Lesson Exemplar
for Mathematics
1
Quarter 2
Lesson
1
Lesson Exemplar for Mathematics Grade 8
Quarter 2: Lesson 1 (Week 1)
SY 2025-2026
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Development Team
Writer:
 Yahweh M. Pasahol (Pedro Guevara Memorial National High School)
Validator:
 Roldan S. Cardona (Philippine Normal University – North Luzon)
Management Team
Philippine Normal University
Research Institute for Teacher Quality
SiMERR National Research Centre
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MATHEMATICS / QUARTER 2 / GRADE 8
I. CURRICULUM CONTENT, STANDARDS, AND LESSON COMPETENCIES
A. Content
Standards
The learners demonstrate knowledge and understanding of plotting points, and finding distance and the midpoint of
line segments on the Cartesian coordinate plane.
B. Performance
Standards
By the end of the quarter, the learners are able to plot points, find the distance between two points, and find the
midpoint of line segments, on the Cartesian coordinate plane. (NA)
C. Learning
Competencies
and Objectives
Learning Competency
At the end of the lesson, the learners are able to:
1. illustrate and describe the Cartesian coordinate plane.
Lesson Objective 1: Illustrate a Cartesian coordinate plane.
Lesson Objective 2: Identify each part of a Cartesian plane.
Lesson Objective 3: Define a Cartesian plane and describe each part.
2. plot points on the Cartesian coordinate plane and determine the coordinates of a point on the plane.
Lesson Objective 1: Understand that the coordinate grid is used to describe the location of a point in the Cartesian plane.
Lesson Objective 2: Plot points on a Cartesian plane.
Lesson Objective 3: Write ordered pairs to describe the location of points in a Cartesian plane.
Lesson Objective 4: Understand four distinct quadrants in the coordinate plane.
Lesson Objective 5: Identify the location of a point in a Cartesian plane.
D. Content
1. Cartesian coordinate plane including its parts.
2. Points on the Cartesian coordinate plane.
3. Coordinates of a point on the Cartesian plane.
4. Location of a point on the Cartesian plane.
E. Integration
II. LEARNING RESOURCES
Alferez, M. S. (2007). MSA Elementary Algebra (2007 ed.). Quezon City.
https://cdn.slidesharecdn.com/ss_thumbnails/poster-130606213607-phpapp01-thumbnail.jpg?width=560&fit=bounds
K5 Learning, (2022, July 27). Grade 5 integers number line. https://www.k5learning.com/free-math-worksheets/fifth-grade-5/integers
Kuta Soft ware – Infinite Geometry. (2012). 3-Points in the Coordinate Plane.pdf. https://cdn.kutasoftware.com/Worksheets/Geo/3Points%20in%20the%20Coordinate%20Plane.pdf
1
Math Bondi. (2024). Parts of a coordinate plane notes. Teachers Pay Teachers. https://www.teacherspayteachers.com/Product/Parts-of-aCoordinate-Plane-Notes-6986541?st=78ba1cf56bd02256f79a3040724f84bc
Nagwa Label. (2024). Lesson Plan: Coordinate Planes | Nagwa. Nagwa_Label. https://www.nagwa.com/en/plans/645121802137/
Nagwa_Label. (2024). Lesson Plan: The Coordinate Plane: First Quadrant | Nagwa. Nagwa_Label.
https://www.nagwa.com/en/plans/390145919494/
Nagwa_Label. (2024). Lesson Plan: The Coordinate Plane: Four Quadrants | Nagwa. Nagwa_Label.
https://www.nagwa.com/en/plans/425148312362/
Nivera, G., PhD. (2018). Grade 8 Mathematics Patterns and Practicalities. Makati City.
Oronce, O. A. (2007). E-math I' 2007 Ed. (elementary algebra) (1st ed.). Sampaloc,Manila.
III. TEACHING AND LEARNING PROCEDURE
A. Activating Prior
Knowledge
NOTES TO TEACHERS
DAY 1
1. Short Review
A. Plot the given integers on the number line. Use the letters to represent the Answer Key:
given integers.
A.
