MATH 8 QUARTER 3-WEEK 1

1. GRADE 8
DAILY LESSON
LOG
School Grade Level EIGHT (8)
Teacher JAYPEE S. COLIS Learning Area MATHEMATICS
Teaching Dates and Time April 24-28, 2023 Quarter 3RD
SESSION 1 SESSION 2 SESSION 3 SESSION 4
I. 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 axiomatic structure of geometry and
triangle congruence.
The learner demonstrates
understanding of key concepts of
axiomatic structure of geometry and
triangle congruence.
The learner demonstrates understanding of
key concepts of axiomatic structure of
geometry and triangle congruence.
The learner demonstrates understanding
of key concepts of axiomatic structure of
geometry and triangle congruence.
B. Performance
Standard
The learner is able to formulate an organized
plan to handle a real-life situation.
The learner is able to formulate an
organized plan to handle a real-life
situation
The learner is able to formulate an
organized plan to handle a real-life situation
The learner is able to formulate an
organized plan to handle a real-life
situation
C. Learning
Competency/
Objectives
Write the LC code for
each.
Learning Competencies: The learner
1. describes a mathematical system
M8GE-IIIa-1
Specific Objectives: At the end of the session,
at least 80% of the students will be able to
1. describe correctly the mathematical system
using a graphic organizer
2. formulate a real-life example/situation of a
postulate and a theorem
3. participate actively in the group activity and
in the discussion
Learning Competencies: The
learner
1. illustrates the need for an
axiomatic
structure of a mathematical
system in
general, and in Geometry in
particular
(a) undefined terms; (b) define
terms;
(c) postulates, and (d) theorems
M8GE-IIIa-c-1
Specific Objectives: At the end of
the
session, at least 80% of the
students
will be able to
1. describe correctly the undefined
terms: point. line, and plane
2. identify whether the given object
represents a point, a line, or a
Learning Competencies: The learner
1. illustrates the need for an axiomatic
structure of a mathematical system in
general, and in Geometry in particular
(a) undefined terms; (b) define terms;
(c) postulates, and (d) theorems
M8GE-IIIa-c-1
Specific Objectives: At the end of the
session, at least 80% of the students
will be able to
1. define terms about angles through the
given group activity
2. illustrate correctly the given definitions
about angles
3. apply the different definitions about
angles in solving problems
4. participate actively in all activities and
discussions
Learning Competencies: The learner
1. illustrates the need for an axiomatic
structure of a mathematical system in
general, and in Geometry in particular
(a) undefined terms; (b) define terms;
(c) postulates, and (d) theorems
M8GE-IIIa-c-1
Specific Objectives: At the end of the
session, at least 80% of the students
will be able to
1. familiarize the different postulates
and theorems about angles
2. illustrate correctly the given
postulates about angles
3. apply the different postulates and
theorems about angles in solving
problems
4. participate actively in all activities and
discussions

2. plane
3. illustrate correctly the given
statements using the postulates
and
theorems of points, lines, and
planes
4. participate actively in all
activities and
Discussions
II. 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.
MATHEMATICAL SYSTEM UNDEFINED TERMS (with
its Postulates, theorems,
and related Definitions)
DEFINITIONS (about Angles) POSTULATES & THEOREMS
(about Angles)
III. LEARNING
RESOURCES
List the materials to be used in different days. Varied sources of materials sustain children’s interest in the lesson and in learning. Ensure that there is a mix of concrete and manipulative materials as well as paper-based
materials. Hands-on learning promotes concept development
A. References
1. Teacher’s Guide
pages
2. Learner’s Materials
pages
3. Textbook pages -Geometry (New High School
Mathematics III) pp. 1-4;
-Geometry III.2009 pp. 3-6
-Geometry III.2009 pp. 3-6; 62-63 Geometry III.2009 pp. 64-69
4. Additional Materials
from Learning
Resource (LR)portal
B. Other Learning
Resource
http://web.cerritos.edu/dford/SitePages/
Math_70_F13/Math70Lecture-1-2-1-3_
SymbolsandPostulates.pdf
https://www.youtube.com/watch?
v=37gTYBJsLrg
IV.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.
A. Reviewing previous
lesson or presenting the
new lesson
Getting Started Activity
-The teacher will let the students watch the video
about Mathematical System found on
https://www.youtube.com/watch?v=37gTYBJsLrg
-The teacher will ask the students this question:
 Based from the video what can you
Reviewing Previous Lesson
Strategy: Game (by group of 5
members each)
Title: Can You Still Recognize Me?
In here, the teacher will give
questions about the mathematical
Reviewing Previous Lesson:
Strategy: Picture/Illustration Analysis
(by group of 5 members each)
Title: What Am I?
In here, the teacher will show
pictures/illustrations of the different
Reviewing Previous Lesson:
Strategy: Q and A (Question and
Answer)/Oral Recitation
In here, the students will be given
questions. The first one to raise his/her
hand will be the one to give the answer

