School BUNGA ELEMENTARY SCHOOL
GRADE 8
DAILY
LESSON LOG
Teacher RACHEL E. REPAREP
Quarter FIRST
Teaching Dates and Time Week 5 (September 25-29, 2023)
MONDAY
TUESDAY
Grade Level 8
Learning Area MATHEMATICS
WEDNESDAY
THURSDAY
FRIDAY
I. OBJECTIVES
1. Content Standards The learner demonstrates
The learner demonstrates
The learner demonstrates
The learner demonstrates
Summative Test/Remediation
understanding of key concepts understanding of key concepts understanding of key concepts understanding of key concepts
of factors of polynomials,
of factors of polynomials,
of factors of polynomials,
of factors of polynomials,
rational algebraic expressions, rational algebraic expressions, rational algebraic expressions, rational algebraic expressions,
linear equations and inequalities linear equations and inequalities linear equations and inequalities linear equations and inequalities
in two variables, systems of
in two variables, systems of
in two variables, systems of
in two variables, systems of
linear equations and inequalities linear equations and inequalities linear equations and inequalities linear equations and inequalities
in two variables and linear
in two variables and linear
in two variables and linear
in two variables and linear
functions.
functions.
functions.
functions.
2. Performance
The learner is able to formulate The learner is able to formulate The learner is able to formulate The learner is able to formulate
real-life problems involving
real-life problems involving
real-life problems involving
real-life problems involving
Standards
operations on rational algebraic operations on rational algebraic operations on rational algebraic operations on rational algebraic
expressions, and solve these
expressions, and solve these
expressions, and solve these
expressions, and solve these
problems accurately using a
problems accurately using a
problems accurately using a
problems accurately using a
variety of strategies.
variety of strategies.
variety of strategies.
variety of strategies.
3. Learning
Performs operations on rational Performs operations on rational Performs operations on rational Performs operations on rational
algebraic expressions.
algebraic expressions.
algebraic expressions.
algebraic expressions.
Competencies /
(M8AL-Ic-d-1 )
(M8AL-Ic-d-1 )
(M8AL-Ic-d-1 )
(M8AL-Ic-d-1 )
Objectives
a. Reduce the fraction in
simplest form.
b. Add or subtract the rational
expression with similar
denominators.
c. Develop cooperative learning
in group activity.
II. CONTENT
a. Identify the least common
denominator of rational
algebraic expressions.
b. Add or subtract the rational
algebraic expressions with
dissimilar denominators.
c. Apply laws of exponent and
factoring in simplifying
rational algebraic expression.
Adding and Subtracting
Adding and Subtracting
Similar Rational Algebraic Dissimilar Rational Algebraic
Expressions
Expressions
a. Identify the least common
denominator of rational
algebraic expressions.
b. Add or subtract the rational
algebraic expressions with
dissimilar denominators.
a. Identify the least common
denominator of rational
algebraic expressions.
b. Add or subtract the rational
algebraic expressions with
dissimilar denominators.
c. Apply laws of exponent and
factoring in simplifying
rational algebraic expression.
Adding and Subtracting
Dissimilar Rational Algebraic
Expressions
c. Apply laws of exponent and
factoring in simplifying
rational algebraic expression.
Adding and Subtracting
Dissimilar Rational Algebraic
Expressions
III. LEARNING RESOURCES
A. References
1.
Teacher’s
Guide pages
2.
Learner’s
95-97
Materials pages
3.
Textbook pages Oronce and Mendoza, e-math,
pp. 111-114;
Chua, et.al, Mastering
Intermediate Algebra II, pp. 9293;
Mendoza, et.al, Intermediate
Algebra, pp. 176-177
94-114
94-114
94-114
94-114
95-97
95-97
95-97
4.
Additional
http://www.mathportal.org/alge https://www.mathplanet.com/ed https://www.mathplanet.com/ed https://www.mathplanet.com/ed
ucation/algebra-1/rationalucation/algebra-1/rationalMaterials from bra/rational-expressions/adding- ucation/algebra-1/rationalexpressions/add-and-subtract- expressions/add-and-subtract- expressions/add-and-subtractLearning
subtracting-rational.php
rational-expressions
rational-expressions
rational-expressions
Resource (LR)
http://creativecommons.org/lice
http://creativecommons.org/lice
http://creativecommons.org/lice
portal
nses/by/3.0/
nses/by/3.0/
nses/by/3.0/
B. Other Learning
Grade 8 LCTG by DepEd
Grade 8 LCTG by DepEd
Grade 8 LCTG by DepEd
Grade 8 LCTG by DepEd
Cavite Mathematics 2016
Cavite Mathematics 2016
Cavite Mathematics 2016
Cavite Mathematics 2016
Resources
Teacher made Worksheet,
laptop, monitor, pictures
laptop, monitor, pictures
laptop, monitor, pictures
Laptop, monitor
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
A. Preliminaries
“Answer Mo, Show Mo!”
Find the factor of the
following expression.
1. x2-x-6
2. a2-25
3. x3 + 6x2 +12x +8
4. x2-y2
5. x3 + 3x2 +3x +1
A. Preliminaries
Perform the operation on the
following fraction.
1. ½ + 4/3
2. 5/8 + 3/2
3. −4/8 + 3/10
4. ½ − 4/3
5. ¼ − 3/2
Preliminaries
Preliminaries
“We have…they have…”
“Fixing a broken heart”
Direction: The class will be
Directions: Fix the broken heart
group into 3. Each group will by matching the factor and
receive 2 sets of phrase attached product that contains in each
with rational expression, one is half of heart.
for the given and the other one
is an answer. The group with
a given will say “We
have…(followed by the
given), and the group holding
the correct answer will say
“they have...(the given),and
we have (the answer)”.The
phrase will be posted on the
board until the class completes
it.
Note: Every group will solve
for the answer, so that they
could able to prove that they
handling the correct answer.
1 In adding or
subtracting is your
3 4
aim,