A. 7
B. -1
C. 4
D. -6
E. 8
F. -3
G. 5
H. 11
I. -11
J. -2
B. Use the number line to determine the integer that is being described in the
following:
1. 2 units to the right of 0
2. 1 unit to the left of 3
3. 7 units to the left of 2
4. 3 units to the right of 4
5. 1 unit to the left of -10
2
B.
1. 2
2. 2
3. -5
4. 4
5. -11
Questions:
1. What integer is usually positioned at the center of the number line from 10 to 10?
2. What integers are found on the left of zero of the number line from -10 to
10?
3. What integers are found on the right of zero? of the number line from -10
to 10?
1. 0
2. negative integers (-1,-2,-3,..
-10)
3. positive integers (1,2,3,..10)
2. Feedback (Optional)
B. Establishing
Lesson Purpose
1. Lesson Purpose
Think about this! Since you are already familiar with the number line, draw a
vertical number line in your notebook with integers from -10 to 10.
1. What do you think will be the integer in the middle of the vertical number
line from -10 to 10?
2. Which integers do you think are placed above zero?
3. Which integers are placed below zero?
4. What if the horizontal and the vertical number lines are combined, what
will it look like?
2. Unlocking Content Vocabulary
 CARTESIAN PLANE or RECTANGULAR COORDINATE PLANE – formed by
two perpendicular number lines, one horizontal and one vertical that
intersect at a point. It is named after Rene Descartes, a French
mathematician, scientist, and philosopher who first developed it in the
1600s.
 X–AXIS – the horizontal number line.
 Y–AXIS – the vertical number line.
 ORIGIN – the point (0,0) or the point of intersection of the x-axis and the yaxis.
 QUADRANT – a region defined by the two axes (x-axis and y-axis) of the
coordinate plane. There are four regions in a Cartesian plane which are
numbered in a counterclockwise direction.
 ORDERED PAIR or COORDINATES – a pair of numbers that is used to
represent a point on a Cartesian plane.
 ABSCISSA or X-COORDINATE – the horizontal distance from the y-axis.
 ORDINATE or Y-COORDINATE – the vertical distance from the x-axis.
3
Answer Key:
1. 0
2. positive integers from 1 to 10
3. negative integers from -1 to 10.
4. It will form perpendicular
lines.
C. Developing and
Deepening
Understanding
SUB-TOPIC 1: Illustrate the Cartesian coordinate plane including its parts.
1. Explicitation
Draw a horizontal number line. Label the integers on the number line. Draw
a vertical number line perpendicular to your horizontal number line intersecting
at zero. Label also the vertical number line with integers where the integers above
the intersection zero are positive integers starting with +1 and those below zero
are negative integers starting with -1.
Questions:
1. What integers are located on the right
of zero in the number lines?
2. What integers are located on the left of
zero on the number lines?
3. What integers are located above zero
on the number lines?
4. What integers are below zero on the
number lines?
5. How will you name this illustration if
the horizontal number line and the
vertical number line are intersected
perpendicularly?
2. Worked Example
From the task you have made in the
“Explicitation”, if the horizontal number line
and the vertical number are combined, a
Cartesian plane is formed. It can also be
named as a rectangular coordinate plane.
The Cartesian plane is named after Rene
Descartes,
a
French
mathematician,
scientist, and philosopher who first
introduced the coordinate system in the
1600s.
In the Cartesian plane, the horizontal
number line is known as the x-axis. The
vertical number is the y-axis. The
intersection of the x-axis and the y-axis is
4
Answer Key:
1. positive integers
2. negative integers
3. positive integers
4. negative integers
5. Cartesian coordinate plane
called the origin. Observe that in the Cartesian plane, the x-axis and the y-axis
divide the plane into four regions. Each region is called a quadrant. These
quadrants are numbered in a counterclockwise direction.
3. Lesson Activity
Activity 1: The Earth-Friendly Plan
Use a graphing paper to perform Activity 1.
Sample Illustration
Earth Warriors Club Inc. has a plan of creating an ecological park in the
rectangular lot they bought. Imagine you are the leader of the Sustainable
Development Team and you are task to design the layout of the eco-park using
a Cartesian plane.
You have in mind that a small circular fishpond will be placed at the origin.
Trees will be located in Quadrant I. This will help improve the quality of the air
and can preserve the soil. Flowering plants will be placed in Quadrant IV. There
will be picnic area surrounded by flowering plants in Quadrant III. A mini
playground will be placed in Quadrant II. The mini playground will be
surrounded by trees to give more shade to the place.
