GRADE 8
DAILY LESSON LOG
School
Teacher
Teaching Dates and Time
Session 1
Grade Level
Learning Area
Quarter
Session 2
Session 3
8
MATHEMATICS
FIRST
Session 4
I. OBJECTIVES
1. Content
Standards
The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions,
linear equations and inequalities in two variables and linear functions.
The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions,
2. Performance
linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and
Standards
linear functions, and solve these problems accurately using a variety of strategies.
3. Learning
The learner solves
The learner solves
The learner illustrates the
The learner illustrates
Competencies /
problems involving rational problems involving
rectangular coordinate
linear equations in two
Objectives
algebraic expression.
rational algebraic
system and its uses.
variables.
(M8AL-Id-2)
expression.
(M8AL-Ie-1)
(M8AL-Ie-3)
(M8AL-Id-2)
a. Perform operations in
a. Describe and illustrate
a. Determine the solution of
solving word problem
a. Perform operations in
rectangular coordinate
Linear Equation in two
involving Rational
solving word problem
system.
variables
Expressions
involving Rational
b. Give the coordinates of a b. Illustrate linear equation
b. Analyze and solve word
Expressions
point on the plane and
in two variables
problems involving
b. Analyze and solve
plot points on the
c. Find pleasure in working
Rational Expressions.
word problems
Cartesian plane.
with linear equation in
c. Appreciate the value
involving Rational
c. Appreciate the concept
two variables.
and importance of
Expressions.
of rectangular coordinate
Rational Expression in
c. Appreciate the value
system in real-life
real life situation.
and importance of
situation.
Rational Expression in
real life situation.
II. CONTENT
Problems involving
Rational Algebraic
Expression
Problems involving
Rational Algebraic
Expression
Rectangular Coordinate
System and its Uses
Linear Equations in Two
variables
III. LEARNING
RESOURCES
A. References
1.
Teacher’s Guide
pages
2.
Learner’s Materials
106 - 108
pages
Alferez M.,
MSA Intermediate
Algebra pages 159
Textbook pages
Bernabe, J.,
Intermediate Algebra
pages 88-94
3.
4.
138 – 154
106 - 108
Alferez, M.,
MSA Intermediate
Algebra pages 159
Bernabe, J.,
Intermediate Algebra
pages 88-94
119 - 136
119 - 120
Crisostomo, R. et.al.
Our World of Math 8,
pages 93 – 99
Sabangan, L. et.al.,
Math Time pages 39-42
Laptop, Projector, visual
aids, Grade 8 LCTG by
DepEd Cavite
Mathematics, 2016
Laptop, Projector, Visual
aids, Grade 8 LCTG by
DepEd Cavite
Mathematics, 2016
Additional
Materials from
Learning Resource
(LR) portal
B. Other Learning
Resources
Laptop, projector, Visual
aids, Grade 8 LCTG by
DepEd Cavite
Mathematics, 2016
Laptop, projector, Visual
aids, Grade 8 LCTG by
DepEd Cavite
Mathematics, 2016
Let’s travel!!!
Preliminaries:
Pick a Pair
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
Two vehicles travelled
(𝑥 + 4) kilometers.
The first vehicle travelled
for (𝑥 2 − 16) hours
while the second
Preliminaries
Can you cross your
arms? What happened
when you cross your
arms horizontally and
vertically? How do you
describe your arms?
Preliminaries
Check the ordered pair
that is a solution to the
given linear equation.
1. 𝑥 − 𝑦 = 8
(9,1)
(-9,1)
travelled for (
2
)
𝑥−4
hours.
Given the following grid,
can you complete its
label to illustrate the
parts and terms involve
in Rectangular
Coordinate System?
(Answers are being jot
down on the board.)
Complete the table
below.
How did you compute
the speed of the two
vehicles?
From the box above, pick
the correct rational
expression to be placed
on the spaces provided
to make the equation
true.
1.
2.
3.
4.
𝑥+6
+ ___ =
3𝑥−6
3
𝑥+7
+
___ −
3𝑥 2 𝑦
2𝑎𝑏
4
𝑥−8
𝑥+3𝑦
6𝑥 3 𝑦
2. 4𝑥 − 9𝑦 = −3
(5,2)
(2,5)
3.
