DETAILED LESSON PLAN IN MATHEMATICS
SUBJECT
MATHEMATICS
TIME
GRADE LEVEL
10
DATE
CONTENT STANDARD
The learner demonstrates understanding of key concepts of circles of
coordinate geometry.
PERFORMANCE STANDARD
The learner is able to formulate and find solutions to challenging situations
involving circles and other related terms in different disciplines through
appropriate and accurate representations.
LEARNING COMPETENCY
Determines the center and radius of a circle given its equation and vice
versa.
I.
OBJECTIVES
At the end of the lesson the student should be able to:
K. Determine the center and the radius of a circle given its equation;
S. Solve and write the equation of the circle in standard form;
A. Appreciate the concept of equations of the circle in real life situation.
II.
SUBJECT MATTER
A. TOPIC
B. LEARNING RESOURCES
B.1 References
1. Teacher’s Guide/Pages
2. Learner’s
Materials/Pages
3. Textbooks
4. Additional
Materials from
Learning Resource
(LR) Portal
B.2 Other Learning
Resources
Equation of a Circle
GRADE 10 Teacher’s Guide in MATHEMATICS – Quarter 2
Mathematics 10 Learning Modules Quarter 2
Visual aid, Activity sheet, color pen, pentel pen , pictures,


III.
https://saylordotorg.github.io/text_intermediatealgebra/s11-02-circles.html
https://www.bbc.co.uk/bitesize/guides/z9pssbk/revision/2
PROCEDURE
Teacher’s Activity
A. PREPARATORY ACTIVITIES
a.1 Prayer
May I request everyone to please stand and
start our day with a prayer.
Student’s Activity
(The students will stand for a prayer)
(Student A), kindly lead the prayer.
(Student A will lead the prayer)
Lets bow down our head and feel the presence of our
Lord Jesus Christ.
In the name of Father the
Son the Holy Spirit
Amen.
Lord we thank you and praise you for everything
we have now, sorry for all the sins we’ve done to
you. Please be in our lessons and help us
toconcentrate and learn. Watch over us as we share,
play and laugh together. In Jesus name Amen.
Thank you , student A.
Good morning class.
Good morning, ma'am Carnaje.
a.2 Energizer
Please remain standing. Let’s wake up our minds
and bodies for this simple warm-up. We will do a
karatae.
Do you know how to do a karatae?
(Some students says Yes, some says No)
Ok, I will teach you how to do the karatae.
Are you ready ?
Yes , Ma’am.
( The teacher execute the steps)
(Students follow the step)
(After the students learn the step, the teacher will
incorporate music so that it will be lively.)
Oh right very good class. Did you enjoyed it?
Yes, Ma’am!
a.3 Checking of Attendance
Go back to your proper seat so that I can recognize
who is absent today.
(Students go to their proper seats.)
(The teacher has student’s seat plan)
Very good class because all of you are present
today.
B.
DEVELOPMENTAL ACTIVITIES
b.1 Classroom Management
Before anything else, I want to discuss to you some
things to do during our class so that we will have an
organize flow of discussion.
Things to do:

Listen and be quite when the teacher or
anyone in the class is speaking.

Be respectful to everyone, especially to
anyone's idea.

Always raise your right hand if you want to
speak, and answer or ask a question.

Do not answer in chorus.

