This document provides information about Laguna State Polytechnic University, including its vision, mission, goals, and objectives for the Bachelor of Secondary Education program. The university aims to provide advanced education, professional, technological, and vocational instruction. Its mission is to primarily serve the Philippines and global economy. The College of Education is committed to developing students' full potential and equipping them with knowledge, skills, and attitudes for teacher education and related fields to meet changing demands. The Bachelor of Secondary Education program objectives are to produce graduates who can serve as role models, provide a wholesome learning environment, facilitate diverse learning, use various teaching methods and materials, use assessment data to improve plans, and strengthen school-community links.

1. Republic of the Philippines
LAGUNA STATE POLYTECHNIC UNIVERSITY
Siniloan (Host) Campus
Siniloan, Laguna
FIELd STUdY
ANd
PRE-SERVICE
TEACHING PORTFOLIO
Prepared by:
ALELI M. ARIOLA
Pre-Service Teacher
ARLENE G. ADVENTO
BSEd – Mathematics, Pre-Service Teacher Supervisor
CORAZON N. SAN AGUSTIN, Ph. D.
Dean, College of Teacher Education

2. VISION
A premier university in
CALABARZON offering academic
programs and related services designed
to respond to the requirements of the
Philippines and the global economy
particularly Asian countries.
MISSION
The university shall primarily
provide advanced education,
professional, technological and
vocational instruction in agriculture,
fisheries, forestry, science, engineering,
industrial technologies, teaching
education, medicine, law, arts and
sciences, information technology and
other related fields. It shall also
undertaken research and extension
services, and provides progressive
leadership in its area of specialization.

3. GOALS
In pursuit of the College Vision-Mission, the College of
education is committed to develop the full potentials of
individual and equip them with knowledge, skills, and
attitudes in teacher education allied fields to effectively
respond to the increasing demands, challenges and
opportunities of changing times for global competitiveness.
OBJECTIVES OF BACHELOR OF SECONdARY EdUCATION
Produce graduates who can demonstrate and practice the
professional and ethical requirements for the Bachelor of
Secondary Education such as:
1. To serve as positive and powerful role models in the
pursuit of learning thereby maintaining high regard
to professional growth.
2. Focus on the significance of providing wholesome and
desirable learning environment.
3. Facilitates learning process in diverse types of
learners.
4. Use varied learning approaches and activities,
instructional materials and learning resources.
5. Use assessment data, plan and revise teaching-
learning plans.
6. Direct and strengthen the links between school and
community activities.
7. Conduct research and development in teacher
education and other related activities.

4. ACKNOWLEdGMENT
Author would like to express his whole - heartedly thanks to the following people
who were able to give their willingness to help, for their unwavering and undying
support, encouragement, financial assistance and precious time for the accomplishment of
this narrative report.
To DR. NESTOR M. DE VERA, University President, for his vision and mission
of attaining more quality and relevant education in the University.
To CORAZON N. SAN AGUSTIN PH.D., Dean of College of Teacher Education, for
allowing her to participate and cooperate in this field of teaching. And also for her moral support
and encouragement to the whole studentry.
To MRS. LEONORA MONTEFALCON. Pre-service Teacher Coordinator for her
untiring guidance, concern, support, encouragement, understanding and most of all for the love
that she gave to all the practice teacher’s.
To MRS. ARLENE G. ADVENTO. Pre–service Teacher Supervisor for her untiring
supervise, concern, support, encouragement, understanding and most of all for her patient in
checking the lesson plan.
To DR. MILAGROS B. PUON PH.D., the principal of Mabitac National High
School, Mabitac, Laguna, for allowing her to conduct his observation and practice
teaching in the said school.
To MRS. LANI C. CABIEDEZ, her cooperating Teacher, for her patience, and
untiring support through her sacrificing her time and giving hints and ideas on how he
will execute every topics properly.

5. To All the Faculty members and staff of Mabitac National High School
Mabitac,Laguna, for their guidance and support in making this teaching portfolio.
To all the students of Mabitac National High School, for their kindness,
cooperation and respect given to the author that inspires her to continue her chosen
career. Also she would like to extend her appreciation to her Second Year Students (II-
Sampaguita, II-Cattleya and II-Lilac) that she had handled, for their cooperation and for
being not only a student but a “ Friends and barkadas” that is always there in her side in
times of happiness and sorrow and also they are the one who gave hope and strength to
pursue her profession.
To the authors’ dearest and closest friends: Ronalyn, Shane, Yvon and Are Edz, for their
companionship, and for inspiring the author to make this teaching portfolio.
To the authors’ loving and supportive guardians: Tatay Dodie and Nanay Amy; her
brothers: Kuya Pido, Armar, Anton; and my sister Aliza, for their untiring support, financial
assistance, for their love, care, advice and encouragement to make this teaching portfolio. Thank
you so much! And I Love you.
To all his classmates and friends, “Math Majors”,Ate glai, Janeth, Rona, Maricon, aleli,
and etc you know who you are, for their assistance, love and endless encouragement and help
which inspired the author to complete and finish this teaching portfolio.
And above all, to our God Almighty, for giving the strength, patience, guidance, and for
the continuous blessings and undying love.
The Author

6. TABLE OF CONTENTS
Title Page
Certificate of Completion
Approval Sheet
Acknowledgment
Table of Content
I. Statement of Purpose of the Portfolio
Student Intention of Making the Portfolio
II. Prayer of the Pre-Service Teacher
Teacher’s Creed
Personal Educational Philosophy
III. Resume and Evidences
Evidences of Community Outreach
IV. Personal Reflection in the Pre-Service Teaching
Personal Reflection in the Field Study Experiences
V. Brief Description of the Site of Practice Teaching
VI. Sample Lesson Plan
a. Detailed Lesson Plan
b. Semi-detailed Lesson Plan
c. Brief Lesson Plan
VII. Best Lesson Plan Using Creative Strategy with the Use of Complete Set of
Materials
a. Pictures of Sample of Materials Used

