CO-2024-LS-G9-NMP_Q1_W1.pdf NATIONAL MATHEMATICS PROGRAM
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About This Presentation
gr 9 nmp lesson script
Slide Content
9
Quarter 1 Week 1
NATIONAL MATHEMATICS PROGRAM
Lesson Script in Mathematics
Quarter 1 Week 1
NATIONAL MATHEMATICS PROGRAM
Lesson Script in Mathematics
National Mathematics Program
Lesson Script in Mathematics
Quarter 1: Week 1
SY 2024-2025
This material is intended exclusively for the use of teachers in the implementation of the MATATAG K to 10 Curriculum. It aims to assist in delivering the curriculum
content, standards, and lesson competencies.
The Intellectual Property Code of the Philippines states that “No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the
government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as
a condition the payment of royalties.”
Borrowed materials (e.g., texts, illustrations, musical notations, photos, and other copyrightable, patentable contents) included in this learning resource are owned by their
respective copyright and intellectual property right holders. Where applicable, DepEd has sought permission from these owners specifically for the development and printing of
this learning resource. As such, using these materials in any form other than agreed framework requires another permission and/or licensing.
No part of this material, including its original and borrowed contents, may be reproduced in any form without written permission from the Department of Education.
Every care has been taken to ensure the accuracy of the information provided in this material. For inquiries or feedback, please call the Office of the Director of the Bureau of
Learning Delivery via telephone numbers (02) 8636-6540 and (02) 6540 or send an email to [email protected].
Published by the Department of Education
Development Team
Writer: Bryan M. Caoile, Marcela II P. Asayas, Irene C. Mier, Alma S. Barbarona
Reviewers: Bonifacio G. Gabales Jr., Charlyn Y. Emata, Hernan G. Pacatang, Jeffrey E. Santiago
Illustrator:
Layout Artist: Althea L. Baguio, Russellier C. Matas
Management Team: Allan G. Farnazo Alona C. Uy Rommel R. Jandayan
Rebonfamil R. Baguio Niel Michael A. De Asis Ramel M. Pilo
Mary Jeanne B. Aldeguer Christine C. Bagacay Felix I. Antecristo
Herminia A. Bantiding Charlyn Y. Emata Ernie E. Agsaulio
Analiza C. Almazan
Lesson Script in Mathematics
Quarter 1: Week 1
SY 2024-2025
This material is intended exclusively for the use of teachers in the implementation of the MATATAG K to 10 Curriculum. It aims to assist in delivering the curriculum
content, standards, and lesson competencies.
The Intellectual Property Code of the Philippines states that “No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the
government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as
a condition the payment of royalties.”
Borrowed materials (e.g., texts, illustrations, musical notations, photos, and other copyrightable, patentable contents) included in this learning resource are owned by their
respective copyright and intellectual property right holders. Where applicable, DepEd has sought permission from these owners specifically for the development and printing of
this learning resource. As such, using these materials in any form other than agreed framework requires another permission and/or licensing.
No part of this material, including its original and borrowed contents, may be reproduced in any form without written permission from the Department of Education.
Every care has been taken to ensure the accuracy of the information provided in this material. For inquiries or feedback, please call the Office of the Director of the Bureau of
Learning Delivery via telephone numbers (02) 8636-6540 and (02) 6540 or send an email to [email protected].
Published by the Department of Education
Development Team
Writer: Bryan M. Caoile, Marcela II P. Asayas, Irene C. Mier, Alma S. Barbarona
Reviewers: Bonifacio G. Gabales Jr., Charlyn Y. Emata, Hernan G. Pacatang, Jeffrey E. Santiago
Illustrator:
Layout Artist: Althea L. Baguio, Russellier C. Matas
Management Team: Allan G. Farnazo Alona C. Uy Rommel R. Jandayan
Rebonfamil R. Baguio Niel Michael A. De Asis Ramel M. Pilo
Mary Jeanne B. Aldeguer Christine C. Bagacay Felix I. Antecristo
Herminia A. Bantiding Charlyn Y. Emata Ernie E. Agsaulio
Analiza C. Almazan
LESSON SCRIPT IN NMP 9
1
Week 1 DAY 1
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A. Content
Standards
The learners demonstrate knowledge and understanding of
● simple geometric concepts and notations.
B. Performance
Standards
By the end of the quarter, the learners are able to:
● illustrate and describe points, lines, rays, line segments, angles, and planes.
C. Learning
Competencies
The learners will be able to:
● illustrate and describe point, line, ray, line segment, angle, and plane using models and geometric
notations.
D. Learning
Objectives
At the end of the lesson, the learners are able to:
● illustrate and describe point, line, ray, line segment, angle, and plane using models and geometric
notations.
II. CONTENT: Measurement and Geometry
III. LEARNING RESOURCES
A. References
Department of Education. Basic Education Assistance for Mindanao Third Year - Mathematics Iii Geometry of
Shape and Size Module 1 - Points, Lines, Planes and Angles Learning Guide. Accessed July 4, 2024.
https://lrmds.deped.gov.ph/detail/7374
Department of Education. Mathematics 7 Quarter 3 – Module 1: Basic Concepts and Terms in Geometry.
Department of Education: Koronadal City, 2020
Department of Education. " sharpened pencil." LR Portal. October 30, 2013.
https://lrmds.deped.gov.ph/create/detail/14
Department of Education. " hospital sign." LR Portal. November 7, 2013.
https://lrmds.deped.gov.ph/create/detail/94
Department of Education. " street light." LR Portal. October 30, 2013.
https://lrmds.deped.gov.ph/create/detail/1027
Department of Education. " flute." LR Portal. December 2, 2013.
https://lrmds.deped.gov.ph/create/detail/388
Department of Education. " cabinet." LR Portal. November 15, 2013.
https://lrmds.deped.gov.ph/create/detail/209
Department of Education. " Icon." LR Portal. January 23, 2013.
https://lrmds.deped.gov.ph/create/detail/606
1
Week 1 DAY 1
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A. Content
Standards
The learners demonstrate knowledge and understanding of
● simple geometric concepts and notations.
B. Performance
Standards
By the end of the quarter, the learners are able to:
● illustrate and describe points, lines, rays, line segments, angles, and planes.
C. Learning
Competencies
The learners will be able to:
● illustrate and describe point, line, ray, line segment, angle, and plane using models and geometric
notations.
D. Learning
Objectives
At the end of the lesson, the learners are able to:
● illustrate and describe point, line, ray, line segment, angle, and plane using models and geometric
notations.
II. CONTENT: Measurement and Geometry
III. LEARNING RESOURCES
A. References
Department of Education. Basic Education Assistance for Mindanao Third Year - Mathematics Iii Geometry of
Shape and Size Module 1 - Points, Lines, Planes and Angles Learning Guide. Accessed July 4, 2024.
https://lrmds.deped.gov.ph/detail/7374
Department of Education. Mathematics 7 Quarter 3 – Module 1: Basic Concepts and Terms in Geometry.
Department of Education: Koronadal City, 2020
Department of Education. " sharpened pencil." LR Portal. October 30, 2013.
https://lrmds.deped.gov.ph/create/detail/14
Department of Education. " hospital sign." LR Portal. November 7, 2013.
https://lrmds.deped.gov.ph/create/detail/94
Department of Education. " street light." LR Portal. October 30, 2013.
https://lrmds.deped.gov.ph/create/detail/1027
Department of Education. " flute." LR Portal. December 2, 2013.
https://lrmds.deped.gov.ph/create/detail/388
Department of Education. " cabinet." LR Portal. November 15, 2013.
https://lrmds.deped.gov.ph/create/detail/209
Department of Education. " Icon." LR Portal. January 23, 2013.
https://lrmds.deped.gov.ph/create/detail/606
LESSON SCRIPT IN NMP 9
2
B. Other Learning
Resources
Activity sheets, LCD Projector
IV. TEACHING AND LEARNING PROCEDURES
Before/Pre-Lesson Proper
Activating Prior
Knowledge
(5 minutes)
Good morning, everyone! Welcome to today's National Mathematics Program class.
Today, we will describe and identify basic geometric figures: point, line, ray, line segment, angle, and plane, and
we will also learn to illustrate these geometric figures using models and geometric notations.
Now, let us familiarize ourselves with some words related to the lesson through this anagram. In this activity, we
form words by rearranging their letters, or by arranging letters based on notations, models, or descriptions.
Intervention Group Consolidation Group Enhancement Group
Your task is to rearrange the
anagram letters to form the word
using its given notation.
Note:
Notation will be the basis for
identifying the anagram word(s).
Your task is to rearrange the
anagram letters to form a word
using the given figure.
Note:
Figure will be the basis for
identifying the anagram word/s.
Your task is to rearrange the
anagram letters to form the word
using its given description.
The description will be the basis for
identifying the anagram word(s).
2
B. Other Learning
Resources
Activity sheets, LCD Projector
IV. TEACHING AND LEARNING PROCEDURES
Before/Pre-Lesson Proper
Activating Prior
Knowledge
(5 minutes)
Good morning, everyone! Welcome to today's National Mathematics Program class.
Today, we will describe and identify basic geometric figures: point, line, ray, line segment, angle, and plane, and
we will also learn to illustrate these geometric figures using models and geometric notations.
Now, let us familiarize ourselves with some words related to the lesson through this anagram. In this activity, we
form words by rearranging their letters, or by arranging letters based on notations, models, or descriptions.
Intervention Group Consolidation Group Enhancement Group
Your task is to rearrange the
anagram letters to form the word
using its given notation.
Note:
Notation will be the basis for
identifying the anagram word(s).
Your task is to rearrange the
anagram letters to form a word
using the given figure.
Note:
Figure will be the basis for
identifying the anagram word/s.
Your task is to rearrange the
anagram letters to form the word
using its given description.
The description will be the basis for
identifying the anagram word(s).
LESSON SCRIPT IN NMP 9
3
(After the answers were posted, process the learner’s output and give appropriate feedback.) Let's verify your
answers.
NOTES TO THE TEACHER: This activity will review the 7th grade competency of representing points, lines, and
planes using concrete and pictorial models. Before the class completes the board work, the teacher must display
various tables with different instructions. For this, choose the most convenient number of groups. The teacher may
have more than one group per learner classification, 3–4 learners per group is recommended.
Lesson
Purpose/Intention
(1 minute)
When you were in 7th grade, you represented points, lines, and planes using concrete and pictorial models. This
time, we will use models and geometric notations to illustrate and describe a point, line, ray, line segment, angle,
and plane.
Let's get started!
Let's read the lesson objective with Jillian.
NOTES TO THE TEACHER: The competency to master is to illustrate and describe points, lines, rays, line
segments, angles, and planes using models and geometric notations.
Lesson Language
Practice
(1 minute)
To remind everyone, let us recall the meaning of the following terms before we go further to our discussion.
➢ Point - It has no dimension and is usually represented by a dot.
➢ Line - It is a set of connected points that extend infinitely in opposite directions.
➢ Segment/Line Segment - It is formed when two distinct points are connected with a line.
➢ Ray - It has only one endpoint and an arrowhead which extends infinitely in one direction.
➢ Plane - It is a flat surface that extends infinitely in all directions.
➢ Angle - A figure formed by two rays with a common endpoint.
NOTES TO THE TEACHER: This section introduces the key terms or terms that are new into the lesson.
During/Lesson Proper
Reading the Key
Idea/Stem
3 minutes
Let us look at Figure 1 on the board. I have completed the first row for you, identifying the point as the given term,
along with its corresponding notation and figure/model. Your task now is to complete the table below by naming
and identifying the notation and/or the figure or model using the given terms in the first column.
3
(After the answers were posted, process the learner’s output and give appropriate feedback.) Let's verify your
answers.
NOTES TO THE TEACHER: This activity will review the 7th grade competency of representing points, lines, and
planes using concrete and pictorial models. Before the class completes the board work, the teacher must display
various tables with different instructions. For this, choose the most convenient number of groups. The teacher may
have more than one group per learner classification, 3–4 learners per group is recommended.
