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1. 1. Republic of the Philippines Department of Education DepEd Complex, Meralco Avenue Pasig City K to 12 Curriculum Guide MATHEMATICS (Grade 1) January 31, 2012
2. 2. K TO 12 MATHEMATICS CONCEPTUAL FRAMEWORK Mathematics is one subject that pervades life at any age, in any circumstance. Thus, its value goes beyond the classroom and the school. Mathematics as a school subject, therefore, must be learned comprehensively and with much depth. The twin goals of mathematics in the basic education levels, K-10 are Critical Thinking and Problem Solving. We adopt the definition of critical thinking by Scriven and Paul (1987): Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. On the other hand, we define Problem Solving in mathematics using Polya’s (1945 & 1962) definition: Mathematical problem solving is finding a way around a difficulty, around an obstacle, and finding a solution to a problem that is unknown. These two goals are to be achieved with an organized and rigorous curriculum content, a well-defined set of high-level skills and processes, desirable values and attitudes, and appropriate tools, recognizing as well the different contexts of Filipino learners. There are five content areas in the curriculum, as adopted from the framework prepared by MATHTED & SEI (2010): Numbers and Number Sense, Measurement, Geometry, Patterns and Algebra, and Probability and Statistics. The specific skills and processes to be developed are: Knowing and Understanding; Estimating, Computing and Solving; Visualizing and Modelling; Representing and Communicating; Conjecturing, Reasoning, Proving and Decision-making, and: Applying and Connecting. The following values and attitudes are to be honed as well: Accuracy, Creativity, Objectivity, Perseverance, and Productivity. We recognize that the use of appropriate tools is needed in teaching mathematics. These include: manipulative objects, measuring devices, calculators and computers, Smartphones and tablet PCs, and the Internet. We define context as a locale, situation or set of conditions of Filipino learners that may influence their study and use of mathematics to develop critical thinking and problem solving skills. Contexts refer to beliefs, environment, language and culture that include traditions and practices, and learner’s prior knowledge and experiences. *K to 12 Curriculum Guide – version as of January 31, 2012 2
3. 3. K TO 12 MATHEMATICS The framework is supported by the following underlying learning principles and theories: Experiential and Situated Learning, Reflective Learning, Constructivism, Cooperative Learning and Discovery and Inquiry-based Learning. The mathematics curriculum is grounded in these theories. Experiential learning as advocated by David Kolb is learning that occurs by making sense of direct everyday experiences. Experiential learning theory defines learning as "the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of grasping and transforming experience" (Kolb, 1984, p. 41). Situated learning, theorized by Lave and Wenger, is learning in the same context on which concepts and theories are applied. Reflective learning refers to learning that is facilitated by reflective thinking. It is not enough that learners encounter real-life situations. Deeper learning occurs when learners are able to think about their experiences and process these allowing them the opportunity to make sense and meaning of their experiences. Constructivism is the theory that argues that knowledge is constructed when the learner is able to draw ideas from his own experiences and connects them to new ideas that are encountered. Cooperative Learning puts premium on active learning achieved by working with fellow learners as they all engage in a shared task. The mathematics curriculum allows for students to learn by asking relevant questions and discovering new ideas. Discovery and Inquiry-based learning (Bruner, 1961) support the idea that students learn when they make use of personal experiences to discover facts, relationships and concepts. *K to 12 Curriculum Guide – version as of January 31, 2012 3
4. 4. K TO 12 MATHEMATICS Figure 1. The Conceptual Framework of Mathematics Education *K to 12 Curriculum Guide – version as of January 31, 2012 4