3. say about a mathematical system?
This question will be answered orally.
system and let the students give the
answer. Every correct answer worth
1 point. The group that will earn the
highest points will win the game.
Sample Questions:
1. These are the building blocks of
Geometry.
2. It is statement that needs to be
proven.
3. It is a statement accepted without
proofs.
4. It is also known as a “helping
theorem”.
5. It is a theorem that is easily
proved as
the consequence of another
theorem.
(Note: The teacher will give more
questions about what have been
discussed last meeting. Above are
samples only.)
definitions, postulates, and theorems about
points, lines, and planes. Then, the teacher
will let the students identify what term,
postulate, or theorem is being
shown/illustrated in the picture/illustration.
Sample Pictures:
1.
. Expected Answer:A line contains an infinite
number of Points(theorem)
2.
Expected Answer: Segment Addition Postulate
3.
Expected Answer: A Ray
(Note: The teacher will give more
pictures/illustrations. Above are samples
only.)
and will be given 2 points for every correct
answer.
(Note: The questions that will be given are
about the definitions of the angles.)
B. Establishing a purpose for
the
Lesson
The teacher will present the lesson objectives to
the students by posting it on the board.
The teacher will present the lesson
objectives to the students by posting
it on the board.
The teacher will present the lesson
objectives to the students by posting it on
the board.
The teacher will present the lesson
objectives to the students by posting it on
the board.
C. Presenting
examples/Instances of
the new lesson
Group Activity (5 Groups only)
Strategy: Carousel Brainstorming
Title: What Do You Know About Me?
The teacher will divide the class into 5 groups.
Each group will be given 1 manila paper and
marker. Each given manila paper has a written
question to be answered in 1 minute only. After 1
minute, the students will move to another group
in a clockwise direction to answer another
question in another 1minute, and so on until all
groups will be able to answer the 5 different
questions.
(Note: Each group will move like a carousel,
holding one another from one station to another.
In answering each question, the group must
brainstorm in order to come up with a good
answer. They can give more than 1 answer per
question. In case of a large class size, the
teacher may do it outside the classroom or let
the students stay on their group and let them
pass the manila papers to another group clock
wise every after 1 minute.)
The teacher will ask: What are the
undefined terms in Geometry?
Expected Answer: points, lines, and planes
Then, the teacher will call three
volunteers to draw/illustrate a point,
a line, and a plane on the board.
ACTIVITY (by Pair)
Strategy: Think-Pair-Share
Title: Describe Me
The teacher will let the students
describe the point, the line and the
plane drawn on the board.
After 3 minutes, discussion will
follow.
Group Activity 1 (5 members in each
group)
Strategy: Brainstorming
Title: Define Me
In this activity, the teacher will let the
students define the following:
After 3 minutes, discussion of answers will
follow. The teacher will also discuss hw to
name an angle.
For Practice: The teacher will give angles
with measurements and will let the students
classify them as acute, right or obtuse
The teacher will let the students share to
the class the different postulates and
theorems about angles that they have
researched.
Then, the teacher will discuss further the
POSTULATES about ANGLES
1. Angle Addition Postulate (AAP)
- If T is in the interior of BAC
 , then
TAC
m
BAT
m
BAC
m 




2. Supplement Postulate
- If 1
 and 2
 form a linear pair,
then 1
 and 2
 are supplementary
angles.
3. Linear Pair Postulate – If two angles
form a linear pair, then they are
supplementary
Group Activity 1 (5 members)
The teacher will give the students some
statements about the angle’s postulates
Define the following:
1. angle
2. acute angle
3. right angle
4. obtuse angle
5. perpendicular line segments

