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Republic of the Philippines Department of Education

DepEd Complex, Meralco Avenue

Pasig City

K to 12 CURRICULUM GUIDE

MATHEMATICS

(Grade 1 to 2)

December 2012

K TO 12 MATHEMATICS

K to 12 Curriculum Guide version as of December 2012 MATHEMATICS 2

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 modeling; 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.

K TO 12 MATHEMATICS


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.

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.

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 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, critical thinking, communicating, reasoning, making connections, representations, and decisions in real life. KEY STAGE STANDARDS:

K – 3 4 – 6 7 – 10

At the end of Grade 3, the learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense, measurement, geometry, patterns and algebra, statistics and probability 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 numbers and number sense, measurement, geometry, patterns and algebra, statistics and probability 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 numbers and number sense, measurement, patterns and 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 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 decisions 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 decisions 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 decisions 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 decisions 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.

GRADE 6 The learner; demonstrates understanding and appreciation of 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,

K TO 12 MATHEMATICS


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.

GRADE 10 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.

Time Allotment:

Grade 1 2 3 4 5 6 7 8 9 10

Daily 50 min

50 min

50 min

50 min

50 min

50 min

Weekly 4 hours

4 hours

4 hours

4 hours

K TO 12 MATHEMATICS


GRADE 1

CONTENT

CONTENT STANDARDS

PERFORMANCE STANDARDS

LEARNING COMPETENCIES

The learner …

The learner is able to…

The learner…

Numbers and

Number Sense demonstrates an

understanding of the key concepts of numbers.

explore the concepts of numbers and compare these in various context.

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 hundreds using objects.

compares two sets using the expressions “less than,” “more than,” and “as many as.”

orders sets from least to greatest and vice versa.

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 one- and two-digit numbers.

renames numbers into tens and ones.

compares numbers up to 100 using relation symbols.

arranges numbers up to 100 in an increasing order and vice versa.

demonstrates an understanding of the terms and language used in relation to money.

explore the concepts of coins and bills up to P100.

recognizes coins and bills up to P100 (pesos and centavos)

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

reads and writes ordinal numbers: 1st, 2nd, 3rd up to

10th.

identifies the 1st , 2nd, 3rd, up to 10th object in a given

set from a given point of reference.

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 expression using addition and subtraction.

identifies and creates patterns to compose and

decompose using addition.

adds two one-digit numbers with sums up to 18 using the order and zero properties of addition.

adds two to three one-digit numbers horizontally and vertically with sums up to 18.

adds three one digit numbers having sums up to 18 using the order and grouping properties of addition.

uses expanded form to explain the meaning of addition with regrouping.

adds numbers with sums through 99 without or with regrouping.

adds mentally two to three one- digit numbers with sums up to 18.

adds mentally two-digit numbers and one-digit numbers with regrouping.

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

analyzes and solves one-step word problems involving numbers including money with sums up to 99 using appropriate problem solving strategies.

subtracts one-digit numbers with minuends through 18

(basic facts)

subtracts one to two-digit numbers with minuends up to 99 without regrouping.

uses the expanded form to explain subtraction with regrouping.

subtracts one to two-digit numbers with minuends up to 99 with regrouping.

subtracts mentally one-digit numbers from minuends up to 18 without regrouping.

subtracts mentally one-digit numbers from two-digit minuends without regrouping.

analyzes and solves word problems involving subtraction of whole numbers including money with minuends up to 99 with and without regrouping using appropriate problem solving strategies.

demonstrates an

understanding of the key concepts of halves and fourths.

visualize, models and represent the concept of halves and fourths using whole objects and sets.

visualizes and identifies ½ and ¼ of a whole object.

divides a whole into halves and fourths.

divides the elements of objects into two groups of equal quantities to show halves of sets.

divides the elements of a set of object into four groups of equal quantities to show fourths of sets.

draws the whole region or set given half of a region or a set.

