DLL-WK 1-LC 1.doc

GRADES 9
DAILY LESSON LOG
School Grade Level 9
Teacher Learning Area MATHEMATICS
Teaching Dates and
Time
Quarter FIRST
Teaching Day and Time
Grade Level Section
Session 1 Session 2 Session 3 Session 4
I. OBJECTIVES
1. Content Standards The learner demonstrates understanding of the key concepts of quadratic equations, inequalities and functions,
and rational algebraic equations.
2. Performance
Standards
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.
Illustrates quadratic
equations. (M9AL-Ia-1)
a. Write a quadratic
equation in standard
form.
b. Identify quadratic
equations.
c. Appreciate the
importance of quadratic
equations.
Solves quadratic equations
by: (a) extracting square
roots; (b) factoring; (c)
completing the square; and
(d) using the quadratic
formula. (M9AL-Ia-b-1)
a. Express quadratic
equation in the form
x2
= k .
b. Solve quadratic equation
by extracting square
roots.
c. Appreciate the
importance of solving
quadratic equations by
extracting square roots.
a. Find the factors of
quadratic expressions.
b. Apply the zero product
property in solving
quadratic equations.
c. Be attentive and
cooperative in doing the
given task with the group.
a. Find the factors of
quadratic expressions.
b. Solve quadratic equations
by factoring.
c. Appreciate how does
solving quadratic equation
help in making decision.

II. CONTENT
Illustrations of Quadratic
Equations
Solving Quadratic
Equations by Extracting
Square Roots
Solving Quadratic
Equations by Factoring
Solving Quadratic
Equations by Factoring
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pp. 14-18 pp. 19-23 pp. 24-27 pp. 24-27
2. Learner’s
Materials pp. 11-15 pp. 18-23 pp. 27-31 pp. 27-31
3. Textbook Math III SEDP Series
Capalad, Lanniene, et., al.
21st Century Math III
pp. 167-172
Ho, Ju Se T. et., al
Math PACE (Algebra II – 8)
pp. 7
Accelerated Christian
Education, Inc.
4. Additional
Materials from
Learning
Resource (LR)
portal
http://math.tutorvista.com/al
gebra/quadraticequation.ht
m


http://library.thinkquest.org/2
0991/alg2/quad.htm
http://www.purplemath.com/
moduleiquadraticform.htm
http://www.algebrahelp.com/
lessons/equation/quadratic
http://www.purplemath.com/
modules/solvquad.html
http://www.webmath.com/qu
adri.html
https://cdn.kutasoftware.co
m/worksheets/Alg1/Solving
%20Quadratic%20Factoring
.pdf
B. Other Learning
Resources
Grade 9 LCTG by DepEd
Cavite Mathematics 2016,
laptop, Monitor/Projector,
Activity Sheets
Activity Sheets
Activity Sheets
Activity Sheets
IV. PROCEDURES

A.Reviewing previous
lesson or presenting
the new lesson Do You Remember These
Products?
Find each indicated product
then answer the questions
that follow.
1. 3(x2
+7)
2. 2s(s-4)
3. (w+7)(w+3)
4. (x+9)(x-2)
5. (2t-1)(t+5)
6. (x+4)(x+4)
7. (2r-5)(2r-5)
8. (3-4m)2
9. (2h+7)(2h-7)
10.(8-3x)(8+3x)
a. How did you find each
product?
b. In finding each product,
what mathematics concepts
or principles did you apply?
Explain.
c. How would you describe
the products obtained?
Find My Roots!
Find the following square
roots. Answer the questions
that follow.
a .How did you find each
square root?
b. How many square roots
does a number have?
c. Does a negative number
have a square root? Why?
d. Describe the following
numbers:
.
Are the numbers rational or
irrational?
How do you describe
rational numbers?
How about numbers that
are irrational?
a. What are the factors
that contribute to
garbage segregation
and disposal?
b. As an ordinary
citizen, what can we
do to help solve the
garbage problem in
our community?
Students are grouped into 2
(boys vs girls).
Using flashcards, have each
group give the factors of the
following polynomials
mentally.
a. x2
+ 8x – 9 = 0
b. x 2
+ 9x = 10
c. x2
= 3 – 2x
d. x2
– 6 = – 5x
e. x2
+ 6x – 7 = 0
f. x2
+ x – 12 = 0
B.Establishing a
purpose for the
lesson
Another Kind of Equation!
Below are different
equations. Use these
equations to answer the
What Would Make a
Statement True?
Factor each polynomial.
a. x2
– 9x + 20
b. x2
– 8x + 12
1. 6.
2. 7.
3. 8.
4. 9.
5. 10.