Question: Have you designed the eco-park plan correctly based on the give data?
SUB-TOPIC 2: Describe the Cartesian coordinate plane.
1. Explicitation
A. In your own words, describe each term:
1. Cartesian Plane
2. X-Axis
3. Y-Axis
4. Origin
5. Quadrant
Search image of Hemispheres on the world map. Sample figure:
https://cdn.slidesharecdn.com/ss_thumbnails/poster-130606213607-phpapp01thumbnail.jpg?width=560&fit=bounds
B. Observe the given illustration.
5
Search image:
Upper left – playground
Upper right – trees
Lower left – park
Lower right – garden
Answer Key:
1. It is formed by two
perpendicular number lines,
the x-axis and the y-axis,
that intersect at a point.
2. The horizontal number line
3. The vertical number line
4. The intersection of the x-axis
and y-axis.
Questions:
1. What does the picture tell us?
2. Which continents belong to the northeastern hemisphere?
3. Which continents belong to the northwest hemisphere?
4. Which continents belong to the southeastern hemisphere?
5. How can you exactly locate a country on the given map?
2. Worked Example
The given map in the “Explicitation” is a real-life example of a Cartesian
plane. Similar to the map, the Cartesian plane is divided into four quadrants.
Similar to the map that you can locate a country, points can also be located in
a Cartesian plane. Each point in the Cartesian plane can be identified by a pair
of numbers called ordered pair. The first number in an ordered pair is called
abscissa or x-coordinate. It denotes the distance of the point from the y-axis.
The second number in the ordered pair is the ordinate or the y-coordinate. It is
the distance of the point from the x-axis.
5. The region formed from
intersection of the x-axis and
the y-axis
Answer Key:
1. The map which represents
the location of a continent in
a hemisphere.
2. Europe, Africa, Asia
3. North America
4. Australia
5. Using the latitude and
longitude in the map.
In the illustration, each quadrant is shaded with different colors to easily
identify the regions bounded by each quadrant.
Questions:
1. What are the values of the abscissa
and the ordinate in the first quadrant
or Quadrant I?
2. What are the values of the abscissa
and the ordinate in the second
quadrant or Quadrant II?
3. What are the values of the abscissa
and the ordinate in the third
quadrant or Quadrant III?
4. What are the values of the abscissa
and the ordinate in the fourth
quadrant or Quadrant IV?
Answer Key:
1. (+x, +y)
2. (-x, +y)
3. (-x, -y)
4. (+x, -y)
6
3. Lesson Activity
Create your own Cartesian plane and include the values of the abscissa and the
ordinate in each quadrant.
DAY 2
SUB-TOPIC 3: Plot points on the Cartesian coordinate plane.
1. Explicitation
Chess is a famous board game where two players compete to attack the
opponent’s King. Here is an example of chess board game.
In a chess game, the knight piece looks like a horse head. The white knight
is moved by a player at (e, 6) since it is in column e and row 6. The black knight
is moved by an opponent player at (a, 4) because it is in column a and row 4.
Answer:
Question: How can the chess game be related to points in the Cartesian plane? The chess board is similar to
Cartesian plane because it also
has its horizontal line or its row
2. Worked Example
Similar to the chess pieces on a chess board, points can also be plot in the and the column is similar to the
Cartesian plane. The column in the chess board is similar to the y-axis while the vertical line.
row in the chess board represents the x-axis. The only thing that differ from a
chess board and a Cartesian plane is that in the Cartesian plane location in the
x-axis comes first followed by the location in the y-axis.
Take Note that in each quadrant:
Quadrant I (+x, +y)
Quadrant II (-x, +y)
Quadrant III (-x, -y)
Quadrant IV (+x, -y)
7
Example 1: Plot the point (3,4).
Steps:
a) Start at the origin.
b) Move 3 units to the right since in the point (3,4)
the abscissa is 3.
c) From 3, move 4 units upward since the ordinate
in (3, 4) is 4.
Example 2: Plot the point (-1, 2).
Steps:
a) Start at the origin.
b) Move 1 unit to the left since in the point (-1,2) the
abscissa is -1.
c) From -1, move 2 units upward since the ordinate
in (-1,2) is 2.