Lesson
Purpose/Intention
(1 minute)
When you were in 7th grade, you represented points, lines, and planes using concrete and pictorial models. This
time, we will use models and geometric notations to illustrate and describe a point, line, ray, line segment, angle,
and plane.
Let's get started!
Let's read the lesson objective with Jillian.
NOTES TO THE TEACHER: The competency to master is to illustrate and describe points, lines, rays, line
segments, angles, and planes using models and geometric notations.
Lesson Language
Practice
(1 minute)
To remind everyone, let us recall the meaning of the following terms before we go further to our discussion.
➢ Point - It has no dimension and is usually represented by a dot.
➢ Line - It is a set of connected points that extend infinitely in opposite directions.
➢ Segment/Line Segment - It is formed when two distinct points are connected with a line.
➢ Ray - It has only one endpoint and an arrowhead which extends infinitely in one direction.
➢ Plane - It is a flat surface that extends infinitely in all directions.
➢ Angle - A figure formed by two rays with a common endpoint.
NOTES TO THE TEACHER: This section introduces the key terms or terms that are new into the lesson.
During/Lesson Proper
Reading the Key
Idea/Stem
3 minutes
Let us look at Figure 1 on the board. I have completed the first row for you, identifying the point as the given term,
along with its corresponding notation and figure/model. Your task now is to complete the table below by naming
and identifying the notation and/or the figure or model using the given terms in the first column.
LESSON SCRIPT IN NMP 9
4
Figure 1:
Very good! Now that you already know the different symbols, models, and notations for describing and illustrating
points, lines, rays, line segments, angles, and planes using either models, figures, or notations, let's do an activity
to check your understanding further.
NOTES TO THE TEACHER: The activity helps the learners name and identify points, lines, segments, rays, planes,
and angles through the figure presented based on their context.
4
Figure 1:
Very good! Now that you already know the different symbols, models, and notations for describing and illustrating
points, lines, rays, line segments, angles, and planes using either models, figures, or notations, let's do an activity
to check your understanding further.
NOTES TO THE TEACHER: The activity helps the learners name and identify points, lines, segments, rays, planes,
and angles through the figure presented based on their context.
LESSON SCRIPT IN NMP 9
5
Developing
Understanding of the
Key Idea/Stem
10 minutes
In the subsequent tasks, examine the table and provide the requested information.
NOTES TO THE TEACHER: These items are given to provide more examples to the learners. Differentiation of
given and unknown was classified in the intervention or consolidation group, and no given model and notation
for the enhancement group.
5
Developing
Understanding of the
Key Idea/Stem
10 minutes
In the subsequent tasks, examine the table and provide the requested information.
NOTES TO THE TEACHER: These items are given to provide more examples to the learners. Differentiation of
given and unknown was classified in the intervention or consolidation group, and no given model and notation
for the enhancement group.
LESSON SCRIPT IN NMP 9
6
Deepening
Understanding of the
Key Idea/Stem
5 minutes
To deepen your understanding of today's lesson, let's have another activity.
6
Deepening
Understanding of the
Key Idea/Stem
5 minutes
To deepen your understanding of today's lesson, let's have another activity.
LESSON SCRIPT IN NMP 9
7
Expected answers:
NOTES TO THE TEACHER: These items aimed to provide more examples to the learners. The difference between
given and unknown was classified in the intervention or consolidation group, and no given model and notation for
the enhancement group. The teacher may have more than 1 group per learner classification, 3-4 learners per group
are recommended.
Intervention Group Consolidation Group Enhancement Group
1. E
2. F
3. D
4. B
5. C
1. E
2. F
3. D
4. B
5. C
1.
2. E F
3.
4. T
5. S T
After/Post-Lesson Proper
Making
Generalizations and
Abstractions
2 minutes
Congratulations everyone! I’m glad you found those activities helpful in describing and illustrating points, lines,
rays, line segments, angles, and planes using models and geometric notations. Let’s give everyone a very good
clap!
Very Good! (clapping hands at the same time)
Very Good! (clapping hands at the same time)
Very Good! Very Good! Very Good! (clapping hands at the same time)
m
7
Expected answers:
NOTES TO THE TEACHER: These items aimed to provide more examples to the learners. The difference between
given and unknown was classified in the intervention or consolidation group, and no given model and notation for
the enhancement group. The teacher may have more than 1 group per learner classification, 3-4 learners per group
are recommended.
Intervention Group Consolidation Group Enhancement Group
1. E
2. F
3. D
4. B
5. C
1. E
2. F
3. D
4. B
5. C
1.
2. E F
3.
4. T
5. S T
After/Post-Lesson Proper
Making
Generalizations and
Abstractions
2 minutes
Congratulations everyone! I’m glad you found those activities helpful in describing and illustrating points, lines,
rays, line segments, angles, and planes using models and geometric notations. Let’s give everyone a very good
clap!
Very Good! (clapping hands at the same time)
Very Good! (clapping hands at the same time)
Very Good! Very Good! Very Good! (clapping hands at the same time)
m
LESSON SCRIPT IN NMP 9
8
Let’s wrap up what we’ve learned from the previous activities.
The box below lists the various models and notations used to describe and illustrate points, lines, rays, line
segments, angles, and planes using figures and geometric notations. In the table, write down the notations or
models that correspond to the given terms.
Terms
Models/Figures Notations
1.point
2. line
3. line segment
4. ray
5. angle
6. plane
8
Let’s wrap up what we’ve learned from the previous activities.
The box below lists the various models and notations used to describe and illustrate points, lines, rays, line
segments, angles, and planes using figures and geometric notations. In the table, write down the notations or
models that correspond to the given terms.
Terms
Models/Figures Notations
1.point
2. line
3. line segment
4. ray
5. angle
6. plane
LESSON SCRIPT IN NMP 9
9
Expected answers:
Terms Models/Figures Notations
1.point
2. line ,
3. line segment
4. ray
5. angle
6. plane
Evaluating Learning
4 minutes
By answering the following tasks, let us test our understanding of describing and illustrating points, lines, rays,
line segments, angles, and planes using models and geometric notations. Write your answers on the activity sheet.
Intervention Group Consolidation Group Enhancement Group
Encircle the letter of your correct
answer.
1. What do you call the term that
has no dimension and is usually
represented by a dot?
A. line B. segment C. point
Complete the blank with the correct
information.
1.An ________ is a figure formed by
two rays with a common endpoint.
Complete the table with information
from the figure below.
9
Expected answers:
Terms Models/Figures Notations
1.point
2. line ,
3. line segment
4. ray
5. angle
6. plane
Evaluating Learning
4 minutes
By answering the following tasks, let us test our understanding of describing and illustrating points, lines, rays,
line segments, angles, and planes using models and geometric notations. Write your answers on the activity sheet.
Intervention Group Consolidation Group Enhancement Group
Encircle the letter of your correct
answer.
1. What do you call the term that
has no dimension and is usually
represented by a dot?
A. line B. segment C. point
Complete the blank with the correct
information.
1.An ________ is a figure formed by
two rays with a common endpoint.
Complete the table with information
from the figure below.
LESSON SCRIPT IN NMP 9
10
2. Which notations represents a
ray?
A.
B.
C.
3. What is the model or figure of the
notation line b with points F and G
on it.
A.
B.
C.
2. The model/figure of plane
TRB can be illustrated as
____________.
3. The geometric notation of the
model M B is ___________.
Terms Models/
figures
Notation
points
lines
rays
line
segments
angles
plane
s
10
2. Which notations represents a
ray?
A.
B.
C.
3. What is the model or figure of the
notation line b with points F and G
on it.
A.
B.
C.
2. The model/figure of plane
TRB can be illustrated as
____________.
3. The geometric notation of the
model M B is ___________.
Terms Models/
figures
Notation
points
lines
rays
line
segments
angles
plane
s
LESSON SCRIPT IN NMP 9
11
Expected answers:
Intervention Group Consolidation Group Enhancement Group
1. C
2. B
3. A
1. angle
2.
3. line s or M B
Additional Activities for
Application or
11
Expected answers:
Intervention Group Consolidation Group Enhancement Group
1. C
2. B
3. A
1. angle
2.
3. line s or M B
Additional Activities for
Application or
LESSON SCRIPT IN NMP 9
12
Remediation (if
applicable)
Remarks
Reflection
12
Remediation (if
applicable)
Remarks
Reflection
13
LESSON SCRIPT IN NMP 9
Week 1 DAY 2
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A. Content
Standards
The learners demonstrate knowledge and understanding of
● simple geometric concepts and notations.
B. Performance
Standards
By the end of the quarter, the learners are able to:
● illustrate and describe points, lines, rays, line segments, angles, and planes.
C. Learning
Competencies
The learners will be able to:
● illustrate and describe point, line, ray, line segment, angle, and plane using models and geometric notations.
D. Learning
Objectives
At the end of the lesson, the learners are able to:
● illustrate a geometric model involving points, lines, rays, line segments, angles and planes.
II. CONTENT: Points, Lines, Rays, Line Segments, Angles, and Planes.
III. LEARNING RESOURCES
A. References
Department of Education. "Basic Education Assistance for Mindanao Third Year - Mathematics Iii
Geometry Of Shape and Size Module 1 - Points, Lines, Planes and Angles Learning Guide" Accessed
August 4, 2024. https://lrmds.deped.gov.ph/detail/7374)
Department of Education. Mathematics Quarter 3 – Module 1: Basic Concepts and Terms in Geometry.
Department of Education : Koronadal City, 2020
Department of Education. "Dining room/area." LR Portal. June 30, 2021.
https://lrmds.deped.gov.ph/create/detail/1445
Department of Education. "Piko." LR Portal. December 26, 2013.
https://lrmds.deped.gov.ph/create/detail/505
Department of Education. "Sweeping." LR Portal. November 25, 2013.
https://lrmds.deped.gov.ph/create/detail/320
B. Other
Learning
Resources
LESSON SCRIPT IN NMP 9
Week 1 DAY 2
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A. Content
Standards
The learners demonstrate knowledge and understanding of
● simple geometric concepts and notations.
B. Performance
Standards
By the end of the quarter, the learners are able to:
● illustrate and describe points, lines, rays, line segments, angles, and planes.
C. Learning
Competencies
The learners will be able to:
● illustrate and describe point, line, ray, line segment, angle, and plane using models and geometric notations.
D. Learning
Objectives
At the end of the lesson, the learners are able to:
● illustrate a geometric model involving points, lines, rays, line segments, angles and planes.
II. CONTENT: Points, Lines, Rays, Line Segments, Angles, and Planes.
III. LEARNING RESOURCES
A. References
Department of Education. "Basic Education Assistance for Mindanao Third Year - Mathematics Iii
Geometry Of Shape and Size Module 1 - Points, Lines, Planes and Angles Learning Guide" Accessed
August 4, 2024. https://lrmds.deped.gov.ph/detail/7374)
Department of Education. Mathematics Quarter 3 – Module 1: Basic Concepts and Terms in Geometry.
Department of Education : Koronadal City, 2020
Department of Education. "Dining room/area." LR Portal. June 30, 2021.
https://lrmds.deped.gov.ph/create/detail/1445
Department of Education. "Piko." LR Portal. December 26, 2013.
https://lrmds.deped.gov.ph/create/detail/505
Department of Education. "Sweeping." LR Portal. November 25, 2013.
https://lrmds.deped.gov.ph/create/detail/320
B. Other
Learning
Resources
14
LESSON SCRIPT IN NMP 9
IV. TEACHING AND LEARNING PROCEDURES
Before/Pre-Lesson Proper
Activating Prior
Knowledge
(5 minutes)
Good morning/afternoon, class! Are you excited about our National Mathematics Program class today
Today, you will illustrate a geometric model involving points, lines, rays, line segments, angles, and planes
Let's talk about the basic ideas in geometry that don't have strict definitions but are really important to understand
geometry. Things like points, lines, and planes are like the building blocks of geometry. They help us create more
complex shapes and ideas in geometry. Knowing these basic concepts well is crucial for doing geometry tasks and
solving problems successfully
There is a figure in the left box. Your task is to list the names of points, lines, rays, line segments, angles, and planes
that you see in the left box. Write your answers inside the right box.