questions that follow.
1. Which of the given
equations are linear?
2. How do you describe
linear equations?
3. Which of the given
equations are not
linear? Why?
How are these
equations different
from those which are
linear? What common
characteristics do
these equations
have?
Solve each of the following
equations in as many ways
as you can. Answer the
questions that follow.
a. How did you solve each
equation?
b. What mathematics
concepts or principles did
you apply to come up with
the solution of each
equation?
c. Compare the solutions
you got with those of your
classmates. Did you arrive
at the same answer? If not,
why?
d. Which equations did you
find difficult? Why?
c. x2
+ 14x +48
d. x2
– x – 6
e. x2
+ 7x – 18
C.Presenting examples/
instances of the
lesson
A quadratic equation in one
variable is a mathematical
sentence of degree 2 that
can be written in the
following standard form
ax2
+ bx + c = 0, where a, b,
and c are real numbers and
a ≠ 0. In the equation, ax2 is
Equations such as ,
, and are the
simplest forms of quadratic
equations. To solve this
equations, we extract the
square roots of both sides.
Hence we get,
Illustrative Example:
The quadratic equation
x2
+ 4x = 5 can be solved by
factoring using the following
procedure:
Write the equation in
Illustrative Example:
Find the solutions of
2x2
+ x = 6 by factoring.
a. Transform the
equation into
standard form
ax2
+bx+ c = 0.
x2-5x+3=0 9r2-25=0
c=12n-5
9-4x=15 r2=144
8k-3=12
t2-7t+6=0 2s+3t=-7
6p-q=10
1. 6.
2. 7.
3. 8.
4. 9.
5. 10.

the quadratic term, bx is the
linear term, and c is the
constant term.
Example 1
2x2
– 6x – 15 = 0 is a
quadratic equation in
standard form with a =2
b = -6 and c =-15.
Example 2
2x (x – 4) = 18 is a quadratic
equation. However, it is not
written in standard form. To
write the equation in
standard form, expand the
product and make one side
of the equation zero as
shown below.
2x(x – 4)= 18→ 2x2
– 8x = 18
2x2
– 8x – 18 = 18 -18
2x2
– 8x – 18 = 0
The equation becomes
2x2
– 8x –18 = 0 which is in
standard form.
In the equation
2x2
- 8x -18 = 0
a = 2, b = - 8, c = - 18.
Example 2. Find the
solutions of the equation
by extracting
square roots.
Write the equation in the
form .
Adding both sides results in
.
Recall that the square of
any real number, whether it
is positive or negative, is
always a positive number.
For example
.
Hence, there is no real
number x which satisfies
. Therefore, the
equation has no real root.
standard form:
x2
+ 4x – 5 = 0
Factor the quadratic
polynomial:
(x + 5) (x – 1)= 0
Set each factor equal to 0:
(x +5=0) or (x-1=0)
Solve each equation:
x = -5 or x = 1
Write the solution set:{ -5, 1}
Each member of the
solution set can be checked
by substituting for x in the
original equation.
Let x = -5 Let x = 1
x2
+ 4x = 5 x2
+ 4x = 5
(-5)2
+4(-5)=5 (1)2
+4(1)=5
25 - 20 = 5 1 + 4 = 5
5 = 5 5 = 5
2x2
+ x – 6 = 0
b. Factor the quadratic
expression 2x2
+x–6.
(2x – 3) (x + 2)
c. Apply the zero
product property by
setting each factor of
the quadratic
expression equal to
0.
2x – 3 = 0 ; x + 2 = 0
d. Solve each resulting
equation.
2x – 3 + 3 = 0 + 3
2x = 3
x = 3/2
x + 2 – 2 = 0 – 2
x = - 2
e. Check the values of
the variable obtained
by substituting each
in the equation
2x2
+ x = 6.
For x = 3/2
2x2
+ x = 6
2(3/2)2
+ 3/2 = 6
2(9/4) + 3/2 = 6
9/2 + 3/2 = 6
6 = 6
For x = -2