Example 3: Plot the point (-2,-4).
Steps:
a) Start at the origin.
b) Move 2 units to the left since in the point (-2,-4)
the abscissa is -2.
c) From -2, move 4 units downward since the
ordinate in (-2,-4) is -4.
(3,4)
(-1, 2)
(-2,-4)
Example 4: Plot the point (3,-3).
Steps:
a) Start at the origin.
b) Move 3 units to the right since in the point (3,-3)
the abscissa is 3.
c) From 3, move 3 units downward since the
ordinate in (3,-3) is -3.
Example 5: Plot the point (0,4).
Steps:
a) Start at the origin.
(3,-3)
(0,4)
8
Questions:
1) Are you going to move either to the right or to the left of the origin?
2) By how many units do you think you will move from the origin?
Since the abscissa in (0,4) is zero, therefore you will not move neither to the
right nor to the left. From the origin, move 4 units upward since the ordinate
in (0,4) is 4.
Example 6: Plot the point (-3,0).
Steps:
a) Start at the origin.
b) From the origin, move 3 units to the left since in
(-3,0), the abscissa is -3.
(-3,0)
Questions:
1) Are you going to move either upward or downward from -3?
2) By how many units do you think you will move from -3?
Since the ordinate in (-3,0) is 0, then there will be no movement neither
upward nor downward.
Question: How will you plot the point (0,0) in the Cartesian plane?
3. Lesson Activity
Activity 2: Playful Pet
An animal is hiding in a Cartesian plane. To see it, plot the given points in a
Cartesian plane. Use a graphing paper to easily create a Cartesian plane.
Connect each point and its next consecutive point with a line segment.
Points to be plot:
1.
(-2,0)
16. (-5,5)
1.
(-1,-1)
1.
(5,-7)
16. (5,2)
2.
(0,2)
17. (-6,6)
2.
(-1,-2)
2.
(7,-7)
17. (2,2)
3.
(0,4)
18. (-7,6)
3.
(0,-3)
3.
(7,-6)
18. (1,1)
4.
(2,6)
19. (-8,5)
4.
(0,-6)
4.
(6,-5)
19. (0,2)
5.
(1,9)
20. (-8,3)
5.
(-1,-7)
5.
(6,-3)
end
6.
(-2,9)
21. (-7,2)
6.
(-1,-8)
6.
(7,-2)
7.
(-1,7)
22. (-5,4)
7.
(2,-8)
7.
(7,0)
8.
(0,7)
23. (-4,1)
8.
(2,-4)
8.
(8,3)
9.
(0,6)
24. (-6,-1)
9.
(2,-8)
9.
(8,5)
9
Answer:
1) No.
2) There will be no movement to
the right or left since the abscissa
is 0.
Answer:
1) No
2) There will be no movement
upward or downward since the
ordinate is 0.
Answer: It is in the origin.
10.
11.
12.
13.
14.
15
(-2,6)
(-2,7)
(-4,10)
(-7,10)
(-6,8)
(-5,8)
25.
26.
27.
28.
(-4,1)
(-3,0)
(-2,0)
end
10.
11.
12.
13.
14.
(5,-8)
(5,-7)
(4,-6)
(4,-3)
end
10.
11.
12.
13.
14.
15.
(5,9)
(2,9)
(3,8)
(4,8)
(7,4)
(6,1)
Question: What animal is it?
Answer: It is a dog.
DAY 3
SUB-TOPIC 4: Determine the coordinates of a point on the plane.
1. Explicitation
Going back to the chess game.
Questions:
1. Where do you think is white knight located?
2. What about the location of the black knight?
3. What helped you in finding the location of the knights in the chess board?
2. Worked Example
Points in the Cartesian plane are the like the knights in the chess board.
Just like the knights in the chess board at (g,7) and (d,3), the ordered pair or the
coordinates that represents the point in the Cartesian plane can also be named.
Always start at the origin. Count the number units that you moved from the
origin to the given point.
Take Note: If the abscissa is positive, it is on the right of the origin. If the
abscissa is negative, then it is on the left of the origin. If the ordinate is positive,
then it is moved upward. If the ordinate is negative, it is moved downward.
