Download Inductive,Deductive Reasoning and Polya's Problem Solving Strategy and more Slides Mathematics in PDF only on Docsity!
INDUCTIVE AND DEDUCTIVE
REASONING,
RECREATIONAL PROBLEMS USING
MATHEMATICS
&
POLYA’S PROBLEM SOLVING
At the end of this lesson, you should be able to: 1.Define Inductive and Deductive reasoning.2. Differentiate deductive and inductive reasoning3. Use Inductive and Deductive to make conjecture.4. Solve problems involving patterns and problems following Polya’s Strategy.5. To become a better solver. LEARNING OBJECTIVES: Use Inductive Reasoning to Predict a Number a. 3,6,9,12,15,___? b. 1,3,6,10,15,___?18 2 1 Use Inductive Reasoning to make a Conjecture • Consider the following procedure : 1. Pick a number 2. Multiply the number by 8 3. Add 6 to the product 4. Divide the sum by 2 5. And subtract 3. • Use inductive reasoning to make a conjecture about the realtionship between the size of the esulting number and the size of the original number. SOLUTION: Original number: Multiply by 8: Add 6: Divide by 2: Subtraxt 3: 5 8 x 5 = 40 40 + 6 = 46 40 ÷ 2 = 23 - 3 = 20 DEDUCTIVE REASONING From general information to specific conclusion Concluding a specific fact out of the general information EXAMPLE 1: 1st Premise: All number ending in 0 or 5 are divisible by 5 2nd Premise: The number 35 ends with 5. Conclusion: Therefore, 35 is divisible by 5. EXAMPLE 2: 1st Premise: All squares are rectangles 2nd Premise: All rectangles have 4 sides Conclusion: Therefore, All square have 4 sides. LOGIC PUZZLES can be solved by using deductive reasoning and a chart that enables us to display the given information in a visual manner SOLVE LOGIC PUZZLE 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. X(1) X(1) 2.Sarah, who is the last to get home from work, is not the editor. X(2 ) 3. The dentist and Sarah leave for work at the same time. X(3) 4.The banker lives next door to Brian. X(4) X ✓ X X X ✓ X X ✓ X✓ Sean is the banker, Maria is the editor, Sarah is the chef, and Brian is the dentist EXERCISES: This type of reasoning that uses specific examples to reach a general conclusion is called _______________?Inductive Reasoning _______________?it is distinguished from Inductive Reasoning in that it is the process of reaching a conclusion by applying general principles and procedures. Deductive Reasoning TOWER OF HANOI!
https: Awww. mathsisfun.com/games/towerofhanoci.htm|
The tower of Hanoi is a logical puzzle, frequently studied in
cognitive psychology and used as a test af problem - solving
ability, consisting of three pegs, on one of which are placed a
number of discs of varying diameter, the largest at the bottom and
the smallest at the top.
POLYAS
PROBLEM
SOLVING
STRATEGY
~\-
One of the foremost recent mathematicians to make
a study of problem solving was
George Polya (1887-1985).
He was born in Hungary and moved to the United States in 1940.
In his book
How to Solve It”, George Polya enumerates the four steps of
problem -solving
EXAMPLE:
Apply Polya's Strategy
TRIANGLE CIRCLE SQUARE MATH GAME
A+A +A=30
A:+®@ a Ig
@-
A:®@ +i= ?
Step 1: Understand the problem
TRIANGLE CIRCLE SQUARE MATH GAME
Step 2: Devise a plan
>Lett=Py 1@ s=[] Seta lel
TRIANGLE CIRCLE SQUARE MATH GAME
A‘: A +A4=30 eco
A+ 1 ey rier e—k tsi AGA a ES