7. b. Pictures in Final Demonstration Teaching
c. Sample of Learners’ Work
VIII. Titles and Brief Synopsis of Professional Reading and References
IX. Professional Development Plan (Career Plan)
X. Additional Entries
a. Application Letters
b. Commendations Relevant to Field Study Experiences
c. Commendations Relevant to Practice Teaching
This practice teaching portfolio was prepared and developed to
provide and share experiences for those who will undergo the same
undertakings. Some classroom difficulties and problems that she had
encountered are mentioned, and the lesson that she had learned. The
greatest value of this practice teaching portfolio is that it serves as the
mirror of the practice teacher for their progress and achievement in
their practice teaching. And also this practice teaching portfolio was
prepared to expose the pre-service teacher experiences so that they can
STATEMENT OF THE PURPOSE/S OF PORTFOLIO/
STUdENT’S INTENTION OF MAKING THE PORTFOLIO
use it in relating their theories learned inside the classroom to become
globally competitive.
Another purpose of this practice teaching portfolio is that it
assess the pre-service teacher’s learning for the preparation in future
life in facing the real world of teaching. The pre-service teacher must
do always their best in imparting knowledge to the students. Just love
your students so in return your students will be embracing you too,
with the great things you’ve done to them not only in cognitive side
but in affective and psychomotor development.

8. PRAYER OF THE PRE-SERVICE TEACHER
Help me to be a fine teacher, to keep peace in the classroom,
peace between my students and myself, to be kind and gentle
to each and every one of my students.
Help me to be merciful to my students, to balance mercy and

9. discipline in the right measure for each student, to give genuine praise a
s much as possible, to give constructive criticism in a manner
that is patatable to my students.
Help me remain conscientious enough to keep my lessons
I am a teacher.
always interesting, to recognize what motivates each of my students,
to accept my student's limitations and not hold it
against them.
I accept the challenge to be sagacious
Help me not to judge my students too harshly, to be fair to all,
to be a good role model, but most of all Lord, help me to show
and tenacious in teaching every student
your love to all of my students.
Amen.
because I believe every child can learn.
TEACHER’S CREEd
I accept the responsibility to
Create a learning environment

10. TEACHER’S PHILOSOPHY OF EdUCATION
The philosophy is that people must believe in something. According to John Dewey,
education is by its nature an endless circle spiral. It is an activity, which includes science, because
in its process, it raises problems to be studied which then reacts upon demanding more through,
more science in an everlasting sequence.
This definition of education makes it imperative to a person to have a philosophy of
education and beliefs in the function of teaching.

11. A teacher should believe in the intended processes and activities to produce desirable
changes in the behavior of students. We must believe in the capacity to effect these changes,
promote and facilitate these changes through the mastery of the subject matter and the use of
appropriate methods and techniques of teaching.
A teacher also functions as manipulator of teaching learning situations. As a
manipulator, she believes in her ability to create a series of operations directed to change specific
behavior. These are just the parts of a teacher’s educational philosophy.
As a student teacher, she must believe in something that will eventually help her in
setting the goal of her life. This will focus on the values and objectives of the new social order;
the will help the teacher in analyzing and organizing her objectives; crystallizing the thoughts that
will serve as a guide to prevent a teacher from getting lost their maze of her many-faceted chores.
The school occupies premier place in the construction of the society, particularly in the matter of
changing the attitudes toward community. The role of the teacher plays will be a crystallizer and
an evaluator of the educational program under the democratic society.

12. ALELI MARCELINO ARIOLA
#016 Brgy. San Antonio Mabitac, Laguna
Contact Numbers: 09293433651
E-mail address; ariola_aleli_@yahoo.com
OBJECTIVE
 To use the skills, knowledge and experience I have gained through tertiary study
and work experience to educate and provide students with the necessary learning
they require to develop in today’s society. I have a strong interest in all areas of
education and am passionately committed to promoting a positive and dynamic
learning environment for secondary school students. And to obtain a teaching
position in high school.

13. PERSONAL DATA
Date of Birth December 21, 1991
Place of Birth Mabitac, Laguna
Age 20
Gender Female
Civil Status Single
Nationality Filipino
Height 5’
Weight 40 kgs.
EDUCATIONAL ATTAINMENT
Tertiary Level: Laguna State Polytechnic University
Siniloan, Laguna
Course: Bachelor of Secondary Education
Major: Major in Mathematics
2008- Present
Secondary Level: Mabitac National High School
Mabitac, Laguna
2004 – 2008
Primary Level: San Antonio Elementary School
San Antonio Mabitac, Laguna
1996 – 2002
SEMINAR AND WORKSHPS ATTENDED
“Exploring Mathematics and Science through Enviromental Awareness and Creativity
Enhancement” (Participants)
Mini – Theater, Laguna State Polytechnic University
Host Campus, Siniloan, Laguna
October 11-12, 2011
“Love Can Wait” (Participants)
Mini – Theater, Laguna State Polytechnic University
Host Campus, Siniloan, Laguna
February 10, 2011
“Bridging Nation’s Growth through Sports” (Participants)