Left Box Right Box
A B
C D
E F
Point Line
Plane
Ray
Line Segment
Angle
LESSON SCRIPT IN NMP 9
IV. TEACHING AND LEARNING PROCEDURES
Before/Pre-Lesson Proper
Activating Prior
Knowledge
(5 minutes)
Good morning/afternoon, class! Are you excited about our National Mathematics Program class today
Today, you will illustrate a geometric model involving points, lines, rays, line segments, angles, and planes
Let's talk about the basic ideas in geometry that don't have strict definitions but are really important to understand
geometry. Things like points, lines, and planes are like the building blocks of geometry. They help us create more
complex shapes and ideas in geometry. Knowing these basic concepts well is crucial for doing geometry tasks and
solving problems successfully
There is a figure in the left box. Your task is to list the names of points, lines, rays, line segments, angles, and planes
that you see in the left box. Write your answers inside the right box.
Left Box Right Box
A B
C D
E F
Point Line
Plane
Ray
Line Segment
Angle
15
LESSON SCRIPT IN NMP 9
(After posting the answers, process the learner’s output and give appropriate feedback.) Say, “Let us see if you got
them right.”
Expected answers:
Points: A, B, C, D, E, and F
Lines: AB, CD, EF, AE, BD, BF, and DF
Line Segments: AB, CD, EF, AE, BD, BF, and DF
Rays: AB, BA, CD, DC, EF, and FE
Angles: <BAE, <AEF, <EFB, <FBA, and <CDB
Planes: Plane BAE
NOTES TO THE TEACHER: This activity serves as a review for the Grade 3 Mathematics competency on recognizing and drawing points, lines, line
segments, and rays using models. The teacher should prepare visual materials to be displayed on the board. This is an individual task where different
students can provide their answers on the board, making it a Boardwork Activity.
Lesson
Purpose/Intention
(1 minute)
When you were in grade 3, you could recognize models of points, lines, line segments, and rays. Let's try to put that
knowledge into practice now!
NOTES TO THE TEACHER: This part of the lesson introduces the competency students are expected to master: illustrating geometric models involving
points, lines, rays, line segments, angles, and planes.
Lesson Language
Practice
(1 minute)
Before we proceed with our discussion, let's review the definitions of the following undefined terms to refresh our
understanding
Point - It has no dimension and is usually represented by a dot.
Line – It is made of set of points which extends in opposite direction infinitely. It has length but no width or thickness.
Line Segment - A part of a line that is bounded by two distinct endpoints.
Ray - It is a part of line that has one endpoint and extends infinitely in one direction.
Angle – A geometrical figure formed when two rays meet at a common point called the vertex.
Plane - It is a flat surface that extends infinitely in all directions.
NOTES TO THE TEACHER: This part introduces the key terms to be used in the lesson or terms that are new in the lesson.
LESSON SCRIPT IN NMP 9
(After posting the answers, process the learner’s output and give appropriate feedback.) Say, “Let us see if you got
them right.”
Expected answers:
Points: A, B, C, D, E, and F
Lines: AB, CD, EF, AE, BD, BF, and DF
Line Segments: AB, CD, EF, AE, BD, BF, and DF
Rays: AB, BA, CD, DC, EF, and FE
Angles: <BAE, <AEF, <EFB, <FBA, and <CDB
Planes: Plane BAE
NOTES TO THE TEACHER: This activity serves as a review for the Grade 3 Mathematics competency on recognizing and drawing points, lines, line
segments, and rays using models. The teacher should prepare visual materials to be displayed on the board. This is an individual task where different
students can provide their answers on the board, making it a Boardwork Activity.
Lesson
Purpose/Intention
(1 minute)
When you were in grade 3, you could recognize models of points, lines, line segments, and rays. Let's try to put that
knowledge into practice now!
NOTES TO THE TEACHER: This part of the lesson introduces the competency students are expected to master: illustrating geometric models involving
points, lines, rays, line segments, angles, and planes.
Lesson Language
Practice
(1 minute)
Before we proceed with our discussion, let's review the definitions of the following undefined terms to refresh our
understanding
Point - It has no dimension and is usually represented by a dot.
Line – It is made of set of points which extends in opposite direction infinitely. It has length but no width or thickness.
Line Segment - A part of a line that is bounded by two distinct endpoints.
Ray - It is a part of line that has one endpoint and extends infinitely in one direction.
Angle – A geometrical figure formed when two rays meet at a common point called the vertex.
Plane - It is a flat surface that extends infinitely in all directions.
NOTES TO THE TEACHER: This part introduces the key terms to be used in the lesson or terms that are new in the lesson.
16
LESSON SCRIPT IN NMP 9
During/Lesson Proper
Reading the Key
Idea/Stem
In geometry, precise notations are used to describe and define various geometric terms. These notations help convey
specific properties and relationships of geometric figures. For example, a line segment AB is denoted as AB, where A
and B are the endpoints. A ray can be represented as ray CD, with C as the initial point and the arrow indicating the
direction of the ray. Geometric notations provide a standardized way to communicate about shapes, angles, and lines
in a clear and concise manner.
Processing Questions:
What is the notation for a line segment with endpoints P and Q?
Expected answers: PQ or PQ
How is a ray represented with an initial point E?
Expected answers: Ray EF or EF, where E is the initial point.
Why are geometric notations important in geometry?
Expected answers: Geometric notations provide a standardized way to communicate properties and relationships of
geometric figures.
You have now basic knowledge about undefined terms in Geometry. Let us try to complete a task.
You will be grouped according to your camp and you will perform the task assigned to your camp. I have prepared
two boxes for each group.
LESSON SCRIPT IN NMP 9
During/Lesson Proper
Reading the Key
Idea/Stem
In geometry, precise notations are used to describe and define various geometric terms. These notations help convey
specific properties and relationships of geometric figures. For example, a line segment AB is denoted as AB, where A
and B are the endpoints. A ray can be represented as ray CD, with C as the initial point and the arrow indicating the
direction of the ray. Geometric notations provide a standardized way to communicate about shapes, angles, and lines
in a clear and concise manner.
Processing Questions:
What is the notation for a line segment with endpoints P and Q?
Expected answers: PQ or PQ
How is a ray represented with an initial point E?
Expected answers: Ray EF or EF, where E is the initial point.
Why are geometric notations important in geometry?
Expected answers: Geometric notations provide a standardized way to communicate properties and relationships of
geometric figures.
You have now basic knowledge about undefined terms in Geometry. Let us try to complete a task.
You will be grouped according to your camp and you will perform the task assigned to your camp. I have prepared
two boxes for each group.
17
LESSON SCRIPT IN NMP 9
3 minutes
Intervention Group Consolidation Group Enhancement Group
Write the geometric symbols for the
terms listed in the Left Box. Write
your answers inside the right box.
Left Box Right Box
Provide the geometric symbols for
the terms shown in the Left Box.
Write your answers inside the right
box.
Left Box Right Box
Use a marker to highlight the terms
representing point, line, ray, line
segment, angle, and plane in the
illustration. Then, list the geometric
notations for each highlighted term.
Left Box
Department of Education. "Dining room/area."
https://lrmds.deped.gov.ph/create/detail/1445
Right Box
In Euclidean Geometry, point, line, and plane are mental concepts without a precise physical form. We can use real
objects to represent these ideas, but they remain abstract. Thus, these undefined terms can only be described.
1. Point A
2. Line BC
3. Ray DE
4. Line Segment FG
5. Angle HIJ
6. Plane K
A B
C
D
E F
G
LESSON SCRIPT IN NMP 9
3 minutes
Intervention Group Consolidation Group Enhancement Group
Write the geometric symbols for the
terms listed in the Left Box. Write
your answers inside the right box.
Left Box Right Box
Provide the geometric symbols for
the terms shown in the Left Box.
Write your answers inside the right
box.
Left Box Right Box
Use a marker to highlight the terms
representing point, line, ray, line
segment, angle, and plane in the
illustration. Then, list the geometric
notations for each highlighted term.
Left Box
Department of Education. "Dining room/area."
https://lrmds.deped.gov.ph/create/detail/1445
Right Box
In Euclidean Geometry, point, line, and plane are mental concepts without a precise physical form. We can use real
objects to represent these ideas, but they remain abstract. Thus, these undefined terms can only be described.
1. Point A
2. Line BC
3. Ray DE
4. Line Segment FG
5. Angle HIJ
6. Plane K
A B
C
D
E F
G
18
LESSON SCRIPT IN NMP 9
Points, lines, line segments, rays, angles, and planes can be represented by figures. Examine Figure 1 and consider
what it suggests. Can the point, line, line segment, and ray be depicted within a single figure? Why or why not? Let
us consider this dot (•) as a point this time. A line is an infinite set of points that extends indefinitely, while a line
segment and a ray are subsets of a line.
Look at Figure 1,
points A and B are
connected in one
straight line.
Processing Questions:
1. What do you think the figure suggests herein?
2. Why the given figure above is called a line? What is a line?
3. Do you believe that a single figure can display the concepts of a point, line, line segment, and ray simultaneously?
Explain your reasoning.
4. Can you create a diagram where a single line can visually represent all its individual components, including points,
line segments, and rays?
NOTES TO THE TEACHER: This activity assists learners in visualizing the notation using both words and symbols.
Figure Notation
Word Geometric(Symbol)
Figure 1: Line AB
Point A
Point B
•A
•B
Line Segment AB
AB
Ray AB
Ray BA
AB
BA
Line AB
AB
Developing
Understanding of
the Key Idea/Stem
10 minutes
In addition, points, lines, line segments, rays, angles, and planes can be represented by real-life illustrations. An
angle is formed when two rays share a common endpoint, and a plane is formed by at least three intersecting lines.
Look at Illustration 1 below. It shows two children playing a traditional Filipino game known as Piko. Have you ever
played Piko in your neighborhood? Can you describe the rules of the game?
LESSON SCRIPT IN NMP 9
Points, lines, line segments, rays, angles, and planes can be represented by figures. Examine Figure 1 and consider
what it suggests. Can the point, line, line segment, and ray be depicted within a single figure? Why or why not? Let
us consider this dot (•) as a point this time. A line is an infinite set of points that extends indefinitely, while a line
segment and a ray are subsets of a line.
Look at Figure 1,
points A and B are
connected in one
straight line.
Processing Questions:
1. What do you think the figure suggests herein?
2. Why the given figure above is called a line? What is a line?
3. Do you believe that a single figure can display the concepts of a point, line, line segment, and ray simultaneously?
Explain your reasoning.
4. Can you create a diagram where a single line can visually represent all its individual components, including points,
line segments, and rays?
NOTES TO THE TEACHER: This activity assists learners in visualizing the notation using both words and symbols.
Figure Notation
Word Geometric(Symbol)
Figure 1: Line AB
Point A
Point B
•A
•B
Line Segment AB
AB
Ray AB
Ray BA
AB
BA
Line AB
AB
Developing
Understanding of
the Key Idea/Stem
10 minutes
In addition, points, lines, line segments, rays, angles, and planes can be represented by real-life illustrations. An
angle is formed when two rays share a common endpoint, and a plane is formed by at least three intersecting lines.
Look at Illustration 1 below. It shows two children playing a traditional Filipino game known as Piko. Have you ever
played Piko in your neighborhood? Can you describe the rules of the game?
19
LESSON SCRIPT IN NMP 9
Expected answers:
▪ Yes! We have enjoyably played piko in our town Teacher.
▪ Piko involves throwing a stone or other marker into numbered boxes drawn on the ground and hopping
between the boxes on one foot.
▪ Players take turns throwing their markers into the boxes and hopping through the game.
You got it right! Piko, also known as hopscotch, is a popular game in the Philippines enjoyed by both girls and boys.
Players draw rectangular-shaped boxes with ten sections on the ground using chalk or charcoal. The game can be
played individually or in teams, and requires a stone (pamato) for players to toss as part of the gameplay.
In the illustration, Chard and Lai are having fun playing Piko in their backyard. From their Piko mark on the ground,
there is a depiction of four intersecting lines that create a rectangle.
