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Do Now

Do Now. Set your homework assignment on your desk ready to be stamped. Solve for x. Give a reason for each step. 3(2x + 1) + 2(2x + 1) + 7 = 42 – 5x. Homework questions?. Deductive Reasoning. Today’s Objectives. Explain the difference between inductive and deductive reasoning.

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Do Now

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  1. Do Now • Set your homework assignment on your desk ready to be stamped. • Solve for x. Give a reason for each step. 3(2x + 1) + 2(2x + 1) + 7 = 42 – 5x

  2. Homework questions?

  3. Deductive Reasoning

  4. Today’s Objectives • Explain the difference between inductive and deductive reasoning. • Judge the validity of conditional statements, including the biconditional. • Use the deductive reasoning process. • Use Problem Solving Skills

  5. Deductive Reasoning • Involves logic and orderly reasoning from accepted truths. • Ex: “Explaining your reasoning” in the do now • Based on accepted truths or facts • Always leads to accurate conclusions

  6. Example • <A and <B are complementary, m<A = 25o. What is m<B? • 65o • What type of reasoning do you use? • Deductive Reasoning

  7. Investigation: Overlapping Segments • In each segment, AB ≅ CD • Step 1: From the markings on each diagram, determine the lengths of AC and BD. What do you discover about these segments? • Step 2: Draw a new segment. Label it AD. Place your own points B and C on AD so that AB ≅ CD • Step 3: Measure AC and BD. How do these lengths compare?

  8. Investigation: Overlapping Segments • Step 4: Complete the conclusion of this conjecture: If AD has points A, B, C, and D in that order with AB ≅CD, then ___________________ • The overlapping segments AC and BD are congruent.

  9. Inductive or Deductive? • Every Monday so far this year, Erick eats an apple during lunch. This Monday, he is going to eat an apple during lunch. • Mr. Castillo is older than Ms. Reynoso. Ms. Reynoso is older than Ms. Forsyth. Therefore, Mr. Castillo is older than Ms. Forsyth.

  10. Inductive or Deductive? • Valery has longer hair than Angelica. Angelica has longer hair than Edgar. So, Valery has longer hair than Edgar. • When we walk into Geometry class, Ms. Forsyth gives us raffle tickets. Today we have Geometry class, so Ms. Forsyth is going to give us raffle tickets.

  11. Inductive or Deductive? • In order to teach Geometry, you have to have a teaching credential. Ms. Forsyth teaches Geometry. She must have a teaching credential. • All college students must have a High School Diploma or GED. Alex is a college student. So he either has a High School diploma or a GED.

  12. Practice

  13. Today’s Objectives • Explain the difference between inductive and deductive reasoning. • Judge the validity of conditional statements, including the biconditional. • Use the deductive reasoning process. • Use Problem Solving Skills

  14. Exit Slip • Explain the difference between inductive and deductive reasoning. • Give an example of inductive reasoning. • Give an example of deductive reasoning. • Which type of reasoning and why? To be a game designer you have to go to an art institute. Edgar is a game designer. He must have gone to an art institute.

  15. Do Now • Set your homework assignment on your desk ready to be stamped. • Solve for x. Give a reason for each step. 3(2x + 1) + 2(2x + 1) + 7 = 42 – 5x

  16. Exit Slip Error Analysis

  17. Homework questions?

  18. Deductive Reasoning

  19. Today’s Objectives • Explain the difference between inductive and deductive reasoning. • Judge the validity of conditional statements. • Use the deductive reasoning process. • Use Problem Solving Skills

  20. Deductive Reasoning • Involves logic and orderly reasoning from accepted truths. • Ex: “Explaining your reasoning” in the do now • Based on accepted truths or facts • Always leads to accurate conclusions

  21. Example • <A and <B are complementary, m<A = 25o. What is m<B? • 65o • What type of reasoning do you use? • Deductive Reasoning

  22. Investigation: Overlapping Segments • In each segment, AB ≅ CD • Step 1: From the markings on each diagram, determine the lengths of AC and BD. What do you discover about these segments? • Step 2: Draw a new segment. Label it AD. Place your own points B and C on AD so that AB ≅ CD • Step 3: Measure AC and BD. How do these lengths compare?

  23. Investigation: Overlapping Segments • Step 4: Complete the conclusion of this conjecture: If AD has points A, B, C, and D in that order with AB ≅CD, then ___________________ • The overlapping segments AC and BD are congruent.

  24. Inductive or Deductive? • Valery has longer hair than Angelica. Angelica has longer hair than Edgar. So, Valery has longer hair than Edgar. • When we walk into Geometry class, Ms. Forsyth gives us raffle tickets. Today we have Geometry class, so Ms. Forsyth is going to give us raffle tickets.