5. 5. K TO 12 MATHEMATICS BRIEF COURSE DESCRIPTION Mathematics from K-10 is a skills subject. By itself, it is all about quantities, shapes and figures, functions, logic and reasoning. Mathematics is also a tool of science and a language complete with its own notations and symbols and “grammar” rules, with which concepts and ideas are effectively expressed. The contents of mathematics include Numbers and Number Sense, Measurement, Geometry, Patterns & Algebra and Statistics and Probability. Numbers and Number Sense as a strand includes concepts of numbers, properties, operations, estimation and their applications. Measurement as a strand includes the use of numbers and measures to describe, understand and compare mathematical and concrete objects. It focuses on attributes such as length, mass and weight, capacity, time, money and temperature among others, as well as applications involving perimeter, area, surface area, volume and angle measure. Geometry as a strand includes properties of two- and three-dimensional figures and their relationships, spatial visualization, reasoning and geometric modeling and proofs. Patterns and Algebra as a strand studies patterns, relationships and changes among shapes and quantities and includes the use of algebraic notations and symbols, equations and most importantly, functions, to represent and analyze relationships. Statistics and Probability as a strand is all about developing skills in collecting and organizing data using charts, tables and graphs, understanding, analyzing and interpreting data, dealing with uncertainty and making predictions and outcomes. The K to 10 Mathematics Curriculum provides a solid foundation for Mathematics at Grades 11 to 12. More importantly, it provides necessary concepts and life skills needed by Filipino learners as they proceed to the next stage in their life as learners and as citizens of our beloved country, the Philippines. *K to 12 Curriculum Guide – version as of January 31, 2012 5
6. 6. K TO 12 MATHEMATICS LEARNING AREA STANDARD: The learner demonstrates understanding and appreciation of key concepts and principles of mathematics as applied, using appropriate technology, in problem solving, communicating, reasoning, making connections, representations, and decisions in real life. KEY STAGE STANDARDS: K–3 4–6 7 – 10 The learner demonstrates understanding. . . The learner demonstrates understanding. . . The learner demonstrates understanding. . . At the end of Grade 3, the learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to ten thousand, fractions, measurement, simple geometric figures, pre-algebra concepts and data representation and analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. At the end of Grade 6, the learner demonstrates understanding and appreciation of key concepts and skills involving rational numbers, measurement, geometric figures, pre-algebra concepts, simple probability and data analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. At the end of grade 10, the learner demonstrates understanding and appreciation of key concepts and skills involving number sense, measurement, algebra, geometry, probability and statistics, and trigonometry as applied, using appropriate technology, in critical thinking, problem solving, communicating, reasoning, making connections, representations, and decisions in real life. *K to 12 Curriculum Guide – version as of January 31, 2012 6
7. 7. K TO 12 MATHEMATICS GRADE LEVEL STANDARDS: Grade Level Grade Level Standards K The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 20, space and measurement, simple geometric figures, pre-algebra concepts and data collection as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in real life. Grade 1 The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 100, fractions, measurement, simple geometric figures, pre-algebra concepts, data collection and representation as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in real life. Grade 2 The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 1 000, fractions, measurement and geometric figures, pre-algebra concepts, data collection, representation and analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in real life. Grade 3 The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 10 000, fractions, measurement, geometric figures, pre-algebra concepts, data collection, representation and analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in real life. Grade 4 The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 100 000, fractions, decimals including money, ratio, angles, plane figures like square, rectangle, and triangle, measurement (perimeter, area of triangle, parallelogram and trapezoids, volume of cubes and rectangular prisms, pre-algebra concepts, data collection, representation and analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. Grade 5 The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 10 000 000, fractions, decimals including money, ratio, percent, geometry (circles and five or more-sided polygons), measurement (circumference, area of circle, volume of cubes and rectangular prisms, temperature) ,pre-algebra concepts, data collection, representation and analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. *K to 12 Curriculum Guide – version as of January 31, 2012 7
8. 8. K TO 12 MATHEMATICS Grade Level Grade Level Standards Grade 6 The learner is expected to have mastered the concepts and operations on whole numbers; demonstrates understanding and appreciation of the key concepts and skills involving fractions, decimals including money, ratio and proportion, percent, rate, integers, geometry (spatial figures), measurement (surface area, volume, meter reading), pre-algebra concepts, data collection, representation and analysis, probability, expressions and equations as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. Grade 7 The learner demonstrates understanding of key concepts and principles of number sense, measurement, algebra, geometry, probability and statistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. Grade 8 The learner demonstrates understanding of key concepts and principles of algebra, geometry, probability and statistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. Grade 9 The learner demonstrates understanding of key concepts and principles of algebra, geometry, and trigonometry as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. Grade10 The learner demonstrates understanding of key concepts and principles of number sense, algebra, geometry, probability and statistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. *K to 12 Curriculum Guide – version as of January 31, 2012 8
9. 9. K TO 12 MATHEMATICS GRADE 1 Content Content Standards Performance Standards Learning Competencies The learner demonstrates understanding of… The learner is able to… The learner…    recognizes cardinal numbers from 0 to 100.  counts and tells the number of objects in a given set by ones and tens.  identifies the number that is one more or one less from a given number.  composes and decomposes a given number.  regroups sets of ones into sets of tens and sets of tens into hundred using objects.  compares two sets using the expressions “fewer than,” “more than,” and “as many as.”  orders sets from least to greatest and viceversa.  counts by 2’s, 5’s and 10’s through 100.  reads and writes numbers up to 100 in symbols and in words.  identifies the place value and finds the value of a digit in a one- and two-digit numbers.   Numbers and Number Sense renames numbers into tens and ones. compares numbers up to 100 using relation symbols. number notation and place value, cardinal and ordinal numbers, and comparing and ordering numbers up to 100. *K to 12 Curriculum Guide – version as of January 31, 2012 explore the concept of cardinal numbers up to 100 and compare these numbers in various contexts. 9
10. 10. K TO 12 MATHEMATICS Content Content Standards The learner demonstrates understanding of… Performance Standards The learner is able to… Learning Competencies The learner …   *K to 12 Curriculum Guide – version as of January 31, 2012  illustrates addition as putting together and subtraction as taking away, comparing and adding up. illustrates the relationship of joining sets to addition of whole numbers. illustrates that addition and subtraction are inverse operations. identifies and constructs equivalent number expressions using addition and subtractions.  illustrate addition and subtraction of whole numbers. determines the position of an object using 1st to 10th from a given point of reference.   identifies the 1st, 2nd, 3rd up to the 10th object in a given set from a given point of reference.  addition and subtraction up to 100. reads and writes ordinal numbers 1st, 2nd, 3rd up to 10th.     explore the concept of ordinal numbers. recognizes coins and bills up to P100 (pesos and centavos).   arranges numbers up to 100 in increasing order and vice versa. identifies and creates patterns to compose and decomposes numbers using addition. 10
