School BULAWAN INTEGRATED SCHOOL Grade Level 8

GRADE 8
Teacher SANDY ME H. CARBONILLA Learning Area MATHEMATICS
DAILY LESSON LOG
Teaching Dates and Time WEEK 5 Quarter FIRST

MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY

I. OBJECTIVES
1. Content Standards The learner demonstrates The learner demonstrates The learner demonstrates The learner demonstrates INSTRUCTIONAL
understanding of key understanding of key understanding of key understanding of key COOPERATIVE
concepts of factors of concepts of factors of concepts of factors of concepts of factors of LEARNING (ICL)
polynomials, rational polynomials, rational polynomials, rational polynomials, rational
algebraic expressions, linear algebraic expressions, algebraic expressions, algebraic expressions,
equations and inequalities in linear equations and linear equations and linear equations and
two variables, systems of inequalities in two variables, inequalities in two variables, inequalities in two variables,
linear equations and systems of linear equations systems of linear equations systems of linear equations
inequalities in two variables and inequalities in two and inequalities in two and inequalities in two
and linear functions. variables and linear variables and linear variables and linear
functions. functions. functions.
2. Performance The learner is able to The learner is able to The learner is able to The learner is able to
Standards formulate real-life problems formulate real-life problems formulate real-life problems formulate real-life problems
involving operations on involving operations on involving operations on involving operations on
rational algebraic rational algebraic rational algebraic rational algebraic
expressions, and solve expressions, and solve expressions, and solve expressions, and solve
these problems accurately these problems accurately these problems accurately these problems accurately
using a variety of strategies. using a variety of strategies. using a variety of strategies. using a variety of strategies.
3. Learning Performs operations on Performs operations on Performs operations on Performs operations on
Competencies / rational algebraic rational algebraic rational algebraic rational algebraic
Objectives expressions. expressions. expressions. expressions.
(M8AL-Ic-d-1 ) (M8AL-Ic-d-1 ) (M8AL-Ic-d-1 ) (M8AL-Ic-d-1 )

a. Reduce the fraction in a. Identify the least common a. Identify the least common a. Identify the least common
simplest form. denominator of rational denominator of rational denominator of rational
b. Add or subtract the algebraic expressions. algebraic expressions. algebraic expressions.
rational expression with b. Add or subtract the b. Add or subtract the b. Add or subtract the
 similar denominators. rational algebraic rational algebraic rational algebraic
c. Develop cooperative expressions with dissimilar expressions with dissimilar expressions with dissimilar
learning in group activity.denominators. denominators. denominators.
c. Apply laws of exponent c. Apply laws of exponent c. Apply laws of exponent
and factoring in and factoring in and factoring in
simplifying rational simplifying rational simplifying rational
algebraic expression. algebraic expression. algebraic expression.
II. CONTENT Adding and Subtracting Adding and Subtracting Adding and Subtracting Adding and Subtracting
Similar Rational Algebraic Dissimilar Rational Dissimilar Rational Dissimilar Rational
Expressions Algebraic Expressions Algebraic Expressions Algebraic Expressions
III. LEARNING
RESOURCES
A. References
1. Teacher’s 94-114 94-114 94-114 94-114
Guide pages