2𝑥 + 𝑦 = 8
(2,4)
(-2,4)
4. 𝑥 + 𝑦 = 6
(4,2)
(-4,2)
5. 7𝑥 − 2𝑦 = 10
(0,-5)
(5,0)
2𝑥+7
3𝑥−6
= ___
=−
∙ ___ =
1
𝑥3
12𝑎𝑥
5𝑦
𝑥 2 −4𝑥+4
B. Establishing a
purpose for the
lesson
Guide Questions:
How did you compute the
speed of the two vehicles?
5.
÷ 𝑥 − 2 = __
2𝑥−4
Guide Question:
Developmental Activity:
1. Do you think rational
expression can be
1. What do you call the two
intersecting number
Questions:
1. How will you find the
value of x?
What method did you
use to find the speed of
the two vehicles?
applied in solving real
word problems? How?
lines? the point of
intersection?
2. Into how many parts or
regions is the plane
divided? How do we call
these regions?
3. How can you describe a
quadrant? How are you
going to label/name these
quadrants?
4. How do you describe now
a Cartesian plane? How
about a point in the
Cartesian plane?
5. How is a point plotted in
the plane?
6. Are the coordinates
( 0, 2 ) and ( 2, 0 ) the
same? Why?
7. Can you plot these points
in the plane?
8. How do we call now the
first component of an
ordered pair? How about
the second component?
2. How will you find the
value of y?
C. Presenting
examples/ instances
of the lesson







Think-Pair-Share
Illustrative Example 1
Pancho and Bruce were
asked to fill the tank with
water. Pancho can fill the
tank in x minutes alone,
while Bruce is slower by
two minutes compared to
Pancho.
Alden and Maine were
dusting the garage. In
an hour, Alden dusted
What part of the job can
Pancho finish in one
minute?
What part of the job can
bruce finish in one
minute?
Pancho and Bruce can
finish filling the tank
together within y
minutes.
How will you represent
algebraically, in simplest
form, the job done by the
two if they worked
together?
One side of the triangle
is 2cm longer than the
second side. The third is
3/5 as long as the first
4
𝑥−5
Determine the solution of
linear equation in two
variables.
1. 5𝑥 – 𝑦 = −1
x
y
of the garage and
1
2
Maine dusted the
remaining. How much
portion of the garage did
Maine dust in an hour?
2. 4𝑥 + 5𝑦 = 10
Solution:
3. 𝑦 = 3𝑥 + 2
x
y
x
y
Alden dusted in an hour
=
4
𝑥−5
Maine dusted in an hour
=1−
=
4
𝑥−5
𝑥−5−4
𝑥−5
=
𝑥−9
𝑥−5
1.
2.
3.
4.
5.
Referring to the
illustration above, in what
quadrant will you locate
the following points?
P ( 3, 4 )
R ( -2, -6)
A ( 1, -5 )
Y ( -4, 3 )
S ( 0, 5 )
5
2
10
4
side. If the perimeter of
the triangle is 24cm, Find
the lengths of the three
sides.
Solution: Write an
equation designating the
three sides as a, b, c
"One side of the triangle
is 2cm longer than the
second side."
a=b+2
rearrange to get b in
terms of a
𝑏 = 𝑎 − 2
"The third is 3/5 as long
as the first side."
3
c= 𝑎
5
"If the perimeter of the
triangle is 24cm,"
𝑎 + 𝑏 + 𝑐 = 24
Replace b and c, using
the above equations
3
a + (a – 2) + 5 𝑎 = 24
3
a + a + 𝑎 = 24 + 2
5
Pair Work:
The length of
rectangular pool area in
terms of x is
𝑥 2 −𝑥−6
𝑥+4
and the width is
𝑥 2 +𝑥−12
𝑥+2
, what is
the area of the
rectangular pool in
terms of x? Give your
answer in factored form.
3
2a + 𝑎 = 26
5
a = 10
b=8
c=6
D. Discussing new
concepts and practicing
new skills #1
Solve the following
problems.
Pipe A can fill a tank in
40 minutes. Pipe B can
fill the tank in x minutes.
What part of the tank is
filled if either of the pipes
is opened in ten
minutes?
E. Discussing new
Solve the following
concepts and practicing problems.
new skills #2
1. If Anna’s height in terms
7
of x is ( ) cm and
3
Corazon’s height in
terms of x is (
8
)cm.
12𝑥−8
What is the difference in
their height?