10
Answer Key:
1. White knight is at (g, 7).
2. Black knight is at (d, 3).
3. The column and the row of the
chess board made it easy to locate
the knights.
Examples: Name the ordered pairs that
represent the points in the Cartesian plane.
Solution:
1. Point A has the coordinates (3,2) since
from the origin, point was moved 3 units
to the right and 2 units upward.
2. Point B has the coordinates (1,-1) since
from the origin, the point was moved 1
unit to the right and 1 unit downward.
3. Point C has the coordinates (-2,3) since
from the origin, the point was moved 2
units to the left and 3 units upward.
4. Point D has the coordinates (-4,-2) since from the origin, the point was
moved 4 units to the left and 2 units downward.
5. Point E has the coordinates (0,0) since it did not moved neither to the right
nor to left and no movement upward or downward from the origin. This
means that the coordinates of the origin is (0,0).
6. Point F has the coordinates (0,-4) since from the origin, no movement was
done to the left nor to the right but it moved 4 units downward.
7. Point G has the coordinates (4,0) since from the origin, the point was moved
4 units to the right but did not moved upward nor downward.
3. Lesson Activity
Activity 3: Naming the coordinates of
a point
Name the coordinates of the
following points in the Cartesian plane.
Activity 3 Answer Key:
A(2,5)
K(1,1)
B(-3,2)
L(5,-4)
C(6,0)
M(3,3)
D(-4,-5) N(-4,4)
E((-5,0)
O(0,-5)
F(0,4)
P(2,4)
G(3,-5)
Q(0,-1)
H(0,0)
R(4,2)
I(-3,-3)
S(1,-2)
J(4,-2)
T(-1,-2)
11
SUB-TOPIC 5: Determine the quadrant of a point on the plane.
1. Explicitation
Using the map in the previous lesson, analyze each continent where they
belong.
Questions:
1. Where does most the South America continent belong to?
Answer Key:
2. Where does the continent Asia belong to?
3. Is it also possible to locate points on the Cartesian plane just like the 1. South Western Hemisphere
2. North Eastern Hemisphere
continents in the map?
3. Yes
Search image of Hemispheres on the world map. Sample figure:
https://cdn.slidesharecdn.com/ss_thumbnails/poster-130606213607-phpapp01thumbnail.jpg?width=560&fit=bounds
2. Worked Example
Just like the continents in the map in the “Explicitation”, points in the
Cartesian plane can also be located. Take note of the values of the abscissa and
ordinate in each quadrant.
Question: Why do you think that
Roman Numerals are used for naming
the quadrants and not the HinduArabic Numerals?
Answer:
To lessen confusion, the ordered
pairs are written in Hindu-Arabic
numerals, while the location of
points is written as Roman
Numerals.
12
Example 1: Identify the location of the following points in the Cartesian plane.
Answers:
 Point A is located in Quadrant I.
 Point B is located in Quadrant IV.
 Point C is located in Quadrant II.
 Point D is located in Quadrant III.
 Point E is at the origin since it is in the
intersection of the x-axis and the y-axis.
 Point F is not located in any of the quadrants
because it is y-axis. Therefore, it is located
in the y-axis.
 Point G is not located in any of the
quadrants. It is located in the x-axis.
Example 2: Given the ordered pairs, identify its location in the Cartesian plane.
1. (5,7)
6. (0,0)
2. (-4,-4)
7. (0,-6)
3. (9,0)
8. (3, 8)
4. (-1,1)
9. (-7, 0)
5. (3,-6)
10. (-2,4)
Answers:
1. Quadrant I
6. origin
2. Quadrant III
7. y-axis
3. x-axis
8. Quadrant I
4. Quadrant II
9. x-axis
5. Quadrant IV
10. Quadrant II
3. Lesson Activity
Activity 4. Indicate the location of the following points.
1. (-3,2)
6. (-5,0)
11. x = 0, y = 0
2. (2,6)
7. (-3,-1)
12. x > 0, y < 0
3. (-3,-5)
8. (1, 1)
13. x < 0, y < 0
4. (0,-7)
9. (4,0)
14. x = 0, y > 0
5. (2,-1)
10. (5,-4)
15. x > 0, y = 0
13
Activity 4 Answer Key:
1. Q II
6. x-axis 11.origin
2. Q I
7. Q III
12. Q IV
3. Q III
8. Q I
13. Q III
4. y-axis 9.x-axis
14.y-axis
5. Q IV
10. Q IV 15.x-axis
D. Making
Generalizations
DAY 4
Learners’ Takeaways and Reflection on Learning
Use the Frayer Diagram to show what you learned.