2. Learner’s 95-97 95-97 95-97 95-97

Materials pages
3. Textbook pages Oronce and Mendoza, e-
math, pp. 111-114;
Chua, et.al, Mastering
Intermediate Algebra II, pp.
92-93;
Mendoza, et.al, Intermediate
Algebra, pp. 176-177
4. Additional http://www.mathportal.org/ https:// https:// https://
Materials from algebra/rational- www.mathplanet.com/ www.mathplanet.com/ www.mathplanet.com/
Learning expressions/adding- education/algebra-1/ education/algebra-1/ education/algebra-1/
Resource (LR) subtracting-rational.php rational-expressions/add- rational-expressions/add- rational-expressions/add-
portal and-subtract-rational- and-subtract-rational- and-subtract-rational-
expressions expressions expressions
http://creativecommons.org/ http://creativecommons.org/ http://creativecommons.org/
licenses/by/3.0/ licenses/by/3.0/ licenses/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
Resources Cavite Mathematics 2016 Cavite Mathematics 2016 Cavite Mathematics 2016 Cavite Mathematics 2016
Teacher made Worksheet, laptop, monitor, pictures laptop, monitor, pictures laptop, monitor, pictures
Laptop, monitor
IV. PROCEDURES
A. Reviewing previous A. Preliminaries A. Preliminaries Preliminaries Preliminaries
lesson or presenting “Answer Mo, Show Mo!” Perform the operation on “We have…they have…” “Fixing a broken heart”
the new lesson Find the factor of the the following fraction. Direction: The class will be Directions: Fix the broken
following expression. 1. ½ + 4/3 group into 3. Each group heart by matching the factor
1. x2-x-6 2. 5/8 + 3/2 will receive 2 sets of phrase and product that contains in
2. a2-25 3. −4/8 + 3/10 attached with rational each half of heart.
3. x3 + 6x2 +12x +8 expression, one is for the
4. x2-y2 4. ½ − 4/3 given and the other one is
5. x3 + 3x2 +3x +1 5. ¼ − 3/2 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. x 2 +5 x +6
5 x−10 2
x −4
1 In adding or
subtracting is your
aim, 3 4
+
x 2x 5( x−2 )
x 2 +5 x +6
( x+2)( x−2 )
 2 Change the bottom
using multiply or
divide, 5 5
+
6r 8r

3 And don’t forget to

simplify,
8 3
−
x −4 x+2
2

But the same to the

top must be applied,
5
24 r

Before it’s time to say

goodbye! 14−3 x
( x +2)( x−2 )

The bottom expressions

must be the same!
3x+4
x2
B. Establishing a The sum of two rational 1. How do you add or What is the important 1. How will you add
purpose for the expressions is the product subtract dissimilar fractions? rules in adding or dissimilar fractions with
lesson of the numerators divided 2. What are the laws of subtracting dissimilar more than two addends?
by the product of the exponent? rational algebraic 2. How will you perform
denominators. expression? combination of addition and
subtraction dissimilar
 fraction?
3.What is the relation of
factoring in adding or
subtracting dissimilar
rational expressions?
C. Presenting examples/ The teacher will show The teacher will show The teacher will show The teacher will show
instances of the illustrative example of illustrative example of illustrative example of illustrative example of
lesson addition and subtraction of addition and subtraction of addition and subtraction of addition and subtraction of
rational expressions with the rational expressions with the rational expressions with the rational expressions with the
common denominator. different denominator. different denominator. different denominator.
Example 1: Example:
Example 1: 1 1 Example 1:
Add + Simplify, state the result in
2 3 a 4 b 5 6
Add x +3 x−2 + 4 x +12 Add + simplest form
x2 +3 x−10 x 2 +3 x−10 c+ 2 c−3
 Since the denominators 2 x2 x 1
Factor the common are not the same, find  Since the denominators + −
x −4 x−2 x +2
2
Denominator the LCD. are not the same, find
x2 +3 x−2 4 x +12  Since 3a and 4b have the LCD.
+ no common factors, the  The LCM of c+2 and c- Find the least
( x +5)( x−2 ) ( x +5 )( x−2)
LCM is simply their 3 is (c +2) (c-3) common multiple
Write as a single product: 3a ⋅ 4b  That is, the LCD of the by factoring each
fraction  That is, the LCD of the fraction (c +2) (c-3) denominator.
( x 2 +3 x−2 )+(4 x +12 ) fractions is 12ab.  Rewrite the fractions
( x +5 )( x−2)  Rewrite the fractions using the LCD.
Remove the parentheses using the LCD.
in the numerator ( 5 c−3
⋅ )(+
6 c +2
⋅ ) x2 - 4= (x+2)(x-2)

