Republic of the Philippines Department of Education DepEd Complex, Meralco Avenue Pasig City
K to 12 Curriculum Guide
MATHEMATICS (Grade 7)
January 31, 2012
K TO 12 MATHEMATICS
CONCEPTUAL FRAMEWORK
Mathematics is one subject that pervades life at any age, in any any circumstance. Thus, its value goes beyond 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 t o 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 diff erent 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 S tatistics. 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 I nternet. 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 pri or knowledge and experiences.
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 MATHEMATICS
Figure 1. The Conceptual Framework of Mathematics Education
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. Sense, Measurement, Measurement, Geometry, Geometry, Patterns & Algebra and Statistics and Probability. Probability. The contents of mathematics include Numbers and Number Sense, 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 Curriculum provides a solid solid foundation for Mathematics at Grades 11 11 to 12. More importantly, it provides necessary 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 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, technology, in critical thinking, problem solving, communicating, reasoning, making connections, representations, and decisions in real life.
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 an d measurement, simple geometric figures, pre-algebra concepts concepts and data collection as applied, using appropriate technology, 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, fract ions, 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, frac tions, 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 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, m easurement (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 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 MATHEMATICS
Grade Level
Grade Level Standards
Grade 6
The learner is expected to have mastered the concepts concepts and operations on whole numbers; demonstrates 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 equations as applied, using appropriate technology, in critical thinking, 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 MATHEMATICS
GRADE 7 Content Numbers and Number Sense
Content Standards The learner demonstrates understanding of…
Performance Standards The learner is able to…
the key concepts of sets, the real number system, estimation / approximation of a square of a number and the measures of quantities, and the applications of real numbers to measurements.
explore set concepts and set operations.
Learning Competencies The learner…
apply various procedures and manipulations on the different subsets of the set of real numbers.
describes and illustrates well-defined sets, subsets, universal set and the null set. defines and describes the union and intersection of sets and the complement of a set. uses Venn Diagrams to represent sets, subsets and set operations. solves problems involving sets.
describes and illustrates the absolute value of a number on a number line as the distance of the number from 0. performs fundamental operations on integers: addition, subtraction, multiplication, division. states and illustrates the different properties of the operations on integers (commutative, associative, distributive, identity, inverse). defines and illustrates rational numbers and arrange them on a number line.
K TO 12 MATHEMATICS
Content
Content Standards The learner demonstrates f… understanding o f…
Performance Standards The learner is able to…
Learning Competencies The learner …
expresses rational numbers (both repeating and terminating/non-repeating and nonterminating) from fraction form to decimal form and vice versa. performs operations on rational numbers and illustrate their properties. describes principal roots and tells whether they are rational or irrational. determines between what two integers the square root of a number is. estimates the square root of a number t o the nearest tenth. illustrates and graphs irrational numbers (square roots) on a number line with and without appropriate technology. describes, represents and compares the different subsets of real numbers. finds the union, intersection and complement of the set of real numbers and its subsets. arranges real numbers in increasing or decreasing order. determines the significant digits in a given situation.
K TO 12 MATHEMATICS
Content
Content Standards The learner demonstrates understanding of…
Performance Standards The learner is able to…
Learning Competencies The learner …
Measurement
the different types of measures.
extend concepts of measurements to include different types of measures and all the subsets of the set of real numbers to solve measurement problems.
writes very large or very small numbers in scientific notation. describes and represents real-life situations which involve integers, rational numbers, square roots of a rational numbers and irrational numbers.
solves problems involving real numbers.
describes what it means to measure.
describes the development of measurement from the primitive to the present international system of units. estimates or approximates the measures of quantities particularly length, weight/mass, volume, time, angle and temperature. uses appropriate instruments to measure quantities such as length, weight/mass, volume, time, angle and temperature. converts measurements from one unit to another for each type of measurement including the English system. solves problems involving measurements such as perimeter, area, weight, time, speed, temperature, volume/capacity and utilities usage (meter reading).
K TO 12 MATHEMATICS
Content Algebra
Content Standards The learner demonstrates understanding of…
Performance Standards The learner is able to…
the key concepts of algebraic expressions as applied in solving problems.
simplify and evaluate algebraic expressions in one or more variables.
Learning Competencies The learner …
explore the concept of and manipulate polynomials.
translates verbal phrases to mathematical phrases and vice versa. differentiates between constants and variables in a given algebraic expression. evaluates algebraic expressions for given values of the variables. gives examples of polynomials, monomial, binomial, trinomial. identifies the base, coefficient, terms and exponents in a given polynomial. defines and interprets the meaning of an where n is a positive integer. derives inductively the laws of exponents (Exponents restricted to positive integers).
illustrates the laws of exponents.
adds and subtracts polynomials.
multiplies and divides polynomials.
finds inductively using models the (a) product of two binomials; (b) product of a sum and difference of two terms; (c) square of a binomial; (d) cube of a binomial; (e) product of a binomial and a trinomial.