1. What is being asked in Analysis:
the given problems
How do you describe
above?
the Cartesian
2. What operation is to be
Coordinate System?
used to solve the
State the steps in
problem?
plotting of points.
3. Give the steps in adding
similar and dissimilar
Is it possible that when
rational expression?
you plot points, you
Multiplying rational
became creative and
expression?
you are ready for future
orientation on how to
use resources wisely?
Solve the following
problems.
Group the class into 5.
Present five Cartesian
1. Joshua can wash a car planes. In each plane,
in 3 hours if the works
give the coordinates of
alone while Caleb can do
each point and arrange
the same job in 4 hours.
the letters to form the
How long will it take them
magic word. From the
to wash the car if they
magic word, create an
work together?
acrostic or use in a
sentence and whoever
2. What number must be
finished the work first will
added to both the
get a prize.
numerator and
In example no. 1, how
will you determine the
value of x and y?
In example no. 2, which
is easy to get, the value
of x or y?
In example no. 3, how
will you determine the
value of x and y?
Illustrate linear equations
in two variables.
1. 𝑦 = 4𝑥 + 1
x
y
-2
-1
2. 𝑦 = −2𝑥 + 6
x
y
2
4
denominator of
14
11
to
make the result equal to
7
?
2
3. If Anna’s height in
terms of x is
(73) cm and
Corazon’s height in terms
of x is (
8
) cm.
12𝑥−8
What is the difference in
their heights?
F. Developing mastery
(Leads to Formative
Assessment 3)
Solve the following
problems.
Solve the following
problems.
2. Mae took (
3
) hours
𝑥+6
3.
4. in reading wattpad story
in the morning and
continue reading (
7
)
𝑥−2
5.
6. hours in the afternoon.
How many hours did
Mae take to finish
reading a story for the
whole day?
G. Finding practical
applications of
concepts and skills
in daily living
Solve the following
problem.
Kim can sew a scarf in 4
hrs. if she works alone.
Cheska finish the same
job 6 hrs. if they works
together, how long will it
take them to finish the
job?
1. Find two
consecutive even
integers if one fourth of
the smaller is equal to
one fifth of the larger
one.
2.
Bryan can paint the
room in five hours
while Andrei can do the
same job in four hours
if both of them work
together, how long will
it take them to finish it?
Solve the following
problem.
1. Wally drives his
Hammer 260 kilometers
in the same time that
Jose drives his BMW 290
kilometer. If Wally
averages 5 kms per
hours faster than Jose,
Find their rates.
Determine the
quadrant where the
following points are
located.
1. M ( -4, 5 )
2. L ( -3, 1 )
3. N ( -3, -6 )
4. K ( -4, -1 )
5. R ( -2, -5 )
6. J ( 5, -1 )
7. S ( 5, 3 )
8. A ( 3, -2 )
9. T ( 7, -2 )
10. F ( 2, -4 )
PLOTTING OF POINTS
IN CARTESIAN PLANE
Plot and label the
following points. Then
connect each of them
consecutively to form a
figure.
Illustrate linear equations
in two variables.
1. 𝑦 = 5𝑥 – 3
x
y
1
2
2. 3𝑥 + 𝑦 = 9
x
y
1
3
Illustrate linear equations in
two variables.
1. 2𝑥 – 3𝑦 = 6
x
y
2
3
2. 𝑦 = 3𝑥 + 2
x
y
2
4
Points
A(-7,7)
B(-5,9)
C(0,9
D(5,9
E(7,7
H. Making
For word problems with
generalizations and rational expression.
abstractions about
the lesson
1. Read through the
problem and set up a
word equation — that is,
an equation that contains
words as well as
numbers.
2.
3. Plug in numbers in place
of words wherever
possible to set up a
regular equation.
4. Solve the rational
expression.
5.
6. Answer the question the
problem asks.
For word problems with
rational expression.
1. Read through the
problem and set up a
word equation — that is,
an equation that
contains words as well
as numbers.
2. Plug in numbers in
place of words wherever
possible to set up a
regular equation.
3. Solve the rational
expression.
4.
Answer the
question the problem
asks.
F(7,3)
G(7,-3
H(7,-7)
I(5,-9
J(0,-9)
K(-5,-9)
L(-7,-7)
M(-7,-3)
N(-7,3)
The rectangular
coordinate system is a
two-dimensional system
consists of two number
lines drawn
perpendicular to each
other on a plane.