( )( )
1 4b 1 3a c +2 c−3 c−3 c +2
x2 +3 x−2+4 x +12 ⋅ + ⋅ x-2 = x-2
( x+5 )( x−2 ) 3 a 4 b 4 b 3 a 5(c−3 ) 6(c +2 )
Combine like terms = + x+ 2= x+2
4b 3a 3 a+4 b ( c+2 )(c−3 ) (c +2 )(c−3 )
x2 +7 x+10 + = LCM: (x+2)(x-2)
( x +5)( x−2 ) 12 ab 12 ab 12 ab  Simplify each
Factor the numerator numerator
( x +5 )( x +2 ) 5 c−15 6 c+12
2 x2 x 1
Example 2: = +
( x +5)( x−2 ) ( c+2 )(c−3 ) (c +2 )(c−3 ) + −
( x +2)( x−2 ) x−2 x+2
Divide out common 5 y 2x  Add the numerators
−
6 3 y3 5 c−15+6 c+12
=
(c +2 )(c−3 )
factors Subtract
( x  5)( x  2) x  2
  Since the denominators  Simplify The LCM becomes
( x  5)( x  2) x  2
are not the same, find 11 c−3 the common
Example 2: the LCD. =
( c+2 )(c−3 ) denominator.
x 2 −2 x+3 x 2 −4 x−5  Since 6 and 3y3 have Multiply each
− no common factors, the Example 2:
x2 +7 x+ 12 x 2 +7 x +12 expression by the
LCM is simply their 2 t−2
Subtract t+1 − 2 equivalent of 1 that
product: 6 ⋅ 3y 3
t −t−2 will give in the
Write as a single
 That is, the LCD of the  Find the factorization common
fraction
( x 2−2 x +3 )−( x 2 −4 x −5) fractions is 18y3. of each denominator. denominator.
x 2 + 7 x+12
 Rewrite the fractions t+1 cannot be
Remove the parentheses using the LCD. factored any further,
in the numerator but t2- t- 2 can be.

( )( )
3
2 2
x −2 x+ 3−x + 4 x +5 5y 3y 2x 6
⋅ 3 − ⋅ 2 t−2
x 2 + 7 x +12 6 3y 3 y3 6 = −
t+1 (t+1 )(t−2 )
2 x2
(
+
x x +2
⋅
( x +2)( x−2 ) x −2 x +2
−)(1 x−2
⋅
x+2 x−2 )
Combine like terms
2 x+ 8  Find the least
2
x +7 x+ 12
15 y 4 12 x common multiple. t+1 Rewrite the original
= − problem with the
Factor 18 y 3 18 y 3 appears exactly once
2( x +4 ) in both of the common
( x +3)( x +4 ) 15 y 4 −12 x expression, so it will denominator. It
= 3
Factor both
appear once in the makes sense to keep
Divide out common 18
3(5y y 4 −4 x )
numerator
factors = and LCD.( t - 2) also the denominator in
2( x  4 ) 2 3(53(6y 4 −4
y 3 )x ) denominator. appears once, this factored form in order
 = means that (t+1)
xy 3x) to check for common
( x  3)( x  4) x  3 53y(64 −4 (t-2) is the LCD.
=
=
5 y 46−4y3 x Reduce,
dividing out
= ( t+12 ⋅t−2
t−2 ) ( (t+1 )(t−2) )
−
t−2
2 x2 x ( x+2 ) 1( x−2)
6 xy 3 2(t−2) t−2 + −
( x +2)( x−2 ) ( x +2)( x−2) ( x+2)( x−2 )
= −
(t +1)(t−2 ) (t+1 )(t−2)
 Subtract the
numerators and Combine the
simplify. Remember numerators
that parentheses
need to be included
2 x 2 +x ( x +2)−1( x−2)
( x +2 )( x−2)
 around the second (t-
2) in the numerator
because the whole
quantity is
Simplify the
subtracted.
numerators