K TO 12 MATHEMATICS
Content
Content Standards The learner demonstrates understanding of…
Performance Standards The learner is able to…
Learning Competencies The learner …
solve equations and inequalities.
finds algebraically the (a) product of two binomials; (b) product of a sum and difference of two terms; (c) square of a binomial; (d) cube of a binomial; (e) product of a binomial and a trinomial.
differentiates between mathematical expressions and mathematical equations. translates English sentences to mathematical sentences and vice versa. differentiates between equations and inequalities. defines and illustrates illustrates the meaning of absolute value. finds the solution of an equation or inequality involving one variable, including one that involves absolute value (a) from a given replacement; (b) intuitively by guess and check; (c) by algebraic procedures (applying the properties of equalities and inequalities); (d) graphing. solves problems that use equations and inequalities.
K TO 12 MATHEMATICS
Content Geometry
Content Standards The learner demonstrates understanding of…
Performance Standards The learner is able to…
the key concepts of geometry of shapes and sizes, geometric construction and the application of measurements in geometric figures.
analyze and investigate in a more formal environment the basic concepts in geometry.
Learning Competencies The learner …
analyze and investigate the different kinds of triangles, quadrilaterals, convex polygons and circles.
represents a point, line and plane using concrete and pictorial models. defines, identifies and names the subsets of a line. illustrates, names, identifies and defines the different kinds of angles. derives relationships of geometric figures using measurements and by inductive reasoning: supplementary angles, complementary angles, equal angles, adjacent angles, linear pairs, perpendicular lines and parallel lines. derives relationships between vertical angles and among angles formed by parallel lines cut by a transversal using measurement and by inductive reasoning.
uses a compass and straightedge to bisect line segments and angles and construct perpendiculars and parallels. classifies triangles according to their angles and according to their sides. illustrates, names and identifies different kinds of triangles and define the terms associated with a triangle.
K TO 12 MATHEMATICS
Content
Content Standards The learner demonstrates understanding of…
Performance Standards The learner is able to…
Learning Competencies The learner …
Statistics and Probability
the key concepts, uses and importance of statistics and probability, data collection/gathering and the different forms of data representation.
engage in statistical investigations.
derives relationships among the sides and angles of a triangle using measurement and inductive reasoning. illustrates, names and identifies the different kinds of quadrilaterals. derives relationships among the angles and among the sides of a quadrilateral using measurement and inductive reasoning. defines and illustrates convex polygons. derives the relationship of exterior and interior angles of any convex polygon using measurement and inductive reasoning. illustrates a circle and defines the terms related to it: radius, diameter, center, arc and central angle.
explains the basic concepts, uses and importance of Statistics. poses questions and problems that may be answered using Statistics. collects or gathers statistical data and organizes the data in a frequency table according to some systematic considerations.
K TO 12 MATHEMATICS
Content
Content Standards
Performance Standards The learner is able to…
Learning Competencies The learner …
uses appropriate graphs to represent organized data: pie chart, bar graph, line graph and a histogram. finds the mean, median and mode of statistical data. describes the data using information from the mean, median and mode. analyzes, interprets accurately and draws conclusions from graphic and tabular presentations of statistical data.
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. – the use of notations, symbols, figures, equations and functions to convey mathematical ideas. Communicating –
Computing – – the skill of calculating using correct algorithms, procedures and tools to arrive at a final exact result. – the skill of formulating mathematical theories that still need to be proven. Conjecturing –
Connecting – – the skill of integrating mathematics to ot her school subjects and other areas in life. – the theory that knowledge is constructed when the learner is able to draw ideas from his/her own experiences and connects them to new Constructivism – ideas that are encountered.
Context 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 - 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 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 g uide 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). Estimating – – the skill of roughly calculating or judging a numerical value or quantity.
K TO 12 MATHEMATICS
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 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 am ong 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. – firmness in finishing a task despite diff iculties and obstacles. Perseverance –
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 f alsity 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 Visualizing - using one’s creativity and imagination to produce images, pictures and other means to represent and understand mathematical c oncepts (MATHTED & SEI, 2010).
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 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%252 gJ:people.exeter.ac.uk/PErnest/pome23/Chamberlin%2520What%2520is% 0What%2520is% 2520Math%2520Prob%2520Solving.doc+mathematical+Problem+Solving+ 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 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 S olve It. Princeton, NJ: Princeton University Press. Polya, G. (1962). Mathematical discovery: On understanding, learning and teaching problem solving: Volume I. New York: John W iley and Sons, Inc. http://www.criticalthinking.org/aboutct/define_critical_thinking.cfm
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 Competencies Venue: Development Academy of the Philippines,Tagaytay City Date: August 8-12, 2011 NAME 1. 2. 3. 4.