2x2
+ x = 6
2(-2)2
+ (-2) = 6
2 (4) – 2 = 6
8 – 2 = 6
6 = 6
D.Discussing new
concepts and
practicing new skills
#1
Tell whether each equation
is quadratic or not quadratic.
If the equation is not
quadratic, explain.
a. x2
+ 7x + 12 = 0
b. -3x (x + 5) = 0
c. 12 – 4x = 0
d. (x + 7) (x – 7) = 3x
e. 2x+ (x + 4) =
(x – 3)+ (x – 3)
Extract Me!
Solve the following
quadratic equations by
Have them find a partner
and do the following.
Solve each equation by
factoring.
1. x2
-11x + 30 = 0
2. x2
– x – 12 = 0
3. x2
+ 5x – 14 = 0
4. x2
+ 2x + 1 = 0
5. x2
– 4x – 12 = 0
factoring.
1. 2x2
-7x - 4 = 0
2. 3x2
+ x – 2 = 0
3. 4x2
– 1 = 0
4. 2x2
- 3x + 1 = 0
5. 10x2
– 14x + 4 = 0
E.Discussing new
concepts and
practicing new skills
#2
a. What is a quadratic
equation?
b. What is the standard form
of quadratic equation?
c. In the standard form of
quadratic equation, which is
the quadratic term?
linear term? constant term?
d. Why is a in the standard
form cannot be equal to 0?
1. What is the simplest form
of quadratic equation?
2. How do you get the
solutions of these
equations?
3. How many solutions/roots
does the equation
have if k > 0?
k = 0? k < 0?
Factor each of the following
polynomials:
a. x2
+ 5x -6
Find the factors of -6
whose sum is 5
b. y2
– 6y – 27
Think of the factors of -
27 whose sum is -6
c. x2
+ 14x + 49
Find identical factors of
49 and having the sum
of 14
d. x2
– 5x – 14
Determine the factors of
a. How do we solve a
quadratic equation?
b. What are the
procedures in
solving quadratic
equation by
factoring?
c. How many solution/s
does a quadratic
equation have?
d. How do you call each
solution?
e. How do we know if
the solution is
correct?
1. 6.
2. 7.
3. 8.
4. 9.
5. 10.
6.

-14 whose sum is -5
e. 2x2
- 7x + 6
Find the missing factors
(2x __)(x __)
F. Developing mastery
(Leads to Formative
Assessment 3)
Write each equation in
standard form then identify
the values of a, b, and c.
a. 2x2
+ 5x – 3 = 0
b. 3 -2x2
= 7
c. x (4x + 6) = 28
d. (3x-7)(5x+2)
“Extract then Match”
Find the solutions of the
following quadratic
equations by matching
column B with column A.
Correct roots will also reveal
the cities primary delicious
fruits.
A B
Tagaytay Strawberry
Davao Mangosteen
Cebu Pineapple
Zamboanga Durian
Baguio Mango
Banana
Solve the following
quadratic equation by
factoring.
1. x2
+ 9x – 36 = 0
2. x2
– 6x = 27
3. x2
+ 4x – 60 = 0
4. 2x2
– 5x – 18 = 0
5. x2
+ 6x = 16
Determine the solution set
of each equation.
1. 7r2
- 14r = -7
2. x2
– 25 = 0
3. 3y2
= 3y + 60
4. y2
– 11y + 19 = -5
5. 8x2
= 6x - x2
G.Finding practical
applications of
concepts and skills in
New houses are being
constructed in CalleSerye.
The residents of this new
Solve the problem.
Cora has a piece of cloth
Solve the following problem:
One positive number
Solve the problem:
The length of a rectangle

