Problem Solving & Reasoning Chapter 3 PDF

PROBLEM SOLVING & REASONING Chapter 3 Mathematical Reasoning & Logic Puzzles PROBLEM SOLVING  Problem solving has been an integral part of the mathematics curriculum that must be taught alongside the various mathematical concepts and skills that are so necessary for succe...

PROBLEM SOLVING & REASONING Chapter 3 Mathematical Reasoning & Logic Puzzles PROBLEM SOLVING  Problem solving has been an integral part of the mathematics curriculum that must be taught alongside the various mathematical concepts and skills that are so necessary for success in school and in real life afterwards. Most occupations require good problem-solving skills. This chapter aims at helping you become a better problem solver and to show that problem solving can be an enjoyable experience. WHAT IS PROBLEM SOLVING?  In cognitive psychology, problem refers to the mental process that people go through to discover, analyze, and solve problems.  George Polya defined it as: - an act to find a way out of difficulty; - find a way around an obstacle; - find a way where none is known; and - attain a desired end that is not immediately attainable by direct means. MATHEMATICAL REASONING  All problem solving, whether in mathematics or dailylife, involves reasoning.  These problems generally present several facts that can be used together to reach a conclusion.  Combining reasoning skills with other strategies will help us find the desired solution.  There are two reasoning that will help us solve the problem. These are: INDUCTIVE REASONING and DEDUCTIVE REASONING. INDUCTIVE REASONING  The type of reasoning that forms a conclusion based on the examination of specific examples is called inductive reasoning.  The conclusion formed by using inductive reasoning is often called a conjecture, since it may or may not be correct.  When you examine a list of numbers and predict the next number in the list according to some pattern you have observed, you are using inductive reasoning. Example: MLM INDUCTIVE REASONING MLM DEDUCTIVE REASONING Another type of reasoning is called deductive reasoning. Deductive reasoning is distinguished from inductive reasoning in that it is the process of reaching a conclusion by applying general principles and procedures. DEDUCTIVE REASONING LOGIC PUZZLES A logic puzzle is derived from the mathematics field of deduction. It can be solved by using deductive reasoning and by organizing the data in a given situation. A logic puzzle is basically a description of an event or any situation. Using the clues provided, one has to piece together what actually happened.  EXAMPLE 1: SOLUTION: Each of four neighbors, Sean, Maria, Sarah, and Brian, has a different occupation (editor, banker, chef, or dentist). From the following clues, determine the occupation of each neighbor. 1. Maria gets home from work after the banker but before the dentist. 2. Sarah, who is the last to get home from work, is not the editor. 3. The dentist and Sarah leave for work at the same time. 4. The banker lives next door to Brian. EXAMPLE 2: Ana, Eva, Ramon and George were winners in the MasterChef Philippines Contest. SOLUTION: There was a winner in each of the four categories: soup, entrée, salad and dessert. From the following clues, determine which category each person was the winner. a) The soups were judged before Ramon’s winning entry. b) This year’s contest was the first for Eva and for the winner in the dessert category. Ana and the winner of the soup category entered last year’s contest. c) The winning entry took 2 hours to cook, whereas Eva required no cooking at all. EXERCISES: Logic Puzzle & Types of Reasoning 1. Determine whether each of the following arguments is an example of inductive reasoning or deductive reasoning. a) During the past 10 years, a tree has produced plums every other year. Last year the tree did not produce plums, so this year the tree will produce plums. b) All home improvements cost more than the estimate. The contractor estimated that my home improvement will cost P35,000. Thus my home improvement will cost more than P35,000. EXERCISES: Logic Puzzle & Types of Reasoning 2. The four children in the Rivera family are Reynaldo, Ramiro, Shakira, and Sasha. The ages of the two teenagers are 13 and 15 while the ages of the younger children are 5 and 7. From the following clues, determine the age of each of the children. a.Reynaldo is older than Ramiro. b.Sasha is younger than Shakira. c.Sasha is 2 years older than Ramiro. d.Shakira is older than Reynaldo.