Remylinda Soriano Teresita Tagulao Robesa Hilario Elizabeth Catao
5. 6. 7. 8.
Sonia Javier Melvin Callanta Nicanor San Gabriel Jr. Dr. Maxima Acelajado 9. Dr. Catherine Vistro – Yu 10. Lydia Landrito 11. Dr. Florante C. Marmeto
DESIGNATION
OFFICE/SCHOOL
Education Program Specialist I Education Program Specialist I Education Program Specialist Education Program Specialist
DCS - Manila DCS - Pasig DepEd – BEE – CDD DepEd – BSE – CDD
Head Teacher III Head Teacher VI Teacher I Professor
JSHS Mangaldan High School Araullo High School De La Salle University
Professor I Science Education Specialist Principal IV
Ateneo De Manila University University of the Philippines - NISMED Sucat Elementary School
B. Workshop on the Development of Learning Competencies and Teaching Teaching Guides Venue: Development Academy of the Philippines,Tagaytay City Date: July 18-22, 2011
NAME 1. Teresita P. Tagulao 2. Remylinda T. Soriano 3. Melvin Calanta 4. Nicanor M. San Gabriel Jr. 5. Maxima J. Acelajado
DESIGNATION
OFFICE/SCHOOL D.O. Pasig City D.O. Manila Mangaldan High School Araullo High School DLSU
K TO 12 MATHEMATICS
6. 7. 8. 9.
Elizabeth Catao Sonia E. Javier Catherine P. Vistro - Yu Robesa Hilario
BSE JSHS Ateneo de Manila BEE - CDD
10. Thomas Manuel L. Quiton
BEE
C. Workshop on the the Development of Learning Competencies Grades K to 3 Venue: Development Academy of the Philippines,Tagaytay City Date: July 11-15, 2011 NAME 1. 2. 3. 4.
DESIGNATION
OFFICE/SCHOOL
Teresita P. Tagulao Remylinda T. Soriano Robesa Hilario Abelardo B. Medes
D.O. Pasig City D.O. Manila BEE - CDD BEE – CDD
5. Thomas Manuel L. Quiton
BEE
D. Experts’ Review of the Curriculum Standards Venue: Bulwagan ng ng Karunungan, Karunungan, DepEd Complex, Pasig City City Date: July 15, 2011 NAME 1. Dr. Evangeline P. Bautista
DESIGNATION
OFFICE/SCHOOL
Associate Professor
Ateneo de Manila University
2. Mr. Melvin M. Callanta 3. Ms. Elizabeth G. Catao 4. 5. 6. 7.
Sr. Iluminada C. Coronel Dr. Rosemarievic V. Diaz Ms. Janet D. Dionio Dr. Ruth G. de Lara
8. Mr. Emmanuel V. Dionisio 9. Dr. Juanita A. Ferido
DepEd BSE DepEd BSE President
Retired Education Supervisor
Mathematics Teachers Assoc. of the Phils. Philippine Normal University Manuel Roxas High School DCS Manila
Head Teacher III Education Supervisor II
A.F.G. Bernardino Memorial Trade School DepEd NCR
K TO 12 MATHEMATICS
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
Assistant Professor Associate Professor
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
Science Education Specialist Professor Professor I
Philippine Normal University DepEd BSE-CDD Rizal High School Ateneo de Manila University UP NISMED UP NISMED
Master Teacher II Director Professor
Ateneo de Manila University UP NISMED
E. Writeshop on the Finalization of the Curriculum Standards Venue: Regional Education Learning Center, Center, Region IV-A (CALABARZON), Malvar, Malvar, Batangas Date: May 19-21,2011 NAME 1. Dr. Ian June L. Garces 2. 3. 4. 5. 6. 7.