14. Multi – Purpose Gymnasium, Laguna State Polytechnic University
Host Campus, Siniloan, Laguna
“Teaching Multi – grade Classes” (Participants)
Mini – Theater, Laguna State Polytechnic University
Host Campus, Siniloan, Laguna
February 05, 2010
“Technology Integration in Mathematics Teaching” (Facilitator)
Host Campus, Siniloan, Laguna
October 07, 2011
“Modern ways in Teaching Mathematics” (Facilitator)
Host Campus, Siniloan, Laguna
September 26, 2011
“Technology Integration in Mathematics Teaching” (Facilitator)
Discrete Mathematics and Algebra
Host Campus, Siniloan, Laguna
August 06, 2011
“Alternative Learning System in Aeta Community” (Participants)
Equalizing Education into Cultural Minority Groups
Mini – Theater, Laguna State Polytechnic University
Host Campus, Siniloan, Laguna
February 11, 2011
“Multi – Channel Learning for Remote Areas” (Participants)
Mini – Theater, Laguna State Polytechnic University
Host Campus, Siniloan, Laguna
February 10, 2011
“The Challenges of the Globally Competitive Teachers” (Participants)
Global Changes; the Effect of Popular Media in Teaching”
Laguna State Polytechnic University
Host Campus, Siniloan Laguna
February 5, 2010
“Teaching Indigenous People” (Participants)
Mini – Theater, Laguna State Polytechnic University
Host Campus, Siniloan Laguna
February 25, 2009
“Seminars on Strengthened Vocational Education Program (STVEP) and Alternative
Learning System ( ALS)” (Participants)
ALS Building, Siniloan Elementary School

15. Siniloan, Laguna
September 22, 2011
“K – 12 and UBD Seminar – Workshop” (Participants)
Mini – Theater, Laguna State Polytechnic University
Host Campus, Siniloan Laguna
October 22, 2011
“Pre – Elementary Education” (Participants)
Mini – Theater, Laguna State Polytechnic University
Host Campus, Siniloan Laguna
February 25, 2009
“Seminars on The Enhanced K – 12 Basic Education Program” (Participants)
Batangas Sports Center
Batangas, City
September 30, 2011
“Makabagong Filipino para sa Bagong Pilipino: Napapnahong Pag – aaral sa Wika at
Panitikan Gamit ang 2009 Gabay sa Ortographiyang Filipino” (Participants)
Mini – Theater, Laguna State Polytechnic University
Host Campus, Siniloan Laguna
February 11, 2011
“SPED: Understanding the hearts of Exceptional Learners” (Participants)
Mini – Theater, Laguna State Polytechnic University
Host Campus, Siniloan Laguna
February 11, 2011
SKILLS
 Ability to communicate both written and oral
 Can speak English and Tagalog fluently
 Computer literate (MS Word, MS Excel, MS PowerPoint, MS Publisher,
Adobe Photoshop, Adobe PageMaker, Software Installation, PC Hardware
Servicing)
CHARACTER REFERENCES
CORAZON N. SAN AGUSTIN Ph. D.
Dean, of College of Education
MRS. ARLENE G. ADVENTO
Pre-service Teacher Supervisor

16. MRS. MILAGROS PUON PH.D.
Principal
Mabitac National High School
Mabitac, Laguna
I hereby certify that the above information is true and correct to the best of my
knowledge and belief.
________________________
Applicant’s Signature
EVIdENCES OF COMMUNITY OUTREACH

19. Personal
Reflection
of
Field Study
Experiences
FIELd STUdY 1
The Learner’s Development and Environment

20. Field Study 1 is focus on Learner’s Development and Environment, the learning
environment as well as the psychological environment that may affect the students’ way
of learning.
.A physical environment that is conducive for learning may be the product of
physical and psychological atmosphere that creates interaction between student to student
and teacher to students, it had a great impact to teaching-learning process.
Every students are unique they are differ from each other. Teacher must consider
the differences of the students, respect them and treat them equally.
FIELd STUdY 2
Experiencing the Teacher-Learning Process
Field study 2 is design to help the field study students observe how the different
principle of teaching and learning are applied to make the teaching and learning process
interactive, meaningful, exciting and enjoyable.
In teaching, teacher must consider the feelings, ideas, interest and needs of
students. Having on actual learning will lead them to better understanding. When it
comes to teaching strategies, there is no such thing as best method. The best method is
the one that works, the one that yields result and the one that promote harmonious
relationship between the teacher and the students.
FIELd STUdY 3
Technology in the Learning Environment

21. This course is designed to realize the importance of technology in teaching and
learning. The teacher must apply the different principle in utilizing instructional materials
suit to the needs of the learners. And these also enrich the student’s experiences in
developing appropriate technology to facilitate learning. It shall also provide students
exposure and hand – on opportunities in the use of information communication
technology.
FIELd STUdY 4
Exploring the curriculum
This field study have the concept of curriculum is a dynamic as the changes that
occur in the society. It is refers to the total learning experiences of individuals not only in
schools but in society as well.
Field study 4 is about the effective curriculum design and assessment. It includes
the different persons involve in the implementation and assessment of the curriculum.
FIELd STUdY 5
Learning Assessment Strategies
Field study 5 provide us an opportunities to acquire knowledge about the different
kind of students while assessing them, and one of the best assessment to learning is the
assessment in affective domain which emphasized measurements of reasoning and the

22. mental faculties of the students, it emphasized feeling, an emotion or a degree of
acceptance and rejection. In this kind of assessment and strategies the student can
broadcast their opinion and their shared their own knowledge, information and ideas to
other learners.
FIELd STUdY 6
On becoming a Teacher
New teachers overwhelmingly say they love what they do. They say it allows
them to contribute to society and help others. I am now entering on the step of the real
world teachers directly affect the lives of the students they teach. Think about how much
time students spend in school; most of that time is spent with a teacher.
Field study 6 provide us in – dept understanding, series of experiences that will motivate,
encourage and enable to go on and appreciate more the valuable things/experiences about
on becoming a professional teacher on the future.
In teaching profession you must have dedication to public interest, and strong
commitment to the profession, moral and ethical values.
OBSERVATION
It was November __, 2010 when I started my observation. It was assigned by the
principal, Dr. Milagros B. Puon, of Mabitac National High School to observe of all year
level to see the teachers’ strategies and technique in handling such different kinds of

23. students with different learning styles and behaviors. I was very excited and quite
nervous because we were in the beginning of a difficult task of our studying.
On the first day, I was endorsed to Mrs. Lani C. Cabiedez and Ms. Vivien B.
Claro, a Mathematics Teachers, to be my cooperating teachers. I was very happy in
observing their class, they easily disciplines their students but in the good way. I really
admired them when they was teaching Mathematics because they always used motivation
to catch their attention and to arouse the interest of their students. They always equipped
with visual materials that is needed in the lesson. They mastered the subject matter and
executed every lesson very well. When it comes to students, they are very active and
talented bur some of them are slow learners.
I had finished my observation last March __, 2011. I learned that as a teacher, you
have to used teaching strategy that is suited for the student because of what we called
“Individual Differences”, your voice must be well modulated, this is very important for a
teacher and most of all you want to stay in this profession you need an ended patience.
I really enjoyed my observation in Mabitac National High School. I learned
beautiful things from all the teachers there and I would like to say thank you to Mrs. Lani
C. Cabiedez, Ms. Vivien B. Claro and Dr. Milagros B. Puon.