Illustration Notation
Illustration 1: Kids playing Piko
Department of Education. "Piko." https://lrmds.deped.gov.ph/create/detail/505
Word Geometric(Symbol)
Point P
Point L
Point A
Point Y
•P
•L
•A
•Y
Line Segment PL
Line Segment LA
Line Segment AY
Line Segment YA
PL
LA
AY
YA
Ray LA
Ray AL
Ray PY
Ray YP
LA
AL
PY
YP
Line LA
Line PY
LA
PY
Point A
Point B
•A
•B
Line Segment PL
PL
L
A
Y P
LESSON SCRIPT IN NMP 9
Expected answers:
▪ Yes! We have enjoyably played piko in our town Teacher.
▪ Piko involves throwing a stone or other marker into numbered boxes drawn on the ground and hopping
between the boxes on one foot.
▪ Players take turns throwing their markers into the boxes and hopping through the game.
You got it right! Piko, also known as hopscotch, is a popular game in the Philippines enjoyed by both girls and boys.
Players draw rectangular-shaped boxes with ten sections on the ground using chalk or charcoal. The game can be
played individually or in teams, and requires a stone (pamato) for players to toss as part of the gameplay.
In the illustration, Chard and Lai are having fun playing Piko in their backyard. From their Piko mark on the ground,
there is a depiction of four intersecting lines that create a rectangle.
Illustration Notation
Illustration 1: Kids playing Piko
Department of Education. "Piko." https://lrmds.deped.gov.ph/create/detail/505
Word Geometric(Symbol)
Point P
Point L
Point A
Point Y
•P
•L
•A
•Y
Line Segment PL
Line Segment LA
Line Segment AY
Line Segment YA
PL
LA
AY
YA
Ray LA
Ray AL
Ray PY
Ray YP
LA
AL
PY
YP
Line LA
Line PY
LA
PY
Point A
Point B
•A
•B
Line Segment PL
PL
L
A
Y P
20
LESSON SCRIPT IN NMP 9
Line Segment LA
Line Segment AY
Line Segment YP
LA
AY
YP
Angle P or Angle LPY
Angle L or Angle ALP
Angle A or Angle LAY
Angle Y or Angle AYP
P or LPY
L or ALP
A or LAY
Y or AYP
Processing Questions:
1. What do you think the illustration suggests herein?
2. Why the given illustration above represents real encounter of undefined term in Geometry?
3. Do you think a single visual representation can effectively showcase the abstract concepts of undefined terms in Geometry at
the same time? Justify your answer.
4. Could you describe real-life situations or encounters that exemplify the concepts of point, line, line segment, ray, angle, and
plane?
NOTES TO THE TEACHER: The illustration revisits a past Physical Education session for Grade 4 students during the First Quarter. The competency
focused on physical activities using target game concepts with agility, balance, coordination, and speed for active and healthy living: a. locomotor skills by
avoiding an object or obstacles, and b. manipulative skills by sending or propelling an object to an intended area. Students can understand how shapes and
spaces relate to their movements in activities. By looking at angles, paths, and distances in their actions, they can connect these skills to geometric ideas like
shapes and directions. Playing Philippine Traditional Games is a fun way for students to practice these geometric concepts in action.
NOTES TO THE TEACHER: The activity helps learners visualize the notation using words and symbols.
Deepening
Understanding of
the Key Idea/Stem
Let's see how well you’ve understood today’s lesson.
You will be divided into groups based on your camps, and each group will complete the task assigned to your camp.
Good luck, and enjoy learning Mathematics!
LESSON SCRIPT IN NMP 9
Line Segment LA
Line Segment AY
Line Segment YP
LA
AY
YP
Angle P or Angle LPY
Angle L or Angle ALP
Angle A or Angle LAY
Angle Y or Angle AYP
P or LPY
L or ALP
A or LAY
Y or AYP
Processing Questions:
1. What do you think the illustration suggests herein?
2. Why the given illustration above represents real encounter of undefined term in Geometry?
3. Do you think a single visual representation can effectively showcase the abstract concepts of undefined terms in Geometry at
the same time? Justify your answer.
4. Could you describe real-life situations or encounters that exemplify the concepts of point, line, line segment, ray, angle, and
plane?
NOTES TO THE TEACHER: The illustration revisits a past Physical Education session for Grade 4 students during the First Quarter. The competency
focused on physical activities using target game concepts with agility, balance, coordination, and speed for active and healthy living: a. locomotor skills by
avoiding an object or obstacles, and b. manipulative skills by sending or propelling an object to an intended area. Students can understand how shapes and
spaces relate to their movements in activities. By looking at angles, paths, and distances in their actions, they can connect these skills to geometric ideas like
shapes and directions. Playing Philippine Traditional Games is a fun way for students to practice these geometric concepts in action.
NOTES TO THE TEACHER: The activity helps learners visualize the notation using words and symbols.
Deepening
Understanding of
the Key Idea/Stem
Let's see how well you’ve understood today’s lesson.
You will be divided into groups based on your camps, and each group will complete the task assigned to your camp.
Good luck, and enjoy learning Mathematics!
21
LESSON SCRIPT IN NMP 9
5 minutes Intervention Group Consolidation Group Enhancement Group
Let’s Practice…
A. List of real-life objects
representing a point, line, or plane
is written below. Your task is to
write each object in its
corresponding column.
• hair strand
• tip of a ballpen
• electric wire
• corner of a table
• surface of the table
• edge of a paper
• screen of a smartphone
• plywood
• thread
• intersection of a side wall and
the ceiling
Objects
that
could
represent
a
POINT
Objects
that
could
represent
a
LINE
Objects
that
could
represent
a
PLANE
Let’s Practice…
A. Roam around classroom and find
real-life objects represent a point,
line, or plane. Place each object in
its corresponding tray or box.
NOTES TO THE TEACHER: Prepare 3 trays or
boxes and label them as Point, Line, and Plane.
Let’s Practice…
A. Create a drawing on a clean,
short bond paper in landscape
orientation. Illustrate real-life
objects that represent a point, line,
or plane. Use a marker to highlight
point, line, ray, line segment, angle,
and plane in the scenery.
NOTES TO THE TEACHER: Prepare short bond
papers, coloring, and art materials. You may
instruct students to bring the necessary materials
a day befo re conducting this NMP.
Objects that could represent a
POINT
Objects that could represent a
Line
Objects that could represent a
PLANE
LESSON SCRIPT IN NMP 9
5 minutes Intervention Group Consolidation Group Enhancement Group
Let’s Practice…
A. List of real-life objects
representing a point, line, or plane
is written below. Your task is to
write each object in its
corresponding column.
• hair strand
• tip of a ballpen
• electric wire
• corner of a table
• surface of the table
• edge of a paper
• screen of a smartphone
• plywood
• thread
• intersection of a side wall and
the ceiling
Objects
that
could
represent
a
POINT
Objects
that
could
represent
a
LINE
Objects
that
could
represent
a
PLANE
Let’s Practice…
A. Roam around classroom and find
real-life objects represent a point,
line, or plane. Place each object in
its corresponding tray or box.
NOTES TO THE TEACHER: Prepare 3 trays or
boxes and label them as Point, Line, and Plane.
Let’s Practice…
A. Create a drawing on a clean,
short bond paper in landscape
orientation. Illustrate real-life
objects that represent a point, line,
or plane. Use a marker to highlight
point, line, ray, line segment, angle,
and plane in the scenery.
NOTES TO THE TEACHER: Prepare short bond
papers, coloring, and art materials. You may
instruct students to bring the necessary materials
a day befo re conducting this NMP.
Objects that could represent a
POINT
Objects that could represent a
Line
Objects that could represent a
PLANE
22
LESSON SCRIPT IN NMP 9
After/Post-Lesson Proper
Making
Generalizations and
Abstractions
2 minutes
You did a great job! You've demonstrated a solid understanding of geometric models involving points, lines,
rays, line segments, angles, and planes.
1. How can you justify that a star can represent a geometric model of a point?
2. Can you cite a real-life object or situation where you can describe and illustrate a geometric model involving
points, lines, rays, line segments, angles, and planes
Expected answers:
1. A star can be seen as a geometric model of a point because, like a point, it is a single, dimensionless entity
representing a specific location in space without size or dimensions.
2. Student may vary their justifications. Accept and validate their reasoning.
Evaluating Learning
4 minutes
Now, we will test your understanding of illustrating geometric models involving points, lines, rays, line segments, angles
and planes by answering the following tasks.
Intervention Group Consolidation Group Enhancement Group
A. Multiple choice. Read each item
carefully. Choose the letter of the
best answer and write it on a
separate sheet of paper.
1. Which of the following does not
represent a point?
A. dot
B. the edge of a notebook
C. intersection of two lines
D. tip of a pen
2. What is the geometric term
represented by a nylon string?
A. point
B. line
C. plane
D. ray
A. Multiple choice. Read each
item carefully. Choose the letter
of the best answer and write it on
a separate sheet of paper.
1. Which of the following does not
represent a point?
A. dot
B. edge of a notebook
C. intersection of two lines
D. tip of a pen
2. What is the geometric term
represented by a nylon string?
A. point
B. line
C. plane
D. ray
A. Multiple choice. Read each item
carefully. Choose the letter of the best
answer and write it on a separate sheet of
paper.
1. Which of the following does not
represent a point?
A. dot
B. edge of a notebook
C. intersection of two lines
D. tip of a pen
2. What is the geometric term represented
by a nylon string?
A. point
B. line
C. plane
D. ray
LESSON SCRIPT IN NMP 9
After/Post-Lesson Proper
Making
Generalizations and
Abstractions
2 minutes
You did a great job! You've demonstrated a solid understanding of geometric models involving points, lines,
rays, line segments, angles, and planes.
1. How can you justify that a star can represent a geometric model of a point?
2. Can you cite a real-life object or situation where you can describe and illustrate a geometric model involving
points, lines, rays, line segments, angles, and planes
Expected answers:
1. A star can be seen as a geometric model of a point because, like a point, it is a single, dimensionless entity
representing a specific location in space without size or dimensions.
2. Student may vary their justifications. Accept and validate their reasoning.
Evaluating Learning
4 minutes
Now, we will test your understanding of illustrating geometric models involving points, lines, rays, line segments, angles
and planes by answering the following tasks.
Intervention Group Consolidation Group Enhancement Group
A. Multiple choice. Read each item
carefully. Choose the letter of the
best answer and write it on a
separate sheet of paper.
1. Which of the following does not
represent a point?
A. dot
B. the edge of a notebook
C. intersection of two lines
D. tip of a pen
2. What is the geometric term
represented by a nylon string?
A. point
B. line
C. plane
D. ray
A. Multiple choice. Read each
item carefully. Choose the letter
of the best answer and write it on
a separate sheet of paper.
1. Which of the following does not
represent a point?
A. dot
B. edge of a notebook
C. intersection of two lines
D. tip of a pen
2. What is the geometric term
represented by a nylon string?
A. point
B. line
C. plane
D. ray
A. Multiple choice. Read each item
carefully. Choose the letter of the best
answer and write it on a separate sheet of
paper.
1. Which of the following does not
represent a point?
A. dot
B. edge of a notebook
C. intersection of two lines
D. tip of a pen
2. What is the geometric term represented
by a nylon string?
A. point
B. line
C. plane
D. ray
23
LESSON SCRIPT IN NMP 9
Illustration 2 Illustration 2 Illustration 2
For numbers 3-4, refer to the
Illustration 2 below.
3. Which of the following is the
name of the plane?
A. plane A
B. plane B
C. plane C
D. plane F
4. Which of the following is not a
point?
A. A
B. B
C. C
D. p
For number 5, refer to Illustration
3 below.
5. Label each numbered item with
its corresponding geometric term:
point, line, line segment, ray,
angle, or plane.
For numbers 3-4, refer to the
Illustration 2 below.
3. Which of the following is the
name of the plane?
A. plane A
B. plane B
C. plane C
D. plane F
4. Which of the following is not a
point?
A. A
B. B
C. C
D. p
For number 5, refer to Illustration
3 below.
5. Encircle and label parts in the
illustration that represent point,
line, line segment, ray, angle, and
plane.