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

Geometry demonstrates an

understanding of 2-dimensional and 3-dimensional shapes.

model and represent 2-dimensional and 3-dimensional objects.

identifies, names and describes the four basic shapes (square, rectangle, triangle and circle) in a 2-dimensional and a 3-dimensional objects.

compares and classifies 2-dimensional and 3-dimensional figures according to common attributes.

draws the four basic shapes.

constructs the three dimensional objects using manipulative materials.

Patterns and

Algebra

demonstrates an understanding of patterns and mathematical sentences.

create patterns using numbers colors. shapes, etc.

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 and orientation.

determines the next term ( figure/number) in a given sequence and gives reason.

Measurements demonstrates an

understanding of the concepts of time, length, weight and capacity.

measure and use non-standard units in measuring length , weight, and capacity.

names and tells the number of days in a week; months in a year in the right order.

uses a calendar to determine a day or a month.

tells the time by an hour, half-hour and quarter-hour.

compares objects using comparative words: short, shorter, shortest; long, longer, longest; heavy, heavier, heaviest; light, lighter, lightest.

estimates and measures length using non- standard units of linear measures.

estimates and measures mass using non-standard units of linear measures.

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

shows and finds capacity using non-standard unit.

Statistics and

Probability

demonstrates an understanding of key concepts of pictographs, outcomes and chances in games.

collect, organize, represent, interpret, analyze data and make conjectures.

collects and organizes data using tallies and tables.

represents data using pictographs without using scale.

reads and interprets pictographs.

identifies cause and effect relationships.

predicts and records outcome of experiments and chance games.

K TO 12 MATHEMATICS


GRADE 2

CONTENT

CONTENT STANDARDS

PERFORMANCE STANDARDS


The learner …


The learner…

Numbers and Number Sense

demonstrates an understanding of the concept of whole numbers up to 1000.

explore the concept of whole numbers up to 1000 and compare these in various contexts.

visualizes and identifies numbers from 101 through 1000.

associates numbers with sets having 101 up to 500 objects and gives the number of objects.

associates numbers with sets having 501 up to 1000 subjects and gives the number of objects.

counts and groups objects in ones, tens, and hundreds.

gives the place value and finds the value of a digit in three-digit numbers.

counts numbers by 10s, 50s, and 100s.

reads and writes numbers from 101 through 1000 in symbols and in words.

writes three-digit numbers in expanded form.

compares numbers using >, < and =.

orders numbers up to 1000 from least to greatest and vice versa.

demonstrates an

understanding of the concept of ordinal numbers

explore the concept of ordinal numbers and use these in various contexts.

visualizes and identifies the 1st through the 20th object of a given set from a given point of reference.

reads and writes ordinal numbers from 1st through the 20th.

identifies and uses the pattern of naming ordinal numbers from 1st to the 20th.

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

demonstrates an

understanding of the concept of the four fundamental operations of whole numbers and the identity and zero properties of multiplication.

compute sums and solve addition problems involving numbers of up to 1000.

adds 2-digit by 3-digit numbers with sums up to 1000 without and with regrouping.

adds 3-digit by 3-digit numbers with sums up to 1000 without and with regrouping.

uses the following properties of addition in computing for sums of up to 1000: zero/identify property of addition, commutative property of addition, associative property of addition.

adds mentally 1- to 2-digit numbers with sums up to 50.

adds mentally 3-digit numbers by 1-digit numbers.

adds mentally three -digit numbers by tens (multiples of 10 up to 90).

adds mentally 3-digit numbers by hundreds (multiples of 100 up to 900).

analyzes and solves word problems involving addition of whole numbers including money with sums up to 1000 without and with regrouping using appropriate problem solving strategies.

compute for

differences and solve subtraction problems.

subtracts 2- to 3-digit numbers with minuends up to 999 without and with regrouping.

subtracts mentally 1-digit numbers from 1 to 2-digit numbers with minuends up to 50.

subtracts mentally 3-digit numbers by ones without regrouping.

subtracts mentally 3-digit numbers by tens without regrouping.