2t−4−t+2 2 x 2 + x 2 + 2 x−x +2
=
(t +1)(t−2 ) ( x +2 )( x−2)
t−2 Check for
=
(t +1)(t−2 ) simplest form.
 The numerator and
denominator have a 3 x2 +x+2
common factor of t -
2, so the rational ( x +2)( x−2 )
expression can be
simplified.
1
=
(t +1) Since neither
(x+2) nor (x-2) is a
factor of 3x2 + x+ 2,
this expression is in
simplest form.
3 x2 +x+2
( x +2)( x−2 )
D. Discussing new 1. How do you think sum 1. How do you think sum 1. How do you think sum or 1. What are the different
concepts and or the difference is or the difference is the difference is obtained? techniques used to solve for
practicing new skills obtained? obtained? 2. What are the different combining multiple rational
#1 2. What are the different 2. What are the different techniques used to solve for expressions?
techniques used to solve techniques used to solve sum or difference? 2. Enumerate the pattern
for sum or difference? for sum or difference? 3. Describe the pattern; you observed in combining
3. Describe the pattern; Enumerate the pattern multiple rational
Enumerate the pattern observed. expressions.
observed.
 E. Discussing new Perform the indicated Perform the indicated Perform the indicated Simplify, state the result in
concepts and operations and reduce operations and reduce operations and reduce simplest form
practicing new skills answer in lowest terms. answer in lowest terms. answer in lowest terms.
5 5 a+1 2m 5m y 2 2 15
#2 1. 2 + 2 1. + 3 7 1. − −
a +3 a+2 a +3 a+ 2 3 2m 2 1. + 3y x 9
x−8 x +3
6 x +5 2 6x x +2 x+ 3
2. − 2 2. − 4 2 2. −
2
x +8 x +4 x + 8 x + 4 3 y 3 4 xy 2. − 2
2 x +13 x +20 2 x+ 5
x+1 x +2
10 2 x+ 9 5 x−7 3.
3a
−5 a 3 6 3 7
3. − +
12 a 2 b
3. + 3. −
x−3 x−3 x−3 b−5 3 b−8 4 v −4 v 2
2

x−7 8 1 5
4. + 4. + 4−a2 a−2 2z 3z 3
4 x 6 xy 2
2 4. − 4. − − 2
4 x 2 −4 4 x 2−4 a2−9 3−a 1−2 z 2 z +1 4 z −1

x +1 x+6 2 3 3 x +2 x 4y 2 2
5. + 2 5. − 5. + 5. − −
2
4 x +28+ 49 4 x +28+49 a a−5 3 x+ 6 4−x2 y −1 y y +1
2

F. Developing mastery Perform the indicated Perform the indicated Perform the indicated Perform the indicated
(Leads to Formative operations and reduce operations and reduce operations and reduce operations and reduce
Assessment 3) answer in lowest terms. answer in lowest terms. answer in lowest terms. answer in lowest terms.
8 y 2 +11 y 4 y 2 −5 y 4 7b 5 a+5 7n 2 4 5
1. − 2 1. − 1. + 1. + −
2
2 x + 13 x +20 2 x +13 x+20 5 a 4 a2 5 n +35−40 3 n
2
a+3 a+3 a−3
−5 x+ 4 x 2 +12 4+ x2 +5 x 8 5
2. − 2 2. + 2 2 4
3
9t 6t 2. + t 2 +4 t 2 t−7 t 2−1
3 x 2 +2 x−8 3 x +2 x −8 y +8 2+i 2. + −
a+2 a−4 t−1 t−1 t+1
4 a2 −11a−3 4 a2 +13 a+3 3. − 7c 8 a+ 2 a−4 a+5
3. − 2 4 3. + 3. − +
b +4 b+4 c +1 c −7 2 4 8
2 2
x + y 3 x +5 y +6 3 4 3 3 2z 3z 5z
4. − 4. + 2 4. − 4. − +
2 x −3 y 2 x−3 y x x 8 3 x+4 z−1 z+1 z 2 −1
2 3 x+1 x +1
6 x +2 5. + 5. − 8 3 2
5. − x−5 4 x x−4 x 2−7 x +12 5. − +
x−5 x−5 2
x −4 x +2 x−2

