This document provides a daily lesson log for an 8th grade mathematics class that focuses on teaching students about if-then statements, their converse, inverse, and contrapositive. The lesson log outlines the objectives, content standards, learning competencies, procedures, activities and assessments that will be used across a week to ensure students understand how to determine and illustrate the relationships between conditional statements and their logic equivalents. The formative and summative assessments are aimed at measuring whether students have mastered the ability to write out conditional statements and their forms, determine truth values, and illustrate the equivalences between statements and their contrapositives or converses and inverses.

1. GRADE 8
DAILY LESSON LOG
SCHOOL GRADE LEVEL Eight (8)
TEACHER GROUP 1, SECTON 1 LEARNING AREA Mathematics
TEACHING DATES AND TIME QUARTER Second -Geometry
Monday Tuesday Wednesday Thursday Friday
Objectives Objectives must be met over the week and connected to the curriculum standards. To meet the objectives necessary procedures must be
followed and if needed, additional lessons, exercises, and remedial activities may be done for developing content knowledge and competencies.
These are assessed using Formative Assessment strategies. Valuing objectives support the learning of content and competencies and enable
children to find significance and joy in learning the lessons. Weekly objectives shall be derived from the curriculum guides.
A. Content Standard The learner demonstrates understanding of key concepts of logic and reasoning.
B. Performance Standard The learner is able to communicate mathematical thinking with coherence and clarity in formulating and analyzing arguments.
C. Learning Competency
The learner
36. determines the inverse,
converse, and
contrapositive of an
if-then statement.
M8GE-IIg-1
37. illustrates the
equivalences of:
(a) the statement and
its
contrapositive; and
(b) the converse and
inverse of a
statement.
M8GE-IIg-2
Objectives
M8GE-IIg-1
At the end of the session,
learners will be able to:
 Determine the
inverse, converse, and
contrapositive of an
if-then statement.
M8GE-IIg-1
 Write the inverse, converse, and
contrapositive of an if-then
statement and determine which
are true and which are false.
M8GE-IIg-2
 Illustrate the
equivalences of:
(a) the statement
and its
contrapositive;
and
M8GE-IIg-2
 Illustrate the
equivalences of:
(b) the converse
and
inverse of a
statement.
SUMMATIVE TEST
 100% of the class will
be able to get at least
75% correct items in
the test.
 Appreciate the value
of honesty.
CONTENT
Content is what the lesson is all about. It pertains to the subject matter that the teacher aims to teach in the CG, the content can be tackled in a
week or two.
REASONING: If-Then Statement, Converse, Inverse and Contrapositive

2. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
LEARNING RESOURCES
A. References Mathematics 8 Mathematics 8 Mathematics 8 Mathematics 8
1. Teacher’s Guide pages 355 - 357 355 - 357 355 - 357 355 - 357
2. Learner’s Materials
pages
321 - 327 321 - 327 321 - 327 321 - 327
3. Textbook pages
4. Additional Materials
from Learning
Resource portal
MTAP review materials MTAP review materials MTAP review materials MTAP review materials
B. Other Learning
Resource
Geometry by Edna B. Zuela & Luis Allan B. Melosantos
PP 8-21 PP 8-21 PP 8-21 pp 8-21
Geometry based on the 2002 BEC by Jose Marasigan & Antonio C. Coronel
Pp 79-81 Pp 79-81 Pp 79-81 Pp 79-81 pp
PROCEDURES
These steps should be done across the week. Spread out the activities appropriately so that students will learn well. Always be guided by
demonstration of learning by the students which you can infer from formative assessment activities. Sustain learning systematically by
providing students with multiple ways to learn new things, practice their learning, question their learning processes, and draw conclusions about
what they learned in relation to their life experiences and previous knowledge. Indicate the time allotment for each step.
Reviewing previous lesson
or presenting the new
lesson
Pre-assigned: Let students
write on their journal
notebook a personal wish
or condition in an “if-then”
statement.
Students group themselves
by and share what they
have written.
*Each group will choose 1
statement and present to the
whole class.
State the converse,
inverse, and contrapositive
of this statement:
If you are a lawyer, then
you passed the bar exam.
Recall the process of
writing the inverse,
converse, and
contrapositive of each
conditional.

3. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
Establishing a purpose for
the lesson
To learn key concepts on
writing the inverse,
converse, and contrapositive
of an if-then statement.
To determine the truth
value of the statement
To illustrate the
equivalences of the
statement and its
contrapositive.
To illustrate the
equivalences of the
converse and inverse of a
statement.
Presenting examples/
Instances of the new
lesson
Explain that each statement
can be re-stated to mean the
same thought.
Take 1 from the students’
examples.
If I get a 90 in math, then my
parents would buy me a new
cellphone.
Guide the class in formulating
the other forms:
*put “NOT” of each part of the
statement;
*interchange the if part and the
then part;
*put “NOT” on each part of
the third statement.
Using the statements deal
with in the previous
meeting, students will be
guided on evaluation
whether the statement is
true or false
1. If two angles are
congruent, then they
have the same
measure.
2. If you live in Manila,
then you live in the
Philippines.
3. If you drink milk, then
you grow.
Present and discuss the
example:
Statement
A triangle is a polygon.
If-then form
If an object is a triangle,
then it is a polygon.
Converse
If an object is a polygon,
then it is a triangle.
Inverse
If an object is not a triangle,
then it is not a polygon.
Contrapositive
If an object is not a
polygon, then it is not a
triangle.
Present and discuss the
example:
Statement
A triangle is a polygon.
If-then form
If an object is a triangle,
then it is a polygon.
Converse
If an object is a polygon,
then it is a triangle.
Inverse
If an object is not a triangle,
then it is not a polygon.
Contrapositive
If an object is not a polygon,
then it is not a triangle.
Teacher -made test will be
used
Discussing new concepts
and practicing new skills #
1
Introduce the names/terms
used for each form of the
statement:
If p then q : conditional
If q then p : converse
If not p then not q : inverse
If not q then not p :
contrapositive
Discuss the meaning of
truth value:
If the statement is always
true, then the true value is
TRUE.
If a statement is true but
sometimes false, the truth
value is FALSE.
Illustrate the equivalences of
the statement and its
contrapositive.
If-then form
If an object is a triangle,
then it is a polygon.
Contrapositive
If an object is not a polygon,
then it is not a triangle.
Illustrate the equivalences
of the converse and
inverse of a statement.
Converse
If an object is a polygon,
then it is a triangle.
Inverse
If an object is not a triangle,
then it is not a polygon.

4. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
Discussing new concepts
and practicing new skills #
2
Let students write the three
forms of statement of the
conditionals they have
written.
With the statements
students wrote the previous
meeting, let them do
brainstorming of the truth
value of each form of the
statement.
Illustrate the equivalences
of the statement and its
contrapositive.
If two angles are
congruent, then they have
the same measure.
Illustrate the equivalences
of the converse and
inverse of a statement.
If two angles are
congruent, then they have
the same measure.
Developing mastery
(leads to Formative
Assessment )
A. Fill up the table.
Statement
Converse
Inverse
Contrapositive
Statements:
1. If two angles are
congruent, then they
have the same measure.
2. If two points lie in a
plane, then the line
containing them lies in
the plane.
3. If you live in Manila,
then you live in the
Philippines.
4. If you drink milk, then
you grow.
5. If a triangle is a right
triangle, then one of its
interior angles is a 90-
degree angle.
On the table which they
did the previous meeting,
add a third column and
evaluate the truth value of
each statement.
Statement
Converse
Inverse
Contrapositive
1. If two angles are
congruent, then they
have the same
measure.
2. If two points lie in a
plane, then the line
containing them lies in
the plane.
3. If a triangle is a right
triangle, then one of
its interior angles is a
90-degree angle.
Rewrite each conditional
statement in if-then form
and state its contrapositive.
1. A rectangle is a
parallelogram with
four right angles.
2. 2𝑥 − 3𝑥 =
6 𝑖𝑚𝑝𝑙𝑖𝑒𝑠 𝑥 = −6.
3. A triangular prism is a
polyhedron with two
triangular bases that
are congruent and
parallel.
4. Skew lines are
noncoplanar lines.
5. If a number ends in
either 0 or 5, then it is
divisible by 5.
Rewrite each conditional
statement in if-then form
and state its converse and
inverse
1. A rectangle is a
parallelogram with
four right angles.
2. 2𝑥 − 3𝑥 =
6 𝑖𝑚𝑝𝑙𝑖𝑒𝑠 𝑥 = −6.
3. A triangular prism is a
polyhedron with two
triangular bases that
are congruent and
parallel.
4. Skew lines are
noncoplanar lines.
5. If a number ends in
either 0 or 5, then it is
divisible by 5.

5. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
Finding practical
application of concepts
and skills in daily living
In your daily life experience,
make a conditional statement
and share its truth value and
make judgments or sound
decision
Give real-life situation
related to the topic that
shows equality
Making generalizations
and abstractions about the
lesson
How can you determine
the inverse, converse, and
contrapositive of a
conditional?
The converse of a
conditional is formed by
interchanging the
hypothesis and the
conclusion.
The inverse of a
conditional is formed by
negating both the
hypothesis and the
conclusion.
The contrapositive of
a conditional is formed
by interchanging the
hypothesis and the
conclusion and negating
both.
Let students share reflections
& realization by answering
the guide questions:
When the conditional is true,
are the other forms of the
statement always true?
And vice versa.
How can you illustrate the
equivalences of the
statement and its
contrapositive?
To easily rewrite a
statement and its
contrapositive.
Given statement:
If p, then q.
Contrapositive:
If not q, then not p.
To form the contrapositive
of a conditional statement,
first, get its inverse, Then,
interchange its hypothesis
and conclusion.
If a statement is true, its
contrapositive is also true.
How can you illustrate the
equivalences of the
converse and inverse of a
statement?
To easily rewrite a
statement and its
contrapositive.
Given statement:
If p, then q.
Inverse:
If not p, then not q.
Converse:
If q, then p.

6. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
A. Evaluating learning State the converse,
inverse, and contrapositive
of the following
statements.
1. If you live in Davao,
then you live in
Mindanao.
2. If you live in Cebu, then
you live in Visayas.
3. If you have a fever, then
you are sick.
4. If you finish a
marathon, then you
have strong legs.
5. If you are a horse, then
you do not know how to
fly.
Evaluate the following
statements according to
its truth value.
1. If your age is 14, then
you are too young to
vote.
2. If two angles are
vertical, then they are
congruent.
3. If two angles form a
linear pair, then the
angles are
supplementary.
4. If a point is in the
interior of an angle,
then it cannot be in its
exterior.
5. If a triangle is obtuse,
then it has two acute
angles.
Illustrate the equivalences
of the statement and its
contrapositive.
1. If m∠A + m∠B = 90,
then ∠A and ∠B are
complementary.
2. If m∠A < 90, then ∠A
is an acute angle.
3. If you are in El Nido,
then you are in Palawan.
4. If two line segments
have the same length,
then they are congruent.
5. If you are a second year
high school student,
then you are a
sophomore.
Illustrate the equivalences
of the converse and inverse
of a statement.
1. If m∠A + m∠B = 90,
then ∠A and ∠B are
complementary.
2. If m∠A < 90, then ∠A
is an acute angle.
3. If you are in El Nido,
then you are in Palawan.
4. If two line segments
have the same length,
then they are congruent.
5. If you are a second year
high school student,
then you are a
sophomore.
B. Additional activities
for application or
remediation
Think About This
Is the inverse of a
conditional always true?
Is the contrapositive
of a conditional always
true?
From the given example,
illustrate the equivalences
of the converse and inverse
of a statement.

7. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
REMARKS
REFLECTION
A. No. of learners who
earned 80% in the
evaluation
B. No. of learners who
require additional
activities for
remediation who
scored below 80%
C. Did the remedial
lessons work? No. of
learners who have
caught up with the
lesson
D. No. of learners who
continue to require
remediation
E. Which of my teaching
strategies worked
well? Why did these
work?
F. What difficulties did I
encounter which my
principal or supervisor
can help me solve?
G. What innovation or
localized materials did
I use/discover which I
wish to share with
other teachers?