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

subtracts mentally 3-digit numbers by hundreds without regrouping.

analyzes and solves one-step word problems involving subtraction of whole numbers including money with minuends up to 1,000 without and with regrouping using appropriate problem solving strategies. .

compute for sums

and differences and solve problems involving both addition and subtraction of numbers.

performs orders of operations involving addition and subtractions of small numbers.

analyzes and solves two-step word problems involving addition and subtraction of 2- to 3-digit numbers including money using appropriate problem solving strategies.

explore and illustrate

the concept of multiplication of whole numbers.

illustrates multiplication as repeated addition, arrays, counting by multiples, and equal jumps on the number line.

writes a related equation for each type of multiplication: repeated addition, array, counting by multiples, and equal jumps on the number line.

illustrates the property of multiplication that any number multiplied by one (1) is the same number.

illustrates the property of multiplication that zero multiplied by any number is zero.

illustrates the commutative property of multiplication.

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

compute products of

numbers involving 2,3,4,5 and 10 and solve problems involving multiplication of these numbers.

constructs and fills up the multiplication tables of 2,3,4,5, and 10.

multiplies mentally to fill up multiplication tables of 2,3,4,5 and 10.

analyzes and solves one-step word problems involving multiplication of whole numbers as well as addition and subtraction including money.

explore and model

the concept of division of whole numbers.

models and describes division situations in which sets are separated into equal parts.

represents division as equal sharing, repeated subtraction, equal jumps on the number line, and formation of equal groups of objects.

writes a related equation for each type of situation: equal sharing, repeated subtraction, equal jumps on the number line, and formation of equal groups of objects.

divides numbers found in the multiplication tables of 2,3,4,5, and 10.

compute quotients of

numbers found in the multiplication tables involving 2,3,4,5 and 10 and solve problems involving division of these numbers.

divides mentally numbers found in the multiplication tables 2,3,4,5 and 10.

analyzes and solves one-step word problems involving division of numbers found in the multiplication tables 2,3,4,5 and 10.

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

demonstrates an

understanding of the concepts of halves and fourths.

visualize, model and represent the concept of halves and fourths using whole objects and sets.

visualizes and identifies unit fractions with denominators 10 and below.

reads and writes unit fractions.

compares unit fractions using relation symbols

orders unit fractions.

visualizes and identifies other fractions less than one with

denominators 10 and below.

visualizes and identifies similar fractions (using group of objects and number line).

reads and writes similar fractions.

compares similar fractions using relation symbols.

apply number

concepts in problem situation involving money.

reads and writes money in symbols and in words through 100.

counts and tells the value of a set of bills or a set of coins through 100 in peso (coins only, bills only and coins and bills).

counts and tell the value of a set of bills or a set of coins through 100 in centavo (coins).

counts and tell the value of a set of bills or a set of coins through 100 in combinations of pesos and centavos (peso and centavo-coins only, bills and centavo-coins, coins and bills).

compares values of different denominations of coins and paper bills through100 using relation symbols >.< and = .

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

Geometry demonstrates an understanding of 2-dimensional and 3-dimensional objects.

model and represents 2-dimensional and 3-dimensional objects.

visualizes, identifies, classifies and describes half circles and quarter circles.

constructs squares, rectangles, triangle, circles half-circles, and quarter circles using cut-outs and square grids.

explore the concept of symmetry.

identifies shapes/figures that show symmetry in a line.

creates figures that show symmetry in a line.

visualize, model and represent tessellations.

recognizes shapes that can tessellate.

tessellates a surface using triangles and squares.

explore the concepts of lines, curves and surface on 3-dimensional objects.

identifies straight lines and curves, flat and curved surfaces in a 3-dimensional object.

explains the differences between straight lines and curved lines, flat surfaces and curved surfaces.

Patterns and Algebra

demonstrates an understanding of patterns and mathematical sentences.

create patterns using numbers, colors, shapes, etc.

identifies and explains simple repeating patterns.

determines the next term (figure/number) in a given sequence and gives a reason.

finds and completes patterns according to one or two of the following attributes: shape, size, color, and orientation.

Measurement deepens understanding of time, length, weight and capacity

measure time tells and writes the time in minutes including a.m. and p.m. using analog and digital clocks.

finds the duration of time elapsed using calendar, analog and digital clocks.

solves simple word problems involving time.