x x2
2 Change the bottom
using
multiply
or
divide,
5
5

6 r 8r
3 And don’t forget to
simplify,
8
3

2
x 4 x2
But the same to the top
must be applied,
5
24 r
Before it’s time to say
14  3x
goodbye!
( x  2)( x  2)
The bottom
expressions must be
the same!
3x  4
x2
B. Establishing a purpose The sum of two rational
expressions is the product
for the lesson
of the numerators divided by
the product of the
denominators.
C. Presenting examples/ The teacher will show
instances of the lesson illustrative example of addition
and subtraction of rational
expressions with the common
denominator.
1. How do you add or subtract
dissimilar fractions?
2. What are the laws of
exponent?
What is the important rules
in adding or subtracting
dissimilar rational algebraic
expression?
1. How will you add dissimilar
fractions with more than two
addends?
2. How will you perform
combination of addition and
subtraction dissimilar fraction?
3.What is the relation of
factoring in adding or
subtracting dissimilar rational
expressions?
The teacher will show
illustrative example of addition
and subtraction of rational
expressions with the different
denominator.
Example 1:
The teacher will show
illustrative example of addition
and subtraction of rational
expressions with the different
denominator.
The teacher will show
illustrative example of addition
and subtraction of rational
expressions with the different
denominator.
Example:
Example 1:
Add
Add x  3x  2  4 x  12
x 2  3x  10 x 2  3x  10
Factor the common
Denominator
2
x 2  3x  2
4 x  12

( x  5)( x  2) ( x  5)( x  2)
Write as a single
fraction
( x 2  3x  2)  (4 x  12)
( x  5)( x  2)
Remove the parentheses
in the numerator
x 2  3x  2  4 x  12
( x  5)( x  2)
1
1

3a 4b
 Since the denominators are
not the same, find the
LCD.
 Since 3a and 4b have no
common factors, the LCM
is simply their product: 3a
⋅ 4b
 That is, the LCD of the
fractions is 12ab.
 Rewrite the fractions using
the LCD.
 1 4b   1 3a 
    