IV. EVALUATING LEARNING: FORMATIVE ASSESSMENT AND TEACHER’S REFLECTION
A. Evaluating
Learning
1. Formative Assessment
A. Fill in the blank with the correct answer.
_____1. The vertical number line.
_____2. The intersection of the horizontal and vertical number line.
_____3. The horizontal number line.
_____4. The region formed from the intersection of the x-axis and y-axis.
_____5. The horizontal distance from the y-axis.
_____6. The vertical distance from the y-axis.
_____7. The coordinates of the origin.
_____8. The location of a point when x < 0 and y > 0.
_____9. The location of the point (5,0).
14
The teacher will ask the learners
of the important lessons they’ve
learned.
NOTES TO TEACHERS
Answer Keys:
A.
1. y-axis
2. origin
3. x-axis
4. quadrant
5. abscissa or x-coordinate
6. ordinate or y-coordinate
7. (0,0)
8. Quadrant II
9. x-axis
10. Cartesian plane
_____10. It is formed by two intersecting perpendicular lines.
B. Give the coordinates of the following points.
B.
A (-4,4)
B (0,0)
C (-3,0)
D (2,3)
E (4,-2)
C. Identify the location of the following points.
1. (-1, -1)
6. (5,8)
2. (-3, 0)
7. (-2,-3)
3. (6, -5)
8. (1, -1)
4. (0, -7)
9. (-3,-7)
5. (-4, 6)
10. (0,3)
11. x > 0, y > 0
12. x < 0, y > 0
13. x > 0, y < 0
14. x = 0, y = 0
15. x < 0, y = 0
2. Homework (Optional)
Use the coordinate plane and your creativity to construct an image using the
points in the Cartesian plane. Write the coordinates of each point you used for
the chosen illustrated object. Color the object you chose to illustrate.
Rubrics:
Accuracy of
naming the
coordinates
10 points
All points have
complete and
correct
coordinates
9 points
All points in the
picture missed 1 to
3 correct
coordinates
Creativity
and
originality
10 points
The object is
original and
artistically
9 points
The object is
artistically crafted
but there are some
15
8 points
All points in the
picture missed
more than 4
correct
coordinates
8 points
The object is
quite vague to
be identified.
7 points
The picture has
no label in the
coordinates of
the points.
7 points
The art work is
not finished so
C.
1. Q III
2. x-axis
3. Q IV
4. y-axis
5. Q II
F (0,-4)
G (-4,-3)
H (3,1)
I (-1,2)
J (1,-2)
6. QI
7. Q III
8. Q IV
9. Q III
10. y-axis
11. QI
12. QII
13.Q IV
14.origin
15. x-axis
Neatness of
work
B. Teacher’s
Remarks
crafted in the
Cartesian plane.
10 points
The output is
done neatly and
orderly.
Note observations on any
of the following areas:
similarities from
online samples.
9 points
The output has 1
to 3 erasures.
8 points
The output has
more than 4
erasures.
the whole object
is unclear.
7 points
The output
needs major
revision due to
many erasures.
materials used
The teacher may take note of
some observations related to the
effective practices and problems
encountered after utilizing the
different strategies, materials
used, learner engagement, and
other related stuff.
learner engagement/
interaction
Teachers may also suggest ways
to improve the different activities
explored/lesson exemplar.
Effective Practices
strategies explored
Problems Encountered
others
C. Teacher’s
Reflection
Reflection guide or prompt can be on:
 principles behind the teaching
What principles and beliefs informed my lesson?
Why did I teach the lesson the way I did?

students
What roles did my students play in my lesson?
What did my students learn? How did they learn?

ways forward
What could I have done differently?
What can I explore in the next lesson?
16
Teacher’s reflection in every
lesson conducted/facilitated is
essential and necessary to
improve practice. You may also
consider this as an input for the
LAC/Collab sessions.