daily lesson log for grade 8 math Week-7.2.docx

math grade 8

1. GRADE 8
DAILY LESSON
LOG
School SURABAY NATIONAL HIGH SCHOOL Grade Level 8
Teacher BEN YHAZEER S. CHIONG Learning AreaMATHEMATICS
Week 7 (November 4 - 8, 2024) Quarter SECOND
GOPHER (M, 11:00 – 111:45)GOPHER (T, 11:00 – 111:45)
I. OBJECTIVES
1.Content Standards The learner demonstrates understanding of key concepts of logic and reasoning.
2.Performance Standards The learner is able to communicate mathematical thinking with coherence and clarity in formulating and analyzing arguments.
3.Learning
Competencies /
Objectives
The learner determines the relationship between the hypothesis
and the conclusion of an if-then statement.
(M8GE-IIf-1)
1. Define conditional or if-then statement, hypothesis and
conclusion.
2. Identify the hypothesis and conclusion of an if-then
statement.
3. Write a conditional statement given the hypothesis and
conclusion.
4. Explain the reasonableness of the agreement about the
conditions under p→q which is true.
Determines the contrapositive of
an if-then statement.
(M8GE-IIg-1)
a. Identify the hypothesis and
conclusion of a conditional
statement
b. Formulate the contrapositive of
the if-then statement
c. Find pleasure in formulating the
contrapositive of the if-then
statement
Illustrates the equivalences of: (a) the
statement and its contrapositive; and
(b) the converse and inverse of a
statement.
(M8GE-IIg-2)
a. Identify the hypothesis and
conclusion of a conditional
statement
b. Formulate the converse, inverse and
contrapositive of the if-then
statement
c. Determine the logically equivalent
statements
Illustrates the equivalences of: (a) the statement and its contrapositive; and
(b) the converse and inverse of a statement.
(M8GE-IIg-2)
a. Identify the hypothesis and conclusion of a conditional statement
b. Formulate the converse, inverse and contrapositive of the if-then statement
c. Determine the logically equivalent statements
II. CONTENT
IF-THEN STATEMENTS
IF-THEN STATEMENTS
(PERFORMANCE TASK #4)
Conditional StatementsConditional StatementsConditional StatementsConditional Statements
III. LEARNING
RESOURCES
A.References
1. Teacher’s
Guide
350-357 350-357
2. Learner’s
Materials
321-324 321-327 321-327
3. Textbook Sabangan, Leticia et.al. Math Time pages 5-7Crisostomo , Ricardo M. et.al., Our World of Math 8 pages 231-234Crisostomo, Ricardo M. et.al, Our World of Math 8 pages 231-234
4. Additional
Materials
from
Learning
Resource
(LR) portal
http://www.mathgoodies.com/lessons/vol9/conditional.html
https://www.mathplanet.com/education/geometry/proof/if-then-
statement
www.mpsaz.org/mesa/staff/mjlarson/.../geom_ppt_2.1_conditional
statement.pptx
www.mpsaz.org/mesa/staff/mjlarson/.../geom_ppt_2.1_conditional
statement.pptx
B.Other Learning
Resources
Laptop, tv, visual aids
Laptop, tv, visual aids Laptop, tv, visual aids
IV. PROCEDURES
A.Reviewing
previous
lesson or
Identify the hypothesis and
conclusion in each of the following
conditionals.
Warm Up
Determine if each statement is true or
false.
5 MIN.

2. presenting
the new
lesson
A.r → t
B.If x , then y
C.If it rains , then classes
are suspended.
D.Ann will dance , if she
gets a candy.
Activity #1: Convert each
statement to if-then form, then
underline the hypothesis and
double underline the conclusion.
1. Good citizens obey rules and
regulations.
2. The sum of the measures of
complementary angles is 90◦.
3. Opposite sides of a rectangle
are parallel.
4. A quadrilateral has four sides.
5. A triangle is a polygon with
three sides.
Activity #2 Directions: Evaluate
the following statements. Use the
truth table below.
1. If a shape is a triangle, then it is
a polygon.
2. If Ana studies for her test, then
she will pass the exam.
3. If a number is even, then it is
divisible by 2.
4. If a polygon has eight sides,
then it is an octagon. 5. If a shape
is a rectangle, then it has four
sides.
1. The measure of an obtuse angle is
less than 90°.
2. All perfect-square numbers are
positive.
3. Every prime number is odd.
4. Any three points are coplanar.
Review about converting statements to the other related conditional
statements.
B.Establishin
g a
purpose
for the
lesson
Guide Question:
What have you noticed
about the hypothesis?
Conclusion?
Conditional statement is known as
if-then statements. The “if” part is the
hypothesis denoted by p, and the
“then” part is the conclusion denoted
by q.
In symbol, If p, then q.
Hypothesis tells us what is given
or what is to be assumed. Conclusion
tells us what to follow from the
assumption.
10 MIN.
Complete the table.
Statement:
Today is Tuesday, the next day is Wednesday.
C.Presenting
examples/
instances
of the
lesson
Illustrative Example:
If you get good grades,
then you will get into a good
college.
The part after the "if": you get
good grades - is called a
hypotheses and the part after the
"then" - you will get into a good
college - is called a conclusion.
A conditional statement is false if
hypothesis is true and the
conclusion is false. The example
above would be false if it said "if
you get good grades then you will
not get into a good college".
Example 2:
Given:
a: The sun is made of gas.
Example1.
Conditional Statement: If a triangle is
obtuse, then it has exactly one obtuse
angle.
Contrapositive: If a triangle has no
obtuse angle, then it is not an obtuse
triangle.
Example 2.
Conditional Statement: If two angles
are complementary, then they are
acute.
Contrapositive: If angles are not
acute, then they are not
complementary.
Example 3.
Conditional Statement: If an animal is
a cat, then it has four paws.
Analyze each statement and the truth
value of each.
Example 1.
Conditional Statement:
If it rains, then the ground is wet. (T)
Converse:
If the ground is wet, then it rained. (F)
Inverse:
If it does not rain, then the ground is
not wet.(F)
Contrapositive:
If the ground is not wet, then it did
not rain. (T)
Example 2.
Conditional Statement:
If an animal is a bird, then it has
feathers. (T)
15 MIN.
Give the equivalent statement.
1. Conditional Statement: If a triangle is obtuse, then it has exactly one obtuse
angle.
2. Conditional Statement: If two angles are complementary, then they are
acute.
3. Conditional Statement: If an animal is a cat, then it has four paws.