Dr. Gladys C. Nivera Dr. Ruth G. de Lara Lydia M. Landrito Remylinda T. Soriano Revie G. Santos Emmanuel V. Dionisio
DESIGNATION
OFFICE/SCHOOL
Associate Professor
Ateneo de Manila University
Professor I Retired Education Supervisor Science Education Specialist Education Program Supervisor I Master Teacher II Head Teacher III/ Documentor
Philippine Normal University DCS Manila University of the Philippines DCS Manila Rizal High School A.F.G. Bernardino Memorial Trade School
K TO 12 MATHEMATICS
F. Workshop on the Review and Refinement Refinement of the K to 12 Curriculum Framework and Standards Venue: Development Academy of the Philippines,Tagaytay City Date: May 10-13,2011 NAME
DESIGNATION
OFFICE/SCHOOL
6. Dr. Ian June L. Garces 7. Dr. Gladys C. Nivera
Associate Professor Professor I
Ateneo de Manila University Philippine Normal University
8. Dr. Ruth G. de Lara 9. Nicanor M. San Gabriel 10. Elizabeth Catao 11. Abelardo B. Medes
Retired Education Supervisor
DCS Manila BSE – CDD
12. Robesa R. Hilario 13. Revie G. Santos 14. Emmanuel V. Dionisio
Master Teacher II
BSE – CDD BEE – CDD BEE – CDD Rizal High School
Head Teacher III/ Documentor
A.F.G. Bernardino Memorial Trade School
G. Consultative Workshops for the Validation Validation of the K to 12 Curriculum Curriculum Framework and Standards 1. Regions IV-A, IV-B,V and NCR Venue: BulwaganngKarunungan, DepEd Complex, Complex, Meralco Avenue, Pasig City Date: April 27, 2011 NAME 1. Maria Gregoria P. Malihan 2. Loreto S. Sauz 3. Arnold G. Gerance 4. 5. 6. 7. 8. 9.
Cheryl G. Pauericio Abella A. Amican Arnulfo G. Mariano Sr. Iluminada C. Coronel Revie G. Santos Juanita A. Ferido
10. Larry Samala
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 Dep. Ed. R-IVB
K TO 12 MATHEMATICS
11. Ian June L. Garces
Ateneo de Manila University
2. Regions I,II,III and CAR Venue: Teachers’Camp, Baguio City Date: April 29, 2011 NAME
DESIGNATION
1. Carmelita S. Domantay 2. Rubielyn L. Babaran 3. Romel L. Ricardo 4. Janette T. Fermin 5. Nestor A. Paat
ESP II
6. Nestor G. Villaflor 7. Nestor P. Nuesca
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
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
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
OFFICE/SCHOOL
Education Program Supervisor Education Program Supervisor
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
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
EPS – I Math
K TO 12 MATHEMATICS
4. Regions IX,X and and ARMM Venue: Regional Education Education Learning Center, Cagayan Cagayan de Oro City Date: May 5, 2011 NAME
DESIGNATION
1. Susan P. Kuyong 2. Arnel L. Agaug 3. 4. 5. 6.
OFFICE/SCHOOL DepEd Sulu II DepEd
Rudilene D. Cael Evelyn T. Villa Ma. Theresa B. Miranda Noelli B. Yap
DepEd DepEd DepEd The Abba’s Orchard School DepEd – Dinagat Division Dep. Ed
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
Dep. Ed. R – X CUBED Corpus Christi School OLLES
13. Reymundo B. Gimena 14. Rosalina V. Eviota 15. Arnold C. Solen 16. Noelli B. Yap
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 Education Learning Center, Davao Davao City and CARAGA Date: May 6,2011 NAME
DESIGNATION
OFFICE/SCHOOL
1. Reynante A. Solitario
DepEd ROXI, EPS
2. Araceu J. Dinopol 3. Junelo C. Fornolles 4. Agnes B. Ortega, RN
DepEdSarangani Division Region XII Samal NHS – Ibalos Region XI Cotabato City Region XII
K TO 12 MATHEMATICS
5. Aida M. Pescado
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 Tagaytay City Date: March 16-18, 2011 NAME 1. 2. 3. 4.
Abelardo Medes RobesaHilario ForcefinaFrias RanteMamerto
5. 6. 7. 8.
Elizabeth Catao Melvin Callanta Sonia Javier Dr. Maxima Acelajado
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
9. Dr. Ruth Lara 10. Ms. Lydia Ladrito 11. Dr. Carmela Oracion 12. Dr. Ronald San Jose 13. Jannet Labu
Ateneo de Manila Univ UP College of Edu (UPIS) CDD – BEE SECRETARIAT
K TO 12 MATHEMATICS
NAME
DESIGNATION
1. Rachelle C. Fermin 2. Prescy Ong 3. Frederick G. Del Rosario 4. 5. 6. 7.
DepEd DepEd BAHS – DepEd Support Staff
Emmanuel V. Dionisio Magdalena Mendoza Tristan Suratos Kimberly Pobre
AFGBMTS – DepEd Support Staff DAP DAP DAP
8. Cristina Villasenor 9. Lani Garnace 10. Kidjie Saguin 11. Maria Boncan 12. Daylinda Guevarra 13. Fenerosa Maur
DAP DAP DAP Accountant, DepEd Accountant, DepEd Accountant, DepEd
14. Divina Tomelden 15. Nilva Jimenez
Accountant, DepEd Disbursing Officer, DepEd
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 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
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
K TO 12 MATHEMATICS