It is hard to calculate the size of the market the testing companies are fighting over. Matthew Chingos, a senior fellow at the Urban Institute, added up what states spent to satisfy federal testing requirements in 2012 and came up with a total of $669 million. Adding how much they spent on additional tests, he estimated overall spending at $1.7 billion.

Some researchers argue that states would have saved money by sticking with the national tests, which the Obama administration paid about $350 million to develop — making them free to states in the early years.

But Delaware, for instance, was already paying to provide the SAT to high school students, so it says it will save $100,000 by dropping Smarter Balanced.

In a few states like Delaware that were already giving the SAT or ACT to all high school juniors, getting rid of the Common Core test is, in part, an attempt to address complaints about too much testing. In most states, though, it amounts to replacing one test with another. But those states are betting that high school students will see the SAT or ACT as more relevant to their lives than the Common Core tests — that they are more interested in looking ahead to college than back on whether they have mastered what they were supposed to learn in elementary and secondary school. For state politicians, the SAT and ACT are also much less politically fraught.

The Common Core has come up against parents who complain of overtesting, students opting out of the tests last spring and conservatives objecting to the standards as a federal intrusion into what they said should be a local issue. Those battles have left only about half the states using one of the national tests.

The reauthorization of the federal law regulating public schools, which President Obama signed in December, still requires states to test students annually in Grades 3 through 8, and once in high school, and to test at least 95 percent of all students. But it allowed them to use what the law termed “nationally recognized” assessments, “such as ACT or SAT exams,” for the high school tests.

Most of the students opting not to take Common Core tests are in high school, and many high school students were already taking the SAT or the ACT. So states are betting that by switching to those tests, they can have higher participation rates — and stem complaints about onerous testing.