3. b: 3 is a prime number.
Proble
m:
Write ab as a sentence.
Then construct a truth table for
this conditional.
a b ab
T T T
T F F
F T T
F F T
In Example 2, "The sun is made of
gas" is the hypothesis and "3 is a
prime number" is the conclusion.
Note that the logical meaning of
this conditional statement is not
the same as its intuitive meaning.
In logic, the conditional is defined
to be true unless a true hypothesis
leads to a false conclusion. The
implication of ab is that: since
the sun is made of gas, this makes
3 a prime number. However,
intuitively, we know that this is
false because the sun and the
number three have nothing to do
with one another! Therefore, the
logical conditional allows
implications to be true even when
the hypothesis and the conclusion
have no logical connection.
Activity #3. Direction: Fill in the
blanks with the correct word/s that
will make the statements correct.
Contrapositive: If an animal does not
have four paws, then it is not a cat.
Example 4.
Conditional Statement: If Cardo’s
birthday is February 29, then he was
born in a leap year.
Contrapositive: If Cardo was not born
in a leap year, then his birthday was
not February 29.
Converse: If an animal has feathers,
then it is a bird. (T)
Inverse: If an animal is not a bird, then
it has no feathers.(T)
Contrapositive: If an animal has no
feathers, then it is not a bird.(T)
Example 3.
Conditional Statement: If two angles
are complementary, then their
measures add up to 90 degrees. (T)
Converse: If the measure of two
angles add up to 90 degrees, then they
are complementary.(T)
Inverse: If two angles are not
complementary, then their measure
does not add up to 90 degrees. (T)
Contrapositive: If the measure of two
angles does not add up to 90 degrees,
then they are not complementary. (T)
D.Discussing
new
concepts
and
practicing
new skills
#1
How do you distinguish the
hypothesis from the
conclusion when statement is
not in the if-then form?
Consider the three
statements below.
1.All right angles are congruent
2.Three non-collinear points
determine a plane.
How do you distinguish the
hypothesis and the
conclusion in an if-then
statement?
Can the hypothesis and
conclusion be
interchanged?
What is the importance of
determining the
hypothesis and the
How did you form the
converse, inverse and
contrapositive?
Which of the statements
have the same meaning?
Which are logically equivalent
statements?
5MIN.
How did you form the equivalent statement?
Why can you say that they are equivalent?

4. 3.Perpendicular lines are
intersecting lines.
Discuss with a partner the underlined
part of the sentence. What part of the
sentence are the underlined words.

conclusion of an if-then
form?
E.Discussing
new
concepts
and
practicing
new skills
#2
Guide Questions:
1.What have you noticed about
the statements above?
2.Take one of the statements
and tell something about it.
What is common to all of the
statements?
Give the contrapositive of “If the
measure of an angle is 90
°
, then it is a
right angle.”
Read and analyze the statements
below. Tell whether each statement is
true or false.
1. If it rains, then the ground is wet.
2. If the ground is wet, then it rained.
3. If it does not rain, then the ground
is not wet.
4. If the ground is not wet, then it did
not rain.
Tell whether each statement is true or
false.
10 MIN.
Construct the Converse, Inverse or Contrapositive of the given statement.
Statement :
Two angles that form a linear pair are supplementary.
If-Then Form:
If two angles form a linear pair, then they are supplementary.
Converse:______________ Inverse: _______________
Contrapositive:__________
F.Developin
g mastery
(Leads to
Formativ
e
Assessme
nt 3)
Identify the hypothesis and
conclusion of the following
conditional statements.
1.If we turn of the water in the
shower, then the water will
stop pouring.
Hypothesis
__________________
Conclusion
__________________
_
2.If a population consists of 50%
men then 50% of the
population must be women.
Hypothesis
__________________
Conclusion
__________________
_
3.If the quadrilateral is
equilateral, then their
diagonals are perpendicular.
Hypothesis
Give the contrapositive of “If a
polygon has three sides, then it is a
triangle.”
Which of the following statements are
equivalent?
1. If you are a guitar player, then you
are a musician.
2. If you are a musician, then you are
a guitar player.
3. If you are not a guitar player, then
you are not a musician.
4. If you are not a musician, then you
are not a guitar player.
10 MIN.
Use the given statement to complete the following.
Statement:
Two right angles are congruent.
If-Then Form: ____________________
Converse:____________
Inverse: _______________
Contrapositive:__________

