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1. Republic of the Philippines
Department of Education
Region I
Schools Division of Ilocos Norte
SAN NICOLAS NATIONAL HIGH SCHOOL
Brgy. 24, San Nicolas, Ilocos Norte
LESSON EXEMPLAR IN MATHEMATICS 10
Code M10GE-IIh-1/M10GE-IIh-2 Date: October 14, 2025
Domain Geometry
Cluster Coordinate Geometry
Lesson Equation of a circle and its center-radius form
MELCS Illustrates and determines the center and radius form of the equation form of the circle and
vice versa
ReferencesReferences: DepEd Mathematics 10 Learner’s Module (pp. 275–280), Curriculum Guide,
Quarter 2
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OBJECTIVES:
At the end of the session, the learners must be able to:
1.Identify the parts of the equation of a circle;
2.Transform the general form of a circle’s equation into standard form;
3.Determine the center and radius of a circle from its equation; and
4.Show appreciation of the importance of accuracy in solving mathematical problems.
Annotation: Objectives are aligned with the K to 12 curriculum standards and use Bloom’s
taxonomy (identify → transform → determine → show).
ASSESSMENT: KEY POINTS:
Assessment for: Pre-Activity done by group
Annotation: Activates prior knowledge and connects to
previous lessons on quadratic equations and
coordinates.
Assessment of: Center and Radius of a Circle using
Geogebra as Graphing Tool
Annotation: The integration of GeoGebra promotes
interactive visualization of abstract mathematical
concepts, helping learners concretely understand
relationships between equations and geometric figures.
It supports DepEd’s ICT integration framework and
enhances spatial reasoning.
Assessment as: Activity Sheet
Annotation: The use of activity sheets provides learners
with structured opportunities to apply learned concepts
and practice computational skills independently. It
The center and radius of a circle is
easy to find when the equation of a
circle is written on Standard form or
center- radius form
The center of a circle can be found at
the origin C(0,0) and C(h,k)
The most important concepts on
finding the radius and center of a
circle is transforming the general form
of the equation of a circle to its
standard or center-radius form

2. reinforces mastery through hands-on engagement and
self-paced learning.
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ELICIT: Materials and Teacher’s Tips/Notes
BUDDY TIME!
Annotation: The use of collaborative learning activities
promotes peer interaction and teamwork. It allows
learners to exchange ideas, clarify misconceptions, and
build social skills while reinforcing conceptual
understanding through discussion and cooperation.
Let the students do the Pre-Activity: Finding Radius and
Center of Circle using Geogebra
Annotation: The integration of GeoGebra promotes
interactive visualization of abstract mathematical
concepts, helping learners concretely understand
relationships between equations and geometric figures.
It supports DepEd’s ICT integration framework and
enhances spatial reasoning.
After the activity, ask: How can we find the center and
radius of a circle when given its center and radius
form?
BUDDY TIME!
Note: In grouping, consider students
abilities. Distribute those fast learners to
each group to guide the members in
their activity. Likewise, it is in this way
that learners exercise collaboration.
Annotation: Grouping slow learners with
fast learners encourages peer tutoring and
cooperative learning. It allows more
advanced students to reinforce their
understanding by explaining concepts,
while struggling learners receive
scaffolded support in a non-threatening
environment.
Pre-Activity: Finding the Radius, and
Center of a Circle using Geogebra
Note: The students were told not to
worry about their answers for this
activity will only determine what they
know and what they need to know about
the topic/lesson.
ENGAGE:
Let students realize some real life applications of
knowing the importance of center and radius of a circle.
Example:
Typhoon
Cow on the Field
Annotation: Presenting real-life applications, such as
identifying circular objects or modeling motion paths,
connects mathematical concepts to learners’ everyday
experiences. This promotes relevance and helps students
appreciate the usefulness of mathematics beyond the
classroom.
Based from their activity, ask: Does knowing the center
and radius of a circle is very important?
Present visual graphics of circle applied
on typhoons and a cow on the field.
EXPLORE:
Using a PowerPoint presentation
1.Discuss the Center and Radius of Circle when its
center is at C(0,0) and C(h,k)
2.Transforming General form of the equation of a
circle to its standard form or center and Radius
form
GROUPIE TIME!
Let one member of each group present
their solution on the board.
Annotation: Encouraging active student
participation during discussions allows
learners to express their ideas, clarify
misconceptions, and construct knowledge