24. Personal
Reflection
of
Pre – Service
Teaching
ACTUAL TEACHING
Student Teaching is the actual Teaching and our major role and responsibility.
During this period, we need to cat like a professional teacher.

25. After three months observations, we are now to apply all the knowledge and good
things we got during our observation period. But before that, there is some orientations
that were given to us on how to perform our duties and responsibilities’ as a student
teacher. All teacher with concern especially our pre- service supervisor, Mrs. Arlene G.
Advento, with our dean, Dr. Corazon N. San Agustin, for us to be ready and capable
enough to handle different kinds of student and apply all principles and methods that we
have learned in our years of schooling.
November 29, 2011, it is a pleasure to see once again the teachers and students of
Mabitac National High School.
Together with my co-practice teachers, we choose the year level we want to teach.
And I choose second year because I already familiar with the second year students.
It was December 1, 2011, when I assigned to teach in II - Sampaguita but I
request my cooperating teacher, Mrs. Lani C. Cabiedez, that I will observe her to prepare
myself to teach in the next class which is II – Lilac, then followed by II – Cattleya.
During my first week of teaching, it was very hard for me to act like a real teacher,
making lesson plans and visual aids at night. I felt tired during the first week of my
teaching. I was always thinking what am I going to do on how can I execute my lesson
well. But I was lucky enough to have a very approachable and supportive cooperating
teacher because she was always willing to help and support me, share ideas and
suggestions to the fullest.
Another important part of teaching was on how to deal and building rapport with
my pupils. During this period, I felt the joy as I was imparting knowledge to them and in
return, they gave me support and respect.

26. With this in my actual practice teaching, I realized being a teacher is very
challenging and enjoyable although it is very difficult task but then, with the student
who’s eager to learn, cooperative, funny and sweet as inspire the teacher to teach. This
was the first time I realized and probe to myself what my teacher told us before that
teaching is the most enjoyable and inspiring profession.
The much-awaited time of every student-teacher was the final demonstration
teaching. March 09, 2012 in the morning was the schedule of my general demonstration.
We are ready to the demonstration all the devices, lesson plan well prepared upon seeing
the panelist namely: Mrs. Montefalcon, Ms. Bobadilla and Mrs. Advento me and my co –
student teachers feel nervous, but through the support and encouragement given to us by
the teachers including our students who always there to make us smile we gather all our
strength and confidences to begin our lesson.
After the demonstration we held short meeting to discuss about the result of our
demonstration. We are all happy because our demonstration ended successfully and with
flying colors said by our panelist. They welcome us in the world of teaching and all of
this is through the help of our Jesus Christ. We continue our practice teaching until march
to finish the time needed.

27. A Brief
Description
of the Site of
Practice
Teaching
MABITAC NATIONAL HIGH SCHOOL
VISION
To give our students desirable teaching-learning environment

28. and thereby enable them to create own destiny in the global
community.
MISSION
To prepare our students to become responsible citizen
And good leader who loves his/her family and
Community and is proud to be a Filipino.
GOALS
 Develop a high performance among administrators,
teachers, students, towards a better higher education.
 Strengthen mutually beneficial linkages and agencies at
the Local and Provincial Government.
 Promote support from alumni, friends and adopt school
program and sustained caring school.
History of Mabitac National High School Mabitac,
Laguna

29. MABITAC NATIONAL HIGH SCHOOL can be said to be small
school situated in the corner of two barangay: Brgy. Maligaya and Brgy. Libis ng
Nayon now called Bernardo Sayarot Street. The total land area of the school is 18
238 sq. meters for the main school and 6000 sq meters for the extension site.
These are all donated by the municipal government.
This school started to operate in the year 1971 through the best effort to
Mrs. Lydia V. Carpio. She was the first principal in-charge and the founder of the
said school.
The school was called Alas-As Barangay National High School, first
Barangay High School in Mabitac. The school’s name was changed to Mabitac
National High School through the Sangunian Bayan resolution and approved by
the NHI (National Historical Institute) on November 15, 1994.
This institute started only two (2) classroom borrowed from Mabitac
Cultural School. Also, the Sanguniang Barangay of Lucong was used as
classroom through the leadership of Brgy. Captain Mariano G. Bobadilla, who
adopted the school for ten years. The Barangay Libis ng Nayon and Barangay
Maligaya disowned the school.
Gradually, the school got its integrity. At the start, there are two full time
teachers in the person of Ms. Fe L. Reyes and Mr. Nelson V. Vicuña, other
teachers are: Mrs. Aimee Albayand and Mrs. Rosario De Guzman.
Yearly, enrolment increases. On the third year of operation, the school is
the full pledged high school. In 1974, thirteen students graduated, though there is
no graduation rite. On the school year 1974-1975, forty students graduated with a
graduation ceremony.
As this is increase on enrolment, number of teachers increase too. The first
faculty members are the following: Mrs. Lydia V. Carpio, the principal-in-charge,
Ms. Soledad Rellosa, and Mrs. Esmeralda V. Bobadilla, Ms. Gloria Bauyo, Mrs.

