not less than the value of a half-Shekel (as indicated by the Pasuk in Nechemyah).

The larger coins were used in the time of Nechemyah, a third of which equaled the half-Shekel of the Torah.

We learn from here that a person must give Tzedakah three times yearly.

We also learn that more than three annual Tzedakah campaigns is a burden for the community.

This is the source for three Sela'im, three Kupos and three donations.

(R. Yehudah): The Pasuk alludes to the fact that B'nei Yisrael sinned at midday (hence the half coin).

(R. Nechemyah): The Pasuk requires a half-Shekel which is made of six Garmesin, because their sin took place at the sixth hour.

The coin had the weight of 10 Gera, owing to their violation of the ten commandments.

Because Rachel's firstborn (Yosef) was sold for 20 Kesef, let every firstborn be redeemed for that amount (20 Dinarim = five Sela'im).

Each brother ended up with one Tiv'a, therefore the annual donation must be a Shekel worth a Tiv'a.

The surplus Shekalim are Chulin.

The surplus tenth of an Eifah (poorest offering) as well as the other offerings listed are Nedavah.

As a rule, leftover of any "deficit" offering is Nedavah.

Olah, Mincha, Shelamim, Pesach, Nezirim their surplus is like themselves.

The surplus of a Nazir goes to Nedavah.

Question: What if one set aside his Shekel and then died?

Answer: They are placed in the box of Nedavah.

The surplus from the tenth of an Eifah of the Kohen Gadol:

R. Yochanan holds it is thrown into the Dead Sea.

R. Elazar says that they go to Nedavah.

Question: Our Mishnah (6.b. above) goes against R. Yochanan!?

Answer: The Mishnah is speaking of the surplus from a Yisrael (Minchas Chotei), not of the Kohen Gadol.

Question: How do we know that (surplus) Pesach can be Shelamim?

Answer: The Pasuk [Min ha'Tzon... l'Zevach Shelamim] implies that any Korban which comes from Tzon can be brought as Shelamim.

Question: But an Olah also comes from Tzon!?

Answer: The Pasuk speaks of Korbanos which exclusively come from Tzon.

Question: But an Asham only comes from Tzon!?

Answer: The Pasuk speaks of Korbanos which can come from any Tzon (including Izim), not only from Kevasim and Aylim.

Question: "Min" normally excludes, yet here it includes?!

Answer: Here, too, it excludes (over one year old or a female).

Question: The Pasuk [Min ha'Tzon... l'Olah] can be understood to mean that the surplus Pesach is brought as an Olah!?

Answer #1: Compare edible Korbanos with edible Korbanos.

Answer #2: It makes more sense to switch Kodeshim Kalim to a different Kodeshim Kalim, and not to Kodshei Kodshim.

(R. Yochanan): A Pesach switches to a Shelamim not only if it were slaughtered to be a Shelamim, but even if it were slaughtered as an Olah.

Question: What is R. Yochanan's rationale?

Answer: The Pasuk implies that all forms of Korbanos revert to Shelamim.

Question: What about an invalidating thought regarding an Olah?

If the invalidation is universal (such as Chutz li'Zemano) then it will certainly invalidate here!

Pigul only applies if there is no other invalidation.

If the thought of an Olah renders it Pasul, then it will not become Pigul (and conversely).

Question: What of a Pesach slaughtered (throughout the year) with both Lishmah and she'Lo Lishmah thoughts?

Answer: It is Kosher (given the power of Lishmah to overcome the absence of any thought).

Question: If the "good" thought is so powerful then it should even address a Pesach slaughtered Lishmah with intent to do the Zerikah she'Lo Lishmah, by neutralizing the intent!?

Answer: Shetikah, per se, does not make it Kosher, unless he has undone the Lishmah of the Shechitah.