The Haggadah quotes Rabbi Yehuda who states a mnemonic for the ten plagues that splits them up into three groups (3+3+4) based on the first letters of the plagues, dzakh adash bachav. In the Middle Ages, the Rashbam (on 7:26) seems to follow this division and noted that that by the first two plagues in each set, Moshe warned Pharaoh and by the third plague in each set there was no warning. Seforno (on 8:12) expands on this distinction and notes that the tenth plague is separate from the other nine plagues. This separation can be seen by the fact that there is a lengthy break from the nine plagues, 7:1-10:23, and the tenth plague, 12:29. Thus, the order of the plagues can be thought of as being nine plus one, or 3, 3, 3, 1.
Many commentators (see for example Malbim on 7:14, and Sarna 1986, p. 76) have noticed other distinctions within each of the three sets of three plagues. When G-d tells Moshe to go to Pharaoh by the first plague in each set, the word used is nisav or hityasev, 7:15, 8:16, and 9:13, while by the second plague in each set the word used is bo, 7:26, 9:1 and 10:1. Furthermore, within the warning by the first plague in each set, G-d tells Moshe to tell Pharaoh a reason for the set of three plagues, 7:17, 8:18 and 9:14, while no rationale is recorded within the warning by second plague in each set. (8:6 records Moshe giving a reason for the removal of the frogs which was second plague, but this appears to be from Moshe since there is no indication that G-d instructed to Moshe to say this.)
In addition, and I did not see this mentioned, by the third plague in each set of three plagues not only is there no warning, but the plague comes and goes without any reaction by Pharaoh. By all the other plagues, Pharaoh responds in some way, by negotiating, 7:4, 8:21, 9:27, 10:16, by not being impressed, 7:23, or by noting the damage done by the plague, 9:7. 10:24 records Pharaoh speaking to Moshe after the plague of darkness (the third plague in the third set), but not only is the plague over, but Pharaoh makes no reference to the plague. Similarly, in the plague of kinnim (the third plague in the first set), Pharaoh's advisors state that the plague was "the finger of G-d," 8:15, but Pharaoh says nothing since he never responded to the third plague.
This grouping of three groups of three plagues plus the tenth plague does not include the miracle of changing the staff into a crocodile, 7:8-13, the introduction to the plagues, and hence really the order of the plagues should be 1, 3, 3, 3, 1. This pattern is similar to the structure of the creation of the world, which was 1, 3, 3, 1, see our discussion, "A literary pattern to the description in the Torah of the creation of the world."
Is there an order to the plagues?
A popular answer (see Rashi on 8:16 and Ralbag, comments end of Va-era`) is that the order is based on the escalation in the severity of the plagues. However, while the tenth plague is clearly the most severe plague, the ninth plague, darkness, seems to be less severe than the preceding plagues of locusts, hail and boils. It seems that if one wants to follow this idea of increasing severity, one would have to argue that the psychological effects of the plague of darkness were greater than the physical pain of boils, and then maybe one could divide the three sets of plagues into annoying, the first set, destructive, the second set and psychological, the third set. (The hail and the locusts, from the third set, also destroyed the Egyptian crops, but this was part of the psychological warfare since the people would worry about their future food.) On the other hand, if the second set of plagues was worse than the third set of plagues, than the severity of the plagues would be a parabola. Of course, the only people who can truly answer whether the plagues were escalating in severity were the Egyptians who lived through the plagues.
A different way to understand the order of the plagues is based on the rational for each of the three sets of three plagues in response to Pharaoh's statement in 5:2. (This idea is discussed in many places, see for example Greenberg, 1971, p. 607, and Weitzman, 1999, pp. 87-99.) In 5:2, Pharaoh stated that he did not know G-d, and even if he knew G-d, he would not release the Jewish people since he evidently did not believe that G-d had any power in this world.
The lesson of the first set of three plagues was that Pharaoh should learn of G-d, 7:17, and this lesson occurred in ascending order, first by nature (blood), then in the homes (frogs) and then on the bodies (kinnim).
The lesson of the second set of three plagues was that G-d is present in the world, 8:18, which was to be learned based on the distinction of the plagues by the Jews and the Egyptians, and this too had an ascending order. The first distinction (arov) was between the homes of the Jews and the Egyptians, 8:20, the second distinction (dever) was between the Jewish and Egyptian animals, 9:4, and the third distinction (boils) was between the bodies of the Jews and the Egyptians, 9:11.
The lesson of the third set of three plagues was that G-d was unique, Shemot 9:14, and the first two plagues of the set are reported as being unique Shemot 9:24 (barad), and 10:6 (locusts). The uniqueness here was in reference to G-d's control over the forces of nature. Note that by the plague of barad, the point of the plague was not to cause damage since Moshe warned the people to bring their animals inside, 9:19 (see Ramban on 9:19), and 9:33 can be understood, as explained by Rashi (on 9:33), that G-d even stopped the rain in mid-course. Instead, it was to show G-d's control over the rain, hail, lighting and thunder, 9:23,24. Also, the unique point of the plague of locusts was not its destruction of some of the crops, which occurs by all swarms of locusts, but the massive presence of the locusts throughout Egypt and this was due to the great wind that brought the locusts, 10:13. G-d's power and control of the wind was also evident when G-d removed the tremendous quantities of locusts, as 10:19 records that the locusts were dumped into the sea, which most likely gave the effect of a great tornado. By the third plague in this set of plagues, darkness, the word unique is not mentioned, but complete darkness for three days was also obviously unique, and this plague showed G-d's control of the sun. In this set of plague, the order was the increase in the demonstration of G-d's control of nature, first over the rain, barad, then over the wind, locusts, and then over the sun, darkness.
Accordingly, within each set of three plagues there is an order of ascending message/ lesson. These lessons of the plagues are most likely the rationale for the plagues since G-d did not have to do any plagues to take the people out of Egypt, as He could have told the people to walk and stopped the Egyptians from attacking them. The lessons of the plagues were to prepare the people for the Decalogue and the covenant with G-d, as finally after the miracle of the splitting of the Yam Suf, 14:31 records that the people believed in G-d.
On the other hand, 10:2 states that the reason for the numerous plagues was in order that the Jewish people would remember the plagues, which is different than the three lessons of the three sets of plagues. Also, 9:16 and 10:1 record in reference to Pharaoh and the Egyptians that the plagues were for them to tell the world about G-d. These are additional reasons to the main reason of the plagues, which was to inculcate the belief of G-d in the Jewish people.
Greenberg, Moshe (1928-2010), 1971, Plagues in Encyclopedia Judaica, Jerusalem: Keter Publishing House, 13, pp. 604-613.
Sarna, Nahum (1923-2005), 1986, Exploring Exodus, New York: Schocken Books.
Weitzman, Gideon, 1999, Sparks of Light, Northvale, NJ: Jason Aronson Inc.