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

identify and compare the standard units, centimeter and meter.

shows and uses the appropriate unit of length and their abbreviation cm and m to measure a particular object .

compares length in meters or centimeters.

estimate and compute for lengths of objects and solve problems involving lengths using centimeter and meter.

measures objects using appropriate measuring tools in m or cm.

estimates and measures length using meter or centimeter.

solves simple word problems involving length.

identify, use and compare the standard units, gram and kilogram.

shows and uses the appropriate unit of weight and their abbreviations g and kg to measure a particular object or situation

compares weight in grams or kilograms

estimate and compute for the mass/weight of an object and solve problems involving mass/weight.

measures objects using appropriate measuring units in g or kg.

estimates and measures mass using gram or kilogram.

solves simple words problems involving mass.

explore and illustrate the concept of area

illustrates area as a measure of how much surface is covered or occupied by a plane figure.

shows the area of a given figure using square-tile units¸ i.e. number of square-tiles needed.

K TO 12 MATHEMATICS


CONTENT

CONTENT STANDARDS

PERFORMANCE

STANDARDS


The learner …


The learner…

estimate and compute for the area of a plane figure

estimates the area of a given figure using any shape.

finds the area of a given figure using square- tile units i.e. number of square-tiles needed.

measure capacity shows and finds capacity using appropriate measuring tools, e.g. amount of liquid needed.

Statistics and Probability

demonstrates an understanding of key concepts of pictographs, outcomes and chances in games

collect, organize, represent, interpret, analyze data, and make conjectures

collects and organizes data using tables and pictures.

reads and interprets data in a given pictograph.

represent data using scales.

forms scale representation of objects from the data collected.

makes pictographs using scale representation.

make conjectures and educated guesses about the likelihood of events.

makes a guess on whether an event is less likely, more likely, equally likely or unlikely to happen based on facts.

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).

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 - 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 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

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 Refinement of K to 12 Mathematics

Date: July 9-13, 2012

A.

B.

C.

D.

B. Workshop on the Finalization of Learning Competencies

Venue: Development Academy of the Philippines,Tagaytay City

Date: August 8-12, 2011

NAME DESIGNATION OFFICE/SCHOOL

1. Remylinda Soriano Education Program Specialist I DCS - Manila

2. Teresita Tagulao Education Program Specialist I DCS - Pasig

3. Robesa Hilario Education Program Specialist DepEd – BEE – CDD

4. Elizabeth Catao Education Program Specialist DepEd – BSE – CDD

5. Sonia Javier Head Teacher III JSHS

6. Melvin Callanta Head Teacher VI Mangaldan High School

7. Nicanor San Gabriel Jr. Teacher I Araullo High School

8. Dr. Maxima Acelajado Professor De La Salle University

9. Dr. Catherine Vistro – Yu Professor I Ateneo De Manila University

NAME DESIGNATION SCHOOL/OFFICE

1. Beth Catao BSE-CDD

2. Elsie ESmer BSE-CDD

3. Melvin Callanta BSE-CDD

4. Sonia Javier BSE-CDD

5. Abelardo Medes BEE-CDD

K TO 12 MATHEMATICS


10. Lydia Landrito Science Education Specialist University of the Philippines - NISMED

11. Dr. Florante C. Marmeto Principal IV Sucat Elementary School

C. Workshop on the Development of Learning Competencies and Teaching Guides

Venue: Development Academy of the Philippines,Tagaytay City Date: July 18-22, 2011


