In this chapter, the LORD reiterates the calendar of burnt offerings.
This chapter reminds us of the various sacrifices that have been commanded in various parts of the bible. In particular, it mentions: the daily offering, the weekly Sabbath offering, the monthly offering (more on this below), the Passover and the Feast of Weeks. The next chapter will conclude with the Feast of Trumpets, the Day of Atonement (Yom Kippur) and lastly, the Feast of Booths (Sukkot). These two chapters should be viewed as one long dialogue and between them they list all of the significant festivals of the Hebrew year. I mention this because the first chapter would look incomplete if we saw that it only contained the festivals up through the Feast of Weeks.
Anyway, we can observe right away that this chapter is very similar to Lev 23 (I would recommend reading my commentary on this chapter for background) in how it lays out all of the festivals, even using the same order, which appears to be chronological. This chapter starts by listing the offerings that are made all year round: the daily, weekly and monthly offerings. Then it lists the annual offerings, starting at the beginning of the year with Passover and ending in the next chapter with the Feast of Booths. Virtually everything is the same between these two chapters.
Lev 23 is a list of the "appointed feasts" of Israel, while the current chapter is a list of the various scheduled sacrifices to be made at the tabernacle. For this reason, the list in Lev 23 does not include the ordained sacrifices for each celebration, while this chapter does. What's more interesting is that what sacrifice Lev 23 does mention, for the Feast of Weeks, does not match the sacrifices described in this chapter. Lev 23:12-13 mentions sacrificing a single male lamb with some oil, grain and wine, while this chapter includes a variety of sacrifices for the same feast: two bulls, a ram, seven male lambs and a male goat, plus the customary grain, oil and wine in varying quantities.
It's not clear to me why there is a discrepancy: perhaps this chapter is expanding or revising on the sacrifices mentioned in Lev 23. As I said, Lev 23 is not intended as a reference guide to the sacrifices for these festivals: it's pretty clear this chapter is the reference guide, which makes its subject matter highly Levitical (which is true of other parts of Numbers as well, like Num 18-19. So this chapter and the chapter to follow are both Levitical-style chapters.
As we can see these two lists here and in Lev 23 are substantially the same, which goes to show that every single festival involves animal sacrifice. There are many reasons for this. Animal sacrifice is part of the ritual of atonement through the shedding of blood. As a semi-nomadic society, they have lots of livestock which makes these sacrifices convenient.
Also, many of these festivals are meant to be celebrations, in particular the Feast of Trumpets, the Feast of Weeks (or first fruits) and the Feast of Booths. Most recently in Num 25 we saw that religious celebrations and feasts (i.e. the eating of large meals and particularly meat) are tightly integrated. Therefore we can definitely conclude that these various celebrations involved lots of sacrifices. I should be clear, however, that the sacrifices in these chapters are burnt offerings which would not be eaten by the public at large. A small portion is given to the priest, but that's it. Rather, the burnt offerings would be accompanied by large quantities of peace offerings and freewill offerings which would be consumed by the celebrants. The burnt offering was probably intended as "God's portion" of the feast, in some fashion.
For all of these reasons and possibly more, the rituals of the tabernacle are dominated by animal sacrifice. The list in this chapter has two additions compared to the list in Lev 23: the daily offerings and the monthly offerings. The weekly offerings coincide with the Sabbath, which is considered one of the ordained festivals in Lev 23. More specifically, it is a "day of sacred assembly", when the people are commanded to gather together in celebration. The daily offerings were commanded back in Ex 29:38-42, so while it's not in the Lev 23 list, it is not new to us.
What's more interesting then is the commanded monthly offering, on the first of each month, which coincides with the new moon (since the Hebrews used a lunar calendar), henceforth known as "new moon offerings" for that reason. I think this is interesting for two main reasons.
First, the word for "month" here and elsewhere is "chodesh". This word means "new moon" or "month" interchangeably and is derived from "chadesh" which means "to be new," "to rebuild".
"Chodesh" is used frequently in the bible, starting in Gen 7:11 and continuing nearly everywhere you see the word "month". The reason I find this interesting is that we are never specifically told that Israel runs on a lunar calendar, it is simply baked into the language that their word for month is "new moon". The NASB sometimes translates "chodesh" as "month", as in Gen 7:11, and sometimes as "new moon", as in Num 29:6, 1 Samuel 20:5, simply depending on the context. 1 Sam 20:5 is a good example because in that chapter, David says "Behold, tomorrow is the chodesh". Obviously David isn't saying "the month is tomorrow", he is saying the new moon, signifying the beginning of a new month, is tomorrow. What makes this verse even more apt is that David is specifically discussing the new moon festival, which is the subject of the present chapter.
Second, this is the first time we have heard of the new moon sacrifices, and these sacrifices are never formally instituted anywhere else in the OT. This chapter is just a list of offerings that only mentions it incidentally. What I mean is that this chapter, must like Lev 23, is a summary and listing of various things. It is not commanding the Israelites to hold new moon sacrifices, just as it is not commanding them to obey the Sabbath: the command to obey the Sabbath was written elsewhere, first in Ex 16 and second in Ex 20. This chapter simply reminds the Israelites of what they have already been commanded. Since the new moon festival is listed here with everything else, I believe that it must have been already part of Hebrew society. This again shows the cultural assumptions in the text, that readers are simply expected to know about the new moon festivals at the beginning of every month. It's possible it was commanded by the LORD in some non-biblical text (which has since been lost), or it is a cultural tradition that existed outside of the Jewish faith that was then adopted in. Also note that Num 10:10 refers to the new moon festival, which I didn't notice at the time.
When I wrote my commentary on Lev 23, I said that I would put off writing a comprehensive guide to the sacrificial calendar, and one thing I had in mind was the new moon offerings which are first described in this chapter. I think this is the definitive list for the Pentateuch (basically everything in this chapter and the next), but I will hold off on creating a reference list of scriptures until the very end of Deuteronomy. Also note that there are additional festivals outside of the Pentateuch (Purim, Hanukkah), but the Pentateuch is different in that it makes a fairly complete set as you progress from Passover through Yom Kippur and Sukkot.
Lastly, this chapter institutes what appears to be a new group of sacrifices for the Passover, which previously involved the sacrifice of a male lamb for each family (established in Ex 12, revised in Num 9), but now it also involves a set of communal offerings that are not for any particular family or individual. Rather, these sacrifices would probably be made on behalf of the nation. Other than that, the sacrifices don't seem particularly noteworthy. My readers can probably observe that the sacrifices are very similar from one festival to the next. While the particular amount of lambs, goats, bulls, grain, wine or oil may change, we can clearly see that the sacrifice system (and by inference, Israelite agriculture) is concentrating around these handful of crops and livestock.