12. 12. K TO 12 MATHEMATICS Content Content Standards The learner demonstrates understanding of… Performance Standards The learner is able to… Learning Competencies The learner …  subtracts one to two-digit numbers with minuends up to 99 without regrouping.    visualizes and identifies ½ and ¼ of a whole object.  divides a whole into halves and fourths. divides the elements of a set of objects into two groups of equal quantities to show halves of sets.  *K to 12 Curriculum Guide – version as of January 31, 2012 solves word problems involving subtraction of whole numbers including money with minuends up to 99 with and without regrouping using appropriate problem solving strategy.  visualize, model and represent the concept of halves and fourths using whole objects and sets. mentally subtracts a 1-digit number from 2digit minuends without regrouping.   mentally subtracts 1-digit numbers from minuends up to 18 without regrouping.  the concepts of halves and fourths and applies them in dividing a whole or set equally. subtracts one to two-digit numbers with minuends up to 99 with regrouping.   uses the expanded form to explain subtraction with regrouping. divides the elements of a set of objects into four groups of equal quantities to show fourths of sets. 12
13. 13. K TO 12 MATHEMATICS Content Content Standards The learner demonstrates understanding of… Performance Standards The learner is able to… Learning Competencies The learner…  given half of a region or a set, draws the whole region or set.  identifies, names and describes the four basic shapes in 2- and 3-dimensional objects: square, rectangle, triangle and circle.  compares and classifies 2- and 3dimensional figures according to common attributes.  draws the four basic shapes.  constructs three-dimensional objects using manipulative materials.  identifies and explains simple repeating patterns.  makes patterns of shapes, colors and numbers.  finds the missing number/digit in addition or subtraction problems.  finds and completes patterns of one or two of the following attributes: Shape, Size, Color, Number, Orientation.  determines the next term (figure/number) in a given sequence and give a reason. Geometry  2-D and 3-D shapes through identifying, classifying and constructing figures using cutouts and concrete models.   Patterns and Algebra  simple patterns.   *K to 12 Curriculum Guide – version as of January 31, 2012 explore the properties of 2and 3-dimensional figures. model and represent 2- and 3-dimensional objects. identify and create number and attribute patterns. complete number and attribute patterns. 13
14. 14. K TO 12 MATHEMATICS Content Content Standards Performance Standards The learner demonstrates understanding of… The learner is able to…  Measurement  Learning Competencies The learner …  *K to 12 Curriculum Guide – version as of January 31, 2012   compares objects using the comparative words: Short, shorter, shortest; Long, longer, longest; Tall, taller, tallest; High, higher, highest; Heavy, heavier, heaviest; Light, lighter, lightest. estimates and measures length using nonstandard units of linear measures. estimates and measures mass using nonstandard units of mass/weight measures. shows and finds capacity using nonstandard unit.  collects and organizes data using tallies and tables.  represents data using pictographs without using a scale.  organizing, representing and comparing data using pictographs without scale representations and probability, and explores games and activities. tells the time by an hour, half-hour and quarter-hour.   uses a calendar to determine a day or month.  Statistics and Probability names and tells the number of days in a week; months in a year in the right order.     the concepts of time and measures and compares objects using direct comparison and non-standard units of length, mass and capacity. reads and interprets a pictograph. give different measures of time. estimate and compute for measurements of length, mass and capacity. organize and interpret data. 14
