The Earth's surface is about 500 million square kilometers, which is handy for the arithmetic. The seven largest plates (Pacific, Africa, Antarctica, North America, Eurasia, Australia and South America) add up to about 420 million, which is close enough to the whole thing. The seventh-largest plate, South America, is about 42 million, and the next largest is the Somalia plate at 19 million, so seven seems like a natural cutoff.
But then we get into the quibbles of schoolkids and teachers. "What about India?" they want to know. "I never heard of this Somalia thing," they whine. Okay, to get to India (tenth-largest at 12 million) we have to include the Somalia and Nazca plates. Because India, whatever its status as a plate, is important for reasons that are cultural and pedagogical—it's right in the middle of the map, and you can't teach about continental collisions or the Tibetan plateau without mentioning it. And those top-ten plates add up to more than 90 percent of the Earth, so that should end the discussion.
But now that we've given in so far, we can't stop. In for a penny, in for a pound, as they used to say. Three more important places—the Philippine Sea, Arabia and the Caribbean—come next, riding on their own relatively little plates of 5.5, 4.9 and 2.9 million square kilometers respectively. The Amur and Okhotsk plates (part of China) are 5.3 and 3 million and belong in the list too. But we can't stop at fifteen because only slightly smaller, at 2.9 million, is the Cocos plate, so that makes sixteen. The next-smallest (the Yangtze microplate) is quite a bit smaller at 2.2 million, so I'm cutting things off at 16.
Unfortunately, the whiners have another complaint: "Those aren't all on the map." The canonical plate map that all the textbooks use doesn't show most of the plates I've just recited. A later map produced in 2006 shows just 21 plates. If anyone is reading this from the U.S. Geological Survey, would you please produce a new map?
Another thing is that all the maps insist that the tiny Juan de Fuca "plate," actually just a microplate, belongs on the map with its name carefully pointed out, even though it ranks twenty-second in size. That's for pedagogical reasons, too, stemming from the history of science. The Juan de Fuca plate is where seafloor spreading was first convincingly mapped in the late 1950s, and that old map of seafloor "magnetic stripes" is still pulling its weight in the classroom.
So please, teachers, don't make your students learn a number for the number of plates. There isn't just one. And geologists, if you haven't read Don Anderson's treatment of this question, see "How Many Plates?" which was published in the May 2002 Geology.