With this siman, we conclude the formation of the long section of Shacharis (often skipped and unfamiliar to many) known as the ‘Korbanos’ (sacrificial offerings). After having learned about the section of the ‘Tamid’ (daily offering - and a few others) in siman 48 (see pp. 32-34 in the Artscroll Siddur), the Shulchan Aruch now explains the placement of the two final selections in the Siddur - ‘Eizehu M’koman’ (pp. 42-48) and ‘Rabi Yishmael Omer’ (pp. 48-52). In seeking a brief but comprehensive overview of these technical selections, and the reasons for their inclusion (Ed: perhaps a bit more than the Mishnah Berura offers), I have found the Artscroll commentary to be very informative.
Please allow me to excerpt them below:
‘Eizehu M’koman’ (“What is the Location?”)
The Talmud (Kiddushin 30a) teaches that one should study Scripture, Mishna (i.e. the compilation of laws) and Gemara (i.e. the explanation of the laws) every day. In fulfillment of that injunction, the Sages instituted that appropriate passages from each of these three categories be included in this section of Shacharis. Since Scriptural passages regarding the Temple offerings (Ed: i.e. the ‘Tamid’ section) are part of the service in any case, the Sages chose a chapter of the Mishnah on the same subject. Chapter 5 of ‘Zevachim’ (lit. slaughtered offerings), which begins ‘Eizehu M’koman’ (“What is the location”) was chosen for three reasons: a) It discusses all the sacrifices; b) it is the only chapter in the Mishnah in which there is no halachic dispute; and c) its text is of very ancient origin, possibly even from the days of Moshe. In discussing the various categories of animal offerings, this chapter focuses on the location in the Courtyard where they were slaughtered and the part of the Altar upon which their blood was placed.
‘Rabi Yishmael Omer’ (“Rabbi Yishmael Says”)
As used in the Talmud, Mishnah means a listing of laws and Gemara means the logic behind and the application of the laws. As a selection from the Gemara, the Sages chose one that gives the thirteen methods used in Scriptural interpretation… this one is a basic introduction to an understanding of the derivation of the laws. It shows us how the very brief statements of the Torah can be ‘mined’ to reveal a host of principles and teachings… The Torah was composed by G-d according to the rules of logic and textual analysis contained in Rabbi Yishmael’s ‘baraisa’ (i.e. teaching). The Oral Tradition governs the way in which these rules are applied and we have no authority to use them in a manner that contradicts, or is not sanctioned by, the Oral Law…
We are now ready to begin the more familiar part of the Shacharis service – the Pesukei D’Zimra (Psalms of Praise)!