15. 15. K TO 12 MATHEMATICS Content Content Standards Performance Standards Learning Competencies The learner is able to…  *K to 12 Curriculum Guide – version as of January 31, 2012 The learner …  identifies cause and effect relationships.  predicts and records outcome of experiments and chance games. make conjectures about games and activities. 15
16. 16. K TO 12 MATHEMATICS GLOSSARY Accuracy – the quality of being correct and precise. Applying – the skill of using concepts, procedures, algorithms and other mathematical constructs on practical situations and phenomena. Communicating – the use of notations, symbols, figures, equations and functions to convey mathematical ideas. Computing – the skill of calculating using correct algorithms, procedures and tools to arrive at a final exact result. Conjecturing – the skill of formulating mathematical theories that still need to be proven. Connecting – the skill of integrating mathematics to other school subjects and other areas in life. Constructivism – the theory that knowledge is constructed when the learner is able to draw ideas from his/her own experiences and connects them to new ideas that are encountered. Context - a locale, situation or set of conditions of students that may influence their study and use of mathematics to develop critical thinking and problem solving skills. Cooperative Learning - learning that is achieved by working with fellow learners as they all engage in a shared task. Creativity – the skill of using available procedures in Mathematics and non-conventional methods to solve a problem and produce answers. Critical Thinking - the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action (Scriven & Paul, 1987). Decision-making – the skill of arriving at a choice or decision based on sound, logical procedures and mathematical analyses. Discovery Learning – learning that is achieved by allowing students to discover new ideas using their experiences (Bruner, 1961). *K to 12 Curriculum Guide – version as of January 31, 2012 16
17. 17. K TO 12 MATHEMATICS Estimating – the skill of roughly calculating or judging a numerical value or quantity. Experiential Learning – learning that occurs by making sense of direct everyday experiences (Kolb, 1984) Inquiry-based Learning – learning that focuses on students asking questions and finding answers to their questions using their personal experiences. Knowing and Understanding – meaningful acquisition of concepts that include memorizing and recalling of facts and procedures Mathematical Problem Solving - finding a solution to a problem that is unknown (Polya, 1945 & 1962). Modeling – the use of functions and graphs to represent relationships between and among quantities in a phenomenon. Objectivity – the quality of judging, evaluating and making decisions based on mathematical facts and results without being influenced by subjective conditions. Perseverance – firmness in finishing a task despite difficulties and obstacles. Productivity – the quality of pursuing an activity to arrive at a meaningful and useful result or product. Proving – the skill of demonstrating the truth or falsity of a theory using reasoning and arguments. Reasoning – the process of explaining using sound analyses, following the rules of logic. Reflective Learning – learning that is facilitated by deep thinking. Representing – the use of figures and shapes, variables, equations and functions to concretize and illustrate quantities and their relationships. Situated Learning – learning in the same context on which concepts and theories are applied. Solving – to find the answer to an algebraic or mathematical problem using any procedures and tools available. Visualizing - using one’s creativity and imagination to produce images, pictures and other means to represent and understand mathematical concepts (MATHTED & SEI, 2010). *K to 12 Curriculum Guide – version as of January 31, 2012 17
