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Inductive and Deductive Reasoning.pptx

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This lesson aims to introduce to you the world of reasoning and logic. Reasoning is one vital skill in studying Mathematics and its vast landscape for learning. Even in real world setting, one can use reasoning to prove or disprove concepts or information. As learner of this lesson, you are expected to achieve the minimum competency for this topic which is to use inductive or deductive reasoning in an argument.

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LEARNING OBJECTIVES At the end of this lesson, you will be able to: provide understanding on the definition of inductive and deductive reasoning; identify a statement whether it is inductive or deductive; and
INDUCTIVE AND DEDUCTIVE REASONING
MATH-TIONARY Inductive Reasoning It is the process of gathering specific information, usually through observation and measurement and then making a conjecture based on the gathered information. Deductive Reasoning It is the process of showing that certain
Observe the following statements below. 1. 5, 10, 15, 20, _____. What do you think is the next number? If you answer 25, then you are absolutely correct! 2. Adrian wears red t-shirt today. Yesterday and the other day he also wore red. What can you say about Adrian? If you will say Adrian loves red tshirt, then it could be since he often wears red t- shirts. 3. My mother is a medical front liner. My classmates mothers are also medical front
As defined in our MATH- TIONARY, INDUCTIVE REASONING is the process of gathering specific information, usually through observation and
Example 1 Observe the number of circles in the sequence. What do you think is the next number of circles following the last one?
Example 1 Observe the number of circles in the sequence. What do you think is the next number of circles following the last one? Think of the pattern you can observe starting from the 1st 2 circles up to the last one. From your observation, can you make a conjecture? What do you think is
Example 1 Observe the number of circles in the sequence. What do you think is the next number of circles following the last one? For the conjecture, consider the interval of each term. As one can observe, the interval is 2. It can be assumed that the next term using the interval is 10. You can also predict for the
Example 2 What can you say about the statements above? Can this be considered an inductive reasoning?
Example 2 A conjecture is considered a general statement. This means that the above statements are an
Example 2 But take note, not all statements made through inductive reasoning are foolproof or always true. Yes, inductive reasoning is practical since it is from observations or experience. However, it is not a guarantee or an automatic acceptance of truth. It must go through a validity test. Does the conjecture always true in all
For example, in the conjecture made in Example 2. A rectangle is a square. It can be noted that rectangles and squares have four sides and four angles. But a square has four equal sides, whereas the rectangle has 2 pairs opposite sides equal. This characteristic of rectangle makes the conjecture invalid. Just to be clear, inductive reasoning is practical but not always true in its conjecture.
Inductive and Deductive Reasoning.pptx
What have you observed in the construction of the statement? Does it start with a specific information? The statement started with a general information or an agreed assumption. Playing Mobile Legend may cause addiction.
How about the conjecture? The conjecture is specifically made. It is not a general knowledge, but in a particular situation. This implies that the statement above is from a general information or agreed assumption which made a specific conjecture.
Inductive and Deductive Reasoning.pptx
Example 1 Suppose that the given statements are true. Use deductive reasoning to give a conjecture that must also be true. Conjecture: A carabao has mammary glands.
DEDUCTIVE REASONING is also used in Algebra. This can be seen during the process of finding the value of a variable. When providing reasons
Example 2 Solve the equation for x. Give a reason for each step in the process. Solution: 2 (3x 5) 6 = x + 4 6x 10 6 = x + 4 Apply the distributive property. 6x 16 = x + 4 Combine like terms. 6x x = 4 + 16 Apply addition property of equality. 5x = 20 Combine like terms.
Now, let us do some exercises. Identify each item whether Inductive Reasoning or Deductive Reasoning. Put a check mark () under the appropriate column.
Now, let us do some exercises. Identify each item whether Inductive Reasoning or Deductive Reasoning. Put a check mark () under the appropriate column.

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Inductive and Deductive Reasoning.pptx

  • 1. LEARNING OBJECTIVES At the end of this lesson, you will be able to: provide understanding on the definition of inductive and deductive reasoning; identify a statement whether it is inductive or deductive; and
  • 3. MATH-TIONARY Inductive Reasoning It is the process of gathering specific information, usually through observation and measurement and then making a conjecture based on the gathered information. Deductive Reasoning It is the process of showing that certain
  • 4. Observe the following statements below. 1. 5, 10, 15, 20, _____. What do you think is the next number? If you answer 25, then you are absolutely correct! 2. Adrian wears red t-shirt today. Yesterday and the other day he also wore red. What can you say about Adrian? If you will say Adrian loves red tshirt, then it could be since he often wears red t- shirts. 3. My mother is a medical front liner. My classmates mothers are also medical front
  • 5. As defined in our MATH- TIONARY, INDUCTIVE REASONING is the process of gathering specific information, usually through observation and
  • 6. Example 1 Observe the number of circles in the sequence. What do you think is the next number of circles following the last one?
  • 7. Example 1 Observe the number of circles in the sequence. What do you think is the next number of circles following the last one? Think of the pattern you can observe starting from the 1st 2 circles up to the last one. From your observation, can you make a conjecture? What do you think is
  • 8. Example 1 Observe the number of circles in the sequence. What do you think is the next number of circles following the last one? For the conjecture, consider the interval of each term. As one can observe, the interval is 2. It can be assumed that the next term using the interval is 10. You can also predict for the
  • 9. Example 2 What can you say about the statements above? Can this be considered an inductive reasoning?
  • 10. Example 2 A conjecture is considered a general statement. This means that the above statements are an
  • 11. Example 2 But take note, not all statements made through inductive reasoning are foolproof or always true. Yes, inductive reasoning is practical since it is from observations or experience. However, it is not a guarantee or an automatic acceptance of truth. It must go through a validity test. Does the conjecture always true in all
  • 12. For example, in the conjecture made in Example 2. A rectangle is a square. It can be noted that rectangles and squares have four sides and four angles. But a square has four equal sides, whereas the rectangle has 2 pairs opposite sides equal. This characteristic of rectangle makes the conjecture invalid. Just to be clear, inductive reasoning is practical but not always true in its conjecture.
  • 14. What have you observed in the construction of the statement? Does it start with a specific information? The statement started with a general information or an agreed assumption. Playing Mobile Legend may cause addiction.
  • 15. How about the conjecture? The conjecture is specifically made. It is not a general knowledge, but in a particular situation. This implies that the statement above is from a general information or agreed assumption which made a specific conjecture.
  • 17. Example 1 Suppose that the given statements are true. Use deductive reasoning to give a conjecture that must also be true. Conjecture: A carabao has mammary glands.
  • 18. DEDUCTIVE REASONING is also used in Algebra. This can be seen during the process of finding the value of a variable. When providing reasons
  • 19. Example 2 Solve the equation for x. Give a reason for each step in the process. Solution: 2 (3x 5) 6 = x + 4 6x 10 6 = x + 4 Apply the distributive property. 6x 16 = x + 4 Combine like terms. 6x x = 4 + 16 Apply addition property of equality. 5x = 20 Combine like terms.
  • 20. Now, let us do some exercises. Identify each item whether Inductive Reasoning or Deductive Reasoning. Put a check mark () under the appropriate column.
  • 21. Now, let us do some exercises. Identify each item whether Inductive Reasoning or Deductive Reasoning. Put a check mark () under the appropriate column.