 3a 4b   4b 3a 
Example 1:
Add
5
6

c 2 c3
 Since the denominators
are not the same, find the
LCD.
 The LCM of c+2 and c3 is (c +2) (c-3)
 That is, the LCD of the
fraction (c +2) (c-3)
 Rewrite the fractions
using the LCD.
c 3  6
c2
 5





 c  2 c 3  c 3 c  2
Simplify, state the result in
simplest form
2x2
x
1


2
x 4 x2 x2
Find the least
common multiple
by factoring each
denominator.
Combine like terms
x 2  7 x  10
( x  5)( x  2)
4b
3a
3a  4b


12ab 12ab
12ab
Factor the numerator
( x  5)( x  2)
( x  5)( x  2)
Divide out common
factors
( x  5)( x  2) x  2

( x  5)( x  2) x  2
Example 2:
x 2  2x  3
x 2  4x  5

x 2  7 x  12 x 2  7 x  12
Write as a single
fraction
( x 2  2 x  3)  ( x 2  4 x  5)
x 2  7 x  12
Remove the parentheses
in the numerator
x 2  2x  3  x 2  4x  5
x 2  7 x  12
Combine like terms
2x  8
2
x  7 x  12
Factor
2( x  4)
( x  3)( x  4)
Divide out common
factors
2( x  4)
2

( x  3)( x  4) x  3
Example 2:
Subtract
5 y 2x

6 3y3

5c  15
6c  12

(c  2)(c  3) (c  2)(c  3)
 Simplify each numerator
5(c  3)
6(c  2)


(c  2)(c  3) (c  2)(c  3)
 Add the numerators
5c  15  6c  12
 Since the denominators are

not the same, find the
(c  2)(c  3)
 Simplify
LCD.
11c  3
 Since 6 and 3y3 have no

common factors, the LCM
(c  2)(c  3)
is simply their product: 6 ⋅
Example 2:
3y3
2
t 2
 That is, the LCD of the Subtract
 2
3
t 1 t  t  2
fractions is 18y .
 Find the factorization of
 Rewrite the fractions using
each denominator. t+1
the LCD.
cannot be factored any
3
further, but t2- t- 2 can
 5 y 3 y   2x 6 
  3    3  
be.
 6 3y   3y 6 
4
15 y
12 x
2
t 2




3
3
t  1 (t  1)(t  2)
18 y 18 y
 Find the least common
15 y 4  12 x
multiple. t+1 appears

exactly once in both of
18 y 3
Factor both
the expression, so it
3(5 y 4  4 x) numerator
will appear once in the

and
LCD.( t - 2) also
3(6 y 3 )
denominator
3(5 y 4  4 x) .
appears once, this

3
means that (t+1) (t3(6 xy )
2) is the LCD.
5 y 4  4x

6 y3

5 y  4x
6 xy3
4
Reduce,
dividing out
factor 3.

t 2
 2 t 2 



  
 t  1 t  2   (t  1)(t  2) 


2(t  2)
t 2

(t  1)(t  2) (t  1)(t  2)
Subtract the numerators
and simplify.
Remember that
x2 - 4= (x+2)(x-2)
x-2 = x-2
x+ 2= x+2
LCM: (x+2)(x-2)
2x2
x
1


( x  2)( x  2) x  2 x  2
The LCM becomes
the common
denominator.
Multiply each
expression by the
equivalent of 1 that
will give in the
common
denominator.
2x2
x 2  1
x2
 x





( x  2)( x  2)  x  2 x  2   x  2 x  2 
Rewrite the original
problem with the
common
denominator. It
makes sense to keep
the denominator in
factored form in order
to check for common
2x2
x( x  2)
1( x  2)


( x  2)( x  2) ( x  2)( x  2) ( x  2)( x  2)
parentheses need to be
included around the
second (t-2) in the
numerator because the
whole quantity is
subtracted.

