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My son asks:
The Hagada mentions, toward the end of Magid, three opinions on how many plagues the Egyptians suffered in Egypt and on the Red Sea:
But there's a fourth opinion that isn't mentioned in the Hagada! In Avos 5:4, the unnamed tana says that ten plagues were suffered in Egypt, and ten on the Sea.
Why is this tana's opinion not included in the Hagada?
The opinion in Avos is fundamentally different from those in the Haggada. The opinion in Avos is simply stating that 10 things happened in Egypt and 10 things happened by the sea. The opinions in the Haggada however, are explaining how each thing was really multiple makkos (based on expounding certain words and then using a 1:5 ratio from finger to hand). Perhaps the purpose of these passages in the Haggada is to highlight how not only did God redeem us and perform wonders, he even kept on adding more and more to it (this fits the theme of dayeinu that immediately follows). The opinions quoted in the Haggada demonstrate this, while the opinion in Avos does not. Thus that opinion was not cited.
Perhaps the Mishna in Avos is consistent with all three opinions in the hagadah. All three opinions in the hagadah must agree that there were ten plagues in Mitzraim, yet they argue if there were ten, forty or fifty. The idea is obviously that each plague can be counted for more than one, if broken down into more detail. This would mean, that the given is that there were sets of ten and ten plagues, then the question would be how many each plague of each set would count for. And I'll attempt to prove this.
If you notice, the one to five ratio is derived from the fact that the plagues in Mitzraim are referred to as the finger of G-d and the splitting of the sea as His Hand. This may be hard to understand, since only one plague was referred to as a finger of G-d, not all of them combined, so perhaps the Mitzraim Plagues totaled ten, and the Sea Plagues totaled five?
The answer is, that the actual amount of plagues, when counted broadly as in the Torah, is non-negotiably ten and ten. The question remains as to the severity of each set. So if a Mitzraim Plague can be called a finger, and a Sea plague a hand, then the consensus is that these refer to severity and not amounts, and it can be inferred that the ten of the Sea can be counted as five times that of Mitzraim.
[sorry, this is just an oversimplified version of Alex's answer, with a proof]
Another possibility re Avot.
Frequently in Talmudic literature, multiple ideas that fit a pattern or theme are clustered. Chapter 5 of Avot is a "classic" example. You have groups of 4's, and, as you see, here, groups of 10's. So, this was placed in Avot.
Likewise in the Hagaddah, you find a pattern of different rabbis all using the same verse to compare the number of plagues. So they included these 3. The one from Avot doesn't fit the Hagaddah's pattern.
