7 e’s DETAILED LESSON PLAN
I.
OBJECTIVES
At the end of the lesson the students must be able to:
1. distinguish between inductive and deductive reasoning
2. use inductive or deductive reasoning in an argument
3. distinguish between a direct and an indirect proof
4. take and pass the test with mastery level of 75%
II.
CONTENT
A. Topic: Mathematical Reasoning
B. Subject Integration: English
III.
LEARNING RESOURCES
A. Materials Needed: Power point presentation, videos
B. References: Math World 8; pp.
PROCEDURE
Teachers Activity
Students Activity
A. Introductory Activity
- Greetings
Good afternoon student
How are you today?
-
-
Good afternoon ma’am
Good, Ma’am
Prayer
To formally start our class discussion this afternoon let us
stand for the prayer
Checking of attendance
Now for your attendance let me check if you are present or not
and say present as I call your name.
B. ELICIT
Review
This afternoon let us review your lesson last discussion
Who can recall you’re the lesson?
What is conditional statement?
(Teacher will mention the name of a student who will answer)
Okay very Good
Like for example we have;
Write each statement in if-then form
1. Sixteen-year-olds are eligible to drive
Ma’am our lesson last meeting
is about Conditional Statement.
Conditional Statement or an
if-then statement is a
combination of two statements ---p, which is called the
hypothesis or premise, and q,
which is called the conclusion.
Such statements are also called
an implication.
-if you are sixteen years old
then you are eligible to drive
C. ENGAGE
Explore and Learn
Looking at the Illustration what can you see about it?
Patterns exist in nature such as those of snowflakes, beehives,
leaves, and dunes. People have long analyzed patterns and
made conclusion about them. In mathematics, you also need to
analyzed number patterns and form conclusions about them. In
mathematics, you also need to analyze number patterns and
form conclusion based on the given information.
D. EXPLORE
ACTIVITY
Describe the pattern in the sequence. Then determine the next number
in the sequence.
a. 3, 6, 9, 12 …
b. 5.15.45.135…
What do you think would be the next number in the sequence for letter
A?
What do you think would be the next number in the sequence for letter
B?
How do you come up with that answer?
What operation do you use to determine the next number in the
sequence?
Okay very good
Explanation:
a. To get the second term in the sequence, add 3 to the first term;
that is, 3+3=6.
To get third term, add 3 to the second term; that is 6+3=9
To get the fourth term, add 3 to the third term; that’s is
9+3=12
The pattern is to add 3 to the previous term to get the current
term.
Therefore, the next term is 12+3=15.
b. Notice that 15 is 3 times 5, which is the number just before15.
Also, 45 is 3 times 15 which is the number just before 45.
Similarly, 135 is 3 times 45.
The pattern is to multiply the previous term by 3 to get the
Snowflakes, beehives, leaves
and dunes.
15
405
Addition and Multiplication
current
Hence, the next number, must be 135(3) =405.
Now you already know how to determine the next pattern in
the sequence.
Do you find it hard class in determining the next number in the
sequence?
Okay, Very well said.
E. EPLAIN
This afternoon class we will going to discuss the
topic about Mathematical Reasoning which really
focuses on the following objectives; first is to
distinguish between inductive and deductive
reasoning, second use inductive or deductive
reasoning in an argument, next distinguish between a
direct and an indirect proof and lastly how write a
direct and an indirect proof.
In this lesson we were tackle the inductive and the
deductive reasoning on how to distinguish these
mathematical reasoning.
Inductive reasoning which define as the process of
observing data, recognizing patterns and making
generalizations or conjectures about the patterns. It is
a kind of reasoning that forms general rules from the
specific examples.
If you have remember earlier in your activity we
tackle about the patterns or the sequence of the
number that is one of an example for inductive
reasoning.
Another example for inductive reasoning
Note that conjecture formed through induction may or may not be true.
It is possible that the conjecture is true for some cases only.
 Data: I see fireflies in my backyard every summer.
Hypothesis: This summer, I will probably see fireflies in my
backyard.
 Data: Every dog I meet is friendly.
Hypothesis: Most dogs are usually friendly.
 Data: I tend to catch colds when people around me are sick.
Hypothesis: Colds are infectious.
It is foe the reason that inductive reasoning alone is not accepted as a
valid logical argument, however, inductive reasoning is still a valuable
tool in mathematics. In fact, in many cases, it is through inductive
No Ma’am
reasoning that many mathematical properties were discovered.
Another type of reasoning used in mathematics is
Deductive reasoning is a process of showing that certain statement
follow logically from agreed upon assumption (axioms) and/or proven
facts (theorems). It is kind of reasoning that proves specific statements
from general rules.
Example:
What can you conclude about the following statements?
a. Statement 1: All humans are mortal.
Statement 2: Socrates is human.
Conclusion: Socrates is Mortal
Solutions:
a. Socrates is a “specific example “of a human being
therefore, Socrates must possess the accepted
characteristic of all humans: they are mortal. Hence, you
can conclude that Socrates is mortal.
Here are some examples of deductive reasoning:



Major premise: All mammals have backbones.
Minor premise: Humans are mammals.
Conclusion: Humans have backbones.
Major premise: All birds lay eggs.
Minor premise: Pigeons are birds.
Conclusion: Pigeons lay eggs.
Major premise: All plants perform photosynthesis.
Minor premise: A cactus is a plant.
Conclusion: A cactus performs photosynthesis.
Now identify the kind of reasoning used in each scenario.
a. Carol had corned beef for lunch for the last 4 days. Therefore,
carol will have corned beef for lunch today.
b. Aileen buys only green bags. She bought a new bag yesterday.
Therefore, that bag must be green.
Solutions :
a. Inductive reasoning
b. Deductive reasoning
Mathematical proofs lie at the foundations of mathematics. The truth
of each claim or conjecture may be proven directly or indirectly.
Direct proof- is an argument that employs deductive reasoning. You
begin with the given information or premises that are assumed to be
true, and from there, take logical steps toward establishing the
conclusion by applying postulates, theorems, or definitions.
Indirect Proof-involves assuming that the negation of the conclusion
is true. If the succeeding deductive arguments lead to a contradiction,
then the original statement is proven to be true.
F. ELABORATE
In Mathematical reasoning always remember
Now determine the kind of reasoning used in the following cases:
1. Team star and Team Moon played a basketball game. The
winning team in that game will play against Team Sun on the
next game. Team Sun will play against Team Star on the next
game. Therefore, Team Moon lost to Team Star in the game.
2. Lea finished her first 5 exams in half the allotted time.
Therefore, she will finish the sixth exam in half the allotted
time.
G. EVALUATION
Describe the patterns and determine the next entry in each
sequence.
Pattern
Next Entry
Triangle, quadrilateral,
1.
2.
pentagon,…
3, 0, 3, 0, 0, …
3.
4.
7, 9,13,19,27,…
5.
6.
(January 2, February 4,
7.
8.
March 6, April 8, …)
9. Every Friday, the Quianzon family eats pizza. Today is Friday.
Therefore, Quianzon Family will eat pizza.
10. If a triangle is equilateral, then it is an acute triangle. Triangle
ABC is equilateral. Therefore, it is an acute triangle.
H. EXTEND
Assignment:
1. Give an example of a scenario in which deductive
reasoning is used. (At least 5 examples)
Prepared by: RACHEL ANN S. ARZAGA
Student Teacher
Checked by: MS. RHEA HANNELLE BAGUIORO
Critique Teacher