1. Teresita P. Tagulao D.O. Pasig City

2. Remylinda T. Soriano D.O. Manila

3. Melvin Calanta Mangaldan High School

4. Nicanor M. San Gabriel Jr. Araullo High School

5. Maxima J. Acelajado DLSU

6. Elizabeth Catao BSE

7. Sonia E. Javier JSHS

8. Catherine P. Vistro - Yu Ateneo de Manila

9. Robesa Hilario BEE - CDD

10. Thomas Manuel L. Quiton BEE

D. 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. Teresita P. Tagulao D.O. Pasig City

2. Remylinda T. Soriano D.O. Manila

3. Robesa Hilario BEE - CDD

4. Abelardo B. Medes BEE – CDD

K TO 12 MATHEMATICS


5. Thomas Manuel L. Quiton BEE

E. Experts’ Review of the Curriculum Standards

Venue: Bulwagan ng Karunungan, DepEd Complex, Pasig City Date: July 15, 2011


1. Dr. Evangeline P. Bautista Associate Professor Ateneo de Manila University

2. Mr. Melvin M. Callanta DepEd BSE

3. Ms. Elizabeth G. Catao DepEd BSE

4. Sr. Iluminada C. Coronel President Mathematics Teachers Assoc. of the

Phils.

5. Dr. Rosemarievic V. Diaz Philippine Normal University

6. Ms. Janet D. Dionio Manuel Roxas High School

7. Dr. Ruth G. de Lara Retired Education Supervisor DCS Manila

8. Mr. Emmanuel V. Dionisio Head Teacher III A.F.G. Bernardino Memorial Trade

School

9. Dr. Juanita A. Ferido Education Supervisor II DepEd NCR

10. Dr. Flordeliza F. Francisco Assistant Professor Ateneo de Manila University

11. Dr. Ian June L. Garces Associate Professor Ateneo de Manila University

12. Dr. Milagros D. Ibe UP Diliman and Miriam College

13. Dr. Sonia E. Javier Juan Sumulong High School

14. Dr. Ma. Nympha B. Joaquin UP Diliman

15. Ms. Lydia M. Landrito Science Education Specialist UP NISMED

16. Dr. Queena N. Lee-Chua Professor Ateneo de Manila University

17. Dr. Auxencia A. Limjap De La Salle University

18. Dr. Gladys C. Nivera Professor I Philippine Normal University

19. Mr. Nicanor M. San Gabriel Jr. DepEd BSE-CDD

20. Ms. Revie G. Santos Master Teacher II Rizal High School

21. Dr. Cornelia C. Soto Ateneo de Manila University

K TO 12 MATHEMATICS


22. Dr. Merle C. Tan Director UP NISMED

23. Dr. Soledad A. Ulep UP NISMED

24. Dr. Catherine P. Vistro-Yu Professor Ateneo de Manila University

25. Dr. Aida A. Yap UP NISMED

F. Writeshop on the Finalization of the Curriculum Standards Venue: Regional Education Learning Center, Region IV-A (CALABARZON), Malvar, Batangas Date: May 19-21,2011





