Republic of the Philippines
Department of Education
REGION IV-A CALABARZON
SCHOOLS DIVISION OF BATANGAS PROVINCE
MABALOR-CATANDALA INTEGRATED SCHOOL
CATANDALA, IBAAN, BATANGAS
GRADE9
DAILY LESSON LOG
School
Mabalor-Catandala Integrated School
Teacher
Nicole L. Tanyag
Monday, Wednesday-Friday / 8:20-9:20 am
SEPTEMBER 4-8, 2023
Teaching Dates and Time
MONDAY
WEDNESDAY
Grade Level
THURSDAY
9
Learning Area
MATH
Quarter
FIRST
FRIDAY
I. OBJECTIVES
A. Content Standards
B. Performance
Standards
The learner demonstrates understanding of the key concepts of quadratic equations, inequalities and functions, and rational algebraic
equations.
The learner is able to investigate thoroughly mathematical relationships in various situations, formulate real-life problems involving
quadratic equations, inequalities and functions, and rational algebraic equations and solve them using a variety of strategies.
C. Learning Competencies Solves quadratic equations by: (a) Solves quadratic equations by: (a) Solves quadratic equations by: (a) Solves quadratic equations by: (a)
extracting square roots; (b)
extracting square roots; (b)
extracting square roots; (b)
extracting square roots; (b)
/ Objectives
factoring; (c) completing the
factoring; (c) completing the
factoring; (c) completing the
factoring; (c) completing the
square; and (d) using the
square; and (d) using the
square; and (d) using the
square; and (d) using the
quadratic formula. (M9AL-Ia-b-1) quadratic formula. (M9AL-Ia-b-1) quadratic formula. (M9AL-Ia-b-1) quadratic formula. (M9AL-Ia-b-1)
a. Identify and complete perfect
square trinomial
b. Model the process of
completing the square with
a. Identify and complete perfect
square trinomial
b. Solve a quadratic equation by
completing the square
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a. Identify the values of a, b, and a. Understand that the quadratic
c in quadratic equation.
formula can be used on any
b. Derive ax2 + bx + c = 0 to
quadratic equation
quadratic formula by applying the
Republic of the Philippines
Department of Education
REGION IV-A CALABARZON
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algebra tiles
c. Value accumulated knowledge method of
c. Appreciate the use of algebra as means of new understanding completing the square
tiles
c. Patience in deriving standard
form to
quadratic formula
b. Solve quadratic equation by
using the quadratic formula
c. Appreciate the importance of
solving quadratic equations by
using the quadratic formula
Solving Quadratic Equations by Solving Quadratic Equations by Solving Quadratic Equations by Solving Quadratic Equations by
Completing the Square
Completing the Square
Using the Quadratic Formula
Using the Quadratic Formula
II. CONTENT
III. LEARNING RESOURCES
A. References
1.
2.
3.
Teacher’s Guide
pages
pp. 28-32
pp. 28-32
pp. 33-38
pp. 33-38
Learner’s
Materials pages
pp. 35-40
pp. 35-40
pp. 47-52
pp. 47-52
21st Century Math III
pp. 176
Ho, Ju Se T. et., al
21st Century Math II
pp. 176
Ho, Ju Se T. et., al
Textbook pages
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Math PACE (Algebra II-8)
Math PACE (Algebra II-8)
pp. 12
pp. 12
Accelerated Christian Educ., Inc. Accelerated Christian Educ., Inc.
Republic of the Philippines
Department of Education
4.
REGION IV-A CALABARZON
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Additional
http://www.cpalms.org/Uploads/re http://www.cpalms.org/Uploads/re
Materials from
sources/48564/1/5/docs/Completi sources/48564/1/5/docs/Completi
Learning Resource ng%20the%20square%20guided ng%20the%20square%20guided
(LR) portal
%20practice%20sheet.pdf
%20practice%20sheet.pdf
http://www.purplemath.com/modul http://www.purplemath.com/modul
http://www.cpalms.org/Uploads/re http://www.cpalms.org/Uploads/re
eiquadraticform.htm
eiquadraticform.htm
sources/48564/1/4/docs/Completi sources/48564/1/4/docs/Completi
ng%20the%20Square%20Instruct ng%20the%20Square%20Instruct
or%20notes%20part%203.pdf
or%20notes%20part%203.pdf
B. Other Learning
Resources
Grade 9 LCTG by DepEd Cavite Grade 9 LCTG by DepEd Cavite Grade 9 LCTG by DepEd Cavite
Grade 9 LCTG by DepEd Cavite
Mathematics 2016, laptop,
Mathematics 2016,
Mathematics 2016,
Mathematics 2016, laptop,
Monitor/Projector, Activity Sheets laptop, Monitor/Projector, Activity laptop, Monitor/Projector, Activity
Monitor/Projector, Activity Sheets
Sheets
Sheets
IV. PROCEDURES
A. Reviewing previous lesson
or presenting the new
lesson
What does a square look like?