Another name for this
system is the Cartesian
Coordinate System,
attributed to the French
mathematician and
philosopher Rene
Descartes ( 1576-1650).
The horizontal line is
the x-axis and the
vertical line is the y-axis.
The point of intersection
of the two coordinate
axes is called the origin
whose coordinates are (
0, 0 ). The x and y axes
divide the plane into 4
quadrants named in
counterclockwise
direction starting at the
upper right. They are
Quadrant I, Quadrant II,
The solution of a linear
equation Ax+By=C,
where a, b and c are
constants are the set of
ordered pair (x,y) that will
satisfy the equation or
that will make the
equation true. To find the
solution of a linear
equation in two variables,
we usually express one
variable in terms of the
other variable
Quadrant III and
Quadrant IV.
Each point in the
plane corresponds to
exactly one ordered pair
( x, y ), where x is the
abscissa, which is the
directed distance of the
point from the y- axis,
while y is the ordinate,
which is the directed
distance of the point from
the x – axis.
Any point in Quadrant
I is to the right of the yaxis and above the xaxis, hence the
coordinates are both
positive,
( +, + ). Any
point in Quadrant II is to
the left of the y-axis and
above the x-axis, the
coordinates are ( -, + ).
Any point in Quadrant III
is to the left of yaxis and
below the x-axis, the
coordinates are ( -, - ).
Lastly, any point in
Quadrant IV, is to the
right of y-axis and below
the x-axis, the
coordinates are ( +, - ).
Any point on the x- axis
or on the y-axis is not in
any of the quadrants.
The origin, usually
named by the letter O,
has coordinates ( 0, 0 ).
I. Evaluating learning
Solve the following
problem.
Solve the following
problem.
Kevin wants to calculate
the perimeter of her
rectangular garden, the
length of rectangular
garden in terms of x is
1. The denominator of
a fraction is 5 more than 1.
the numerator. If both the2.
numerator and
3.
denominator of the
4.
fraction are increase by 5.
2, the resulting fraction 6.
equal 1/3 . Find the
7.
fraction.
8.
𝑥+2
𝑦
𝑥−2
𝑦
, and the width is
.
Plot the following sets of
points. Connect the points
and determine the
geometric figure formed.
P ( -2, 3 ), Q ( 8, 3 ),
R ( 6, -2 ) S ( -4, -2 )
F ( -4, 4 ), O ( 4, 4 ),
U ( 4, -4 ), R ( -4, -4 )
S ( -3, 2 ), C ( 0, 3 ),
O ( 3, 2 ), R ( 3, -2 ),
E ( -3, -2 )
Illustrate linear equations
in two variables.
1. 3𝑥 + 4𝑦 = 15
x
y
1
2
2. 𝑦 = 5𝑥 + 3
x
y
-1
1
J. Additional activities
for application or
remediation
Follow up:
Solve the following.
Alex can do a piece of
work in 6 days. When
she and Toni work
together, it takes only 4
day. How long will it take
Toni to do the work if she
works alone?
1.
2.
3.
4.
Study: Look for the
meaning of the following:
Cartesian plane
x - axis
y – axis
function
Follow up:
In Santiago, General
Trias, Cavite, the Gen.
Solve the following.
Trias Dairy Raisers MultiPurpose Cooperative was
Alex can do a piece of
located where dairy
work in 6 days. When she products are being made.
and Toni work together, it These are kesong puti,
takes only 4 day. How
fresh carabao’s milk,choco
long will it take Toni to do milk, strawberry milk, and
the work if she works
pastillas de leche. These
alone?
products are arranged in
freezer with their own
designation so that the
seller will be able to locate
the products easily. Using
the figure that follows, the
seller can determine the
location of each dairy
product. Can you also
determine the location of
the dairy products?
1. Follow Up
Illustrate linear
equations in two
variables
a. 𝑦 = 5𝑥 + 3
x
y
-1
1
b. 𝑦 = −2𝑥 + 4
x
y
1
2
2. How will you illustrate
the slope of a line?
3. Give an example of
illustration of slope of
a line.
V. REMARKS
VI. REFLECTION
1.
No.of learners who
earned 80% on the
formative 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.
7.
What difficulties did I
encounter which my
principal or
supervisor can help
me solve?
What innovation or
localized materials
did I use/discover
which I wish to share
with other teachers?