For numbers 3-4, refer to the
Illustration 2 below.
3. Which of the following is the name of
the plane?
A. plane A
B. plane B
C. plane C
D. plane F
4. Which of the following is not a point?
A. A
B. B
C. C
D. p
For number 5, refer to Illustration 3
below.
5. Encircle and label parts representing
point, line, line segment, ray, angle, and
plane in the illustration.
Explain in words, how you classify the
part of illustration as point, line, line
segment, ray, angle or plane.
________________________________________
________________________________________
_________________________
LESSON SCRIPT IN NMP 9
Illustration 2 Illustration 2 Illustration 2
For numbers 3-4, refer to the
Illustration 2 below.
3. Which of the following is the
name of the plane?
A. plane A
B. plane B
C. plane C
D. plane F
4. Which of the following is not a
point?
A. A
B. B
C. C
D. p
For number 5, refer to Illustration
3 below.
5. Label each numbered item with
its corresponding geometric term:
point, line, line segment, ray,
angle, or plane.
For numbers 3-4, refer to the
Illustration 2 below.
3. Which of the following is the
name of the plane?
A. plane A
B. plane B
C. plane C
D. plane F
4. Which of the following is not a
point?
A. A
B. B
C. C
D. p
For number 5, refer to Illustration
3 below.
5. Encircle and label parts in the
illustration that represent point,
line, line segment, ray, angle, and
plane.
For numbers 3-4, refer to the
Illustration 2 below.
3. Which of the following is the name of
the plane?
A. plane A
B. plane B
C. plane C
D. plane F
4. Which of the following is not a point?
A. A
B. B
C. C
D. p
For number 5, refer to Illustration 3
below.
5. Encircle and label parts representing
point, line, line segment, ray, angle, and
plane in the illustration.
Explain in words, how you classify the
part of illustration as point, line, line
segment, ray, angle or plane.
________________________________________
________________________________________
_________________________
24
LESSON SCRIPT IN NMP 9
Department of Education. "Sweeping."
https://lrmds.deped.gov.ph/create/detail/320
Department of Education. "Sweeping."
https://lrmds.deped.gov.ph/create/detail/32
0
Department of Education. "Sweeping."
https://lrmds.deped.gov.ph/create/detail/320
Rubric in Explanation in Words.
Point Description
1
Inadequate
-The explanation lacks clarity,
coherence, and relevant
details.
2
Developing
-The explanation shows some
understanding but lacks depth
and may contain minor errors.
3
Proficient
-The explanation is clear, well-
organized, and demonstrates a
Illustration 3: A boy sweeping the floor Illustration 3: A boy sweeping the floor
Illustration 3: A boy sweeping the floor
LESSON SCRIPT IN NMP 9
Department of Education. "Sweeping."
https://lrmds.deped.gov.ph/create/detail/320
Department of Education. "Sweeping."
https://lrmds.deped.gov.ph/create/detail/32
0
Department of Education. "Sweeping."
https://lrmds.deped.gov.ph/create/detail/320
Rubric in Explanation in Words.
Point Description
1
Inadequate
-The explanation lacks clarity,
coherence, and relevant
details.
2
Developing
-The explanation shows some
understanding but lacks depth
and may contain minor errors.
3
Proficient
-The explanation is clear, well-
organized, and demonstrates a
Illustration 3: A boy sweeping the floor Illustration 3: A boy sweeping the floor
Illustration 3: A boy sweeping the floor
25
LESSON SCRIPT IN NMP 9
good understanding of the
topic.
4
Advanced
-The explanation is thorough,
insightful, and effectively
communicates complex ideas
with precision.
5
Exceptional
-The explanation is
exceptionally clear, insightful,
and demonstrates a deep
understanding while engaging
the reader effectively.
Additional Activities
for Application or
Remediation (if
applicable)
Remarks
Reflection
LESSON SCRIPT IN NMP 9
good understanding of the
topic.
4
Advanced
-The explanation is thorough,
insightful, and effectively
communicates complex ideas
with precision.
5
Exceptional
-The explanation is
exceptionally clear, insightful,
and demonstrates a deep
understanding while engaging
the reader effectively.
Additional Activities
for Application or
Remediation (if
applicable)
Remarks
Reflection
26
LESSON SCRIPT IN NMP 9
Week 1 DAY 3
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A. Content
Standards
The learners demonstrate knowledge and understanding of
● simple geometric concepts and notations.
● perpendicular and parallel lines, and angles formed by a transversal.
B. Performance
Standards
By the end of the quarter, the learners are able to:
● illustrate and describe points, lines, rays, line segments, angles, and planes.
● construct perpendicular and parallel lines.
● determine the measure of the angles formed by parallel lines cut by a transversal.
C. Learning
Competencies
The learners will be able to:
● construct perpendicular and parallel lines.
D. Learning
Objectives
At the end of the lesson, the learners are able to:
● construct perpendicular and parallel lines.
II. CONTENT: Constructing Parallel Lines and Perpendicular Lines
III. LEARNING RESOURCES
A. References
Quarter 3 – Module 4: Geometric Construction: Bisectors, Perpendicular Lines and Parallel Lines. Koronadal City:
Department of Education, 2020, 10-11.
B. Other Learning
Resources
Ruler, Compass, Pencil, and Eraser
IV. TEACHING AND LEARNING PROCEDURES
Before/Pre-Lesson Proper
Activating Prior
Knowledge
(5 minutes)
Good morning/afternoon, class! It’s wonderful to see all of you again. Welcome to another session of the National
Mathematics Program!
Today, we will begin our session with an activity designed just for you. Let’s begin!
Intervention Group Consolidation Group Enhancement Group
Answer the following questions:
Question No. 1:
A figure that has length only, but no
width and endpoints, and extends
indefinitely in both directions is
called ___________.
Expected Answer: Line
Question No.2:
Answer the following questions:
Question No. 1:
An exact position or location on a
plane surface denoted by a capital
letter is called ___________.
Expected Answer: Point
Question No. 2:
Answer the following questions:
Question No. 1:
A figure that has length only, but no
width and endpoints, and extends
indefinitely in both directions is
called ___________.
Expected Answer: Line
LESSON SCRIPT IN NMP 9
Week 1 DAY 3
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A. Content
Standards
The learners demonstrate knowledge and understanding of
● simple geometric concepts and notations.
● perpendicular and parallel lines, and angles formed by a transversal.
B. Performance
Standards
By the end of the quarter, the learners are able to:
● illustrate and describe points, lines, rays, line segments, angles, and planes.
● construct perpendicular and parallel lines.
● determine the measure of the angles formed by parallel lines cut by a transversal.
C. Learning
Competencies
The learners will be able to:
● construct perpendicular and parallel lines.
D. Learning
Objectives
At the end of the lesson, the learners are able to:
● construct perpendicular and parallel lines.
II. CONTENT: Constructing Parallel Lines and Perpendicular Lines
III. LEARNING RESOURCES
A. References
Quarter 3 – Module 4: Geometric Construction: Bisectors, Perpendicular Lines and Parallel Lines. Koronadal City:
Department of Education, 2020, 10-11.
B. Other Learning
Resources
Ruler, Compass, Pencil, and Eraser
IV. TEACHING AND LEARNING PROCEDURES
Before/Pre-Lesson Proper
Activating Prior
Knowledge
(5 minutes)
Good morning/afternoon, class! It’s wonderful to see all of you again. Welcome to another session of the National
Mathematics Program!
Today, we will begin our session with an activity designed just for you. Let’s begin!
Intervention Group Consolidation Group Enhancement Group
Answer the following questions:
Question No. 1:
A figure that has length only, but no
width and endpoints, and extends
indefinitely in both directions is
called ___________.
Expected Answer: Line
Question No.2:
Answer the following questions:
Question No. 1:
An exact position or location on a
plane surface denoted by a capital
letter is called ___________.
Expected Answer: Point
Question No. 2:
Answer the following questions:
Question No. 1:
A figure that has length only, but no
width and endpoints, and extends
indefinitely in both directions is
called ___________.
Expected Answer: Line
27
LESSON SCRIPT IN NMP 9
A portion of a line with two
endpoints is called ___________.
Expected Answer: Line Segment
Question No. 3:
A part of a line with only one
endpoint that extends endlessly in
only one direction is called
___________.
Expected Answer: Ray
Question No. 4:
An exact position or location on a
plane surface denoted by a capital
letter is called ___________.
Expected Answer: Point
A part of a line with only one
endpoint that extends endlessly in
only one direction is called
___________.
Expected Answer: Ray
For items 3-5, label each of the
following figures, whether it is a
point, line, ray, or a line segment.
C.
Expected Answer: Line
D.
Expected Answer: Line Segment
E.
Expected Answer: Ray
Question No.2:
A portion of a line with two
endpoints is called ___________.
Expected Answer: Line Segment
Question No. 3:
A part of a line with only one
endpoint that extends endlessly in
only one direction is called
___________.
Expected Answer: Ray
Question No. 4:
An exact position or location on a
plane surface denoted by a capital
letter is called ___________.
Expected Answer: Point
For items 5-7, label each of the
following figures, whether it is a
point, line, ray, or a line segment.
5.
Expected Answer: Line
6.
Expected Answer: Line Segment
7.
Expected Answer: Ray
Lesson
Purpose/Intention
(1 minute)
You are now familiar with the undefined terminologies of Geometry, indicating that you are all set for another
exciting lesson! In today’s lesson, we will construct two types of lines, Parallel Lines and Perpendicular Lines.
LESSON SCRIPT IN NMP 9
A portion of a line with two
endpoints is called ___________.
Expected Answer: Line Segment
Question No. 3:
A part of a line with only one
endpoint that extends endlessly in
only one direction is called
___________.
Expected Answer: Ray
Question No. 4:
An exact position or location on a
plane surface denoted by a capital
letter is called ___________.
Expected Answer: Point
A part of a line with only one
endpoint that extends endlessly in
only one direction is called
___________.
Expected Answer: Ray
For items 3-5, label each of the
following figures, whether it is a
point, line, ray, or a line segment.
C.
Expected Answer: Line
D.
Expected Answer: Line Segment
E.
Expected Answer: Ray
Question No.2:
A portion of a line with two
endpoints is called ___________.
Expected Answer: Line Segment
Question No. 3:
A part of a line with only one
endpoint that extends endlessly in
only one direction is called
___________.
Expected Answer: Ray
Question No. 4:
An exact position or location on a
plane surface denoted by a capital
letter is called ___________.
Expected Answer: Point
For items 5-7, label each of the
following figures, whether it is a
point, line, ray, or a line segment.
5.
Expected Answer: Line
6.
Expected Answer: Line Segment
7.
Expected Answer: Ray
Lesson
Purpose/Intention
(1 minute)
You are now familiar with the undefined terminologies of Geometry, indicating that you are all set for another
exciting lesson! In today’s lesson, we will construct two types of lines, Parallel Lines and Perpendicular Lines.
28
LESSON SCRIPT IN NMP 9
Lesson Language
Practice
(1 minute)
Today, we're delving into the fascinating world of constructions in geometry. A Construction is a geometric drawing
that uses a limited set of tools, usually a compass and straightedge. A Straightedge is (a ruler without marks) used
to guide the pencil when drawing straight lines, while a compass is a geometric tool used to draw circles and parts
of a circle called arcs.
Now, let's explore the concepts of parallel and perpendicular lines:
• Parallel lines are two lines that never intersect, and the distance between them always remains the same.
• Perpendicular lines are two lines that intersect, and the angle formed between the two lines is 90 degrees
(right angle).
During/Lesson Proper
Reading the Key
Idea/Stem
3 minutes
Let's learn more about parallel and perpendicular lines through the following postulates.
The Parallel Postulate
Given a point and a line not containing it, there is exactly one line through the given point parallel to the given line.
Two lines are parallel if and only if they are coplanar and they do not intersect. The symbol “||” represents parallel
lines.
The Perpendicular Postulate
Given a point and a line not containing it, there is exactly one line through the given point perpendicular to the
given line. The symbol “⊥” represents perpendicular lines.