18. 18. K TO 12 MATHEMATICS References Bruner, J. S. (1961). "The act of discovery". Harvard Educational Review 31 (1): 21–32. Chamberlin, S. A. (n.d.) What is problem solving in the mathematics classroom. Retrieved July 19, 2011, from http://74.125.153.132/search?q=cache:TKX2hdSKJ- gJ:people.exeter.ac.uk/PErnest/pome23/Chamberlin%2520What%2520is% 2520Math%2520Prob%2520Solving.doc+mathematical+Problem+Solving+ definition&cd=10&hl=tl&ct=clnk&gl=ph. Kolb, D. A. (1984). Experiential learning: Experience as the source of learning and development. New Jersey: Prentice-Hall. MATHTED & SEI. (2010). Mathematics framework for Philippine basic education. Manila: SEI & MATHTED. Polya, G. (1945). How to Solve It. Princeton, NJ: Princeton University Press. Polya, G. (1962). Mathematical discovery: On understanding, learning and teaching problem solving: Volume I. New York: John Wiley and Sons, Inc. http://www.criticalthinking.org/aboutct/define_critical_thinking.cfm *K to 12 Curriculum Guide – version as of January 31, 2012 18
19. 19. K TO 12 MATHEMATICS CURRICULUM DEVELOPERS/WRITERS/REACTORS/REVIEWERS in the DEVELOPMENT of K to 12 CURRICULUM -MATHEMATICS A. Workshop on the Finalization of Learning Competencies Venue: Development Academy of the Philippines,Tagaytay City Date: August 8-12, 2011 NAME 1. Remylinda Soriano 2. Teresita Tagulao 3. Robesa Hilario 4. Elizabeth Catao 5. Sonia Javier 6. Melvin Callanta 7. Nicanor San Gabriel Jr. 8. Dr. Maxima Acelajado 9. Dr. Catherine Vistro – Yu 10. Lydia Landrito 11. Dr. Florante C. Marmeto DESIGNATION Education Program Specialist I Education Program Specialist I Education Program Specialist Education Program Specialist Head Teacher III Head Teacher VI Teacher I Professor Professor I Science Education Specialist Principal IV OFFICE/SCHOOL DCS - Manila DCS - Pasig DepEd – BEE – CDD DepEd – BSE – CDD JSHS Mangaldan High School Araullo High School De La Salle University Ateneo De Manila University University of the Philippines - NISMED Sucat Elementary School B. Workshop on the Development of Learning Competencies and Teaching Guides Venue: Development Academy of the Philippines,Tagaytay City Date: July 18-22, 2011 1. 2. 3. 4. NAME Teresita P. Tagulao Remylinda T. Soriano Melvin Calanta Nicanor M. San Gabriel Jr. *K to 12 Curriculum Guide – version as of January 31, 2012 DESIGNATION OFFICE/SCHOOL D.O. Pasig City D.O. Manila Mangaldan High School Araullo High School 19
20. 20. K TO 12 MATHEMATICS 5. Maxima J. Acelajado 6. Elizabeth Catao 7. Sonia E. Javier 8. Catherine P. Vistro - Yu 9. Robesa Hilario 10. Thomas Manuel L. Quiton DLSU BSE JSHS Ateneo de Manila BEE - CDD BEE C. Workshop on the Development of Learning Competencies Grades K to 3 Venue: Development Academy of the Philippines,Tagaytay City Date: July 11-15, 2011 1. 2. 3. 4. 5. NAME Teresita P. Tagulao Remylinda T. Soriano Robesa Hilario Abelardo B. Medes Thomas Manuel L. Quiton DESIGNATION OFFICE/SCHOOL D.O. Pasig City D.O. Manila BEE - CDD BEE – CDD BEE D. Experts’ Review of the Curriculum Standards Venue: Bulwagan ng Karunungan, DepEd Complex, Pasig City Date: July 15, 2011 1. 2. 3. 4. 5. 6. 7. 8. NAME Dr. Evangeline P. Bautista Mr. Melvin M. Callanta Ms. Elizabeth G. Catao Sr. Iluminada C. Coronel Dr. Rosemarievic V. Diaz Ms. Janet D. Dionio Dr. Ruth G. de Lara Mr. Emmanuel V. Dionisio *K to 12 Curriculum Guide – version as of January 31, 2012 DESIGNATION Associate Professor President Retired Education Supervisor Head Teacher III OFFICE/SCHOOL Ateneo de Manila University DepEd BSE DepEd BSE Mathematics Teachers Assoc. of the Phils. Philippine Normal University Manuel Roxas High School DCS Manila A.F.G. Bernardino Memorial Trade School 20
21. 21. K TO 12 MATHEMATICS 9. Dr. Juanita A. Ferido 10. Dr. Flordeliza F. Francisco 11. Dr. Ian June L. Garces 12. Dr. Milagros D. Ibe 13. Dr. Sonia E. Javier 14. Dr. Ma. Nympha B. Joaquin 15. Ms. Lydia M. Landrito 16. Dr. Queena N. Lee-Chua 17. Dr. Auxencia A. Limjap 18. Dr. Gladys C. Nivera 19. Mr. Nicanor M. San Gabriel Jr. 20. Ms. Revie G. Santos 21. Dr. Cornelia C. Soto 22. Dr. Merle C. Tan 23. Dr. Soledad A. Ulep 24. Dr. Catherine P. Vistro-Yu 25. Dr. Aida A. Yap Education Supervisor II Assistant Professor Associate Professor DepEd NCR Ateneo de Manila University Ateneo de Manila University UP Diliman and Miriam College Juan Sumulong High School UP Diliman UP NISMED Ateneo de Manila University De La Salle University Philippine Normal University DepEd BSE-CDD Rizal High School Ateneo de Manila University UP NISMED UP NISMED Ateneo de Manila University UP NISMED Science Education Specialist Professor Professor I Master Teacher II Director Professor E. Writeshop on the Finalization of the Curriculum Standards Venue: Regional Education Learning Center, Region IV-A (CALABARZON), Malvar, Batangas Date: May 19-21,2011 1. 2. 3. 4. 5. 6. 7. NAME Dr. Ian June L. Garces Dr. Gladys C. Nivera Dr. Ruth G. de Lara Lydia M. Landrito Remylinda T. Soriano Revie G. Santos Emmanuel V. Dionisio *K to 12 Curriculum Guide – version as of January 31, 2012 DESIGNATION Associate Professor Professor I Retired Education Supervisor Science Education Specialist Education Program Supervisor I Master Teacher II Head Teacher III/ Documentor OFFICE/SCHOOL Ateneo de Manila University Philippine Normal University DCS Manila University of the Philippines DCS Manila Rizal High School A.F.G. Bernardino Memorial Trade School 21