30. Yolanda S. Dimaranan, Ms. Fe Reyes, Ms. Fidela G. Gonzales, Ms. Felicidad De
Leon, Mrs. Rosita De Guzman and Mr. Nelson V. Vicuña.
On the school year 1977-1978, Mrs. Carpio decided that the school should
have a permanent site, and the head teacher designed was Mr. Nelson Vicuña.
After a year of being a head teacher, Mr. Vicuña decided to work abroad. Mrs.
Mata was assigned as the teacher-in-charge, on 1979-1980. During her
administration, school record was organized; sewing machines and science
equipments were acquired. Unfortunately, she was not able to pass the Board
Examination for Teachers, so Mrs. Yolanda S. Dimaranan took over the position
and was promoted to Head Teacher to Principal I.
Mrs. Dimaranan is the leader of the school for twenty-six years. She was
able to establish our school on its success. The acquisition of land for the school,
different buildings and all equipments needed were patiently acquired for the use
of the institution. During her administration, students’ development as well as
curriculum development and values were given emphasized.
On December 22, 2006, Mrs. Yolanda S. Dimaranan retired at the age of
65. Due to her retirement, the Division Superintendent,
Dr. Lilia T. Reyes designates Dr. Adelina L. Acelajado, Education
Supervisor in H.E. to be the OIC-Principal and now year 2010 the assigned
principal of Mabitac National High School was Mrs. Milagros B. Puon Ph.D. a
very humble, patience and kind principal of (MNHS).
Presently, the principal of Mabitac National High School is Mrs. Cynthia
Dela Torre from Pagsanjan National High School.

31. Examples
of
Lesson Plan

32. Detailed
Lesson Plan

33. Mean of Grouped Data
I. Learning Objectives
Cognitive: Derived the formula for finding the mean of grouped data;
Affective: Manifest understanding of the mean of grouped data; and
Psychomotor: Compute the mean of grouped data.
II. Learning Content
A. Mathematical Concept
To get the mean for grouped data
1. Using long method
Where
f = frequency of the class interval
x = midpoint of the class interval
n = total number of frequency
2. Using the coded – deviation method
Where
f = frequency of the class interval
x’ = assumed mean
d’ = deviation from thr reference point
i = size of the class interval

34. n = total number of frequency
B. Value Integration: work neatly and systematically
C. Materials: Cartolina, Calculator, pentel pen, coins, computer
D. References:
Bernabe, Julieta G. Advanced Algebra, Trigonometry and
Statistics (Functional, Approach), 2005 pp. 161
Orance, Orlando A. E- Math Advanced Algebra and Trigonometry
2010 pp. 406
III. Procedure
TEACHER’S ACTIVITY STUDENT’S ACTIVITY
A. Daily Routine
1. Prayer
Everybody please stand and
we will pray.
2. Greetings
Good Morning class! Good Morning ma’am!
Good Morning classmate!
3. Attendance I am glad to tell you that nobody
Let me see if everyone is is absent today.
present today. Secretary will
you please check the
attendance
B. Developmental activity
1. Drill
Find the mean The mean or the average age is
a. The following are the ages of 22.
students in culinary class: 24
18 19 20 24 26 27 20 23 19.
Find the mean.
b. The number of student in six The average class size is 55.
fourth year section are 45 57
48 62 58 60. What is the
average class size in the fourth
year? The mean sales amount is P333
c. Last month’s sales for six 709.5
different coffee shop were:

35. P375 910, P351 884
P252 675, P361 148
P392 740, P267 900. Find the
mean sales.
2. Review
Last time we discuss the mean Mean is the sum values of all
of ungrouped data. Again given items divided by the
class, what is mean? number of items.
What is another name for
mean? The other name for mean is
average.
How do we compute the mean
or average for ungrouped In computing the mean get the
data? sum of the values of all given
items divided by the total number
of items.
What formula is used?
What does the mean implies?
The mean is a single number that
represent the characteristics of
given data.
C. Motivation
Given:
7 11 6 11 10 8 17
1. Use coin to duplicate the
seven Stacks given each
stacks represent a number in a
set of data
2. Rearrange the coins so that
each of the seven stacks
contains the same number of The coins are evenly distributed
coins. Describe the stack of over the seven stacks.
the coins. The stacks of coins have the same
height.
Can you find the mean number of
coins? Yes!
What is the mean number of

36. coins? The mean number of coins is 10.
D. Presentation
Finding the mean for a large data
is a tedious job requiring much
patience. Today we are going to
find the mean of a large data.
Do you have any idea on how we Yes ma’am, add the students’
can find the mean score of 100 scores divided by 100.
students in a math quiz?
Very Good!
Another way is to group the data
Adding the 100 items take a lot of to a frequency distribution.
time, to save time is there another
way to find the mean of large
data?
Calculate the mean score of 100
students in a math quiz

37. Class Class
interval interval
f f
x x
fx fx
55 – 59 55 – 59
50 – 54 50 – 54
45 – 49 45 – 49
40 – 44 40 – 44
35 – 39 35 – 39
i=5 i=5
14 14
28 17
17 28
15 15
26 26
n =100 n =100
57
52
47
42
37
798
884
1316
Find the midpoint of the class 630
interval ( x) and multiply to the 962
frequency (fx) 4590
Now, how can we find the mean
score?
Very Good!
Equate it in symbol
Correct!
Yes, that is the first method.
Get the summation of fx divided
How did you get the mean? by the total frequency.

