Republic of the Philippines
Davao Del Norte State College
INSTITUTE OF EDUCATION
Laboratory School

LESSON DESIGN IN MATHEMATICS III

Quarter: Fourth quarter Year & Section: III- Libra and Gemini Topic: Deductive Reasoning Date: March 8, 2013 SY: 2012-2013 Time Frame: 10:00-11:00 am and 2:00-3:00 pm Cooperating Teacher: Ms. Cherry Ann Nicolas

Preparatory Activities:
|Teacher’s Activity |Student’s Activity | |Prayer: | | | | | |May I request Ms. /Mr. _________ to please lead the prayer. |In the name of the father, of the son, of the Holy Spirit. Amen. | |Energizer: |For our energizer this morning, let’s sing __________. Everybody sing!| |I am requesting Ms./Mr._____ to lead an energizer. | | | | | |Greetings: |Good morning ____________. | |Good morning class! | | | | | |Classroom Checking: | | |Before you take your seats, kindly pick up pieces of papers and | | |arrange your chairs properly. | | | | | |You may now take your seats. |Thank you ______. | | | | |Checking of Attendance: | | |Where is the class secretary? Is there anyone who is absent today? |None________. Everybody is present. | | | | |Very good! | |

Summary:
The topic focuses on the geometric application of inductive and deductive reasoning.

STAGE 1
I. Content Standard:

The students should be able to explain, discuss, solve and relate the concept of inductive and deductive reasoning by solving a series of mathematical problems and situations, then write and articulate the particulars and conclusion in a given general statement as well as provide brief explanation how does they get the pattern in solving inductive mathematical problems.

II. Performance Standard:

The students are expected to solve and a complete set statements using their previous knowledge about inductive and deductive reasoning...

...DeductiveReasoning
In order to fully understand deductivereasoning, there are certain points to be noted. First, what is the nature of deductivereasoning? Logical strength is defined as the property of an argument whose premises, if true provide support for its conclusion. Deductive and inductive arguments are also distinguished based on the point that logical strength is a matter of degree. This distinction makes it necessary to understand the nature of deductivereasoning. Therefore, deductive arguments are those whose premises guarantee the truth of the conclusion, and inductive arguments are those whose premises make it reasonable to accept the conclusion though do not absolutely guarantee its truth.
Deductivereasoning is somewhat different from an inductive argument (truth of premises doesn't guarantee the truth of conclusion) for the conclusion can't possibly be false if the premises are true. Consider the following example.
If you like listening to Metallica then you prefer rock music.
If you prefer rock music then you are a rocker.
Therefore, if you like listening to Metallica then you are a rocker.
In this argument, it can be said that the truth of the conclusion is guaranteed if its premises are true, unless at least one of the premises is false. Deductive arguments are...

...DeductiveReasoning
1.The ancient Greeks used Deductivereasoning to solve many things. They learned theses things form the Egyptians and the Babylonians. They learned how to solve geometric constructions like circles, squares, and pyramids, they also learned how to determine they lengths of objects from the Babylonians by using Pythagorean theorem. Building upon what they learned from the Egyptians and Babylonians they found fundamental truths in geometry, and from these truths they mad propositions called axioms, through deductivereasoning the Greeks would use these axioms to find new theorems that could be proven. These theorems would be used to find solutions of both practical and abstract nature.
2. Thales:
Thales of Miletus born in 624 B.C., was the first known Greek philosopher, scientist, and mathematician. After studying in Egypt, Thales was the first philosopher to introduce geometry to the Greeks. Thales discovered how to determine the height of a pyramid through indirect measurement. Thales was also credited with being the first to discover that a circle is bisected by its diameter, and the angle formed by the two radii that makes up the diameter is 180 degrees. But we have little evidence that he proved these axioms.
3. Pythagoras
Pythagoras was born on the island of the Samos in the Aegean Sea, and was a well-known Greek philosopher and mathematician, however...

...ReasoningReasoning is a method of coming to conclusions by the use of logical argument. There are three basic form of reasoning: inductive, deductive and the combination of both called inductive/deductive (Walliman & Baiche, 2001).
Inductive and DeductiveReasoning
Inductive Reasoning
Inductive reasoning is one method of reasoning that researchers use. It is based on making a conclusion or generalization based on a limited number of observations. Thus, it produces from the specific to the general. All research that makes inference or generalizations about the results of a study uses inductive reasoning (Berg & Latin, 2008).
According to American Psychological association (2009), “Inductive reasoning is the form of reasoning in which inferences and general principles are drawn from specific observations and cases. Inductive reasoning is the counter stone of scientific method in that it underlies the process of developing hypothesis from particular facts or observation” (p.246). The conclusions drawn from inductive reasoning are always probable rather than absolute and the degree of probability of any conclusion is the product of the degree of probability granted to each premise (Sprague, Stuart & Bodary, 2010).Occurrence of qualifying phrase like , ‘so it...