3. 3.Discuss on how to find the center and radius of a
circle from general form of the equation of a
circle using its standard form
Provide a wordproblem and group the students into
three.
1
ST
GROUP – answer problem 1
2
nd
GROUP – answer problem 2
3
rd
GROUP – answer problem 3
4
th
GROUP – answer problem 4
5
th
GROUP –answer problem 5
6
th
GROUP – answer problem 6
collaboratively. This promotes critical
thinking and ensures that learning is
learner-centered rather than teacher-
directed.
Acknowledge their work and effort.
Annotation: Acknowledging learners’
efforts during recitation and problem-
solving motivates them to participate
more actively. It fosters a positive
classroom atmosphere where students
feel valued and confident to express their
ideas.
EXPLAIN:
Asked the studenst:
1.Which of the following problems is easy to
solve?
2.Which of the following problems is hard to
solve?
3.What makes the problem hard to solve?
Explain the importance of perseverance and honesty in
solving the given problem.
Annotation: Emphasizing the values of honesty and
perseverance during problem-solving helps students
develop integrity in their academic work. By
encouraging learners to show their complete solutions
and accept both correct and incorrect answers sincerely,
the teacher cultivates ethical behavior and resilience in
learning.
ELABORATE:
Let students appreciate the use of Geogebra application
tool
1.Checking their transformation of general form of
the equation of a circle to its standard form by
graphing it
2.Graphing equation of circle correctly
3.Visualizing the center and radius of a circle
using the application tool
Annotation: The use of graphing tools such as graphing
paper, GeoGebra, and calculators enhances students’
visualization and conceptual understanding of
mathematical relationships. It allows learners to explore
patterns, verify results, and connect algebraic equations
with their graphical representations.

4. EVALUATE:
Students will answer the Activity Sheet on Center and
Radius of a Circle
Annotation: The use of activity sheets provides learners
with structured opportunities to apply learned concepts
and practice computational skills independently. It
reinforces mastery through hands-on engagement and
self-paced learning.
Note: Students will answer the activity
individually.
EXTEND:
PERFORMANCE TASK (Challenge Yourself)
Make a poem, brochures, poster-slogan, and comic
strips on the real life application of Circles

Annotation: Differentiated learning is applied by
designing varied activities and providing multiple
representations of concepts to address learners’ diverse
needs, abilities, and learning styles. Grouping fast
learners with slow learners promotes peer tutoring and
collaboration, ensuring that all students can participate
meaningfully and achieve the lesson objectives at their
own pace.
Note: This activity will be done
individually wherein they will apply
their newly acquired knowledge on the
center and radius of a circle
A rubric for assessment is to be
presented or given to the learners.
Prepared by:
JEFFREY DAGA MANGLIGOT
JHS Teacher I
Checked by: Approved:
NANDING B. RAQUEL FLORANTE R. RIEGO
Head Teacher III School Principal IV

5. ANNOTATIONS
Objectives Annotation
1. Apply knowledge of content within and across
curriculum teaching areas.
I used “Area Approximation” activity to start the
discussion on finding the area under a curve. In this
activity, they were given graphs wherein they will
approximate the area under the curve.
I presented an example where they can apply the topic
that is in the field of statistics - area of a region under a
normal curve which represents probability.
Overall, I incorporated real-world examples and
applications in my lesson, demonstrating how
knowledge extends beyond individual disciplines.
This approach fosters a holistic understanding of the
subject matter, showing students the interconnections of
concepts and promoting a more comprehensive learning
experience.
3. Ensure the positive use of ICT to facilitate the
teaching and learning process.
I introduced and used Riemann Sum Calculator to make
the discussion and learning and to promote interactive
and student-centered learning.
4. Use a range of teaching strategies that enhance
learner achievement in literacy and numeracy skills.
I used “Groupie Activity” to enhance learners
communication skills among themselves. In this way,
both literacy and numeracy skills of learners were
developed.
Also, evaluation of learning in mathematics is a teaching
strategy that enhances learners’ achievement in literacy
and numeracy skills. In the evaluation part, I gave word
problems. If students can read and comprehend the
problems in the activity, they will be able to correctly
solve the given problems. Moreover, if learners can
solve problems correctly, it means that they can read
well and understand at the same time. Thus, there is an
enhancement in literacy and numeracy skills.
5. Use effective verbal and non-verbal classroom
communication strategies to support learner
understanding, participation, engagement and
achievement.
To enhance learner understanding, participation, and
achievement, I employed effective verbal and non-
verbal communication strategies such as clear speech,
appropriate tone, and questioning techniques to ensure
clarity and engagement, while eye-contact, gestures, and
facial expressions reinforce understanding and
motivation.
In addition, acknowledging learners' effort and ideas
during recitation is a way to boost their confidence.
6. Maintain supportive learning environments that
nurture and inspire learners to participate, cooperate,
and collaborate in continued learning.
Maintaining a supportive learning environment involves
fostering respect, trust, and a sense of belongingness
among learners.
7. Apply a range of successful strategies that maintain
learning environments that motivate learners to work
productively by assuming responsibility for their
own learning.
Presenting different ways or strategies for solving areas
under a curve, such as the manual method and using an
online application, will help maintain learning
environments that motivate learners to work

6. productively.
8. Design, adapt, and implement teaching strategies
that are responsive to learners with disabilities,
giftedness, and talents.
In grouping activities, I consider students’ abilities. I
distributed those fast learners to each group to guide the
members in their activity. It is in this way that learners
exercise collaboration.
9. Plan and deliver learning strategies that are
responsive to the special educational needs of
learners in difficult circumstances, including
geographic isolation; chronic illness; displacement
due to armed conflict; urban resettlement or
disasters; child abuse and child labor practices.
To those who cannot use the online application
(Riemann Sum Calculator), I encouraged “sharing and
caring” to the learners by asking those with strong data
connections to share their data through “hotspot”.