Importance Of Reasoning And Problem Solving

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Learning Outcomes:
At the end of the lesson, the students will be able to: Use different types of reasoning to justify statements and arguments made about mathematics and mathematical concepts; Write clear and logical proofs; Know how inductive reasoning differ from deductive reasoning; Solve problems involving patterns and recreational problems following Polya’s four steps; Use reasoning as a cognitive tool to arrive at conclusion or solutions to problems; Increase awareness on the importance of reasoning and problem solving; and Organize one’s methods and approaches for proving and solving problems.

This chapter will enhance our skills in reasoning and problem solving as we continue to discuss the relationships between and among …show more content…

Why reasoning’s and problem solving useful? Why you have to study reasoning and problem solving?

Performance Task

Goal –
You are tasked to make a housing loan comparison and come up with recommendations afterwards.
Role -
You are working as one of the spokesperson of the leading firm of your province. Family Sta. Cruz comes to your office and ask you to assist them in deciding which among the housing loans offered by DBP, Bank of Commerce and PNB will allow them to save money and payoff the loan within 10 years. . Audience –
Your recommendations will be presented to your firm and to Sta. Cruz family. Situation – As a spokesperson, you will coordinate to the head of the three banks you offer to Sta. Cruz family to have a data and computations for the breakdown of their housing loans. Then, ask them for the reasons why Sta. Cruz family will choose their bank.

Performance/Product –
You will create a recommendation for each bank. The recommendation will be written in two columns. The first column contains the computation while the other column will suggest a reason why Sta. Cruz Family will choose one among the following banks: DBP, Bank of Commerce and …show more content…

A conditional statement may sometimes be true or false. To show that a conditional statement is true, the argument should consist of hypothesis followed by a conclusion that holds at all times. If a conditional statement is false, a single counterexample is needed to make the statement true.

Example 3.6: If x^2=9 , then x = 3.

Solution:
As a counterexample, let x=-3. The hypothesis is true because 〖(2)〗^2=4. But the conclusion is false because the value of x can also be -3. Therefore, the conditional statement is false.

Example 3.7: If one-digit number is multiplied, then the product is a two-digit number.

Solution:
As a counterexample, let 2 and 4 be the one-digit number to be. However, the product of 2 and 4 is 8, which is a one-digit number. The hypothesis is true because 2 and 4 are one-digit number. But the conclusion is false because the product of 2 and 4 is not a two-digit number. Therefore, the conditional statement is false.

When we interchange the hypothesis and conclusion of a conditional statement a⇒b, then we have the converse statement b⇒a. Here are some examples:

Example 3.8:
Statement: “If Dory is a fish, then she

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