4. Lydia M. Landrito Science Education Specialist University of the Philippines

5. Remylinda T. Soriano Education Program Supervisor I DCS Manila

6. Revie G. Santos Master Teacher II Rizal High School

7. Emmanuel V. Dionisio Head Teacher III/ Documentor A.F.G. Bernardino Memorial Trade

School

G. 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





9. Nicanor M. San Gabriel BSE – CDD

10. Elizabeth Catao BSE – CDD

11. Abelardo B. Medes BEE – CDD

K TO 12 MATHEMATICS


12. Robesa R. Hilario BEE – CDD

13. Revie G. Santos Master Teacher II Rizal High School

14. Emmanuel V. Dionisio Head Teacher III/ Documentor A.F.G. Bernardino Memorial Trade

School

H. 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. Maria Gregoria P. Malihan St. Jude Catholic School

2. Loreto S. Sauz UST – EHS

3. Arnold G. Gerance AurolioArago, Oriental Mindoro

4. Cheryl G. Pauericio Division of Legazpi City

5. Abella A. Amican Niogan Elementary School

6. Arnulfo G. Mariano Division of Valenzuela City

7. Sr. Iluminada C. Coronel MTAP

8. Revie G. Santos Rizal High School

9. Juanita A. Ferido Dep. Ed. NCR

10. Larry Samala Dep. Ed. R-IVB

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


1. Carmelita S. Domantay Dagupan City NHS – Dagupan City

K TO 12 MATHEMATICS


2. Rubielyn L. Babaran Enrile North Central School – Enrile,

Cagayan

3. Romel L. Ricardo Regional Science High School

Tumauini, Isabela

4. Janette T. Fermin St. Paul University Philippines

Tugeugarao City

5. Nestor A. Paat ESP II DepEdTugeugarao City

6. Nestor G. Villaflor ESP I DepEd – Div. Office, Ilocos Sur

7. Nestor P. Nuesca ESP II DepEd RO III

8. Janice Q. Nonog Teacher II Tabuk c/s, Dagupan West, Tabuk City,

Kalinga

9. Ofelia A. Dolo Master Teacher II La Trinidad, Benquet, CAR

10. Jenny Jesusa J. Catubay Master Teacher II Sta. Maria Elem. School

11. Arnel R. Lumbo University of the Cordilleras – Grade

School Baguio City

12. Susana E. Vanhoutte SLU – Lab. High School

13. Norma Maria P. Rutab University of the Cordilleras

Baguio City

14. Daniel D. Peredo Dept. Head Benguet NHS, La Trinidad, Benquet

15. Lauro C. Cruz Dept. Head Sacred Heart Academy

Poblacion, Sta. Maria, Bulacan

3. Regions VI, VII and VIII

Venue: Ecotech Center, Lahug, Cebu City Date: May 4, 2011


1. Rosemary S. Achacoso Education Program Supervisor Maasin City Division – Region VIII

2. Feliciaro C. Buenate Jr. Education Program Supervisor RO VI – Western Visayas

3. Rufa T. Temblor St. Francis of Assisi School

Lahug, Cebu City. Region VII

K TO 12 MATHEMATICS


4. Ma. Emilie S. Gepison Leon Elem. School

Division of Iloilo, Region VI

5. Jose Leover S. Illut San Roque Child Dev’t School YatiIliloan, Cebu – Region VII

6. Ann Marie C. Bandola EPS – I Math City of Naga Division, Region VII

7. Jeremy M. Movilla Ormoc City Central School

Ormoc City Division, Region VIII

8. Romao D. Castante Calbayog City NHS

Calbayog City Division – RO VIII

9. Suzette C. Martinez

Inocencio V FerrerMem. School of Fisheries

Talisay City, Neg. Occ., Div. of Neg. Occ.

10. Andreo G. Aba

Guihulangan National Agricultural School

Plagatasanon, Guihulangan City, Neg. Or.

Div. of Guih. City

11. Cesar L. Sanchez University of San Jose Recoletos

BasakPardo, Cebu City

12. Adonis A. Torres Tanjay City Science High School

Tanjay City Schools Division – Region VII

13. Lita B. Morales Don Carlos Ledesma NHS

San Carlos City, Neg. Occ. – Region VI

4. Regions IX,X and ARMM

Venue: Regional Education Learning Center, Cagayan de Oro City Date: May 5, 2011


1. Susan P. Kuyong DepEd Sulu II

K TO 12 MATHEMATICS


2. Arnel L. Agaug DepEd

3. Rudilene D. Cael DepEd

4. Evelyn T. Villa DepEd

5. Ma. Theresa B. Miranda DepEd

6. Noelli B. Yap The Abba’s Orchard School

7. Reymundo B. Gimena DepEd – Dinagat Division

8. Gilda L. Taboclaon Dep. Ed

9. Rogelio J. Bahian Dep. Ed. R – X

10. Maria Conchita P. Bas CUBED

11. Editha J. Amper Corpus Christi School

12. Rhodora S. Amantorno OLLES

13. Reymundo B. Gimena Dep. Ed. Dinagat Island

14. Rosalina V. Eviota Dep. Ed. Dinagat Island

15. Arnold C. Solen Dep. Ed. Agusan del Norte

16. Noelli B. Yap The Abba’s Orchard

5. Regions XI,XII, ARMM (ShariffKabunsuan,Maguindanao) Venue: Regional Education Learning Center, Davao City and CARAGA Date: May 6,2011