Is this a square?
Express each of the following
perfect square trinomial as a
square of binomial.
What about this one?
This one?
a.
b.
c.
d.
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x2 + 6x + 9
x2 – 14x + 49
x2 + 2x + 1
x2 – 18x + 81
Answer the question.
“How does finding solutions of
quadratic equations facilitate
solving real-life problems and
making decisions?”
Simplify each of the following
expressions.
Republic of the Philippines
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Why isn’t the last picture a
e. 25x2 – 30xy + 9y
square?
What would we need to do to
make this a square?
B. Establishing a purpose for We can model a quadratic
expression like this
the lesson
x2 + 4x + 4 with tiles like this
Follow the Standards!
Write the following quadratic
Not all quadratic equations can
equations in standard form ax2 +
be easily solved by factoring or by
bx + c = 0. Then identify the
extracting the square roots. When
values of a, b, and c.
these methods are not possible,
how do you solve the equation?
1. 2x2 + 9x = 10
2. -2x2 = 2 – 7x
3. 6x – 1 = 2x2
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4. 10 + 7x – 3x2 = 0
5. 2x (x – 6) = 5
Consider this problem.
C. Presenting examples/ Illustrative Example:
instances of the lesson
x2 + 6x – 8 = 0
We will use algebra tiles to help
us with the non factorable
problem. The algebra tiles will
help us get a new c value that will
help us factor into a new perfect
square.
ax2 + bx + c
a=
b=
c=
so for x2 + 6x – 8 ; a = 1
b = 6 c = -8
using algebra tiles we have
The product of a number and four
less than the number is equal to
2. What is the number?
The problem can be written in
mathematical sentence as x(x –
4)= 2.
In standard form, the equation
becomes
x2 – 4x – 2 = 0.
The expression x2 – 4x – 2
cannot be factored. We can
employ another method called
completing the square to find the
solutions.
To use this method, we must aim
to produce a trinomial that is a
perfect square. Take note that
perfect square trinomials can be
expressed as the square of a
binomial.(refer to a–e of no.1 in
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In order to use the quadratic
formula in solving the quadratic
equation, we need to identify the
The solutions of any quadratic
2
equation ax + bx + c = 0 can be values of a, 2b, and c in the
equation ax + bx + c = 0. Then
determined using the quadratic
solve.
formula
Illustrative Example:
6x2 = 10 + 11x
6x2 – 11x – 10 = 0
This formula can be derived by
Rewrite in the form
applying the method of
ax2 + bx + c = 0
completing the square as shown
below.
So a = 6, b = -11, c = - 10
Identify a, b, and c.
Republic of the Philippines
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A). Note that these quadratic
trinomials are of the form ax2 + bx
+ c. Moreover, the constant term
in every perfect square trinomial
is the square of one-half the
coefficient of the x.
Recall that
the square of the binomial (x + y)2
is x2 + 2xy + y2
Let us take a look at the
We are missing a space in our
expression x2 + bx,
square.
If we add (b/2)2, that is, the
square of half of the coefficient of
How many s would we really
x, then we have
need to complete the square?
x2 + bx + (b/2)2= (x + b/2)2.
Answer = 9 s
Thus the expression becomes a
perfect square trinomial that can
So x2 + 6x – 8 = 0 would factor
be written as the square of a
out easier if it were
binomial. We can now solve the
x2 + 6x + 9. So we bring the -8 to equation
the other side.
x2 – 4x – 2 = 0 by completing the
square.
x2 + 6x + 9 = 8 + 9
x2– 4x + ___ = 2
because what we do to one side Transpose the constant 2 to the
we must also do to the other.
right side of the equation.
x2 4x + 4 = 2 + 4
Which factors out to be
Complete the square by adding
(x + 3)(x + 3) = 17
the square of half coefficient of x,
(x + 3)2
= 17
that is,
(x + 3) School
= ±√17
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[1/2(- 4) ]2 = 4 to both sides of the
x = - 3 ±√17
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equation.
