מדרש אויף דברים 16:1

(Fol. 9a) R. Abba said: "All agree that the deliverance of Israel out of Egypt took place in the evening, as it is said (Deu. 16, 1.) Did the Lord, thy God, bring thee forth out of Egypt by night; and [they also agree] that they did not leave [Egypt] before the next morning, as it is said (Num. 33, 3.) On the morrow after the Passover sacrifice, the children of Israel went out with a high hand, but they differ as to the meaning of Chipazon (In haste, Ex. 12, 11). R. Elazar b. Azariah holds that Chipazon (In haste), refers to the Egyptians who [after realizing the plague of the first-born] hurried the children of Israel to leave; and R. Akiba holds Chipazon (In haste), refers to the Israelites [who were in haste to leave]." We have also a Baraitha to the same effect: Did the Lord, thy God, bring thee forth out of Egypt by night (Deu. 16, 1). "Did they really go out at night? Behold! it was in the morning, for it is said (Num. 33, 3.) On the morrow after the Passover sacrifice, did the children of Israel go out with a high hand. We must therefore say that the beginning of the deliverance was in the evening."

(Exodus 12:2) "the beginning of months": I might think, for the minimum of months, two (i.e., the most distinctive of months, Sivan and Tishrei). It is, therefore, written (Ibid.) "of (all) the months of the year." (Exodus 12:2) "It is the first": What is the intent of this? It is written (Devarim 16:1) "Observe the month of Aviv (spring) and offer the Pesach to the L–rd your G–d, etc." Observe Pesach for Aviv, and Aviv for Pesach, that Aviv fall out in its proper time. How so? Intercalate Adar, so that Aviv fall out in its proper time. If they intercalated Adar and Aviv did not fall out in its proper time, I might think that they should intercalate the New Moon of Nissan. R. Yishmael says: If you say this, you make Nissan twice; but the Torah has said: "It is the first (i.e., one) to you" (and not two).

R. Nathan says "Observe the month of Aviv" — Observe the month which is closest to Aviv. And which is that? Adar. But we have not heard how many (days) are to be intercalated. From "Observe the month (of Aviv"), we infer that a month (of days, i.e., thirty) are to be intercalated. And this follows, viz.: A month is intercalated and a year is intercalated. Just as a month, (with) one of its units (i.e., days), so, a year, with one of its units (i.e., months). But perhaps, just as (with a) month — one thirtieth of it, so, (with) a year, one thirtieth of it? It is, therefore, written "Observe the month." (A month is intercalated and not one thirtieth of it. But perhaps, just as a year, one twelfth of it, so, a month, one twelfth of it? It is, therefore, written (Numbers 28:17) "And on the fifteenth day of this month" — You intercalate a day for a month, and not one twelfth of it.