Be cooperative.
Did I make myself clear ?
Yes, Ma’am!
b.2 Review
Before we start, let us first review the last topic that
we’ve discussed yesterday.
So, what was our last topic?
( The students raise their hands.)
Yes, Student B?
Ma’am, it’s all about the distance Formula.
Okay, thank you!
And what is the distance formula? Yes, Student C?
Very Good.
b.3 Unlocking of Difficulty
So,what is the distance between two points
(5,-3) , (5,6) ?
Who can solve it on the board?
( The students raise their hands.)
Yes, Student D.
D = √(5 − 5)2 +(6 + 3)2
D = √(0)2 +(9)2
D = √92
D = √81
D=9
Very Good, Student D. That is correct.
Any questions class about distance formula?
None, Ma’am.
It seems that you have fully understand what is the
distance formula and how to solve it. Ok! let us
have an activity.
C.
MOTIVATION
I have here some pictures. All you have to do is
guess what the picture represents It is okay with
you class ?
Yes, Ma’aam!
FIRST PICTURE
What the first picture represent?
Anyone?
( The students raise their hands)
Yes, Student E.
Equation, Ma’am.
Correct. Equation.
(The teacher give Student E a reward)
SECOND PICTURE
How about the second picture?
( The students raise their hands)
Yes, Student F.
It represents circle, Ma’am.
Yes, that is correct. Circle.
Then now, who can guess what is our topic for
today?
( The students raise their hands)
Yes, Student G.
EQUATION OF A CIRCLE, Ma’am.
Yes, that’s right. Today the topic I will be
discussing with you is all about the EQUATION
OF A CIRCLE.
D. ACTIVITY
But before we proceed to our proper discussion, let’s
have another activity.
First, let’s divide the class. So row 1 will be the Group
A, and row 2 will be the Group B.
I have here two activity sheet. All you have to do is to
follow all the instructions in the activity sheet.
Am I clear class?
Yes, Ma’am!
I will give you 5 minutes to do the task.
(Now, the teacher distribute the activity sheet)
So your time starts now!
GROUP A
GROUP A
Answer:
Center (0,0)
Radius: 3

Using the Cartesian Coordinate
plane determine the center of the
circle.

Determine the radius, by counting
the units from the center upto
the edge of te circle
*note: Write the name of your
members at the back of your activity
sheet.
GROUP B

At the figure above label where
is the center and radius of the
circle.( Use the color pen)
*note: Write the name of your
members at the back of your activity
sheet.
Time is up. Please pass all your work forward.
E.
ANALYSIS
In your activity I assigned you to label and determine
the center and radius of a circle. Let’s check if your
answers are correct.
Who can point out where is the center of the circle?
Yes, Student M?
( The students raise their hands)
( Student M pointed out where is the center)
That is Correct.
How about the radius?
( The students raise their hands)
Yes, student N ?
( Student N pointed out where is the radius)
Very Good student N.
So,What will be the center of a circle if it is located at
the origin? Student P?
Yes, that’s correct.
(0,0) Ma’am.
F. ABSTRACTION
EQUATION OF A CIRCLE
A circle is the set of points in a plane that lie a
fixed distance, called the radius, from any point,
called the center.
In a rectangular coordinate plane, where the center
of a circle with radius r is (h,k) we have:
Squaring both sides leads us to the equation of
a circle in standard form,
(𝒙 − 𝒉)𝟐 + (𝒚 − 𝒌)𝟐 = 𝒓𝟐
To find the equation of a circle when you know the
radius and centre, use the formula
(x − h)2 + (y − k)2 = r 2 ,where (h,k) represents
the centre of the circle, and r is the radius.
This equation is the same as the general equation
of a circle, it's just written in a different form.
Example No. 1
Example No. 2
Find the equation for the circle with
centre =(0,0) and radius = 4
(𝒙 − 𝒉)𝟐 + (𝒚 − 𝒌)𝟐 = 𝒓𝟐
(𝒙 − 𝟎)𝟐 + (𝒚 − 𝟎)𝟐 = (𝟒)𝟐
𝒙𝟐 + 𝒚𝟐 = 16
G.
APPLICATION
If (𝒙 − 𝟒)𝟐 + (𝒚 + 𝟕)𝟐 =9 is the equation of circle,
then what is the center of circle?
Given,(𝒙 − 𝟒)𝟐 + (𝒚 + 𝟕)𝟐 =9 is the equation of
circle. If we compare this equation with the
standard equation we get:
(𝒙 − 𝒉)𝟐 + (𝒚 − 𝒌)𝟐 = 𝒓𝟐
𝒉=4 , 𝒌=-7
Therefore, (4,-7) is the center of circle.
How about the radius class, what will be the radius
of that equation? Anyone?
Yes, Student A?
Very good. That’s correct.
Try to answer this one class.