4. The 5 different questions:
1. What are undefined terms in Geometry?
2. What is a definition?
3. What is a postulate?
4. What is a theorem?
5. Give at least three symbols that you know in
Mathematics/Geometry. (Repetition of answers
is not allowed.)
In here, the teacher will act as a facilitator.
Practice 1: Determine whether each
of the following suggests a point, a
line, or a plane.
1. tip of a pen
2. corner of a box
3. string of a guitar
4. top of a table
5. laser beam
Practice 2: Give at least 3 examples
in real-life that represents a point, a
line, and a plane (not mentioned
above).
angle. and will let them illustrate them
After 5 minutes, presentations and checking
of illustrations will follow.
D. Discussing new concepts
and
practicing new skills # 1
After 5 minutes, the teacher will let the students
post on the board the manila papers and ask one
representative per group to present or read the
answers. Analysis of answers will follow in order
to come up with best answer/s.
The teacher will say, “From these 3
undefined terms, there are
definitions, postulates, and theorems
that arise.”
Then, the teacher will discuss them
one-by-one.
DEFINITIONS about Points and
Lines
1. Space – a set of points
2. Segment – is a subset of a line. It
has
two endpoints.
3. Ray – is also a subset of a line. It
has
only one end point
4. Midpoint – the point that divides a
segment into two congruent
segments
5. Segment Bisector – a line, a
segment, a ray, or a point that
divides a segment into two
Group Activity 2 (5 members in each
group)
Strategy: Brainstorming
Title: Define Me
In this activity, the teacher will let the
students define the following:
After 5 minutes, discussion of answers will
follow.
Then, the teacher will present illustrations
and let the students name the
complementary angles, supplementary
Then the teacher will discuss the following
theorems
Strategy: Discussion Method
THEOREMS about ANGLES
1. All right angles are congruent.
2. Vertical Angle Theorem – Vertical
angles are congruent.
Group Activity 2 (same group)
The teacher will give the groups problems
to solve about the theorems presented
above.
After 5 minutes, discussion of answers will
follow.
Undefined Terms
1. Point – has no dimension,
length, width, and thickness.
It is represented by a capital
letter
2. Line – a straight edge. It is
named by using two capital
letters r a small letter
3. Plane – has no thickness; it
contains an infinite number of
points and lines, and it extends
indefinitely in all directions
Define the following:
1. complementary angles
2. supplementary angles
3. linear pair
4. angle bisector
5. congruent angles
6. vertical angles

5. congruent parts
6. Distance - The distance between
two
points is the length of a straight
line
segment that links them
(Note: In each definition above, the
teacher will ask a volunteer to
draw/illustrate on the board.)
angles, linear pair, angle bisector,
congruent angles, and vertical angles.
After 5 minutes, discussion of answers will
follow.
E. Discussing new concepts
and
practicing new skills # 2
Then, the teacher will discuss formally the
Mathematical System.
4 Parts of Mathematical System
1. Undefined Terms
- are building blocks of geometry.
These are points, lines and planes.
2. Definitions
- some terms in geometry are defined
based on the undefined terms e.g.,
angle, line segment, etc.
The four characteristics of a good
definition are:
a. It names the term being defined;
b. It places the term into a set or
category;
c. It distinguishes itself from other
terms in that category ( without
providing unnecessary facts)
d. It is reversible.
Ex: If a triangle is isosceles, then it
has two congruent sides.
If a triangle has two congruent
sides, then it is isosceles
3. Postulates
- statements which are accepted
without proofs
4. Theorems
- statements that follow logically from previous
definitions and principles; statements that can
POSTULATES about Points, Lines.
And Planes
1.Two points are contained in exactly
one line.
2. Every line contains at least two
distinct points.
3. If two points are on a plane, then
the
line containing these points is also
on
the plane.
4. Every plane contains at least three
non-collinear points.
5. Plane Postulate – Any three points
lie
in at least one plane and any three
non-collinear points lie in exactly
one
plane.
6. If two distinct points intersect, then
their intersection is a line.
7. Segment Addition Postulate – If
point
M is between points A and B,
then
AM+MB=AB
THEOREM about Points, Lines.
And Planes
1. A line contains an infinite number
of
Points
Practice 3: State the postulate or
theorem you would use to justify the
statement made about each figure
The teacher will give some problems to
solve as application of the definitions of
complementary angles, supplementary
angles, linear pair, angle bisector,
congruent angles, and vertical angles.
After 10 minutes, discussion of answers will
follow.
The teacher will discuss further the
applications using the postulates and
theorems.
Then, the teacher will give students
problems to solve for Practice. (Refer to
different Geometry book or Geometry
III.2009 pp. 64)
Mathematical system - A structure
formed from one or more sets of
undefined objects, various concepts
which may or may not be defined, and a
set of axioms relating these objects and
concepts.

6. be proved to be true.
a. Corollary
- a theorem that follows from
Another theorem as a “by product”; a
a theorem that is easily
proved as the consequence of another
theorem.
b. Lemma
–a theorem that is introduced and proved
so that a later theorem can be proved
(“helping theorem”)
(Note; The teacher will give example/s of a
postulate, a theorem, a corollary and a lemma in
order for the students to differentiate them.)
The teacher will also discuss the different
symbols used in Mathematics/Geometry like the
symbol of triangle, angle, parallel, perpendicular,
and etc. (Please see attached file: Symbols in
Geometry)
1.
2.
3.
4.
(Note: The teacher may add more.)
F. Developing mastery
(leads to Formative
Assessment 3)
The teacher will give some statements in
geometry and let the students identify whether
they are merely definition, postulate or theorem.
ACTIVITY (by Pair)
Title: Illustrate Me
The teacher will let the students
illustrate the following with their
partners.
1. Point A lies in Plane B
2. Plane Z contains line XY and a
point W.
3. Planes G and M intersects at line
BP.
4. Segment GB has a midpoint L.
5. Ray MP bisects segment AB.
(Note: Above are samples only. The
teacher may add more.)
After 5 minutes, discussion of correct
illustrations will follow.
To develop mastery, the teacher will let the
students answer the following individually:
1. From the given figure, form an
equation in x and solve for the
unknown measure.
2. Find the values of x and y in the given
figure.
To develop mastery, the teacher will let the
students answer the following individually:
1. Point V lies in the interior of ABC
 . If
70

