Levítico 23:6 Midrash: Midrash Tannaim, Mekhilta DeRabbi Yishmael, Sifra & Sifrei Bamidbar

Or [perhaps] just like the year [intercalates] one out of twelve in it, so too with the month one twelfth? [Hence] it teaches to say: on the fifteenth day of that month (Leviticus 23:6) — you intercalate a day for the month; you do not intercalate one twelfth in it.

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.

2) (Vayikra 23:6) ("And on the fifteenth day of this month is the festival of matzoth to the L–rd. Seven days shall you eat matzoh.") "And on the fifteenth day of this month is the festival of matzoth": This day requires matzoh, but the festival of Succoth does not require matzoh. For would it not follow otherwise, a fortiori, viz.: If this (Pesach), which does not require a succah (a booth) requires matzoh, then that (Succoth), which does require a succah, how much more so should it require matzoh! It is, therefore, written "this" ("of this month). It is this festival of matzoth, which requires matzoh, but not the festival of Succoth.