(x – 2)2 = 6
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Write the left side as the square
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of a binomial.
x – 2 = ± √6
Extract the square root of both
side.
x = 2 ±√6
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D. Discussing new concepts
and practicing new skills
#1
A.
1.
2.
3.
4.
5.
B.
E. Discussing new concepts
and practicing new skills
#2
1.
2.
3.
4.
5.
1.
2.
3.
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Complete the square of
Complete Me!
Lead Me to the Formula!
the following:
Find the solutions of each of the Work in groups of 4 in finding the
x2 + 4x + _____
following quadratic equations by solutions of the quadratic
x2 – 6x + _____
completing the square.
equation below by completing the
x2 – 12 x +_____
square.
n2 – 18n + _____
a. x2 – 2x = 3
x2 + 8x + _____
b. s2 + 4s – 21 = 0
2x2 + 9x + 10 = 0
2
c. t + 10t + 9 = 0
Determine a number that
d. x2 + 14x = 32
must be added to both
e. r2 – 10r = -17
sides of each equation to
complete the square?
x2 + 4x = 12
x2 – 2x = 24
x2 – 6x = -8
x2 – 6x = 7
x2 + 6x = 16
What does it mean to
How do we solve a quadratic
1. How did you use
“complete the square”? equation by completing the
completing the square in
How do you describe a
square?
solving the given
perfect square trinomial?
equation?
How can you determine a
a. What are the solutions of
2. What are the solutions of
number that must be
the quadratic equation x2
the given equation?
added to the terms of
– 10x + 19 = 0?
3. How would you describe
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Solve these quadratic equations
by using the quadratic formula.
Write answers in set form.
1.
2.
3.
4.
5.
2x2 – 7x + 3 = 0
6x2 – 7x = 3
3x2 – 4 = -6x
4x2 + 9x + 2 = 0
3x2 = x + 5
How do you solve a quadratic
equation using the quadratic
formula?
Find the solutions of the following
quadratic equations.
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polynomial to make it a
b. Write the solutions by
the solutions obtained? a. x2 + 10x + 9 = 0
perfect square trinomial?
following the procedure
4. In the equation 2x2 + 9x + Identify the values of a, b, and c
2
4. Observe the terms of
x – 10x + 19 = 0
10 = 0, what would be the b. x2 – 12x = - 35
each trinomial. How is the
Transpose 19 to the right
resulting equation if 2, 9, Rewrite in the form ax2 + bx + c =
third term related to the
side of the equation.
and 10 were replaced by 0
coefficient of the middle
Complete the square by
a, b, and c, respectively? c. x2 + 5x – 14 = 0
term?
adding
5. Using the resulting
Use the quadratic formula after
5. How can algebra tiles be
[1/2(10)]2 = 25
equation in item 4, how substituting the values
used to visually represent
Write the left side as the
are you going to find the of a, b, and c
completing the square?
square of binomial.
value of x if you follow the d. 4x2 – 4x + 1 = 0
Extract the square of both
same procedure in finding Divide first by 4.
sides
the same solutions of 2x2
Solve for x.
+ 9x + 10 = 0? What
equation or formula would
give the value of x?
6. Do you think the equation
or formula that would give
the value of x can be
used in solving other
quadratic equations?
F. Developing mastery
(Leads to Formative Assessment
3)
Solve the following quadratic
equation using algebra tiles.
Solve the following quadratic
equations by completing the
square.
1. x2 + 10x – 3 = 0
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Identify the values of a, b, and c
for each equation & substitute
these values in the Quadratic
formula.
Determine the solutions of each
quadratic equation using the
quadratic formula.
1. x2 + 3x – 10 = 0
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2.
3.
4.
5.
G. Finding practical
applications of concepts
and skills in daily living
x2 + 2x – 1 = 0
x2 – 4x – 6 = 0
x2 – 6x – 18 = 0
x2 – 2x – 5 = 0
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a. x2+ 4x – 45 = 0
b. x2 + 8x = - 15
1. 2x2 + 7x + 9 = 0
2
c. x – 2x = 24
2. 4x2 – 4x + 1 = 0
d. p2 + 2p = 48
3. 3x2 – 4x = 0
e. 3x2 – 7x – 6 = 0
4. 9x2 – 72 = 0
5. 2x2 + 4x = 3
Solve the problem below.
Solve the problem below.