1. Reynante A. Solitario DepEd ROXI, EPS

2. Araceu J. Dinopol DepEdSarangani Division Region XII

3. Junelo C. Fornolles Samal NHS – Ibalos Region XI

4. Agnes B. Ortega, RN Cotabato City Region XII

5. Aida M. Pescado MAG. I

6. Nempha F. Gonzales Davao Christian Learning Center, Davao

City

7. Abdul – Aziz H. Iya Bureau of Elementary Education DepEd –

K TO 12 MATHEMATICS


ARMM RO

8. Levi B. Butihen Polomolok West District Division of South

Cotobato

9. Eduard C. Amoguis EPS – Math Division of Davao del Norte

Region XI

10. Genelyn H. Morante Sultan Kudarat Division

11. Glenn A. Bisnan DepEd ROXII – EPS

I. Workshop on the K to 12 Curriculum Mapping Venue: Development Academy of the Philippines, Tagaytay City Date: March 16-18, 2011


1. Abelardo Medes SDD – BEE

2. RobesaHilario CDD – BEE

3. ForcefinaFrias CDD – BEE

4. RanteMamerto Division of Muntinlupa

5. Elizabeth Catao CDD – BSE

6. Melvin Callanta Mangaldan NHS – Pangasinan

7. Sonia Javier Division of Quezon City

8. Dr. Maxima Acelajado Dela Salle University – Taft

9. Dr. Ruth Lara World Bank Consultant – TUP Retired

Professor

10. Ms. Lydia Ladrito UP – NISMED

11. Dr. Carmela Oracion Ateneo de Manila Univ

12. Dr. Ronald San Jose UP College of Edu (UPIS)

13. Jannet Labu CDD – BEE

K TO 12 MATHEMATICS


SECRETARIAT

NAME DESIGNATION

1. Rachelle C. Fermin DepEd

2. Prescy Ong DepEd

3. Rozelyn M. Buyucan DepEd

4. Frederick G. Del Rosario BAHS – DepEd Support Staff

5. Emmanuel V. Dionisio AFGBMTS – DepEd Support Staff

6. Magdalena Mendoza DAP

7. Tristan Suratos DAP

8. Kimberly Pobre DAP

9. Cristina Villasenor DAP

10. Lani Garnace DAP

11. Kidjie Saguin DAP

12. Maria Boncan Accountant, DepEd

13. Daylinda Guevarra Accountant, DepEd

14. Fenerosa Maur Accountant, DepEd

15. Divina Tomelden Accountant, DepEd

16. Nilva Jimenez Disbursing Officer, DepEd

FACILITATORS/SUPPORT TEAM

NAME DESIGNATION

1. Irene C. De Robles CDD – BEE

2. Jose Tuguinayo, Jr. CDD – BSE

3. Marivic Abcede CDD – BSE

4. Mirla Olores SPED – BEE

K TO 12 MATHEMATICS


5. Simeona Ebol CDD – BEE

6. Fe Villalino SDD – BEE

ADVISORY TEAM

NAME DESIGNATION

1. Usec. Yolanda S. Quijano Undersecretary, DepEd OSEC

2. Dr. Lolita Andrada Director, BSE – DepEd, Pasig

3. Dr. Angelita Esdicul Director, BEE – DepEd, Pasig

4. Dr. Ricardo de Lumen OIC, Director III – Tech Voc, DepEd

5. Dr. Paraluman R. Giron Chair, K – 10 TWG

6. Dr. Avelina T. Llagas Consultant, TEC, DepEd

7. Dr. Dina Ocampo Dean, COE, UP Diliman

8. Dr. Ester B. Ogena President, PNU

9. Dr. Brenda B. Corpuz Technical Adviser to the Office of USEC, Pograms and

Standards

10. Dr. Dennis Faustino Headmaster, SMS Sagada, Mt. Prov.

11. Dr. Merle Tan Director, UP – NISMED

12. Dr. Cristina Padolina President, CEU

13. Mr. Napoleon Imperial CHED

14. Diane Decker Consultant, MTB – MLE

15. Dr. Nelia Benito Director, NETRC

16. Dr. Socorro Pilor Director, IMCS

17. Dr. Beatriz Torno Executive Director, TEC

18. Dr. Carolina Guerrero Director, BALS

19. Dr. Irene Isaac Director, TESDA

20. Dr. Imelda Taganas Director, TESDA

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