daily living housing project use a 17m
long path that cuts
diagonally across a vacant
rectangular lot. Before the
diagonal lot was
constructed, they had to
walk a total of 23 m long
along the two sides if they
want to go from one corner
to an opposite corner. Write
the quadratic equation that
represents the problem if
the shorter side is x. Identify
whose area is 32 square
inches. What is the length of
the side of the largest
square that can be formed
using the cloth?
exceeds another by 5. The
sum of their squares is 193.
Find both numbers.
is 6 cm more than the width.
If the area is 55 cm2
, find
the dimensions of the
rectangle.
H.Making
generalizations and
abstractions about
the lesson
A quadratic equation is an
equation of degree 2 that
can be written in the form
ax2
+ bx + c = 0, where a, b,
and c are real numbers and
a ≠ 0.
To solve an incomplete
quadratic equation:
1. Solve the equation for
the square of the
unknown number.
2. Find the square roots of
both members of the
equation.
Some quadratic equations
can be solved easily by
factoring. To solve such
equations, the following
procedure can be followed.
1. Transform the
quadratic equation
using standard form
in which one side is
zero.
2. Factor the non-zero
side.
3. Set each factor to
zero.
4. Solve each resulting
equation.
5. Check the values of
the variable obtained
by substituting each
in the original
When solving a quadratic
equation, keep in mind that:
1. The quadratic
equation must be
expressed in
standard form before
you attempt to factor
the quadratic
polynomial.
2. Every quadratic
equation has two
solutions. Each
solution is called a
root of the equation.
3. The solution set of a
quadratic equation
can be checked by
verifying that each
different root makes
the original equation

equation. a true statement.
I. Evaluating learning Write fact if the equation is
quadratic and bluff if the
equation is not quadratic.
1. x2
+ x – 3 = 0
2. 24x + 81 = x2
3. x2
= 2x (6x2
+ 4)
4. 2x2
= 7x
5. 5 – x + (2x - 3) = 12
1. x2
= 81
2. 4x2
– 100 = 0
3. a2
– 225 = 0
4. 7p2
– 2 = 54p
5. 2r2
+ 3 = 67
Group Activity:
What Name is Given to
Words That are Formed to
Imitate Sounds?
Find the solutions and write
the letter of each solution
set on top of the given
answer in the boxes below
to solve the puzzle.
N
x2
– 2x
= 4
T
x2
+4x–
21 =0
C
x2
– 4x
= 5
P
x2
– 2x
= 8
E
x2
– 3x
= 10
A
x2
– x
= 2
I
x2
– 9x
= -8
O
x2
– 3x
= -2
M
x2
–
5x+6=
0
factoring.
1. 3r2
– 16 r – 7= 5
2. 6b2
– 13b + 3 = -3
3. -4k2
– 8k – 3 = -3-5k2
4. 7x2
+ 2x = 0
5. 15a2
– 3a = 3 – 7a
Fact or bluff

J. Additional activities for
application or
remediation
1. Give 5 examples of
quadratic equations written
in standard form. Identify
2. Study solving quadratic
equation by extracting the
square root.
a. Do you solve a quadratic
equation by extracting the
square root?
b. Give the procedure.
Reference:
Learner’s Material pp. 18-20
Find the solutions of the
following equations by
1. 2(x+3)2 = 18
2. 4a2 – 147 = a2
3. 1 = ½ x2
4. 54a2 – 6 - 24
5. 3c2 – 5 = 25
Follow-Up
1. Find the solutions of
(x + 3)2
= 25.
2. Do you agree that x2
+ 5x – 14 = 0 and 14
– 5x – x2
= 0 have
the same solutions?
Justify your answer.
Factor the following
Quadratic Equation.
1. x2
+ 4x + 4 = 0
2. x2
– 6x + 9 = 0
3. x2
– 8x + 16 = 0
4. x2
+ 2x + 1 = 0
5. x2
– 10x + 25 = 0
What have you noticed with
their factors?
V. REMARKS
VI. REFLECTION
1. No. of learners who
earned 80% on the
formative assessment
require additional
activities for
remediation.
3. Did the remedial
lessons work? No. of
learners who have
caught up with the
lesson.

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 share with
other teachers?

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