22. 22. K TO 12 MATHEMATICS F. Workshop on the Review and Refinement of the K to 12 Curriculum Framework and Standards Venue: Development Academy of the Philippines,Tagaytay City Date: May 10-13,2011 NAME 6. Dr. Ian June L. Garces 7. Dr. Gladys C. Nivera 8. Dr. Ruth G. de Lara 9. Nicanor M. San Gabriel 10. Elizabeth Catao 11. Abelardo B. Medes 12. Robesa R. Hilario 13. Revie G. Santos 14. Emmanuel V. Dionisio DESIGNATION Associate Professor Professor I Retired Education Supervisor Master Teacher II Head Teacher III/ Documentor OFFICE/SCHOOL Ateneo de Manila University Philippine Normal University DCS Manila BSE – CDD BSE – CDD BEE – CDD BEE – CDD Rizal High School A.F.G. Bernardino Memorial Trade School G. Consultative Workshops for the Validation of the K to 12 Curriculum Framework and Standards 1. Regions IV-A, IV-B,V and NCR Venue: BulwaganngKarunungan, DepEd Complex, Meralco Avenue, Pasig City Date: April 27, 2011 1. 2. 3. 4. 5. 6. 7. 8. 9. NAME Maria Gregoria P. Malihan Loreto S. Sauz Arnold G. Gerance Cheryl G. Pauericio Abella A. Amican Arnulfo G. Mariano Sr. Iluminada C. Coronel Revie G. Santos Juanita A. Ferido *K to 12 Curriculum Guide – version as of January 31, 2012 DESIGNATION OFFICE/SCHOOL St. Jude Catholic School UST – EHS AurolioArago, Oriental Mindoro Division of Legazpi City Niogan Elementary School Division of Valenzuela City MTAP Rizal High School Dep. Ed. NCR 22
23. 23. K TO 12 MATHEMATICS 10. Larry Samala 11. Ian June L. Garces Dep. Ed. R-IVB Ateneo de Manila University 2. Regions I,II,III and CAR Venue: Teachers’Camp, Baguio City Date: April 29, 2011 NAME 1. Carmelita S. Domantay DESIGNATION 2. Rubielyn L. Babaran 3. Romel L. Ricardo 4. Janette T. Fermin 5. Nestor A. Paat 6. Nestor G. Villaflor 7. Nestor P. Nuesca ESP II ESP I ESP II 8. Janice Q. Nonog Teacher II 9. Ofelia A. Dolo 10. Jenny Jesusa J. Catubay Master Teacher II Master Teacher II 11. Arnel R. Lumbo 12. Susana E. Vanhoutte 13. Norma Maria P. Rutab 14. Daniel D. Peredo Dept. Head 15. Lauro C. Cruz Dept. Head *K to 12 Curriculum Guide – version as of January 31, 2012 OFFICE/SCHOOL Dagupan City NHS – Dagupan City Enrile North Central School – Enrile, Cagayan Regional Science High School Tumauini, Isabela St. Paul University Philippines Tugeugarao City DepEdTugeugarao City DepEd – Div. Office, Ilocos Sur DepEd RO III Tabuk c/s, Dagupan West, Tabuk City, Kalinga La Trinidad, Benquet, CAR Sta. Maria Elem. School University of the Cordilleras – Grade School Baguio City SLU – Lab. High School University of the Cordilleras Baguio City Benguet NHS, La Trinidad, Benquet Sacred Heart Academy Poblacion, Sta. Maria, Bulacan 23
24. 24. K TO 12 MATHEMATICS 3. Regions VI, VII and VIII Venue: Ecotech Center, Lahug, Cebu City Date: May 4, 2011 NAME 1. Rosemary S. Achacoso 2. Feliciaro C. Buenate Jr. DESIGNATION Education Program Supervisor Education Program Supervisor 3. Rufa T. Temblor 4. Ma. Emilie S. Gepison 5. Jose Leover S. Illut 6. Ann Marie C. Bandola 7. Jeremy M. Movilla 8. Romao D. Castante 9. Suzette C. Martinez 10. Andreo G. Aba 11. Cesar L. Sanchez 12. Adonis A. Torres 13. Lita B. Morales *K to 12 Curriculum Guide – version as of January 31, 2012 EPS – I Math OFFICE/SCHOOL Maasin City Division – Region VIII RO VI – Western Visayas St. Francis of Assisi School Lahug, Cebu City. Region VII Leon Elem. School Division of Iloilo, Region VI San Roque Child Dev’t School YatiIliloan, Cebu – Region VII City of Naga Division, Region VII Ormoc City Central School Ormoc City Division, Region VIII Calbayog City NHS Calbayog City Division – RO VIII Inocencio V FerrerMem. School of Fisheries Talisay City, Neg. Occ., Div. of Neg. Occ. Guihulangan National Agricultural School Plagatasanon, Guihulangan City, Neg. Or. Div. of Guih. City University of San Jose Recoletos BasakPardo, Cebu City Tanjay City Science High School Tanjay City Schools Division – Region VII Don Carlos Ledesma NHS San Carlos City, Neg. Occ. – Region VI 24
