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Republic of the Philippines

LAGUNA STATE POLYTECHNIC UNIVERSITY Siniloan (Host) Campus Siniloan, Laguna









programs and related services designed Prepared by: to respond to the requirements of the Philippines

and the global ALELI M. ARIOLA Pre-Service Teacher particularly Asian countries.


MISSION ARLENE G. ADVENTO The university shall primarily BSEd – Mathematics, Pre-Service Teacher Supervisor provide advanced education, professional, technological and CORAZON N. SAN AGUSTIN, Ph. D. vocational instruction in Education agriculture, Dean, College of Teacher fisheries, forestry, science, engineering,




education, sciences, other




undertaken services,





teaching arts




It and




extension progressive

leadership in its area of specialization.

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







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 teachinglearning plans. 6. Direct and strengthen the links between school and community activities. 7. Conduct research and development in teacher education and other related activities.


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. 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 (IISampaguita, 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

TABLE OF CONTENTS Title Page Certificate of Completion Approval Sheet Acknowledgment Table of Content


Statement of Purpose of the Portfolio Student Intention of Making the Portfolio


Prayer of the Pre-Service Teacher Teacher’s Creed Personal Educational Philosophy


Resume and Evidences Evidences of Community Outreach


Personal Reflection in the Pre-Service Teaching Personal Reflection in the Field Study Experiences


Brief Description of the Site of Practice Teaching


Sample Lesson Plan a. Detailed Lesson Plan b. Semi-detailed Lesson Plan c. Brief Lesson Plan


Best Lesson Plan Using Creative Strategy with the Use of Complete Set of Materials a. Pictures of Sample of Materials Used 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)


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

STATEMENT OF THE PURPOSE/S OF PORTFOLIO/ undertakings. Some classroom difficulties and problems that she had STUdENT’S INTENTION OF MAKING THE PORTFOLIO 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 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.


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 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 always interesting, to recognize what motivates each of my students,

to accept my student's limitations and not hold it against them. 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 I am a teacher.

your love to all of my students.

I accept the challenge to be sagacious


and tenacious in teaching every student

because I believe every child can learn. I accept the responsibility to

TEACHER’S CREEd Create a learning environment conducive to optimum achievement, academically, socially, and emotionally. I actively pursue excellence, for myself and my students.

I provide a model of decorum and respect that guides my students as well as honors them. I affirm superlative expectations for my students and myself. I cherish every child. I am a teacher. I change the world, one student at a time.

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. 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.

ALELI MARCELINO ARIOLA #016 Brgy. San Antonio Mabitac, Laguna Contact Numbers: 09293433651 E-mail address;

OBJECTIVE ď ś 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. PERSONAL DATA Date of Birth Place of Birth Age Gender Civil Status

December 21, 1991 Mabitac, Laguna 20 Female Single

Nationality Height Weight

Filipino 5’ 40 kgs.

EDUCATIONAL ATTAINMENT Tertiary Level: Course: Major:

Laguna State Polytechnic University Siniloan, Laguna Bachelor of Secondary Education 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) 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 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 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


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

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

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

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

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.

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.

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.

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.

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

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 ď ś Develop a high performance among administrators, teachers, students, towards a better higher education. ď ś Strengthen mutually beneficial linkages and agencies at the Local and Provincial Government. ď ś Promote support from alumni, friends and adopt school program and sustained caring school. History of Mabitac National High School Mabitac, Laguna

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. Vicuùa, 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.

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.

Examples of Lesson Plan

Detailed Lesson Plan

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.


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 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 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 a. The following are the ages of students in culinary class: 24 18 19 20 24 26 27 20 23 19. Find the mean. b. The number of student in six fourth year section are 45 57 48 62 58 60. What is the average class size in the fourth year?

The mean or the average age is 22.

The average class size is 55.

The mean sales amount is P333

c. Last month’s sales for six 709.5 different coffee shop were: 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?

C. Motivation

The mean is a single number that represent the characteristics of given data.



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 stacks of coins have the same the coins. height. Can you find the mean number of Yes! coins?

What is the mean number of 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! Adding the 100 items take a lot of 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 Class f x fx interval 55 – 59 14 50 – 54 28 45 – 49 17 40 – 44 15 35 – 39 26 i=5 n =100

Another way is to group the data to a frequency distribution.

Class interval 55 – 59 50 – 54 45 – 49 40 – 44 35 – 39 i=5




14 17 28 15 26 n =100

57 52 47 42 37

798 884 1316 630 962 4590

Find the midpoint of the class interval ( x) and multiply to the frequency (fx) Get the summation of fx divided by the total frequency. Now, how can we find the mean score? Very Good! Equate it in symbol Correct! Yes, that is the first method.