38. Now, another method to find the
mean using the same example.
Class
interval
f In getting the mean find the
x midpoint of the class interval (x)
d’ and multiply to the frequency (fx)
fd’ and then add the fx divided by the
total frequency.
55 – 59
50 – 54 (The student will find the mean
45 – 49 using the coded – deviation
40 – 44 method)
35 – 39
i=5
14
17
28
15
26
n=100
0
1. Locate the class interval with
the highest frequency and
assumed that the mean is in
that class interval.
2. Let us deviate in the assumed
mean and that is 0. Positive
deviation above and negative
deviation below it.
3. Multiply each f by its d’ to get

39. fd’ Class
4. Divide the ∑fd’ by n then interval
multiply to (i) plus the f
assumed mean. x
d’
Compare the answer. fd’
How did you compute the mean,
using coded – deviation method? 55 – 59
50 – 54
45 – 49
Write it in symbol 40 – 44
35 – 39
E. Generalization i=5
14
What are the two methods of 17
computing the mean of group 28
data? 15
26
How do we compute the mean of
grouped data using Long method? 57
Code- deviation method? 52
47
42
Very Good! 37
2
F. Group Activities/Application 1
Now, I will group you into 2 0
( Boys’ group and girls group) -1
-2
a. Activity sheet 28
17
Group I (Boys group) 0
-15
Using the long method find the -52
mean of the given distribution

40. Class
interval
f
X
fx
85 – 89
80 – 84 They are the same.
75 – 79
70 – 74 (the student will give the step to
65 – 69 compute the mean using the
60 – 64 coded – deviation method)
i=5
4
9
7
8
12
10 The two methods are the long
n = 50 method and the coded- deviation
method.
Group II (Girls group)
Using the coded – deviation
method find the mean of the given
distribution.

41. Class
interval
f
x
d’
fd’
85 – 89
80 – 84
75 – 79
70 – 74
65 – 69
60 – 64
i=5
4
9
7
8
12
10
n = 50
(each group will present their
work)
Group I and Group II got the
If your group were done in doing same answer
the activities please go back to
your seat. It implies that if you use either the
long method or the coded –
b. Analysis deviation method we will get the
Post your work on the board. same result.
Read first the instruction
written on the activity sheet The more convenient and the
easier method to use is long
Q1: Examine the answer of your groups method/coded – deviation method
what did you notice with your answer?
Q2: If they have the answer what does it
implies? I feel that I’m belonging to the
group.

42. Q3: Which do you think is more I did the Frequency distribution
convenient to use? Why? table.
Very Good!
G. Valuing
None!
What do you feel while doing
your activity with your group
mates?
How about your cooperation with
your group mates? What did you
contribute to your activity?
Do you have any question?
Get ½ sheet of paper and be ready
for a short quiz.
IV. Evaluation
Using the two methods Long Method and Coded – deviation method find the
mean.
Test Score of 50 students in Algebra II
Class Interval f
78 – 83 4
72 – 77 9
66 – 71 7
60 – 65 6
54 – 59 8
48 – 53 10
42 – 47 6
i=6 n = 50
V. Assignment
Make a simple survey on the ages of your family members. Find the mean
age of your family members. You will work on this activity cooperatively and
present the data in a table.

44. Semi-
Detailed
Lesson Plan

45. “Integrating Values with Subject Matter”
HARMONIC SEQUENCE
I. Specific Objectives
At the end of the lesson, the students should be able to:
1. define and identify a harmonic sequence; and
2. find the nth term of a harmonic sequence.
II. Mathematical Concept
A sequence of numbers is said to be harmonic if their reciprocals form an
arithmetic sequence. In general form, a harmonic sequence may be represented as
, , , ………. .
III. Values Focus
Cooperation and self-discipline
IV. Materials
Algebra II (Functional Approach), chart
V. Teaching Strategies: Exposition and Practice
A. Drill
Identify the common difference in the following:
a. 2, 5, 8, …… c. 18, 24, 30, ……
b. 9, 7, 5, …… d. -8, -5, -2 , ……
B. Review
1. What is an arithmetic sequence?

46. 2. Give examples of an arithmetic sequence.
C. Introduction / Motivation
Besides the simple sequence studied, there are other sequences that
are useful for counting purposes.
D. Presentation
1. Observe the given examples of harmonic sequence together with the
corresponding arithmetic sequence below.
Arithmetic Sequence Harmonic Sequence
1, 4, 7, 10, ….. 1, ¼, 1/7, 1/10, …..
15, 12, 9, 6, 3, 0, ….. 1/15, 1/12, 1/9, 1/6, 1/3, 0, ….
3/2, 7/2, 11/2, 15/2, ….. 2/3, 2/7, 2/11, 2/15, ….
Given nth first term and the common difference, the nth term
can be found.
2. Find the first six terms of a harmonic sequence where a1 is 1/3 and d is
¼.
Solution:
The corresponding arithmetic sequence with a1 = 3 and d = 4
will be 3, 7, 11, 15, 19, 23, ….. Therefore, the harmonic sequence is
1/3, 1/7, 1/11, 1/15, 1/19, 1/23, ….
3. Find the 13th term of a harmonic sequence if a1 = 1/6 and d = 2.
Solution:
The corresponding arithmetic sequence has a1 6, d = ½ and n =
13.
a13 = 6 + (13 -1) ½ = 6 + 12(1/2)
a13 = 6 + 6 + 12
Therefore, the 13th term of the harmonic sequence is 1/12.
E. Exploration
1. What is observed about the given examples?
2. Compare an arithmetic sequence and a harmonic sequence.

47. 3. What is the relation between an arithmetic sequence and a harmonic
sequence?
4. What is the nth term of a harmonic sequence?
F. Generalization
(Refer to Mathematical Concept for the definition of harmonic
sequence.)
To find the nth term of the harmonic sequence use the formula for
arithmetic sequence an = a + (n – 1)d and get the reciprocal of an.
G. Activities
1. Identify whether the given sequences are harmonic or not.
a. 5, 8, 11, 14 c. ½, ¼, 1/8, 1/10 e. -1/7, -1/4, -1, 1/2
b. ¼, `/7, 1/10, 1.13 d. 1, 1/3, ¼, 1/7
2. Find the indicated term of a harmonic sequence if:
a. a1 = ½ and d = 1/5; 15th term
b. a1 = 1/15 and d = -1/2; 13th term
VI. Evaluation
Find the indicated term of a harmonic sequence if:
1. a7 = -1/4 and d = -3; 20th term
2. a16 = 1/17 and d = -1/3; 1st term
3. a21 = -1/48 and a33 = -1/84; 100th term
VII. Assignment / Extension
Answer the following.
1. Find the 30th term of the harmonic sequence 1/3, 1/6, 1/9, 1/12, …..
2. Find the 10th term of the harmonic sequence -2/3, -4/7, -1/2, -4/9, …..
3. Find the 12th term of the harmonic sequence -8/3, -4/3, -8/9, ….