ABV
m and 80

VBC
m ,
what is ABC
m ?
2. In the given figure, WMX
 and
ZMY
 are right angles.
Name two pairs of:

7. (Note: The teacher may add more practices
especially on angle bisector.)
Board work and checking will follow after 5
minutes.
a. complementary angles
b. supplementary angles
c. vertical angles
If 60
3 

m , what is 6

m ?
If 90
1 

m , what is 2

m ?
Board work and checking will follow after 5
minutes.
G. Finding practical
application of
concepts and skills in daily
living
The teacher will let the students formulate at
least one example of a postulate and a theorem
in real-life.
(For Postulate - a real life situation/example
where proof is not anymore necessary because
it is already accepted as true. For Theorem – a
real life situation/example where proofs are
needed in order for it to be accepted as true.)
Strategy: Journal Writing
The teacher will let the students
answer the question below in their
journal:
What is life without points, lines, and
planes?
Strategy: Journal Writing
The teacher will let the students answer the
question below in their journal:
Do angles important in our lives? If yes,
give real-life situations or examples where
angles can be applied and/or needed. If
not, defend your answer.
Strategy: Journal Writing
The teacher will let the students answer
the question below in their journal:
Can we apply in real life the different
postulates and theorems about angles?
Why or why not?
H. Making generalizations
and
abstractions about the lesson
The teacher will let the students answer the
question: Why is it important to study the
mathematical system? What do you think is its
contribution/significance in writing proofs?
To be answered orally:
Why is it that a point, a line, and a
plane are called undefined terms?
The teacher will let the students choose at
least three definitions about angles to be
illustrated based from their own
understanding.
The teacher will let the students answer
this question: Based from all the postulates
and theorems that you have learned, what
generalization can you draw about angles?
I. Evaluating learning Formative Assessment (Quiz No. 1)
Graphic Organizer:
Formative assessment(Quiz No. 2)
I. Determine whether each of the
following
suggests a point, a line, or a plane
1. top of a box
2. star in the sky
3. clothesline
4. a corner of a room
5. cover of a book
II. Illustrate each of the following and
label
the diagram.
6. Point B lies in plane M.
7. Lines m and n intersect at point
E.
8. Plane A and plane B intersect at
line
PR.
III. Construction
Formative assessment(Quiz No. 3)
I. State whether each of the following is
true or false
1. An angle with measures 89o is an
acute angle.
2. If two angles form a linear pair then
they are complementary.
3. An angle formed by two perpendicular
lines are obtuse.
4. The sum of the measures of any
obtuse angle and any acute angle is
180o.
5. Two vertical angles are always
congruent.
II. Solve for x.
Formative assessment(Quiz No. 4)
I. In your own words, state the following
postulates.
1 Angle Addition Postulate (AAP)
2. Supplement Postulate
3. Linear Pair Postulate
II. Solve the following.
4. Point B lies in the interior of AOC
 .
Find AOB
m if 135

AOC
m and
Is 20

BOC
m ?
5. Find the value of x.
If 96

AOD
m , 5
3
1 

 x
m ,
3
4
2 

 x
m , 10
6
3 

 x
m

8. Direction: Describe the mathematical system
using the graphic organizer above. List
down its 4 parts and describe each.
9. Draw segment AC with a
midpoint B.
10. (Refer in number 9) If AC = 10
cm,
what is the measurement of AB?
Board work and checking will follow after 5
minutes. Board work and checking will follow after
10 minutes.
J. Additional activities for
application
or remediation
(Assignment for next lesson)
The teacher will let the students research
the different postulates and theorems about
angles.
(Assignment for next lesson)
The teacher will let the students research
about the definitions and theorems of
angles formed by parallel lines cut by
transversal.
V.REMARKS
(Please check one)
_______Accomplished
_______Not Accomplished If not accomplished indicate the topi c/s:________________________________________ Due to
________________________________________________________________________________________
(Please indicate the reason)
VI.REFLECTION Reflect on your teaching and assess yourself as a teacher. Think about your students’ progress this week. What works? What else needs to be done to help the students learn? Identify what help your instructional supervisors can
provide for you so when you meet them, you can ask them relevant questions.
A. No. of learners who earned
80% on the formative
assessment.
B. No. of learners who require
additional activities for
remediation.
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?
Prepared by: JAYPEE S. COLIS Checked by:
Teacher School Principal