  25. Inductive or Deductive? • In order to teach Geometry, you have to have a teaching credential. Ms. Forsyth teaches Geometry. She must have a teaching credential. • All college students must have a High School Diploma or GED. Alex is a college student. So he either has a High School diploma or a GED.

  26. Inductive or Deductive? • Every Monday so far this year, Erick eats an apple during lunch. This Monday, he is going to eat an apple during lunch. • Mr. Castillo is older than Ms. Reynoso. Ms. Reynoso is older than Ms. Forsyth. Therefore, Mr. Castillo is older than Ms. Forsyth.

  27. Practice

  28. Today’s Objectives • Explain the difference between inductive and deductive reasoning. • Judge the validity of conditional statements. • Use the deductive reasoning process. • Use Problem Solving Skills

  29. Exit Slip • Explain the difference between inductive and deductive reasoning. • Give an example of inductive reasoning. • Give an example of deductive reasoning. • Which type of reasoning and why? To be a game designer you have to go to an art institute. Edgar is a game designer. He must have gone to an art institute.

  30. Do Now • Set your homework assignment on your desk ready to be stamped. • Solve for x. Give a reason for each step. 3(2x + 1) + 2(2x + 1) + 7 = 42 – 5x

  31. Exit Slip Error Analysis

  32. Homework questions?

  33. Deductive Reasoning

  34. Today’s Objectives • Explain the difference between inductive and deductive reasoning. • Judge the validity of conditional statements. • Use the deductive reasoning process. • Use Problem Solving Skills

  35. Deductive Reasoning • Involves logic and orderly reasoning from accepted truths. • Ex: “Explaining your reasoning” in the do now • Based on accepted truths or facts • Always leads to accurate conclusions

  36. Example • <A and <B are complementary, m<A = 25o. What is m<B? • 65o • What type of reasoning do you use? • Deductive Reasoning

  37. Investigation: Overlapping Segments • In each segment, AB ≅ CD • Step 1: From the markings on each diagram, determine the lengths of AC and BD. What do you discover about these segments? • Step 2: Draw a new segment. Label it AD. Place your own points B and C on AD so that AB ≅ CD • Step 3: Measure AC and BD. How do these lengths compare?

  38. Investigation: Overlapping Segments • Step 4: Complete the conclusion of this conjecture: If AD has points A, B, C, and D in that order with AB ≅CD, then ___________________ • The overlapping segments AC and BD are congruent.

  39. Inductive or Deductive? • Valery has longer hair than Angelica. Angelica has longer hair than Edgar. So, Valery has longer hair than Edgar. • When we walk into Geometry class, Ms. Forsyth gives us raffle tickets. Today we have Geometry class, so Ms. Forsyth is going to give us raffle tickets.

  40. Inductive or Deductive? • In order to teach Geometry, you have to have a teaching credential. Ms. Forsyth teaches Geometry. She must have a teaching credential. • All college students must have a High School Diploma or GED. Alex is a college student. So he either has a High School diploma or a GED.

  41. Inductive or Deductive? • Every Monday so far this year, Erick eats an apple during lunch. This Monday, he is going to eat an apple during lunch. • Mr. Castillo is older than Ms. Reynoso. Ms. Reynoso is older than Ms. Forsyth. Therefore, Mr. Castillo is older than Ms. Forsyth.

  42. Practice

  43. Today’s Objectives • Explain the difference between inductive and deductive reasoning. • Judge the validity of conditional statements. • Use the deductive reasoning process. • Use Problem Solving Skills

  44. Exit Slip • Explain the difference between inductive and deductive reasoning. • Give an example of inductive reasoning. • Give an example of deductive reasoning. • Which type of reasoning and why? To be a game designer you have to go to an art institute. Edgar is a game designer. He must have gone to an art institute.

  45. Do Now • Set your homework assignment on your desk ready to be stamped. • Solve for x. Give a reason for each step. 3(2x + 1) + 2(2x + 1) + 7 = 42 – 5x

  46. Exit Slip Error Analysis

  47. Homework questions?

  48. Deductive Reasoning

  49. Today’s Objectives • Explain the difference between inductive and deductive reasoning. • Judge the validity of conditional statements. • Use the deductive reasoning process. • Use Problem Solving Skills

  50. Deductive Reasoning • Involves logic and orderly reasoning from accepted truths. • Ex: “Explaining your reasoning” in the do now • Based on accepted truths or facts • Always leads to accurate conclusions

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