48. Brief
Lesson Plan

49. I. Objectives
At the end of the Lesson the student, should able to:
 Manifest understanding of the mean;
 Define mean;
 Compute the mean of ungrouped data.
II. Subject Matter
Mathematics: Finding the mean of ungrouped data
Advanced Algebra, Trigonometry and Statistics (Functional, Approach)
III. Learning Task
A. Daily Routine
a. Task 1
Discussed what is mean.
b. Task 2
Perform on how to find the mean of the ungrouped data.
IV. Get one whole sheet of paper. And answer the following.
1. Get the average grade of Benjie if he got the following grades: 86, 85, 84,
79, 85, 87, and 90.
2. Den Mark got the following scores in the math quizzes: 20, 19, 17, 19, 18,
15, 19, 20 and 6.
3. A teacher wants to evaluate the performance of the groups of students to
find out which group will best quality for the math quiz bee. After a series
of test the mean score obtained by each member of the group were:
Group I – 85, 92, 88, 88, 90
Group II – 86, 90, 87, 92, 86
4. Mercy aims to obtain a mean grade 88 in math at the end of fourth grading
period for the first three grading periods her mean grade is 87. What
grades should she get for the fourth grading period?

50. Best
Lesson Plan

51. Unit Title: Sequence and Series Year Level: Second Year
Lesson Topic: Geometric Sequence Time Frame: 1 hour
Established Goals (Standard): Technology Standard:
The student demonstrates understanding The student applies Microsoft Excel in
of the key concepts and the general or nth understanding and solving problems
term of the geometric sequence. involving geometric sequence.
Essential Questions: Desired Understanding:
How to determine the fixed number or The students will understand that the
the common ratio in a geometric sequence? geometric sequence is a sequence which
What is the general term used in each term is obtained by multiplying the
geometric sequence? preceding term by a constant number called
common ratio.
Students will know: Students will be able to:
 the characteristics of geometric  identify and describe geometric
sequence; and sequence; and
 the next term in the given geometric  solve for the common ratio and the
sequence. next term of the given sequence.
Teaching/learning Sequence (showing the integration/infusion of technology)
EXPLORE
Provide learners opportunities to recall mathematics concepts related to arithmetic
sequence and geometric sequence.
Drill/Review
Give an example of arithmetic sequence.
What is an arithmetic sequence?
Activity 1
Directions: Determine whether the given sequence is an arithmetic or not. If it is
arithmetic, find the common difference.
1. 30, 26, 22, 18, 14, …

52. 2. 1, 3/2, 2, 5/2, 3, …
3. 10, 8, 6, 4, 2, …
4. 1, 3, 9, 27, 81, …
5. -6, -2, 2, 6, 10, …
Why is it arithmetic or not?
How do you find the common difference?
Activity 2
Directions: Arrange the given numbers in Column A. increasing and Column B.
decreasing order then find the next number.
1. 21, 7, 63, 189, ___
2. 6, 384, 24, 96, ___
3. 125,5, 25, 625___
4. 4, 144, 24, 864, ___
5. 8, 64, 16, 32, ___
What did you notice to the given numbers?
How did you get the next number?
Activity 3
Directions: Study the given numbers and give the missing numbers.
1. 2, 4, 8, ___, 32, 64, …
2. 2, 6, ___, 54, 162, …
3. ¼, ½, 1, ___, 4, …
4. 80, ___, 20, 10, 5, …
5. 2, -4, 8, ___, 32, -64, …
How did you get the missing number in each set of numbers?
Do you observe any pattern in a given sequence? Explain the pattern in a given

53. sequence.
Activity 4
Directions: Perform the activity cooperatively.
A tennis ball is dropped from a height of 160 ft. and always rebounds one half of
the distance fallen. How high does it rebound the fifth time?
A. Let’s do some calculations and look for patterns.
Rebound
1
2
3
4
5
Height
80
How did you get the height of the ball?
Do you use a fixed number? What do you call that fixed number?
Observe the height of the ball after each rebound. Is there a sequence? Why?
FIRM UP
The activities in this part apply various learning strategies to check the learners’
comprehension, rethinking and revision of their understanding in geometric sequence,

54. Activity 5
Directions: Supply the missing number and identify the common ratio in the given
sequence.
1. 7, 14, 28, ___, 112, 224, …
2. 9, 36, 144, ___, 2304, …
3. 5, 30, 180, 1080, ___, …
4. 12, ___, 108, 324, 972, …
5. ___, 44, 176, 704, 2816, …
How did you find the common ratio?
In each given geometric sequence, find the next three terms.
How did you get the next three terms?
Activity 6
Directions: Find the next two terms of the given sequence.
1. 5, 20, 80, 320, 1280, …
2. 250, 50, 10, 2, …
3. 2, 6, 18, 54, 162, …
4. 9, 27, 81, 243, 729, …
5. 6, 12, 24, 48, 96, …
Did you find any pattern? Describe the pattern.
How did you get the next term of the given sequence?
What is the common ratio?
Resources (Websites, Software, etc.)
E – Math II Intermediate Algebra pp. 436 – 443
Algebra II Functional Approach pp. 224 - 227
Microsoft Excel,
Materials/ Equipment Needed:

55. Computer, Flashcards, Tennis ball,
During my
Final

56. Demonstrati
on

57. MY CRITIC ANd MY PANELIST

58. MY STUdENTS ANd I
PICTURES OF SAMPLE OF MATERIALS USEd

59. SAMPLE OF LEARNERS’ WORK

60. PRINCIPLES ANd METHOdS OF TEACHING
This book is intended primarily for students in the college of Education and
beginning teachers, to have s strong foundation and a through grasp on concepts, theories,
principles and teaching-learning process.
This book will also provide teachers who are already in the service for a great
long time and who want to improve their competency and to update themselves on
current trends, new techniques and strategies in the teaching process.
FIELd STUdY
Maria Rita D. Lucas

61. Field Study is a component of the new pre-service teacher education curriculum
that aims to expose the students to actual field study experiences so that they can relate
the theories learned inside the classroom with those experiences. These off-classroom
experiences would emphasize the importance of
CURRICULUM dEVELOPMENT
After graduationPurita P .et al to have a serious
Bilbao, I’m going
Curriculum in order to pass the Licensure Examination which
review Development is an instructional material in module from
complement the 3 – unit course of thewaiting for the resultclosely approximates
for Teacher. While New Teacher Curriculum. It of Board
the syllables of the CMO 30 s – 2004. find way to get a job related
Passers I’m going to
Similarmy other materials in projectto help my family I givetries to
to to course. I’m going write, curriculum development
balance theory and practice. Each Module follows afor them.
them the life that I dreamed distinct pattern or format with a short
introductory part or take off, the advance reading or focus, the activities to strenghthen
the focus or take, reflection for Higher Order Thinking and Self check for evaluation.
If I luckily pass the exam I will be in my
teaching career and I will take also my Masters
degree when I PROFESSIONAL regular job. After
already have my
all of that dEVELOPMENT PLAN
things, I will help my family, friends,
relatives etc and I will let myself to enjoy my life
while I am still single, then if I am already
satisfied with my life of being single I will now
soon to face my future life having my own family.
I will pray to our Dear God that he will give
me the guidance, strength, and love that I need
in order to make this plan come true.

63. LETTER OF APPLICATION
(BLOCK STYLE)
016 Brgy. San Antonio
Mabitac, Laguna
March 09, 2012
The Principal
Mabitac National High School
Mabitac, Laguna
Madam:
The guidance Councilor of your informed me that your school is in need of an
Mathematics teacher who can also teach P.E., and Filipino I would like to be considered
in the said position.

64. I graduated from Laguna State Polytechnic University, Siniloan, Laguna with a
degree of Bachelor of Secondary Education major in Mathematics. I undergone student-
teaching program that trained me to be efficient and effective teacher, a qualification to
teach in your school. Moreover, I also joined different school organization and activities
that helped build my leadership and self-confidence.
For your reference, you can ask the following persons regarding my personality:
1. Dr. Corazon N. San Agustin Laguna state Polytechnic University
2. Prof. Lydia R. Chavez Laguna state Polytechnic University
3. Mrs. Lani C. Cabiedez Mabitac National High School
I have enclosed copies of my college transcript of records for your reference.
I shall be very glad to come for an interview at your most convenient time.
Very truly yours,
Aleli M. Ariola
LETTER OF APPLICATION
(CONVENTIONAL STYLE)
016 Brgy. San Antonio
Mabitac, Laguna
March 09, 2012
The Principal
Mabitac National High School
Mabitac, Laguna
Madam:
The increase of the enrollment in both private and public schools will
undoubtedly necessitate the creation of the new position for classroom teachers to take

65. charge for additional classes. Should this opportunity arise, please consider me as an
applicant for the position, secondary school teacher.
I completed the degree of Bachelor of Secondary Education (BSEd) major in
Mathematics, from Laguna State Polytechnic University, Siniloan, Laguna (LSPU) 2012.
I undergone student-teaching program that trained me to be efficient and effective
teacher, a qualification to teach in your school. Moreover, I also joined different school
organization and activities that helped build my leadership and self-confidence.
I am a Filipino, a Roman Catholic, 21 years old, single and in good health.
For your reference, you can ask the following persons regarding my personality:
1. Dr. Corazon N. San Agustin Laguna state Polytechnic University
2. Prof. Lydia R. Chavez Laguna state Polytechnic University
3. Mrs. Lani C. Cabiedez Mabitac National High School
I shall be very glad to come for an interview at your most convenient time.
Very truly yours,
Aleli M. Ariola
Letter of Inquiry
016 Brgy. San Antonio
Mabitac, Laguna
March 09, 2012
Division Superintendent
DepEd Laguna
Sta. Cruz Laguna
Madam:
I would like to inquire about teaching opportunities in the public school in
Laguna. I am particularly interested in teaching Math subject in high school students.

66. I completed the degree of Bachelor of Secondary Education (BSEd) major in
Mathematics, from Laguna State Polytechnic University, Siniloan, Laguna (LSPU) 2012
and presently preparing myself for this coming Licensure Examination for teachers. My
resume and a copy of my transcript of records are attached herewith.
A self-addressed envelope is also enclosed for the information you will send me
about my request.
I am looking forward for your most favorable response.
Thank you, more power and God Bless!
Respectfully yours,
Aleli M. Ariola

67. OBSERVATION ANd PARTICIPATION PHASE
Observation in student teaching must be directed and systematic. There should be
specific purposes. During this period, the student teacher participates in the classroom
and school activities. They assist the cooperating teacher in the management,
maintenance of the classroom and order discipline, preparation of instructional materials,
construction of test, checking and usage of test results, accomplishment of school forums
and records, extracurricular activities in the school and in the community.
In the actual classroom observation and participation, student teachers must:
1. Follow the schedule of observations; make arrangement in case of changes in
schedule.
2. Visit their room at least one day before the observation day.

68. 3. Confer with the cooperating teacher before observation day.
4. Arrive at least an hour before the class starts.
5. Record the observation silently.
6. Thank the teacher or the cooperating teacher.
7. Observe the cooperating teacher at different occasions.
a. Developing a new lesson.
b. Demonstrating in the shop or laboratory.
c. Administering the test.
d. Supervising practical work.