25. 25. K TO 12 MATHEMATICS 4. Regions IX,X and ARMM Venue: Regional Education Learning Center, Cagayan de Oro City Date: May 5, 2011 NAME 1. Susan P. Kuyong 2. Arnel L. Agaug 3. Rudilene D. Cael 4. Evelyn T. Villa 5. Ma. Theresa B. Miranda 6. Noelli B. Yap 7. Reymundo B. Gimena 8. Gilda L. Taboclaon 9. Rogelio J. Bahian 10. Maria Conchita P. Bas 11. Editha J. Amper 12. Rhodora S. Amantorno 13. Reymundo B. Gimena 14. Rosalina V. Eviota 15. Arnold C. Solen 16. Noelli B. Yap DESIGNATION OFFICE/SCHOOL DepEd Sulu II DepEd DepEd DepEd DepEd The Abba’s Orchard School DepEd – Dinagat Division Dep. Ed Dep. Ed. R – X CUBED Corpus Christi School OLLES Dep. Ed. Dinagat Island Dep. Ed. Dinagat Island Dep. Ed. Agusan del Norte The Abba’s Orchard 5. Regions XI,XII, ARMM (ShariffKabunsuan,Maguindanao) Venue: Regional Education Learning Center, Davao City and CARAGA Date: May 6,2011 NAME 1. Reynante A. Solitario 2. Araceu J. Dinopol 3. Junelo C. Fornolles *K to 12 Curriculum Guide – version as of January 31, 2012 DESIGNATION OFFICE/SCHOOL DepEd ROXI, EPS DepEdSarangani Division Region XII Samal NHS – Ibalos Region XI 25
26. 26. K TO 12 MATHEMATICS 4. Agnes B. Ortega, RN 5. Aida M. Pescado Cotabato City Region XII MAG. I Davao Christian Learning Center, Davao City Bureau of Elementary Education DepEd – ARMM RO Polomolok West District Division of South Cotobato EPS – Math Division of Davao del Norte Region XI Sultan Kudarat Division DepEd ROXII – EPS 6. Nempha F. Gonzales 7. Abdul – Aziz H. Iya 8. Levi B. Butihen 9. Eduard C. Amoguis 10. Genelyn H. Morante 11. Glenn A. Bisnan H. Workshop on the K to 12 Curriculum Mapping Venue: Development Academy of the Philippines, Tagaytay City Date: March 16-18, 2011 NAME 1. Abelardo Medes 2. RobesaHilario 3. ForcefinaFrias 4. RanteMamerto 5. Elizabeth Catao 6. Melvin Callanta 7. Sonia Javier 8. Dr. Maxima Acelajado 9. Dr. Ruth Lara 10. Ms. Lydia Ladrito 11. Dr. Carmela Oracion 12. Dr. Ronald San Jose 13. Jannet Labu *K to 12 Curriculum Guide – version as of January 31, 2012 DESIGNATION OFFICE/SCHOOL SDD – BEE CDD – BEE CDD – BEE Division of Muntinlupa CDD – BSE Mangaldan NHS – Pangasinan Division of Quezon City Dela Salle University – Taft World Bank Consultant – TUP Retired Professor UP – NISMED Ateneo de Manila Univ UP College of Edu (UPIS) CDD – BEE 26
27. 27. K TO 12 MATHEMATICS SECRETARIAT NAME DESIGNATION DepEd DepEd BAHS – DepEd Support Staff AFGBMTS – DepEd Support Staff DAP DAP DAP DAP DAP DAP Accountant, DepEd Accountant, DepEd Accountant, DepEd Accountant, DepEd Disbursing Officer, DepEd 1. Rachelle C. Fermin 2. Prescy Ong 3. Frederick G. Del Rosario 4. Emmanuel V. Dionisio 5. Magdalena Mendoza 6. Tristan Suratos 7. Kimberly Pobre 8. Cristina Villasenor 9. Lani Garnace 10. Kidjie Saguin 11. Maria Boncan 12. Daylinda Guevarra 13. Fenerosa Maur 14. Divina Tomelden 15. Nilva Jimenez FACILITATORS/SUPPORT TEAM NAME 1. 2. 3. 4. 5. 6. DESIGNATION CDD – BEE CDD – BSE CDD – BSE SPED – BEE CDD – BEE SDD – BEE Irene C. De Robles Jose Tuguinayo, Jr. Marivic Abcede Mirla Olores Simeona Ebol Fe Villalino ADVISORY TEAM *K to 12 Curriculum Guide – version as of January 31, 2012 27
28. 28. K TO 12 MATHEMATICS 1. 2. 3. 4. 5. 6. 7. 8. NAME Usec. Yolanda S. Quijano Dr. Lolita Andrada Dr. Angelita Esdicul Dr. Ricardo de Lumen Dr. Paraluman R. Giron Dr. Avelina T. Llagas Dr. Dina Ocampo Dr. Ester B. Ogena 9. Dr. Brenda B. Corpuz 10. Dr. Dennis Faustino 11. Dr. Merle Tan 12. Dr. Cristina Padolina 13. Mr. Napoleon Imperial 14. Diane Decker 15. Dr. Nelia Benito 16. Dr. Socorro Pilor 17. Dr. Beatriz Torno 18. Dr. Carolina Guerrero 19. Dr. Irene Isaac 20. Dr. Imelda Taganas *K to 12 Curriculum Guide – version as of January 31, 2012 DESIGNATION Undersecretary, DepEd OSEC Director, BSE – DepEd, Pasig Director, BEE – DepEd, Pasig OIC, Director III – Tech Voc, DepEd Chair, K – 10 TWG Consultant, TEC, DepEd Dean, COE, UP Diliman President, PNU Technical Adviser to the Office of USEC, Pograms and Standards Headmaster, SMS Sagada, Mt. Prov. Director, UP – NISMED President, CEU CHED Consultant, MTB – MLE Director, NETRC Director, IMCS Executive Director, TEC Director, BALS Director, TESDA Director, TESDA 28