Question

A student asks why he​ can't just make​ "random guesses" rather than​ "intelligent guesses" when using the​ guess-and-check problem-solving strategy. What is the correct response to this​ question?

Answer 1

Making random guesses lacks strategy and efficiency, whereas intelligent guesses are informed by the problem's parameters, thus leading to a more effective problem-solving approach. Intelligent guessing involves estimations that speed up the process and improve critical thinking necessary for real-world problems.

Step-by-step explanation:

The correct response to the question of why a student cannot simply make random guesses instead of intelligent guesses when using the guess-and-check problem-solving strategy is that intelligent guesses are informed by understanding the problem, identifying the knowns and unknowns, and using that information to methodically approach a solution. With random guessing, there is no strategy involved, and it could take an impractical amount of time to arrive at the correct answer, if at all. On the other hand, intelligent guesses are based on meaningful estimations and approximations that guide the solver to the answer more efficiently and effectively.

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For example, if a student is tasked with finding a number that when multiplied by 5 gives a product close to 90, making random guesses could be time-consuming. However, by using an intelligent guess, a student could estimate that 90 divided by 5 is close to 18, and then refine this guess with a precise calculation to confirm that the exact answer is 18. This process helps to develop problem-solving skills and prepares students for real-world situations where problems do not always present with clear-cut numbers.

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Lastly, it's important to check if the answer is reasonable by reassessing the logic behind the guess, especially if suspicions arise that the logic may be leading down the wrong path. This critical thinking component is integral to effective problem-solving.

Answer 2

At an average or in terms of probable outcome, Intelligent guesses often leads to the right answer while random guesses often lead to the wrong answer

Step-by-step explanation:

Guess and Check problem-solving strategy is a form of method or approach to solving problems that individuals or specifically researchers and students can employ to solve mathematical situations by guessing the answer after critical evaluation and analysis have been carried out and then checking that the guess conforms with the conditions of the problem under study.

Therefore, in order to get the right answer or solution to a problem, one has to make intelligent guesses which examining and analyzing each problem and determine important clue statements from the problem, then guess the answer from the critical analysis and evaluation. This often helps or leads the individuals to the right solution.

However, using random guesses is to pick or derived answers randomly, without critically analyzing the problem, which most times leads to wrong answers.

Hence, at an average or in terms of probable outcome, Intelligent guesses often leads to the right answer while random guesses often lead to the wrong answer