...Compare and Contrast the Inductive and Deductive Research Paradigm/Approaches
When underlying assumptions and intellectual structure are built upon research, observation, or development in a field of inquiry a paradigm is created. The way we perceive the world around us or the way facts and theories are established are generated in different ways. Knowledge is constantly being produced, based on assumptions or reasoning. One might see a story in the news of a shark in Southern California that attacks a surfer. A new acquired knowledge or hypothesis may arise that all Southern California sharks attack people. Is generating such a hypothesis a valid reasoning? Or if we flip it -- one could deduct from the generalized fact that if all apples are fruit and all fruits grow on trees, then all apples grow on trees. But is this hypothesis valid? How do we go about testing or generating hypotheses about different topics?
On a scientific level, knowledge and hypotheses are forever being generated or tested. One might hypothesize that "the color of a mineral is determined by its crystal structure." How could this hypothesis be tested? Through deductivereasoning, this can be done -- for the purpose of deductivereasoning is to test a hypothesis. Finding other examples to attempt to prove or disprove this hypothesis is the beginning step to reasoning out this hypothesis....

...Lindsey Lane
October 21, 2012
The Importance of DeductiveReasoning
Critical Thinking
Kevin White
It is important to understand what is known prior to making a decision because the decision could be either wrong or right. Making decisions at times can be a hard thing to do. There are many pros and cons for decision making. In argument five To Cheat or Not to Cheat Jenna has a big decision to make. She has to decide whether or not she wants to continue her class by being honest or to cheat because it will help her out in the end. Her decision can result in failure for the class or if she can prep herself to do better she can pass this class. If she doesn’t think about what the consequences can be she will turn to cheating because it is an easy escape. Making decisions can also come with consequences if you don’t make the right choice. People make choices by impulse which usually comes with a negative reward. Jenna needs to decide what is right for her rather than what Cyndi thinks she should do. If Jenna happened to cheat she would fail the class and have to retake it. Her best bet is to buckle down and do the work herself. With her making the right choice can benefit her in many ways like knowing that she did the work herself and didn’t cheat. Cheating can leave a big chip on your shoulder and she wouldn’t have that if she was honest and did her work by herself. Jenna can set aside an amount of time where she can study...

...Problem-Solving
Despite what folks accomplish as a profession or where they exist, most folks use the majority of their waking hours, at a workplace or at home, tackling situations. Most situations people challenge are little, some are substantial and complex, yet they need to be settled in a tasteful manner. There are a few definitions of a situation or how one individual may distinguish a situation. A situation is a chance for development. A situation may be a true break, the stroke of fortunes, chance thumping, an opportunity to get out of the groove of the ordinary and greatly improve the situation. A situation is the contrast between an individual present state and an individual objective state. A situation can come about because of revamped learning or supposing. At the point that a person knows where they are and where they need to be, they have a situation to fathom in getting to their objective. A situation comes about because of the acknowledgment of a present defective and the credence in the probability of a preferred fate. The function of this paper will explain the different approaches to the study of problem-solving. Explain the role of insight and creativity in the problemsolving process, analyze the dynamics of problem representation and problem solution and analyze the function of reasoning, judgment, and decision making in the...

...The Nature of Reasoning
What is Reasoning?
a mental act whereby starting with several judgments which we relate to one another.
the process which uses arguments, statements, premises and axioms to define weather a statement is true or false, resulting in a logical or illogical reasoning.
the process of using a rational, systematic series of steps based on sound mathematical procedures and given statements to arrive at a conclusion.
the cognitive skills with which we reach sound conclusions in order to make decisions and solve our daily life problems.
In logical reasoning, an if-then statement (also known as a conditional statement) is a statement formed when one thing implies another and can be written and read as "If P then Q." A contrapositive is the conditional statement created when negating both sides of the implication and can be written and read as "If not Q, then not P." Anything that is not proven is known as a conjecture.
In today’s logical reasoning three different types of reasoning can be distinguished, known as deductivereasoning, inductive reasoning and abductive reasoning based on respectively deduction, induction and abduction.
DeductiveReasoningDeductivereasoning originates from...

...an example in which you can use deductivereasoning to draw a conclusion. State the axioms or premises used to reach the conclusion.
Karen knows if she misses cheerleading practice the day before a game that she will not be able to cheer at the game.
Karen misses practice on Tuesday, the day before the game.
Karen was not allowed to cheer at Wednesday’s game.
DeductiveReasoning:
(Premises) Fact: Karen knows if she misses cheerleading practice the day before a game she will not be able to cheer at the next game.
(Premises) Fact: Karen misses cheerleading practice on Tuesday before the game on Wednesday.
Conclusion: Karen was not able to cheer at the game on Wednesday.
Facts
Facts
DeductiveReasoningDeductiveReasoning
Logical Argument
Logical Argument
Accepted Properties
Accepted Properties
Definitions
Definitions
Inductive Reasoning:
(Observation) Larry came into work late
(Observation) Larry didn’t have his lunch.
(Prior Experience) Larry always has his lunch with him when he comes to work.
Inductive Reasoning
Inductive Reasoning
(Conclusion) Larry overslept.
Verify/Modify
Verify/Modify
Conjecture
Conjecture
Pattern
Pattern
Compare and contrast inductive and deductivereasoning. Provide an example of each to illustrate the similarities and...