2023.DLL.Pre-Calculus.11.prelims.W.1.docx

DLL

1. school year 2023 - 2024
Saint Catherine’s School
PRE – SCHOOL, ELEMENTARY, JUNIOR AND SENIOR HIGH SCHOOL
PAASCU ACCREDITED
Real St., Buag, Bambang, Nueva Vizcaya
DAILY LESSON LOG
Department Mathematics Department Grade Level Grade 11
Teacher Jolita I. Lisbog Learning Area Pre-Calculus 11
Teaching Dates and Time September 4 – September 8, 2023 Quarter Prelims
SESSION #1 SESSION #2 SESSION #3 SESSION #4
I.STANDARDS, MELC/s, &
OBJECTIVE/S
A.Content Standards The learners demonstrate an understanding of key concepts of conic sections and systems of nonlinear equations.
B.Performance Standards The learners shall be able to model situations appropriately and solve problems accurately using conic sections and systems of
nonlinear equations.
C.Learning Competencies/
Objectives:
At the end of the lesson, the
learners are expected to:
1. Illustrates the types of conic
sections: parabola, ellipse,
circle, hyperbola, and
degenerate cases.
STEM_PC11AG-Ia-1
a.Define conic
sections,
b.Illustrate the types of
conic sections, and
c.Appreciate the
concept about conic
sections.
At the end of the lesson, the
learners are expected to:
1. Define a circle.
STEM_PC11AG-Ia-2
a.Define circle and
b.Appreciate the concept
about circles.
At the end of the lesson, the
learners are expected to:
1. Determine the standard
form of equation of a
circle.
STEM_PC11AGIa-3
a.Illustrate the standard
form of equation of
a circle.
b.Solve an equation
applying the
standard form of
equation of a circle.
c.Appreciate the concept
about standard form
At the end of the lesson, the
learners are expected to:
1.Define conic sections,
2.Define circle,
3.Illustrate the types of
conic sections,
4.Illustrate the standard
form of equation of a
circle and;
5.Solve an equation
applying the standard
form of equation of a
circle.
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2. school year 2023 - 2024
of equation of a
circle.
II.CONTENT
A.Lesson/Topic An Overview of Conic
Sections
Circles
Standard Form of
Equation of a Circle
Long Quiz
III.LEARNING RESOURCES
A.References Text book: Albay, Eduard M.
(2016). Precalculus. Makati
City, Philippines. Diwa
Learning
Text book: Albay, Eduard M.
(2016). Precalculus. Makati
City, Philippines. Diwa
Learning
Text book: Albay, Eduard M.
(2016). Precalculus. Makati
City, Philippines. Diwa
Learning
1.Teacher’s Guide pages
2.Learner’s Material pages
3.Textbook/Module pages Chua D.T., S. L., et.al. (2018).
B.Other Learning Resources Laptop, PowerPoint, TV,
Blackboard, Chalk
Laptop, PowerPoint, TV,
Blackboard, Chalk
Laptop, PowerPoint, TV,
Blackboard, Chalk
Laptop, PowerPoint, TV,
Blackboard, Chalk
IV.PROCEDURES
A.Reviewing previous lesson or
presenting the new lesson
The teacher will let the students
guess the parts of the cone by
giving them a short activity.
The teacher will let the students
guess the types of conic
sections illustrated by the given
pictures.
The teacher will let the
students recall the circles.
Guide questions:
How can we define
circle?
Review the 4 types of conic
sections, circles and the
standard form of equation of a
circle.
Conic Section
Four Types Of Conic Sections
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3. school year 2023 - 2024
B.Establishing a purpose for the
lesson
The teacher will let the students
realize that recognizing the parts
of a cone is needed to
understand the concept of the
conic sections.
The teacher will let the students
realize that recognizing the
types of conic sections is
needed to understand the
concept of the circles.
The teacher will let the
students realize that
recognizing the types of conic
sections is needed to
understand the concept of the
standard form of equation of a
circle.
Circle
A circle is a conic section that
is formed by intersecting a
cone with a plane that is
perpendicular to the axis of the
cone.
A circle is the set of all points
in a plane that are equidistant
from affixed point called the
center. The distance from the
center to any point on the
circle is called the radius of the
circle center, denoted by r,
where r ¿ 0.
Standard Form of
Equation of a Circle
C.Presenting examples/instances
of the new lesson
The teacher will present a
picture and the students will
guess if what types of conic
sections it is.
The teacher will present a
picture and the students will
analyze it.
The teacher will define with the
students about the circles.
A circle is a conic section that is
formed by intersecting a cone
The teacher will present the
standard form of equation of a
circle.
Let the center C of a circle be
located at point (h,k) and the
radius be equal to r also, let the
point P(x,y) be any point on
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4. school year 2023 - 2024
with a plane that is
perpendicular to the axis of the
cone.
the circle.
Then the distance C to P is r,
that is,
√(x−h)
2
+(y−k)
2
=r
Squaring both sides of the
equation leads to
(x−h)
2
+(y−k)
2
=r
2
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A circle is formed when
a cone is cut by a plane
that is parallel to the
base.