Developing
Understanding of the
Key Idea/Stem
10 minutes
Let us now construct parallel lines. Consider the problem below:
Given line � and point � not on � construct line �
through � with �||�
Step 1: Label two points � and � on �.
LESSON SCRIPT IN NMP 9
Lesson Language
Practice
(1 minute)
Today, we're delving into the fascinating world of constructions in geometry. A Construction is a geometric drawing
that uses a limited set of tools, usually a compass and straightedge. A Straightedge is (a ruler without marks) used
to guide the pencil when drawing straight lines, while a compass is a geometric tool used to draw circles and parts
of a circle called arcs.
Now, let's explore the concepts of parallel and perpendicular lines:
• Parallel lines are two lines that never intersect, and the distance between them always remains the same.
• Perpendicular lines are two lines that intersect, and the angle formed between the two lines is 90 degrees
(right angle).
During/Lesson Proper
Reading the Key
Idea/Stem
3 minutes
Let's learn more about parallel and perpendicular lines through the following postulates.
The Parallel Postulate
Given a point and a line not containing it, there is exactly one line through the given point parallel to the given line.
Two lines are parallel if and only if they are coplanar and they do not intersect. The symbol “||” represents parallel
lines.
The Perpendicular Postulate
Given a point and a line not containing it, there is exactly one line through the given point perpendicular to the
given line. The symbol “⊥” represents perpendicular lines.
Developing
Understanding of the
Key Idea/Stem
10 minutes
Let us now construct parallel lines. Consider the problem below:
Given line � and point � not on � construct line �
through � with �||�
Step 1: Label two points � and � on �.
29
LESSON SCRIPT IN NMP 9
Step 2: Draw ��⃡
Step 3: At �, construct ∠1 congruent to ∠���. Label
the new line �. That is �||�
Fantastic work, class! We've successfully tackled Problem No. 1 on constructing parallel lines. Now, let's ensure
we're all clear about the steps we took in constructing parallel lines.
Since we seem to have a solid grasp of constructing parallel lines, let's seamlessly transition to our next challenge
- constructing perpendicular lines.
Problem 2: Given point � on line �, construct
??????�⃡ with ??????�⃡ ⊥�
Step 1: Construct two points on � that are
equidistant from �. Label the points as � and �.
LESSON SCRIPT IN NMP 9
Step 2: Draw ��⃡
Step 3: At �, construct ∠1 congruent to ∠���. Label
the new line �. That is �||�
Fantastic work, class! We've successfully tackled Problem No. 1 on constructing parallel lines. Now, let's ensure
we're all clear about the steps we took in constructing parallel lines.
Since we seem to have a solid grasp of constructing parallel lines, let's seamlessly transition to our next challenge
- constructing perpendicular lines.
Problem 2: Given point � on line �, construct
??????�⃡ with ??????�⃡ ⊥�
Step 1: Construct two points on � that are
equidistant from �. Label the points as � and �.
30
LESSON SCRIPT IN NMP 9
Step 2: With the compass tip on �, draw an arc
above the point �.
Step 3: This time let us place the compass on
point �. Draw an arc that intersects the arc
from Step 2. Label the point of intersection as
??????.
Step 4. Draw ??????�⃡ .
LESSON SCRIPT IN NMP 9
Step 2: With the compass tip on �, draw an arc
above the point �.
Step 3: This time let us place the compass on
point �. Draw an arc that intersects the arc
from Step 2. Label the point of intersection as
??????.
Step 4. Draw ??????�⃡ .
31
LESSON SCRIPT IN NMP 9
Great job, everyone! We've successfully tackled the challenge of constructing perpendicular lines. Before we move
on to our next activity, let's take a moment to ensure everything is clear on the concepts we've covered. Can someone
volunteer to explain the key steps we followed to construct perpendicular lines? This will reinforce our learning and
boost our confidence in applying geometric principles.
Since there don't seem to be any questions, let's dive into an exciting activity to put our new knowledge to the test.
Deepening
Understanding of the
Key Idea/Stem
5 minutes
Intervention Group Consolidation Group Enhancement Group
Construct the line through point �
and parallel to ��⃡ for each figure
given below.
Figure No.1
Expected Answer:
Using the figure below, construct
the line perpendicular to ��⃡ at point
�.
Construct the line through point �
and parallel to ��⃡ for each figure
given below.
Figure No.1
Expected Answer:
Using the figure below, construct
the line through point � and parallel
to ��⃡ .
Figure No.1
Expected Answer:
LESSON SCRIPT IN NMP 9
Great job, everyone! We've successfully tackled the challenge of constructing perpendicular lines. Before we move
on to our next activity, let's take a moment to ensure everything is clear on the concepts we've covered. Can someone
volunteer to explain the key steps we followed to construct perpendicular lines? This will reinforce our learning and
boost our confidence in applying geometric principles.
Since there don't seem to be any questions, let's dive into an exciting activity to put our new knowledge to the test.
Deepening
Understanding of the
Key Idea/Stem
5 minutes
Intervention Group Consolidation Group Enhancement Group
Construct the line through point �
and parallel to ��⃡ for each figure
given below.
Figure No.1
Expected Answer:
Using the figure below, construct
the line perpendicular to ��⃡ at point
�.
Construct the line through point �
and parallel to ��⃡ for each figure
given below.
Figure No.1
Expected Answer:
Using the figure below, construct
the line through point � and parallel
to ��⃡ .
Figure No.1
Expected Answer:
32
LESSON SCRIPT IN NMP 9
Figure No. 2
Expected Answer:
Construct the line perpendicular to
��⃡ at point � for each figure shown
below.
Figure No.2
Expected Answer:
Using the figure below, construct
the line perpendicular to ��⃡ at point
�.
Figure No. 2
Expected Answer:
Determine whether the following
pair of equations are parallel,
perpendicular, or neither.
�=��+�
�=��−�
Expected Answer:
Parallel lines because their slopes
are equal.
LESSON SCRIPT IN NMP 9
Figure No. 2
Expected Answer:
Construct the line perpendicular to
��⃡ at point � for each figure shown
below.
Figure No.2
Expected Answer:
Using the figure below, construct
the line perpendicular to ��⃡ at point
�.
Figure No. 2
Expected Answer:
Determine whether the following
pair of equations are parallel,
perpendicular, or neither.
�=��+�
�=��−�
Expected Answer:
Parallel lines because their slopes
are equal.
33
LESSON SCRIPT IN NMP 9
Congratulations, everyone! Your hard work and teamwork have indeed paid off! This outstanding achievement
showcases the power of cooperation and collaboration. Your commitment to learning and working together is truly
commendable. Well done!
After/Post-Lesson Proper
Making
Generalizations and
Abstractions
2 minutes
You did a great job! You've demonstrated a solid understanding of constructing parallel and perpendicular lines.
It’s wrap-up time! I have prepared questions for you. If you wish to answer the question, kindly raise your right
hand, okay? Let’s get started!
Question No. 1: State the Parallel Postulate
Expected Answer: Given a point and a line not containing it, there is exactly one line through the given point parallel
to the given line. Two lines are parallel if and only if they are coplanar and they do not intersect.
Question No. 2: State the Perpendicular Postulate.
Expected Answer: Given a point and a line not containing it, there is exactly one line through the given point
perpendicular to the given line.
Question No. 3 What is the symbol for parallel lines? How about the symbol for perpendicular lines?
Expected Answer: The symbol “||” represents parallel lines. The symbol “⊥” represents perpendicular lines.
Question No. 4: Construct an example of parallel lines and perpendicular lines.
Expected Answer: Answers may vary
Evaluating Learning
4 minutes
Let's put your skills to the test! To assess your proficiency in constructing parallel and perpendicular lines, you
will now complete the following task. Write your answer on a 1 whole sheet of paper.
Intervention Group Consolidation Group Enhancement Group
Problem No. 1
Using the figure below, construct
the line through point � and parallel
to ��⃡ .
Problem No. 1
Using the figure below, construct
the line through point � and parallel
to ��⃡ .
Problem No. 1
Using the figure below, construct
the line through point � and parallel
to ��⃡ .
LESSON SCRIPT IN NMP 9
Congratulations, everyone! Your hard work and teamwork have indeed paid off! This outstanding achievement
showcases the power of cooperation and collaboration. Your commitment to learning and working together is truly
commendable. Well done!
After/Post-Lesson Proper
Making
Generalizations and
Abstractions
2 minutes
You did a great job! You've demonstrated a solid understanding of constructing parallel and perpendicular lines.
It’s wrap-up time! I have prepared questions for you. If you wish to answer the question, kindly raise your right
hand, okay? Let’s get started!
Question No. 1: State the Parallel Postulate
Expected Answer: Given a point and a line not containing it, there is exactly one line through the given point parallel
to the given line. Two lines are parallel if and only if they are coplanar and they do not intersect.
Question No. 2: State the Perpendicular Postulate.
Expected Answer: Given a point and a line not containing it, there is exactly one line through the given point
perpendicular to the given line.
Question No. 3 What is the symbol for parallel lines? How about the symbol for perpendicular lines?
Expected Answer: The symbol “||” represents parallel lines. The symbol “⊥” represents perpendicular lines.
Question No. 4: Construct an example of parallel lines and perpendicular lines.
Expected Answer: Answers may vary
Evaluating Learning
4 minutes
Let's put your skills to the test! To assess your proficiency in constructing parallel and perpendicular lines, you
will now complete the following task. Write your answer on a 1 whole sheet of paper.
Intervention Group Consolidation Group Enhancement Group
Problem No. 1
Using the figure below, construct
the line through point � and parallel
to ��⃡ .
Problem No. 1
Using the figure below, construct
the line through point � and parallel
to ��⃡ .
Problem No. 1
Using the figure below, construct
the line through point � and parallel
to ��⃡ .
34
LESSON SCRIPT IN NMP 9
Problem No. 2
Using the figure below, construct
the line perpendicular to ��⃡ at point
�.
Problem No. 2
Using the figure below, construct
the line perpendicular to ��⃡ at point
�.
Problem No. 2
Using the figure below, construct
the line perpendicular to ��⃡ at point
�.
Problem No. 3
Determine whether the following
pair of equations are parallel,
perpendicular, or neither.
�=−��+??????
�=
�
�
�−�
Expected Answers:
Problem No. 1
Expected Answers:
Problem No. 1
Expected Answers:
Problem No. 1
LESSON SCRIPT IN NMP 9
Problem No. 2
Using the figure below, construct
the line perpendicular to ��⃡ at point
�.
Problem No. 2
Using the figure below, construct
the line perpendicular to ��⃡ at point
�.
Problem No. 2
Using the figure below, construct
the line perpendicular to ��⃡ at point
�.
Problem No. 3
Determine whether the following
pair of equations are parallel,
perpendicular, or neither.
�=−��+??????
�=
�
�
�−�
Expected Answers:
Problem No. 1
Expected Answers:
Problem No. 1
Expected Answers:
Problem No. 1
35
LESSON SCRIPT IN NMP 9
Problem No. 2
Problem No. 2
Problem No. 2
Problem No. 3
Perpendicular lines because their
slopes are negative reciprocals.
Great work today, class! I'm proud of your dedication and progress. Keep up the good work! Until our next
meeting and remember to practice what we've learned. See you all next session!
Additional Activities for
Application or
Remediation (if
applicable)
Remarks
Reflection
LESSON SCRIPT IN NMP 9
Problem No. 2
Problem No. 2
Problem No. 2
Problem No. 3
Perpendicular lines because their
slopes are negative reciprocals.
Great work today, class! I'm proud of your dedication and progress. Keep up the good work! Until our next
meeting and remember to practice what we've learned. See you all next session!
Additional Activities for
Application or
Remediation (if
applicable)
Remarks
Reflection
26
LESSON SCRIPT IN NMP 9
Week 1 DAY 4
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A. Content
Standards
The learners demonstrate knowledge and understanding of
● perpendicular and parallel lines, and angles formed by parallel lines cut by a transversal.