Center ( 5,3 ) r=5
Center (-8,9) r=√2
Row 1 will answer No. 1 and Row 2 will answer
No. 2
What will be the equation of the circle ?
( The students raise their hands)
Radius = 3, ma’am.
Who can try to answer it on the board? 1
representative row 1 and row 2
𝒉=5 , 𝒌=3 , r=5
(𝒙 − 𝟓)𝟐 + (𝒚 − 𝟑)𝟐 = (𝟓)𝟐
(𝒙 − 𝟓)𝟐 + (𝒚 − 𝟑)𝟐 = 25
h=-8, k =9 r=√2
(x+8)² + (y-9)² = 2
Correct, Very good class. Did you came up with
the same answer ?
Yes, Ma’am.
Ok, Let’s try another one. Do it by pair or with
seatmate.

Liam wants to paint a ball image at the center
wall of his room, center (0,0) and radius 50cm .
What will be the equation.
Who can try to answer ?
Yes, student X?
center (0,0) r=50cm
X²+Y²=2500cm²
Let’s check the answer of Student X.
(The teacher check and discuss the answer of the
student)
Ok,Correct, Good job student X.
IV. ASSESSMENT
It seems that you have fully understand the Equation of
a Circle and how to solve it. Ok!Get 1/2 Crosswise
Solve for the following:
Determine the center and radius
1. (𝒙 − 𝟏𝟐)𝟐 + (𝒚 − 𝟒)𝟐 = 49
2. (𝒙 + 𝟒)𝟐 + (𝒚 − 𝟏)𝟐 = 4
3. (𝒙 − 𝟗)𝟐 + (𝒚 + 𝟑)𝟐 = 81
ANSWER
1. (12,4) h=12,k=4 radius=7
2. (-4,1) h=-4,k=1 radius=2
3. (9,-3) h=9,k=-3 radius=9
Write the equation of the circle given the center
and radius;
1. Center (7,-8) r=10
2. Center (-2,5) r=7
1. (𝒙 − 𝟕)𝟐 + (𝒚 + 𝟖)𝟐 = 100
2. (𝒙 + 𝟐)𝟐 + (𝒚 − 𝟓)𝟐 = 49
V.
ASSIGNMENT/ENRICHMENT ACTIVITIES
Write the equation of each of the following
circles given the center and the radius. Answer the
questions that follow.
1.
2.
Center (5,-2) r=√2
Center (-1,9) r=2√4
VI.
REMARKS
VII.
REFLECTION
A. No. of learners who earned 80% in the evaluation
B. No. of learners who require additional activities for remediation
C. Did the remedial lessons work? No. of learners who have caught up
the lesson
D. No. of learners who continue to require remediation
E. Which of my teaching strategies worked well? Why did these work?
A. ____ No. of learners who earned 80% in the evaluation
B. ____ No. of learners who require additional activities for
remediation
C. Did the remedial lessons work? _____ No. of learners who
have caught up the lesson.
D. ___ No. of learners who continue to require remediation
Strategies used that work well:
___ Group collaboration
___ Games
___ Poweerpoint presentation
Answering preliminary activities/exercises
___ Discussion
___ Differentiated
Instruction
___ Case Method
___Role Playing /Drama
___ Think-Pair-Share (TPS)
___ Doscivery
Method
___ Rereading of Paragraphs/Poems/Stories ___ Lecture Method
Why?
___ Complete Ims
___ Availability of Materials
F. What difficulties did I encounter which my principal and supervisor
help me solve?
G. What innovation or localized I used/discover which I wish to share
with other teacher?
Prepared by:
MICHELLE D. CARNAJE
BSED MATH IV-A Student
Checked/Observed by:
_____________________
INSTRUCTOR
___ Pupil’s eagerness to learn
___ Group member’s cooperation in doing their tasks
___ Bullying among learners
___ Equipment
(AVR/LCD)
___ Learner’s behavior/attitude
___ Science/Computer/Internet Lab
___ Colorful Ims
___ Additional Clerical
Works
___ Unavailable Technology
___ Reading Readiness