Book groupings in the Old Testament

Modern Jews divide the Old Testament into 3 groupings. They are

1. Torah (Law)
2. Nevi’im (Prophets)
3. Ketuvim (Writings) 

From which they derive the term TaNaKh from the initial letters. Within the Tanakh they divide the Prophets into Former Prophets and Latter Prophets. The Writings are divided into Poetry, 5 scrolls, and other. Within these groupings the books are also ordered.

• Scripture
• Law
• Genesis
• Exodus
• Leviticus
• Numbers
• Deuteronomy
• Prophets
• Former prophets
• Joshua
• Judges
• Samuel
• Kings
• Latter prophets
• Isaiah
• Jeremiah
• Ezekiel
• The Twelve (minor prophets)
• Writings
• Poems
• Psalms
• Proverbs
• Job
• Scrolls
• Song of Songs
• Ruth
• Lamentations
• Ecclesiastes
• Esther
• Other
• Daniel
• Ezra & Nehemiah
• Chronicles

Some argue for a fixed canon of the OT around 100 BC, others to after 100 AD. The early manuscripts were on scrolls and thus not bound. Some books were grouped on scrolls such as the 12 minor prophets. Thus the groupings of the books and the order of the books need not date to the time of any agreement of the canon. Specifically, I am unaware of any documented grouping or order of the Tanakh prior to c. 400 AD. Further, there is evidence of a different grouping prior to and at the time of Jesus.

The term the "Law of Moses" or "Book of the Law" or similar was used by the authors of other Old Testament books: Joshua 1:7, Joshua 8:31, Joshua 8:32, Joshua 22:5, Joshua 23:6, 1 Kings 2:3, 2 Kings 14:6, 2 Kings 21:8, 2 Kings 23:25, 2 Chronicles 23:18, 2 Chronicles 25:4, 2 Chronicles 30:16, 2 Chronicles 33:8, 2 Chronicles 34:14, Ezra 3:2, Ezra 7:6, Nehemiah 8:1, Nehemiah 8:14, Nehemiah 9:14, Nehemiah 10:29, Daniel 9:11, Daniel 9:13, Malachi 4:4. This often refers to a specific book, usually Deuteronomy.

The phrase the Law and the Prophets is attested by the time of the New Testament. Sirach (Ecclesiasticus) was written c. 200 BC. In the prologue written c. 150 BC we read,

Many great teachings have been given to us through the Law and the Prophets and the other books that followed them, and for these we should praise Israel for instruction and wisdom. Now, those who read the scriptures must not only themselves understand them, but must also as lovers of learning be able through the spoken and written word to help the outsiders. So my grandfather Joshua, who had devoted himself especially to the reading of the Law and the Prophets and the other books of our ancestors, and had acquired considerable proficiency in them, was himself also led to write something pertaining to instruction and wisdom, so that by becoming familiar also with his book those who love learning might make even greater progress in living according to the law.

You are invited therefore to read it with goodwill and attention, and to be indulgent in cases where, despite our diligent labour in translating, we may seem to have rendered some phrases imperfectly. For what was originally expressed in Hebrew does not have exactly the same sense when translated into another language. Not only this book, but even the Law itself, the Prophecies, and the rest of the books differ not a little when read in the original.

We also find the term "Law and the Prophets" in the book of 2 Maccabees which was written c. 150 BC.

But Maccabeus had ever sure confidence that the Lord would help him: Wherefore he exhorted his people not to fear the coming of the heathen against them, but to remember the help which in former times they had received from heaven, and now to expect the victory and aid, which should come unto them from the Almighty. And so comforting them out of the law and the prophets, and withal putting them in mind of the battles that they won afore, he made them more cheerful. (2 Maccabees 15:7–9)

The term the Law and the Prophets is also found several times in the New Testament. Mat 5:15; 7:12; 11:13; 22:40; Luk 16:16; Joh 1:45; Act 13:15; 24:14; 28:23; Rom 3:21. Jesus specifically uses this term to sum up the Old Testament: Mat 5:15; 7:12; 11:13; 22:40; Luk 16:16.