B. Performance
Standards
By the end of the quarter, the learners are able to:
● construct perpendicular and parallel lines. (MG)
C. Learning
Competencies
The learners will be able to:
● identify the relationships between angles formed by parallel lines cut by a transversal
D. Learning
Objectives
At the end of the lesson, the learners are able to:
● identify the angles formed by parallel lines cut by a transversal
II. CONTENT: Parallel Lines Cut by a Transversal
III. LEARNING RESOURCES
A. References
Mercado, Ana Cristy P. Mathematics 7 Quarter 3 – Module 3: Parallel Lines Cut By a Transversal. Department of
Education: Tagum City, 2020, 2-5.
Bundang, Frenezi A., Balaba, Karl Jio S. Mathematics 7 Quarter 3 – Module 3: Parallel Lines Cut By a
Transversal. Department of Education: SOCCSKSARGEN , 2020, 4-6.
B. Other Learning
Resources
Ruler, bond paper
IV. TEACHING AND LEARNING PROCEDURES
Before/Pre-Lesson Proper
Activating Prior
Knowledge
(4 minutes)
Good morning/afternoon, class! Are you excited about our National Mathematics Program class today?
Today, we will identify the angles formed by parallel lines cut by a transversal.
I have prepared activities for each group to perform. You will post your answer on the board.
Intervention Group Consolidation Group Enhancement Group
1. Define parallel lines.
2. Construct parallel lines using a
ruler.
1. Define transversal.
2. Construct parallel lines cut by a
transversal using a ruler.
1. Construct parallel lines cut by a
transversal using a ruler.
2. Label the angles formed.
(After the answers are posted, process the learner’s output and give appropriate feedback.) Say, “Let us see if you
got them right.”
Lesson
Purpose/Intention
Now let us identify the angles formed by parallel lines cut by a transversal.
Let us do it!
LESSON SCRIPT IN NMP 9
Week 1 DAY 4
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A. Content
Standards
The learners demonstrate knowledge and understanding of
● perpendicular and parallel lines, and angles formed by parallel lines cut by a transversal.
B. Performance
Standards
By the end of the quarter, the learners are able to:
● construct perpendicular and parallel lines. (MG)
C. Learning
Competencies
The learners will be able to:
● identify the relationships between angles formed by parallel lines cut by a transversal
D. Learning
Objectives
At the end of the lesson, the learners are able to:
● identify the angles formed by parallel lines cut by a transversal
II. CONTENT: Parallel Lines Cut by a Transversal
III. LEARNING RESOURCES
A. References
Mercado, Ana Cristy P. Mathematics 7 Quarter 3 – Module 3: Parallel Lines Cut By a Transversal. Department of
Education: Tagum City, 2020, 2-5.
Bundang, Frenezi A., Balaba, Karl Jio S. Mathematics 7 Quarter 3 – Module 3: Parallel Lines Cut By a
Transversal. Department of Education: SOCCSKSARGEN , 2020, 4-6.
B. Other Learning
Resources
Ruler, bond paper
IV. TEACHING AND LEARNING PROCEDURES
Before/Pre-Lesson Proper
Activating Prior
Knowledge
(4 minutes)
Good morning/afternoon, class! Are you excited about our National Mathematics Program class today?
Today, we will identify the angles formed by parallel lines cut by a transversal.
I have prepared activities for each group to perform. You will post your answer on the board.
Intervention Group Consolidation Group Enhancement Group
1. Define parallel lines.
2. Construct parallel lines using a
ruler.
1. Define transversal.
2. Construct parallel lines cut by a
transversal using a ruler.
1. Construct parallel lines cut by a
transversal using a ruler.
2. Label the angles formed.
(After the answers are posted, process the learner’s output and give appropriate feedback.) Say, “Let us see if you
got them right.”
Lesson
Purpose/Intention
Now let us identify the angles formed by parallel lines cut by a transversal.
Let us do it!
27
LESSON SCRIPT IN NMP 9
(1 minute)
NOTES TO THE TEACHER: This lesson introduces the competency/objective to be mastered: identifying the
angles formed by parallel lines cut by a transversal.
Lesson Language
Practice
(1 minute)
To refresh our memories, let us recall the meaning of the following words before continuing our discussion.
Parallel lines are coplanar lines that do not intersect
Transversal is a line intersecting two or more coplanar lines at different points.
Alternate Interior Angles- a pair of non-adjacent interior angles on opposite sides of a transversal
Corresponding Angles- a pair of non-adjacent interior and exterior angles on the same transversal side.
Same-Side Interior Angles- interior angles on the same- side of the transversal.
Vertical angles are pair of non-adjacent angles formed by two intersecting lines.
NOTES TO THE TEACHER: This part introduces the key terms to be used in the lesson.
During/Lesson Proper
Reading the Key
Idea/Stem
3 minutes
I will show an illustration of parallel lines cut by a transversal. Lines a and x are parallel and cut by transversal t.
Notice that a transversal creates different angle pairs. You will identify the angles formed by parallel lines cut by a
transversal. We will post the answers on the board.
1. How many angles are there?
2. Can you name all the angles?
Expected answers:
1. 8
2. ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8
Excellent, you have named all the angles correctly. So now, let’s proceed to the next activity: discussing of the angles
formed by parallel lines cut by a transversal.
1
7
a
x
3
4
5
6
t
LESSON SCRIPT IN NMP 9
(1 minute)
NOTES TO THE TEACHER: This lesson introduces the competency/objective to be mastered: identifying the
angles formed by parallel lines cut by a transversal.
Lesson Language
Practice
(1 minute)
To refresh our memories, let us recall the meaning of the following words before continuing our discussion.
Parallel lines are coplanar lines that do not intersect
Transversal is a line intersecting two or more coplanar lines at different points.
Alternate Interior Angles- a pair of non-adjacent interior angles on opposite sides of a transversal
Corresponding Angles- a pair of non-adjacent interior and exterior angles on the same transversal side.
Same-Side Interior Angles- interior angles on the same- side of the transversal.
Vertical angles are pair of non-adjacent angles formed by two intersecting lines.
NOTES TO THE TEACHER: This part introduces the key terms to be used in the lesson.
During/Lesson Proper
Reading the Key
Idea/Stem
3 minutes
I will show an illustration of parallel lines cut by a transversal. Lines a and x are parallel and cut by transversal t.
Notice that a transversal creates different angle pairs. You will identify the angles formed by parallel lines cut by a
transversal. We will post the answers on the board.
1. How many angles are there?
2. Can you name all the angles?
Expected answers:
1. 8
2. ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8
Excellent, you have named all the angles correctly. So now, let’s proceed to the next activity: discussing of the angles
formed by parallel lines cut by a transversal.
1
7
a
x
3
4
5
6
t
28
LESSON SCRIPT IN NMP 9
Developing
Understanding of the
Key Idea/Stem
10 minutes
Given the parallel lines a and x, cut by transversal t, identify the following:
1. Interior angles
2. Exterior angles
3. Pairs of same-side interior angles
4. Pairs of alternate interior angles
5. Pairs of same-side exterior angles
6. Pairs of alternate exterior angles
7. Pairs of corresponding angles
8. Vertical angles
Expected Answers:
1. Interior angles: ∠2, ∠4, ∠5, and ∠7
2. Exterior angles: ∠1, ∠3, ∠6, and ∠8
3. Pairs of same-side interior angles: ∠2 and ∠5 ; ∠4 and ∠7
4. Pairs of alternate interior angles: ∠2 and ∠7 ; ∠4 and ∠5
5. Pairs of same-side exterior angles: ∠1 and ∠6 ; ∠3 and ∠8
6. Pairs of alternate exterior angles: ∠1 and ∠8 ; ∠3 and ∠6
7. Pairs of corresponding angles: ∠1 and ∠5 ; ∠2 and ∠6 ; ∠3 and ∠7; ∠4 and∠8
8. Vertical angles: ∠1 and ∠4 ; ∠2 and ∠3 ; ∠5 and ∠8 ; ∠6 and ∠7
To enhance your comprehension, you will complete the activity individually, in pairs, or groups. We will post the
answers on the board to verify if everyone has the correct responses.
NOTES TO THE TEACHER: These items were given to provide more examples to the learners.
1
7
a
x
3
4
5
6
t
LESSON SCRIPT IN NMP 9
Developing
Understanding of the
Key Idea/Stem
10 minutes
Given the parallel lines a and x, cut by transversal t, identify the following:
1. Interior angles
2. Exterior angles
3. Pairs of same-side interior angles
4. Pairs of alternate interior angles
5. Pairs of same-side exterior angles
6. Pairs of alternate exterior angles
7. Pairs of corresponding angles
8. Vertical angles
Expected Answers:
1. Interior angles: ∠2, ∠4, ∠5, and ∠7
2. Exterior angles: ∠1, ∠3, ∠6, and ∠8
3. Pairs of same-side interior angles: ∠2 and ∠5 ; ∠4 and ∠7
4. Pairs of alternate interior angles: ∠2 and ∠7 ; ∠4 and ∠5
5. Pairs of same-side exterior angles: ∠1 and ∠6 ; ∠3 and ∠8
6. Pairs of alternate exterior angles: ∠1 and ∠8 ; ∠3 and ∠6
7. Pairs of corresponding angles: ∠1 and ∠5 ; ∠2 and ∠6 ; ∠3 and ∠7; ∠4 and∠8
8. Vertical angles: ∠1 and ∠4 ; ∠2 and ∠3 ; ∠5 and ∠8 ; ∠6 and ∠7
To enhance your comprehension, you will complete the activity individually, in pairs, or groups. We will post the
answers on the board to verify if everyone has the correct responses.
NOTES TO THE TEACHER: These items were given to provide more examples to the learners.
1
7
a
x
3
4
5
6
t
29
LESSON SCRIPT IN NMP 9
Deepening
Understanding of the
Key Idea/Stem
5 minutes
Intervention Group Consolidation Group Enhancement Group
Let’s Practice…
A. Given the parallel lines a and x, cut
by transversal t, identify the angles
asked in each item.
1. 4 pairs of corresponding angles
∠7 and ∠3 ; ∠6 and ∠ ___ ;
∠8 and ∠____ ; ∠5 and ∠____.
2. All interior angles: ______________
3. 2 pairs of alternate interior
angles
∠8 and ∠ ____ ; ∠5 and ∠____.
4. All exterior angles:_____________
5. 2 pairs of alternate exterior
angles ∠7 and ∠____; ∠6 and ∠____.
Expected Answers:
1. ∠6 and ∠2; ∠8 and ∠4;
∠5 and ∠1
2. ∠2, ∠3 , ∠5, and ∠8
3. ∠8 and ∠2 ; ∠5 and ∠3
Let’s Practice…
A. Given the parallel lines a and x,
cut by transversal t, identify the
angles asked in each item.
1. 4 pairs of vertical angles
2. 2 pairs of same-side interior
angles
3. 2 pairs of same-side exterior
angles
4. 4 pairs of corresponding angles
Expected Answers:
1. ∠7 and ∠5 ; ∠6 and ∠5 ;
∠2 and ∠4; ∠1 and ∠3
2. ∠8 and ∠3 ; ∠5 and ∠2
3. ∠7 and ∠4 ; ∠6 and ∠1
Let’s Practice…
A. If the statement is correct, write
TRUE. If not, write FALSE. Lines a
and x are parallel and are cut by
transversal t.
1. ∠7 and ∠1 are corresponding
angles
2. ∠6 and ∠2 are corresponding
angles
3. ∠8 and ∠2 are alternate interior
angles
4. ∠7 and ∠4 are same-side
exterior angles
5. ∠8 and ∠3 are same-side
interior angles
B. Use the figure above to identify
the following pairs of angles:
1. ∠6 and ∠1
2. ∠7 and ∠3
3. ∠5 and ∠2
4. ∠4 and ∠2
5. ∠5 and ∠1
7
a
x
6
5
3
4
1
t
8
7
a
x
6
5
3
4
1
t
8
7
a
x
6
5
3
4
1
t
8
LESSON SCRIPT IN NMP 9
Deepening
Understanding of the
Key Idea/Stem
5 minutes
Intervention Group Consolidation Group Enhancement Group
Let’s Practice…
A. Given the parallel lines a and x, cut
by transversal t, identify the angles
asked in each item.