G. Finding practical The pathway of a church Your teacher asked the Juan bought a lawn lot in Lorna gives an illustration
applications of has a perimeter of 10 z , if class to find the perimeter of Manila Memorial Park in
z−1 board to Miguel with an area
concepts and skills in 2z the blackboard in your Dasmariñas, Cavite. Find 2
daily living the width is z−1 what is the classroom. the total area of his lawn lot, of . She instructed
length? if he used the lot area 2 x , x2 −25
5 x +4 Miguel to cut the board into

3
 and the remaining lot area is
6x .
2 x +3

6x
2 x +3 2x
5x+4
2z
z−1
two pieces, one for Antonio
with an area of and
the other half is for Miguel.
What is the area of an
illustration board goes to
Miguel?

H. Making Generalization: Generalization: Generalization: Generalization:

generalizations and In adding or subtracting There are a few steps to In adding or In adding or subtracting
abstractions about similar rational expressions, follow when you add or subtracting dissimilar dissimilar rational
the lesson add or subtract the subtract rational rational expressions change expressions change the
numerators and write the expressions with unlike the rational algebraic rational algebraic
answer in the numerator of denominators. expressions into similar expressions into similar
the result over the common rational algebraic rational algebraic
denominator. In symbols, 1. To add or expressions using least expressions using least
a c ( a+c ) subtract rational common denominator or common denominator or
+ = , b≠0 expressions with unlike LCD as in adding dissimilar LCD as in adding dissimilar
b d b
denominators, first find fractions. fractions.
the LCM of the
denominator. The LCM of
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 Let’s Amaze it! “Pick my Pieces” “Four in a Line” “Let’s Gora in Cavite”
(Group Activity) Add or subtract the Directions: Each group will Simplify the given
Complete the maze below following rational add or subtract the given algebraic expression
by adding each rational expressions. Match your rational expressions. Each attached in the provinces of
expression from the start to answer with the expression correct answer will gives the Cavite, and then state the
end. You are free to choose in each piece of a puzzle to group a chance to pin 2 result in simplest form.
your way, there are 11 form it. A hint will help you assigned chips in the game Match the province with its
possible ways. to solve the problem. board. To win this game, the respective landmark.
group need to connect 4
6 5c pieces in a row, column or
1. −
c−1 4 diagonally.
5 7y
2. −
x x +3
7 3
3. +
d e
5
4 . +8
b
4
5 .7−
j−9
Hint:
 ”Isang dalagang may
 Given:
2 4
1. −
5 x +5 x 3 x+3
2

5x 18
2. 2
− 2
x −x −6 x −9

4−a2 a−2
3. −
a2 −9 3−a
3 x+ 2 x
4. +
korona, 3 x+ 6 4−x 2
kahit saan ay may
2 4
mata. “ 5. +
x +3 (x +3 )2
Silang, Cavite is very known
for this fruit.
 J. Additional activities Follow up: Reflection Journal
for application or Add or subtract the following
remediation rational expressions.
Follow up: 2x 3
1. 2 − 2
Add or subtract the following Follow up: x −1 x +5 x+ 4
rational expressions. Add or subtract the following
x−4 x +8 rational expressions. 2 x−3 3 x−1
1. 2 + 2 2. 2 + 2
x −2 x−8 x −2 x−8 5 x−3 1 x +3 x+ 2 x +5 x+ 6
1. −
5 5 a+1 4x 6x
2. 2 + 2
a +3 a+2 a +3 a+2 3 7
2. +
c +6 c−2

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. 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: CHECKED:

SANDY ME H. CARBONILLA RAMIL P. VILLAREAL
Date: DATE: ____________________