4 Maccabees was written c. 100 AD and also uses the phrase.

In the time of my maturity I remained with my husband, and when these sons had grown up their father died. A happy man was he, who lived out his life with good children, and did not have the grief of bereavement. While he was still with you, he taught you the law and the prophets. Maccabees 18:9–10

There is also a variation on the phrase: The Law and the Prophets and the Psalms. Jesus uses it in Luke talking to his disciples after his resurrection.

Then [Jesus] said to them, “These are my words that I spoke to you while I was still with you, that everything written about me in the Law of Moses and the Prophets and the Psalms must be fulfilled.” Then he opened their minds to understand the Scriptures,

Note that the fuller phrase also expands "Law" to "Law of Moses".

In his book Against Apion, Josephus enumerates the holy Scriptures of the Jewish people.

For we have not an innumerable multitude of books among us, disagreeing from, and contradicting one another, as the Greeks have, but only twenty two books, which contain the records of all the past times; which are justly believed to be divine. And of them five belong to Moses, which contain his laws, and the traditions of the origin of mankind, till his death. This interval of time was little short of three thousand years. But as to the time from the death of Moses, till the reign of Artaxerxes, King of Persia, who reigned after Xerxes, the Prophets, who were after Moses, wrote down what was done in their times, in thirteen books. The remaining four books contain hymns to God; and precepts for the conduct of human life. 

It is true, our history has been written since Artaxerxes very particularly, but has not been esteemed of the like authority with the former by our forefathers, because there has not been an exact succession of prophets since that time; and how firmly we have given credit to these books of our own nation is evident by what we do; for during so many ages as have already passed, no one has been so bold as either to add any thing to them, to take any thing from them, or to make any change in them; but it is become natural to all Jews immediately, and from their very birth, to esteem these books to contain Divine doctrines, and to persist in them, and, if occasion be willingly to die for them. For it is no new thing for our captives, many of them in number, and frequently in time, to be seen to endure racks and deaths of all kinds upon the theatres, that they may not be obliged to say one word against our laws and the records that contain them; whereas there are none at all among the Greeks who would undergo the least harm on that account, no, nor in case all the writings that are among them were to be destroyed; for they take them to be such discourses as are framed agreeably to the inclinations of those that write them; and they have justly the same opinion of the ancient writers, since they see some of the present generation bold enough to write about such affairs, wherein they were not present, nor had concern enough to inform themselves about them from those that knew them; examples of which may be had in this late war of ours, where some persons have written histories, and published them, without having been in the places concerned, or having been near them when the actions were done; but these men put a few things together by hearsay, and insolently abuse the world, and call these writings by the name of Histories.

Thus we have the scriptures of the Jews referred to as the Law and the Prophets from at least 150 BC to about 100 AD in various writings. There is a variation of the term: the Law of Moses and the Prophets and the Psalms. Josephus specifies the number of book that this includes which is 5 for the Law of Moses, 13 for the Prophets, and 4 for the Psalms (and related books).

The best way to read this is that the term "the Law and the Prophets" referred to the canon of scripture at the time; all of what is now termed the Old Testament. At times "Psalms" was added to the term, and "Psalms" included the book of Psalms and 3 other books. These 4 books were a subset of the "Prophets".

Jesus and the apostles used the term "the Law and the Prophets" to encompass Scripture. It is probable that "Prophets" in this term refers to all the books excluding the 5 books of the Law of Moses. The more expanded term including "Psalms" recognises that hymns were part of the collection, and Josephus' writings make it likely that Psalms includes 3 other books.

This is not unlike the phrase "the heavens and the earth" which includes everything in heaven and earth. This phrase, or variant of it, is used multiple times in the Bible. Variations include the addition of "sea" or "under the earth" but these additions do not mean that the lack of extra terms limit the scope of "heaven and earth."

The grouping of the books of the Bible fit the early term "the Law and the Prophets" or "the Law and Prophets and Psalms". The modern Judaic grouping of "the Law and the Prophets and the Writings" does not appear to go back to the time of the first century, and the grouping of the "Writings" does not correspond to the term "Psalms".