1. 4 pairs of corresponding angles
∠7 and ∠3 ; ∠6 and ∠ ___ ;
∠8 and ∠____ ; ∠5 and ∠____.
2. All interior angles: ______________
3. 2 pairs of alternate interior
angles
∠8 and ∠ ____ ; ∠5 and ∠____.
4. All exterior angles:_____________
5. 2 pairs of alternate exterior
angles ∠7 and ∠____; ∠6 and ∠____.
Expected Answers:
1. ∠6 and ∠2; ∠8 and ∠4;
∠5 and ∠1
2. ∠2, ∠3 , ∠5, and ∠8
3. ∠8 and ∠2 ; ∠5 and ∠3
Let’s Practice…
A. Given the parallel lines a and x,
cut by transversal t, identify the
angles asked in each item.
1. 4 pairs of vertical angles
2. 2 pairs of same-side interior
angles
3. 2 pairs of same-side exterior
angles
4. 4 pairs of corresponding angles
Expected Answers:
1. ∠7 and ∠5 ; ∠6 and ∠5 ;
∠2 and ∠4; ∠1 and ∠3
2. ∠8 and ∠3 ; ∠5 and ∠2
3. ∠7 and ∠4 ; ∠6 and ∠1
Let’s Practice…
A. If the statement is correct, write
TRUE. If not, write FALSE. Lines a
and x are parallel and are cut by
transversal t.
1. ∠7 and ∠1 are corresponding
angles
2. ∠6 and ∠2 are corresponding
angles
3. ∠8 and ∠2 are alternate interior
angles
4. ∠7 and ∠4 are same-side
exterior angles
5. ∠8 and ∠3 are same-side
interior angles
B. Use the figure above to identify
the following pairs of angles:
1. ∠6 and ∠1
2. ∠7 and ∠3
3. ∠5 and ∠2
4. ∠4 and ∠2
5. ∠5 and ∠1
7
a
x
6
5
3
4
1
t
8
7
a
x
6
5
3
4
1
t
8
7
a
x
6
5
3
4
1
t
8
30
LESSON SCRIPT IN NMP 9
4. ∠7, ∠6, ∠4, and ∠1
5. ∠7 and ∠1 ; ∠6 and ∠4
4. ∠7 and ∠5, ∠6 and ∠2; ∠8 and ∠4;
∠5 and ∠1
Expected Answers:
A.
1. FALSE
2. TRUE
3. TRUE
4. TRUE
5. TRUE
B.
1. same-side exterior angles
2. corresponding angles
3. same-side interior angles
4. vertical angles
5. corresponding angles
After/Post-Lesson Proper
Making
Generalizations and
Abstractions
2 minutes
You did an excellent job! You've shown a strong grasp of recognizing the angles formed by parallel lines cut by a
transversal. Let us conclude the day’s discussion by answering a few questions.
1. What is a transversal line?
2. What angles are formed by parallel lines cut by a transversal?
Expected answers:
3. Transversal is a line intersecting two or more coplanar lines at different points.
4. The angles formed by parallel lines cut by a transversal are: corresponding angles, vertical angles, alternate
interior angles, alternate exterior angles, same-side interior angles, same-side exterior angles, exterior angles,
and interior angles
Evaluating Learning
4 minutes
Now, we will assess your understanding of angles formed by parallel lines cut by a transversal by answering the
following tasks. Read and comprehend each item carefully. Write your answers on a separate sheet of paper.
LESSON SCRIPT IN NMP 9
4. ∠7, ∠6, ∠4, and ∠1
5. ∠7 and ∠1 ; ∠6 and ∠4
4. ∠7 and ∠5, ∠6 and ∠2; ∠8 and ∠4;
∠5 and ∠1
Expected Answers:
A.
1. FALSE
2. TRUE
3. TRUE
4. TRUE
5. TRUE
B.
1. same-side exterior angles
2. corresponding angles
3. same-side interior angles
4. vertical angles
5. corresponding angles
After/Post-Lesson Proper
Making
Generalizations and
Abstractions
2 minutes
You did an excellent job! You've shown a strong grasp of recognizing the angles formed by parallel lines cut by a
transversal. Let us conclude the day’s discussion by answering a few questions.
1. What is a transversal line?
2. What angles are formed by parallel lines cut by a transversal?
Expected answers:
3. Transversal is a line intersecting two or more coplanar lines at different points.
4. The angles formed by parallel lines cut by a transversal are: corresponding angles, vertical angles, alternate
interior angles, alternate exterior angles, same-side interior angles, same-side exterior angles, exterior angles,
and interior angles
Evaluating Learning
4 minutes
Now, we will assess your understanding of angles formed by parallel lines cut by a transversal by answering the
following tasks. Read and comprehend each item carefully. Write your answers on a separate sheet of paper.
31
LESSON SCRIPT IN NMP 9
Intervention Group Consolidation Group Enhancement Group
Given the parallel lines 2 and 3, cut
by transversal 1, answer the
questions below. Write the letter of
the correct answer.
1. Which of the following is NOT an
exterior angle?
A. ∠r B. ∠s C. ∠ w D. ∠z
2. All of the following are interior
angles, EXCEPT:
A. ∠w B. ∠y C. ∠t D. ∠x
3. How many pairs of vertical angles
are there?
A. 6 B. 4 C. 2 D. 1
4. Which of the following pairs of
angles are corresponding angles?
A. ∠u and ∠w C. ∠s and ∠z
B. ∠r and ∠w D. ∠x and ∠y
5. What do you call ∠s and ∠t?
A. corresponding angles
B. alternate interior angles
C. same-side interior angles
D. vertical angles
Expected answers:
1. C
2. B
I. Given the parallel lines 2 and 3,
cut by transversal 1, answer the
following questions. Write the letter
of the correct answer.
1. Which of the following is NOT an
exterior angle?
A. ∠r B. ∠s C. ∠ w D. ∠z
2. All of the following are interior
angles, EXCEPT:
A. ∠w B. ∠y C. ∠t D. ∠x
3. How many pairs of corresponding
angles are there?
A. 6 B. 4 C. 2 D. 1
4. Which of the following pairs of
angles are vertical angles?
A. ∠u and ∠w C. ∠s and ∠z
B. ∠r and ∠w D. ∠x and ∠y
5. What do you call ∠s and ∠x?
A. corresponding angles
B. alternate interior angles
C. vertical angles
D. same-side interior angles
II. List the following pairs of angles:
I. Given the parallel lines 2 and 3,
cut by transversal 1, answer the
following questions. Write the letter
of the correct answer.
1. Which of the following is NOT an
exterior angle?
A. ∠r B. ∠s C. ∠ w D. ∠z
2. All of the following are pairs of
corresponding angles, EXCEPT:
A. ∠r and ∠w C. ∠t and ∠y
C. ∠s and ∠x D. ∠u and ∠x
3. How many pairs of vertical angles
are there?
A. 6 B. 4 C. 2 D. 1
4. Which of the following pairs of
angles are alternate interior angles?
A. ∠u and ∠w C. ∠s and ∠z
B. ∠r and ∠w D. ∠x and ∠y
5. What do you call ∠w and ∠t?
A. corresponding angles
B. alternate interior angles
C. vertical angles
D. same-side interior angles
II. Identify the following pairs of
angles:
r
2
3
s
u
w
y
z
1
t
r
2
3
s
u
w
y
z
1
t
r
2
3
s
u
w
y
z
1
t
LESSON SCRIPT IN NMP 9
Intervention Group Consolidation Group Enhancement Group
Given the parallel lines 2 and 3, cut
by transversal 1, answer the
questions below. Write the letter of
the correct answer.
1. Which of the following is NOT an
exterior angle?
A. ∠r B. ∠s C. ∠ w D. ∠z
2. All of the following are interior
angles, EXCEPT:
A. ∠w B. ∠y C. ∠t D. ∠x
3. How many pairs of vertical angles
are there?
A. 6 B. 4 C. 2 D. 1
4. Which of the following pairs of
angles are corresponding angles?
A. ∠u and ∠w C. ∠s and ∠z
B. ∠r and ∠w D. ∠x and ∠y
5. What do you call ∠s and ∠t?
A. corresponding angles
B. alternate interior angles
C. same-side interior angles
D. vertical angles
Expected answers:
1. C
2. B
I. Given the parallel lines 2 and 3,
cut by transversal 1, answer the
following questions. Write the letter
of the correct answer.
1. Which of the following is NOT an
exterior angle?
A. ∠r B. ∠s C. ∠ w D. ∠z
2. All of the following are interior
angles, EXCEPT:
A. ∠w B. ∠y C. ∠t D. ∠x
3. How many pairs of corresponding
angles are there?
A. 6 B. 4 C. 2 D. 1
4. Which of the following pairs of
angles are vertical angles?
A. ∠u and ∠w C. ∠s and ∠z
B. ∠r and ∠w D. ∠x and ∠y
5. What do you call ∠s and ∠x?
A. corresponding angles
B. alternate interior angles
C. vertical angles
D. same-side interior angles
II. List the following pairs of angles:
I. Given the parallel lines 2 and 3,
cut by transversal 1, answer the
following questions. Write the letter
of the correct answer.
1. Which of the following is NOT an
exterior angle?
A. ∠r B. ∠s C. ∠ w D. ∠z
2. All of the following are pairs of
corresponding angles, EXCEPT:
A. ∠r and ∠w C. ∠t and ∠y
C. ∠s and ∠x D. ∠u and ∠x
3. How many pairs of vertical angles
are there?
A. 6 B. 4 C. 2 D. 1
4. Which of the following pairs of
angles are alternate interior angles?
A. ∠u and ∠w C. ∠s and ∠z
B. ∠r and ∠w D. ∠x and ∠y
5. What do you call ∠w and ∠t?
A. corresponding angles
B. alternate interior angles
C. vertical angles
D. same-side interior angles
II. Identify the following pairs of
angles:
r
2
3
s
u
w
y
z
1
t
r
2
3
s
u
w
y
z
1
t
r
2
3
s
u
w
y
z
1
t
32
LESSON SCRIPT IN NMP 9
3. B
4. B
5. D
1. same-side interior angles
___________________________________
___________________________________
2. same-side exterior angles
___________________________________
___________________________________
Expected answers:
I.
1. C
2. B
3. B
4. D
5. A
II.
1. ∠t and ∠w ; ∠u and ∠x
2. ∠r and ∠y ; ∠s and ∠z
1. corresponding angles
___________________________________
___________________________________
2. vertical angles
___________________________________
___________________________________
Expected answers:
I.
1. C
2. D
3. B
4. A
5. D
II.
1. ∠r and ∠w ; ∠s and ∠x ;
∠t and ∠y ; ∠u and ∠z
2. ∠r and ∠u ; ∠s and ∠t ;
∠w and ∠z ; ∠x and ∠y
Additional Activities
for Application or
Remediation (if
applicable)
Remarks
Reflection
LESSON SCRIPT IN NMP 9
3. B
4. B
5. D
1. same-side interior angles
___________________________________
___________________________________
2. same-side exterior angles
___________________________________
___________________________________
Expected answers:
I.
1. C
2. B
3. B
4. D
5. A
II.
1. ∠t and ∠w ; ∠u and ∠x
2. ∠r and ∠y ; ∠s and ∠z
1. corresponding angles
___________________________________
___________________________________
2. vertical angles
___________________________________
___________________________________
Expected answers:
I.
1. C
2. D
3. B
4. A
5. D
II.
1. ∠r and ∠w ; ∠s and ∠x ;
∠t and ∠y ; ∠u and ∠z
2. ∠r and ∠u ; ∠s and ∠t ;
∠w and ∠z ; ∠x and ∠y
Additional Activities
for Application or
Remediation (if
applicable)
Remarks
Reflection
For inquiries or feedback, please write or call:
Department of Education – Region XI
Office Address: F. Torres St., Davao City
Telefax: (082) 291-1665; (082) 221-6147
E-mail Address: [email protected] | [email protected]
Department of Education – Region XI
Office Address: F. Torres St., Davao City
Telefax: (082) 291-1665; (082) 221-6147
E-mail Address: [email protected] | [email protected]
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