In getting the mean find the

How did you get the mean?

midpoint of the class interval (x) and multiply to the frequency (fx) and then add the fx divided by the total frequency.

Now, another method to find the (The student will find mean using the same example. using the coded – method) Class f x d’ fd’ Class f x interval interval 55 – 59 14 55 – 59 14 57 50 – 54 17 50 – 54 17 52 45 – 49 28 0 45 – 49 28 47 40 – 44 15 40 – 44 15 42 35 – 39 26 35 – 39 26 37 i=5 n=100 i=5

the mean deviation d’


2 1 0 -1 -2

28 17 0 -15 -52


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 fd’ 4. Divide the ∑fd’ by n then multiply to (i) plus the assumed mean. They are the same. Compare the answer. (the student will give the step to How did you compute the mean, compute the mean using the using coded – deviation method? coded – deviation method) Write it in symbol E. Generalization What are the two methods of computing the mean of group The two methods are the long method and the coded- deviation data? method.

How do we compute the mean of grouped data using Long method? Code- deviation method? Very Good! F. Group Activities/Application Now, I will group you into 2 ( Boys’ group and girls group) a. Activity sheet Group I (Boys group) Using the long method find the mean of the given distribution Class interval 85 – 89 80 – 84 75 – 79 70 – 74 65 – 69 60 – 64 i=5




4 9 7 8 12 10 n= 50

Group II (Girls group) Using the coded – deviation method find the mean of the given distribution. Class interval 85 – 89 80 – 84 75 – 79 70 – 74 65 – 69 60 – 64 i=5





4 9 7 8 12 10 n = 50

If your group were done in doing

the activities please go back to your seat. b. Analysis Post your work on the board. Read first the instruction written on the activity sheet

(each group will present their work)

Group I and Group II got the Q1: Examine the answer of your groups same answer what did you notice with your answer? It implies that if you use either the Q2: If they have the answer what does it long method or the coded – implies? deviation method we will get the same result. The more convenient and the Q3: Which do you think is more easier method to use is long convenient to use? Why? method/coded – deviation method Very Good! G. Valuing I feel that I’m belonging to the What do you feel while doing group. your activity with your group mates? I did the Frequency distribution How about your cooperation with table. 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.


Evaluation Using the two methods Long Method and Coded – deviation method find the mean. Test Score of 50 students in Algebra II Class Interval 78 – 83 72 – 77

f 4 9

66 – 71 60 – 65 54 – 59 48 – 53 42 – 47 i=6 V.

7 6 8 10 6 n = 50

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.

SemiDetailed Lesson Plan

“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.


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 ,



, ……….


Values Focus Cooperation and self-discipline


Materials Algebra II (Functional Approach), chart


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? 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.

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

b. ¼, `/7, 1/10, 1.13

d. 1, 1/3, ¼, 1/7

e. -1/7, -1/4, -1, 1/2

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


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, ….

Brief Lesson Plan


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.


Subject Matter Mathematics: Finding the mean of ungrouped data Advanced Algebra, Trigonometry and Statistics (Functional, Approach)


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.


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?

Best Lesson Plan

Unit Title: Sequence and Series Lesson Topic: Geometric Sequence Established Goals (Standard): The student demonstrates understanding

Year Level: Second Year Time Frame: 1 hour Technology Standard: The student applies Microsoft Excel in

of the key concepts and the general or nth understanding term of the geometric sequence. Essential Questions:




involving geometric sequence. 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

Students will know:

common ratio. Students will be able to:

 the characteristics of geometric sequence; and  the next term in the given geometric

 identify and describe geometric sequence; and  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, …

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

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 Height

1 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, 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: Computer, Flashcards, Tennis ball,

During my Final Demonstrati on





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 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 Bilbao, Purita P .et al Curriculum Development is an instructional material in module from which complement the 3 – unit course of the New Teacher Curriculum. It closely approximates the syllables of the CMO 30 s – 2004. Similar to other materials in project write, curriculum development tries to balance theory and practice. Each Module follows a 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.


After graduation I’m going to have a serious review in order to pass the Licensure Examination for Teacher. While waiting for the result of Board Passers I’m going to find way to get a job related to my course. I’m going to help my family I give them the life that I dreamed for them.

If I luckily pass the exam I will be in my teaching career and I will take also my Masters degree when I already have my regular job. After all of that 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.

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. I graduated from Laguna State Polytechnic University, Siniloan, Laguna with a degree of Bachelor of Secondary Education major in Mathematics. I undergone studentteaching 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 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. 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

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. 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.

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