School: Calicanan High School
Name of Teacher:
Gina Dawn Rose B. Mandao
Learning area: MATHEMATICS 8
Grade Level: 8
Quarter: IV
Date: June 13, 2023
Content Standard
The learner demonstrates understanding of key concepts of functions.
Performance Standard
The learner is able to accurately construct mathematical models to
represent real-life situations using functions.
Learning Competency
I. OBJECTIVES
M8AL-VIa-3
The learner perform addition, subtraction, multiplication, division,
and composition of functions.
The learner:
Identifies the rules in operations on functions;
Knowledge:
Skills:
Performs addition, subtraction, multiplication, division and
composition of functions;
Affective:
Develops accuracy in performing operations on functions.
II. CONTENT
III. LEARNING RESOURCES
A. References
1. Teacher’s Guide Pages
2. Learner’s Materials Pages
3. Textbook Pages
4. Additional Materials
5. Learning Resources (LR) portal
B. Other Learning Resources
Operations on Functions
TG in Mathematics 8, pp. 14-22
LM in Mathematics, pp. 13-20
Teacher’s Guide and Learner’s Material
General Mathematics Diwa Publishing Series 2016
IV. PROCEDURES
(Preliminary Activities)
Teachers’ activity
-“Good morning class”
-Let us pray first.
-Checking of attendance
-Are you ready listen and learn?
-I will be showing you some expressions
and try to analyze what expression is it, ok?
Students’ activity
- “Good morning maam”
– One Student will lead the prayer
- Vaccant seats will be marked absent
- Yes maam!
- Yes maam!
A. Establishing a purpose for the lesson
Ask: What is P(x) + Q(x) ?
𝑃(𝑥)
𝑄(𝑥)
?
Expected answer:
The first expression is the sum of two expression or functions. The
second is a quotient of two functions.
B. Discussing new concepts and
practicing new skills #1
Introduce the definition of the operations of two functions given f(x)
and g(x) as two functions.
C. Discussing new concepts and
practicing new skills #2
Present the following problems to the class. Let them work in pairs
for an allotted time. Then, call a volunteer or two to discuss the
answers.
Given: f ( x)  2 x  1 , q( x)  x 2  2 x  2 and r ( x) 
2x 1
x 1
(1) Express the function f1 ( x)  x 2  3 as a sum or difference of the
functions above.
Solution: The solution can involve some trial and
error. Add q( x) and f ( x ) and check if the sum is
x2  3 .
q( x)  f ( x)  ( x 2  2 x  2)  (2 x  1)
 x2  3
 f1 ( x) .
Thus, f1 ( x)  q( x)  f ( x) .
Express the function f 2 ( x)  x 2  4 x  1 as a sum or difference of the
functions above.
Solution: Again, the solution can involve trial and
error. Check if q( x)  f ( x) gives x 2  4 x  1 .
q( x)  f ( x)  ( x 2  2 x  2)  (2 x  1)
 x2  4 x  1
 f 2 ( x) .

D. Finding practical applications of
concepts and skills in daily living
E. Making Generalizations and
abstractions about the lesson
F. F. Evaluating learning
Thus, f 2 ( x)  q( x)  f ( x) .
Students will explain how to perform operations on functions.
See attachment.
G. Additional Activities for application
or remediation
For remediation, assign learners to pick one of two problems given
in part E. Peer tutoring is desired. See to it the learners submit their
output. Random output presentations should be encouraged.
For enrichment, assign Example 11, 12 of TG on page 19. The same
rubric should be used for grading the learners’ outputs.
V.
REMARKS
VI.
REFLECTION
A. No. of learners who earned 80% in
the evaluation
B. No. of learners who require
additional activities for remediation
C. Did the remedial lessons work? No.
of learners who have caught up the
lesson
D. No. of learners who continue to
require remediation
E. Which of my teaching strategies
worked well? Why did these work?
F. What difficulties did I encounter
which my principal and supervisor
help me solve?
G. What innovation or localized I
used/discover which I wish to share
with other teacher?
A. ____ No. of learners who earned 80% in the evaluation
B. ____ No. of learners who require additional activities for
remediation
C. Did the remedial lessons work? _____
No. of learners who have caught up the lesson.
D. ___ No. of learners who continue to require remediation
Strategies used that work well:
___ Group collaboration
___ Games
___ Poweerpoint presentation
Answering preliminary activities/exercises
___ Discussion
___ Differentiated Instruction
___ Case Method
___Role Playing /Drama
___ Think-Pair-Share (TPS)
___ Doscivery Method
___ Rereading of Paragraphs/Poems/Stories ___ Lecture Method
Why?
___ Complete Ims
___ Availability of Materials
___ Pupil’s eagerness to learn
___ Group member’s cooperation in doing their tasks
___ Bullying among learners
___ Equipment (AVR/LCD)
___ Learner’s behavior/attitude
___ Science/Computer/Internet Lab
___ Colorful Ims
___ Additional Clerical Works
___ Unavaailable Technology
___ Reading Readiness
EVALUATION
WORKSHEET No. ___
Use the following functions to answer the task below.





f(x) = x + 3
p(x) = 2x – 7
v(x) = 𝑥 2 + 5𝑥 + 4
g(x) = 𝑥 2 + 2x -8
𝑥+7
h(x) = 2−𝑥

t(x) = 𝑥+3
𝑥−2
Task: Determine the following functions.
a) (v + g)(x)
b) (f. p)(x)
c) (f + h) (x)
d) (p – f)(x)
e) (v/g)(x)
Solution :