# ACT and SAT Would you recommend to your students to actually solve the mathematical problem or use the PITA (plug in the answer) method? Especially for simplifying rational expressions.

I also agree with 4,5, and 6. One note however; you cite simplifying radicals as an example type of problem. Often an answer is given that is not fully simplified, e.g. sqrt(72) might have distractor answers of 3sqrt(8) or 2sqrt(18). A calculator will confirm that these are equivalent to 6sqrt(2) so PITA won't work.

Another concern with PITA is incomplete solutions. 3 is a solution to x^2-x-6=0, so checking this answer confirms that it is correct. However the full solution of 3,-2 will be listed also.

A last concern with PITA is having an answer that works algebraically but is not a solution to the problem -- not in the domain, negative lengths, etc...

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On the actual test, the goal is to get the correct answer as quickly as possible. They have to understand the process, but basically there is no reason not to work backward from the answer until they get the correct one if that is faster than solving it once.
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I agree with post 4. During the exam is not a time for learning. Students should presumably already know the material once they have reached the testing period. During classes, teachers should, of course, teach multiple ways to solve the equation. I agree that PITA will not be effective in a classroom or collegate setting. However, during the SAT and the ACT, it is really all about time. If PITA is an effective way to get the answer, then by all means plug in the answer. The SAT and ACT have flaws in their ability to test students true knowledge. I would certainly advise a student to take advantage of these flaws in order to gain a higher score.
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During the actual exam it is just the time taken that matters. If the PITA method is able to save time I would recommend students using it in the exam. Though it is important for students to realize that they should know how to actually work out problems as a list of answers is provided in only a few instances. And even arriving at the right result using PITA requires a considerable amount of skill. A student cannot use it with no idea about the question.

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I wouldn't encourage students to do this (although many of them probably will), because while getting a good score on the test is important for college admissions, that approach won't help them at all when they get to college.

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This is an interesting question because it does encourage us to think about what our end goal is. What is most important? Is it that students get the right answer through their own methods or that they use an ascribed way of reaching the answer that they are looking for? Surely our job as teachers should be to show them a range of different techniques or strategies and encourage them to come up with the answer using whatever method they choose, be it PITA or otherwise.

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