A space in the shape of a right
Television screen are usually
triangle is to be surrounded on its measured by the length of its
edge by pebbles. The hypotenuse diagonal The television set has a
of the triangle is 6m. One leg is to 60-inch diagonal. The screen is
be 2m longer than the other leg. 12 inches wider than its height.
To the nearest hundredths, what Find the dimensions of the
are the lengths of the two legs? screen.
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2. x2 – 4x – 21 = 0
3. x2 – 2x = 24
4. x2 – 8x = -7
5. 12x + 3x2 = 63
The length of a car park is 120m Read and understand the
longer than it width. The area of situation below then answer the
the car park is 6400m2.
questions that follow.
1. How would you represent Mr. Bonifacio cuts a size of
the width of the car park? rectangular plywood to be used in
How about its length?
the furniture that he makes. The
2. What equation represents length of the plywood is twice its
the area of the car park? width and the area is 4.5 sq. ft.
3. What is the standard form What quadratic equation
of the equation?
represents the area of the piece
4. What are the values of a, of plywood?
b and c?
a. Write the quadratic equation
formulated in standard form. Then
determine the values of a, b, and
c.
b. Solve the quadratic equation
using the quadratic formula
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c. Which of the solutions or roots
obtained represents the width of
the plywood?
H. Making generalizations and
abstractions about the
lesson
I. Evaluating learning
To solve a quadratic equation ax2
+ bx = c by completing the square The equation should be arranged
in the right form: ax2 + bx + c = 0.
a. Transform the equation
into the form
The solutions of any quadratic
To use the quadratic formula, first
Algebra tiles can help us solve
x2 + (�/�) x = −�/�
equation
write the given equation in
non factorable quadratic
b. Add to each side of the ax2 + bx + c = 0 can be
standard form. Then, identify the
equations. It will help us get a
equation the square of
determined using the quadratic
values of a, b, and c and
new value of c that will help us
half the coefficient of x. formula
substitute these values in the
factor into a perfect square.
c. Write the left side as the
quadratic formula.
square of a binomial.
d. Take the square root of
each side of the equation.
Solve the resulting linear
equations.
Group Work: Solve the following
“In time of difficulties, be like a Solve the equation
Use the quadratic formula in
equations. Have one
____ tree.”
2x2 + x = 5 by using the quadratic solving each quadratic equation.
representative from a group come
formula.
1. c2 – 13c – 30 = 0
to the board and explain why/how Write the indicated letter into the
2. x2 – 10x = -9
they got their answer and then
box that corresponds to the
3. m2 – 10m + 16 = 0
they will solve on board.
solutions of the quadratic
4. 4d2 + 18d – 10 = 0
equation solved by completing
5. x2 – 8x + 16 = 0
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1. x2 + 8x – 3 = 0
the square. Show your solutions.
2. x2 – 6x – 9 = 0
M. {5,1 }
x2–13x–30=0
2
3. x = 6x = 1
B. { 1, -5 }
x2+4x=96
O. {3, 2 }
x2–6x+5 = 0
A. { 8, -12 }
2x2+8x =10
O. { 7, 1 }
4x2–32x=-28
R. {-3 -2 }
x2–5x 6=0
B. {15, -2 }
J. Additional activities for
Assignment:
Assignment:
Assignment:
application or remediation
Answer the following.
1. Memorize the Quadratic
Answer.
Formula.
Karen wants to use completing
2. Solve the equation 5x2 –
the square in solving the
Do you agree that any quadratic
2x – 2 = 0 by using the
quadratic equation 4x – 25 = 0.
equation can be solved by
quadratic formula.
Can she use it in finding the
completing the square? Justify
solutions of the equation? Explain your answer.
Reference: Learner’s Material pp.
why or why not.
50-51
V. REMARKS
VI. REFLECTION
1.
No. of learners who earned
80% on the formative
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Assignment:
Answer the following.
Do you think the quadratic
formula is more appropriate to
use in solving quadratic
equations? Explain then give
examples to support your answer.
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assessment
2.
No. of learners who require
additional activities for
remediation.
3.
Did the remedial lessons
work? No. of learners who
have caught up with the
lesson.
4.
No. of learners who
continue to require
remediation
5.
Which of my teaching
strategies worked well? Why
did these work?
6.
What difficulties did I
encounter which my principal
or supervisor can help me
solve?
7.
What innovation or
localized materials did I
use/discover which I wish to
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share with other teachers?
Prepared by:
NICOLE L. TANYAG
Teacher I
Checked by:
MA. VERONICA C. ROXAS
Principal II
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