2t  4  t  2
(t  1)(t  2)
t 2
(t  1)(t  2)
The numerator and
denominator have a
common factor of t - 2,
so the rational
expression can be
simplified.


1

(t  1)
Combine the
numerators
2 x 2  x( x  2)  1( x  2)
( x  2)( x  2)
Simplify the
numerators
2x 2  x 2  2x  x  2
( x  2)( x  2)
Check for
simplest form.
3x 2  x  2
( x  2)( x  2)
Since neither (x+2) nor
(x-2) is a factor of 3x2 + x+
2, this expression is in
simplest form.
3x 2  x  2
( x  2)( x  2)
D. Discussing new
concepts and
practicing new skills
#1
1. How do you think sum
or the difference is
obtained?
2. What are the different
techniques used to solve
for sum or difference?
3. Describe the pattern;
Enumerate the pattern
observed.
1. How do you think sum
or the difference is
obtained?
2. What are the different
techniques used to solve
for sum or difference?
1. What are the different
1. How do you think sum or the
techniques used to solve for
difference is obtained?
combining multiple rational
2. What are the different
expressions?
techniques used to solve for
2. Enumerate the pattern you
sum or difference?
observed in combining multiple
3. Describe the pattern;
Enumerate the pattern observed. rational expressions.
E. Discussing new
Perform the indicated
Perform the indicated
Simplify, state the result in
Perform the indicated
operations
and
reduce
answer
in
operations
and
reduce
answer
in
concepts and
operations and reduce answer in simplest form
lowest
terms.
lowest
terms.
practicing new skills
lowest terms.
y2
2 15
5
5a  1
2
m
5
m
1
.


#2
3
7
1. 2
 2
1.

3
y
9
x
2
1
.

a  3a  2 a  3a  2
3 2m
x

8
x

3
2
6
x
6
x5
x2
x3

x 2  8x  4 x 2  8x  4
10
2 x  9 5x  7
3.


x3 x3
x3
2.
4.
5.
F. Developing mastery
(Leads to Formative
Assessment 3)
x7
8

4x 2  4 4x 2  4

3 y 3 4 xy
3a
3.
 5a
12a 2b
2.
4.
x 1
x6
 2
4 x  28  49 4 x  28  49
1
5

2
4x
6 xy2
5.
2
2
3

a a 5
4
2

x 1 x  2
3
6
3.

b  5 3b  8
2.
4.
5.
4  a2 a  2

a2  9 3  a
3x  2
x

3x  6 4  x 2
2.
2 x 2  13x  20

2x  5
3
7

4v  4v 2
3.
2
2z
3z
3


1  2z 2z  1 4z 2  1
4y
2
2
5. 2
 
y 1 y y 1
4.
Perform the indicated
Perform
the
indicated
Perform the indicated
Perform the indicated
operations and reduce answer in operations and reduce answer in operations and reduce answer in operations and reduce answer in
lowest terms.
lowest terms.
lowest terms.
lowest terms.
1.
8 y 2  11y
4y2  5y
4
7b

1. 
2 x 2  13x  20 2 x 2  13x  20 5a 4a 2
 5 x  4 x 2  12 4  x 2  5 x
8
5
 2
2. 3  2
2
3x  2 x  8
3x  2 x  8 9t 6t
2
2
a2 a4
4a  11a  3 4a  13a  3
3.

3.

2
4
b4
b4
2.
4.
x 2  y 3x 2  5 y  6

2x  3 y
2x  3 y
5.
6
x2

x5 x5
3
4
 2
x
x
2
3
5.

x  5 4x
4.
1.
5a  5
7n

5n  35  40 3n
2
2.
2
4

y 8 2i
3.
7c
8

c 1 c  7
3
3
4. 
8 3x  4
5.
x 1
x 1

x  4 x 2  7 x  12
1.
2
4
5


a 3 a 3 a 3
t 2  4t 2t  7 t 2  1


t 1
t 1
t 1
a2 a4 a5
3.