5. __________________
Conclusion
__________________
_
A.
G.Finding
practical
applicatio
ns of
concepts
and skills
in daily
living.
Identify the hypothesis and
conclusion of the following
conditional statements.
1.If (x + 2)(x – 11) = 0,
then x = -2 or x = 11.
Hypothesis
__________________
Conclusion
___________________
2.If you give me 20 dollars,
then I will be your best friend.
Hypothesis
__________________
Conclusion
___________________
Give the contrapositive of “If a
polygon has four sides, then it is a
quadrilateral.”
Give the equivalent statement.
If you are a Filipino, then you have
black hair.
5 MIN.
From your answers above, determine if each statement is true or false, then
give the equivalent statement of each.

H.Making
generaliza
tions and
abstractio
ns about
the lesson
An if-then statement is
composed of two clauses: the
if-clause and the then-clause.
We can denote a letter for each
clause, p for the if-clause and q
for the then-clause. The
statement is in the form, “If p
then q”. Conditional statements
are formed by joining two
statements p and q using the
words if and then. The p
statement is called the
hypothesis and the q statement
is called the conclusion.
The conditions in which
a conditional is true are illustrated
The contrapositive of a statement is
obtained by both exchanging and
negating the hypothesis and the
conclusion.
In short,
Conditional Statement:
If p, then q.
Contrapositive:
If not q, then not p.
A conditional statement and its
contrapositive are either both true or
both false. The original conditional
statement and its contrapositive will
always have the same meaning.
Similarly, the converse and the
inverse of a conditional statement are
either both true or both false. The
converse and inverse of a conditional
statement will always have the same
meaning.
When two statements are both true
or both false, they are called
equivalent statements.
5 MIN.
Generalization:
A conditional statement and its contrapositive are either both true or both
false. The original conditional statement and its contrapositive will always
have the same meaning.
Similarly, the converse and the inverse of a conditional statement are
either both true or both false. The converse and inverse of a conditional
statement will always have the same meaning.
When two statements are both true or both false, they are called
equivalent statements.

p q p →
q
T T T
T F F
F T T
F F T

6. in the truth table below.
I.Evaluating
learning
Identify the hypothesis and
conclusion of the following
conditional statements.
1. If two even integers
are multiplied, then the product is
also even.
Hypothesis
__________________
Conclusion
___________________
2. If the quadrilaterals are
rectangle, then the quadrilaterals
are equiangular.
Hypothesis
__________________
Conclusion
___________________
3. If the triangles are
equilateral, then the triangles are
isosceles.
Hypothesis
__________________
Conclusion
___________________
Look for a partner. Create an if-then
statement. It may be based from your
experiences, definitions, postulates or
rules. Write its contrapositive
statement.
Write the converse, inverse, and
contrapositive of the conditional
statement “If two angles are
congruent, then they have the same
measure.” Find the truth value of each
and give the equivalent statements.
25 MIN
SUMMATIVE TEST #3
J.Additional
activities
for
applicatio
n or
remediati
on.
Follow up:
1.Identify the hypothesis
and conclusion of the following
conditional statements.
a.If polygons are regular,
then the polygons are
equilateral.
b.If I get my bonus, then I
will buy a new bag.
2.Study:
Inverse, Converse and Contrapositive
of an if-then statement.
Give the contrapositive of “If the
perimeter of a square is 56 cm, then
each side is 14 cm long.”
Write the converse, inverse, and
contrapositive of the conditional
statement “If two angles are a
linear pair, then they are
supplementary.” Find the truth value
of each and give the equivalent
statements.
V. REMARKS
VI. REFLECTION
1.No.of learners who
earned 80% on the

7. formative assessment
2.No.of learners who
require additional
activities for
remediation.
3.Did the remedial
lessons work? No.of
learners who have
caught up with the
lesson.
4.No.of learners who
continue to require
remediation
5.Which of my teaching
strategies worked well?
Why did these work?
6.What difficulties did I
encounter which my
principal or supervisor
can help me solve?
Prepared By:BEN YHAZEER S. CHIONG
Teacher-III
Checked By: Attested By: Noted By:
ARNOLD C. AYAON VENJIE G. BALIDAD RIZA D. MORADOS
Master Teacher I Head Teacher III Principal IV