5. school year 2023 - 2024
D.Discussing new concepts and
practicing new skills #1
The teacher will define with the
students about the conic
sections.
A circle is the set of all points
in a plane that are equidistant
from affixed point called the
center. The distance from the
center to any point on the circle
is called the radius of the circle
center, denoted by r, where r ¿
0.
Therefore, the standard form of
the equation of a circle whose
center is at (h,k) and whose
radius is r is given by
(x−h)
2
+(y−k)
2
=r
2
, where r
¿ 0.
If the center of the circle is at
the origin, that is h=0 and k=0,
and the radius is r, then the
equation of the circle is given
by x
2
+y
2
=r
2
, where r ¿ 0.
The teacher will let the
students answer the given
activities.
E.Discussing new concepts and
practicing new skills #2
The teacher will illustrate with
the students about the types of
conic sections.
Given the center and radius, it
would be easy to determine the
equation of the circle.
Example 1: Determine the
standard equation of the circle
given the coordinates of its
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6. school year 2023 - 2024
center and the length of its
radius.
a.center at (2,-3) and r=3
b.center(0,0) and r=5
Example 2: Given the standard
form of the equations. Find the
coordinates of the center and
the radius of each of the
following circles.
a.x
2
+y
2
=64
b. (x+9)
2
+(y−1)
2
=25
F.Developing mastery
(Leads to Formative
Assessment)
The teacher will let the students
recite orally.
Guide Questions:
What are the four types
of conic sections that
we have discussed?
The teacher will let the students
recite orally.
Guide Questions:
How can we define
circle in your own
understanding?
The teacher will let the
students solve in the
blackboard.
1.center(2,-5) and r=10
2.x
2
+(y−2)
2
=49
G.Valuing
Finding practical
applications of
concepts/skills in daily
The teacher will let the students
give a real life situation about
the conic sections.
Circles represent completeness
encompasses all space and time.
The circle symbolizes unity,
stability, rationality. It is also
the symbol of infinity, without
.
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Water from a fountain
takes a path of parabola
to fall on the earth.
Electrons on the atom
move around the nucleus
in an elliptical path of
orbit.
A guitar is an example of
hyperbola as its side’s
hyperbola.
beginning or end, perfection,
the ultimate geometric symbol.
Core Values Integration
Excellence
Critical Thinking
Excellence
Critical Thinking
Excellence
Critical Thinking
Excellence
Critical Thinking
H.Making generalizations and
abstractions about the lesson
The teacher summarizes the
lesson by asking volunteer
students to answer the
following:
1. What is conic section?
2. What are the four types of
conic sections?
The teacher summarizes the
lesson by asking volunteer
students to answer the
following:
1. How does the conic sections,
circle is being form?
The teacher summarizes the
lesson by the students to state
the formula of a circle at (h,k)
and circle with center at the
center.
I.Evaluating learning The teacher will let the studentsThe teacher will let the studentsThe teacher will let the
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8. school year 2023 - 2024
identify the type of conic
sections illustrated by the given
pictures.
to complete the definition of
circle by filling the blanks.
A ______ is the set of all points
in a plane that are
________from affixed point
called the ______. The distance
from the center to any point on
the circle is called the ______
of the circle center, denoted by
r, __________.
students answer the given
activities.
J.Assignment
Additional activities for application or
remediation
Guide Question:
What is a circle?
Guide Question:
What is the standard form of the
equation circle?
Let the students review their
lessons for the long quiz.
V.REMARKS
Students’ Mastery Level  Beginning
 Developing
 Approaching Proficiency
 Proficient
 Advanced
 Beginning
 Developing
 Approaching Proficiency
 Proficient
 Advanced
 Beginning
 Developing
 Approaching Proficiency
 Proficient
 Advanced
 Beginning
 Developing
 Approaching Proficiency
 Proficient
 Advanced
Intervention/s Made
Prepared by: Checked:
JOLITA INWAY LISBOG OLIVER V. RAZA
Subject Teacher Department Chair
Noted:
CLARISSA S. SILVA, MED – SL
School Principal
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