Inductive and deductive reasoning, Lecture notes of Mathematics

Download Inductive and deductive reasoning and more Lecture notes Mathematics in PDF only on Docsity! Republic of the Philippines Department of Education Region XII Division of Cotabato Amas, Kidapawan City DAILY DETAILED LESSON PLAN School: MATALAM HIGH SCHOOL – JUNIOR HIGH SCHOOL Subject: MATHEMATICS Teacher: ELLEN JOY TORMIS DATE: 02/20-21/2023 CLASS/SECTION / TIME: STEM 8 : MW 7:30 – 9:30 8F : MW 7:30 – 9:30 F 1:00 – 2:00 8A : TTh 7:30 – 9:30 F 8:30 – 9:30 I. OBJECTIVES A. Content Standards The learners will demonstrate understanding of key concepts of logic and reasoning. B. Performance Standards The learners will able to communicate mathematical thinking with coherence and clarity in formulating and analyzing arguments. C. Learning Competencies/ Objectives (M8GE-IIh-1)/ The learners will use Inductive and Deductive reasoning in an argument. Cognitive: Psychomotor: a. Write conclusions to statements using inductive and deductive reasoning. Affective: b. Show appreciation on the importance of inductive and deductive reasoning in real life II. CONTENT/SUBJECT MATTER Inductive and Deductive reasoning (Continuation) III. LEARNING RESOURCES A. References 1. Teacher’s Guide pages p. 302-326 2. Learner’s Material pages 3. Textbook pages Grade 8 Mathematics (Pattern and Practicalities) by Gladys C. Nivera, PhD, p.302-324 4. Additional Materials from Learning Resource Portal http://lrmds.deped.gov.ph/. B. Other Learning Resources Grade 8 LCTG Laptop, LED TV, Powerpoint IV. PROCEDURE A. Reviewing Previous Lesson or Presenting the New Lesson A. Determine whether it applied Inductive reasoning or Deductive reasoning. Just write IR or DR. 1. Students go to school Monday to Friday. Today is Monday, so all students are in school. 2. If you are 48 inches tall, you can ride the new ride at Great America. You rode the new ride, so you are taller than 48 inches. 3.The flamingos here are all pink. All flamingos I’ve ever seen are pink. All flamingos must be pink 4. The left-handed people I know use left-handed scissors; therefore, all left- handed people use left-handed scissors. 5.Gas prices have gone down every day this week. The price of gas will go down tomorrow. B. Establishing a Purpose for the Lesson Consider the following illustrations and try to give the answer for each. ] Guide Questions: 1. Were you able to draw the correct conclusion in each activity? 2. How did you come up with your answers in Activity 1? 3. How did you come up with your conclusion in Activity 2? 4. What do you notice on each of the statement before you give your conclusions? The students will present their outputs D . Discussing New Concepts and Practicing New Skills #1 (The teacher will process the answers of the students and give further input of the topic. In activity 1, you were able to give an answer or draw a conclusion based on specific examples or events. This kind of logical reasoning is called inductive reasoning. While in activity 2, you were given general truth or facts which you utilized in making conclusion on specific situations or examples. This kind of logical reasoning is called deductive reasoning. This section will provide you an in- depth discussion about inductive and deductive reasoning. Inductive reasoning - gathers specific information, usually through observation and measurement, formulate conjecture/s, then draw generalization or conclusion based on the carefully gathered information. Example: 1. In the sequence, 10, 20, 30, …, the next term is 40. 2. John, a math challenger is good in mathematics. Joan, Josh, and Bea who are also math challengers are good in mathematics. Therefore, all math challengers are good in mathematics. 3. The chair in the living room is red. The chair in the dining room is red. Therefore, the color of the chairs in the house is red. Inductive reasoning allows you to make a general rule from specific examples. Like in example 1, you are given a sequence with first three terms are 10, 20 and 30. From these specific examples, you may then generalize that the sequence is a sequence of numbers that are divisible by or multiple of 10. Hence, you conclude that the next term is 40. - In example 2, you are given specific names of math challengers, Jim, Jane, Josh and Bea who are good in mathematics. - From these specific examples, you can then generalize that all math challengers are good in mathematics. - Similarly, in example number 3, you generalize that all chairs in the house are red as you observed that the chairs in the living and dining rooms are red. - Note however that necessary precaution should be done before making a generalization or conclusion. - For example, you may observe that a carabao is black and another carabao is black then you immediately conclude that all carabaos are black. This conclusion is wrong, because not all carabaos are black. Although most of the carabaos are black, there are some that are not. Hence, we have to be careful in making conclusion specially in using the word “All”. - In inductive reasoning, a single case that is not true will invalidate the general conclusion. Thus, analysis and investigation of different cases are important Deductive reasoning uses acceptable facts, proven theorem as proof to draw a specific case or situation. Examples: 1. Sally does not drink soft drinks. Then, it follows that she does not drink Cola. 2. All numbers ending in 0 or 5 are divisible by 5. Number 35 ends with 3. Therefore, it must be divisible by 5. 4. Right angles measure 90°. ∠𝐴 is a right angle. Therefore, ∠𝐴 measures 90°. 5. All mathematics challenge contestants are good in mathematics. Jim, Jane and Jelian are math challenge contestants. Therefore, Jim, Jane and Jelian are good in mathematics. - Deductive reasoning starts from a general statement or fact to conclude into specific example or claim. - For instance, in example 1, you are given that Sally does not drink soft drinks. Since a cola is a specific example of a soft drink, then it follows that Sally does not drink cola. - Similarly, in example 2, it is a fact that all numbers ending with 0 or 5 are divisible by 5. Since 35 is a number ending with 5, you then conclude that number 35 must be divisible by 5. - In number 3, you are given with a general statement that right angles measure 90 degrees. Knowing that ∠𝐴 is a right angle. Then the conclusion is ∠𝐴 measures 90 degrees. - Example 4 provides a general statement that all mathematics challengers are good in math since Jim Jane and Jelian are mathematics challenge contestants. Then you can specifically conclude that, Jim, Jane and Jelian are good in mathematics. Let’s try it! Complete Me! Directions: Draw a conclusion from each given situation and identify the kind of reasoning used. Write your answer on a separate sheet of paper. 1. Complementary angles are two angles whose sum is 90°. ∠𝐴 and ∠𝐵 are complementary. Therefore, ______________. 2. In the sequence 3, 6, 9, 12, … . The next number is __________. 3. All rectangles have congruent diagonals. Square is a rectangle.