2
4
8
2.
4.
2z
3z
5z

 2
z 1 z 1 z 1
5.
8
3
2


x 4 x2 x2
2
G. Finding practical
The pathway of a church has a Your teacher asked the class to
perimeter of
, if 10 z
find the perimeter of the
applications of
z

1
blackboard in your classroom.
concepts and skills in
2z
the width is
what is the
daily living
z 1
length?
Lorna gives an illustration
board to Miguel with an area of
2
x  25
2
Juan bought a lawn lot in
Manila Memorial Park in
Dasmariñas, Cavite. Find the
total area of his lawn lot, if he
used the lot area
,
2x
5x  4
and the remaining lot area is
6x .
2x  3
3
x5
. She instructed Miguel to cut
2z
z 1
the board into two pieces, one
6x
2x  3
for Antonio with an area of
2x
5x  4
and the other half is for Miguel.
What is the area of an
illustration board goes to
Miguel?
H. Making
Generalization:
Generalization:
Generalization:
In adding or subtracting
There are a few steps to
In adding or subtracting
generalizations and
abstractions about the similar rational expressions, add follow when you add or subtract dissimilar rational expressions
or subtract the numerators and rational expressions with unlike change the rational algebraic
Generalization:
lesson
write the answer in the
denominators.
expressions into similar rational In adding or subtracting
numerator of the result over the
algebraic expressions using
dissimilar rational expressions
common denominator. In
1. To add or
least common denominator or change the rational algebraic
symbols,
subtract rational
LCD as in adding dissimilar
expressions into similar rational
expressions with unlike
fractions.
algebraic expressions using
a c (a  c)
 
,b  0
denominators, first find
least common denominator or
b d
b
the LCM of the
LCD as in adding dissimilar
denominator. The LCM of
fractions.
the denominators of
fraction or rational
expressions is also
called least common
denominator, or LCD.
2. Write each expression
using the LCD. Make
sure each term has the
LCD as its denominator.
3. Add or subtract the
numerators.
4. Simplify as needed.
I.
Evaluating learning
“Four in a Line”
“Let’s Gora in Cavite”
Directions: Each group will add
Simplify the given algebraic
“Pick my Pieces”
or subtract the given rational
expression attached in the
Add or subtract the
expressions. Each correct
provinces of Cavite, and then
following rational expressions. answer will gives the group a state the result in simplest form.
Let’s Amaze it!
Match your answer with the
chance to pin 2 assigned chips Match the province with its
(Group Activity)
expression in each piece of a
in the game board. To win this respective landmark.
Complete the maze below by puzzle to form it. A hint will
adding each rational expression help you to solve the problem. game, the group need to connect
4 pieces in a row, column or
from the start to end. You are
diagonally.
6
5c
free to choose your way, there
1
.

are 11 possible ways.
c 1 4
5
7y

x
x3
7 3
3. 
d e
2.
4.
5
8
b
5.7 
4
j 9
Hint:
 ”Isang dalagang may
korona,
kahit saan ay may
mata. “
Silang, Cavite is very known for
this fruit.
Given:
1.
2
4

5 x  5 x 3x  3
2.
2
5x
18
 2
x  x6 x 9
2
4  a2 a  2
3. 2

a 9 3 a
3x  2
x
4.

3x  6 4  x 2
5.
2
4

x  3 ( x  3) 2
J. Additional activities
for application or
remediation
Reflection Journal
Follow up:
Follow up:
Follow up:
Add or subtract the following Add or subtract the following Add or subtract the following
rational expressions.
rational expressions.
rational expressions.
x4
x8
 2
x  2x  8 x  2x  8
5
5a  1
2. 2
 2
a  3a  2 a  3a  2
1.
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
2
5x  3 1

4x
6x
3
7
2.

c6 c2
1.
1.
2x
3
 2
x 1 x  5x  4
2.
2x  3
3x  1
 2
x  3x  2 x  5 x  6
2
2
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?
Prepared by:
RACHEL E. REPAREP
Learning Facilitator
Noted by:
RHONAL LIZA C. ECHALUSE
Head Teacher III