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# K to 12 Mathematics Curriculum Guide for Grades 1 to 10

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K to 12 Mathematics Curriculum Guide for Grades 1-10

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### K to 12 Mathematics Curriculum Guide for Grades 1 to 10

1. 1. Republic of the PhilippinesDepartment of EducationDepEd Complex, Meralco AvenuePasig CityK to 12 Curriculum GuideMATHEMATICS(Grade 1 to Grade 10)January 31, 2012
2. 2. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 2CONCEPTUAL FRAMEWORKMathematics 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 thinkingby Scriven and Paul (1987):Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluatinginformation 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, desirablevalues 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 criticalthinking and problem solving skills. Contexts refer to beliefs, environment, language and culture that include traditions and practices, and learner’s priorknowledge and experiences.
3. 3. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 3The 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 theorydefines learning as "the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of graspingand transforming experience" (Kolb, 1984, p. 41). Situated learning, theorized by Lave and Wenger, is learning in the same context on which concepts andtheories are applied.Reflective learning refers to learning that is facilitated by reflective thinking. It is not enough that learners encounter real-life situations. Deeper learningoccurs when learners are able to think about their experiences and process these allowing them the opportunity to make sense and meaning of theirexperiences.Constructivism is the theory that argues that knowledge is constructed when the learner is able to draw ideas from his own experiences and connectsthem 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-basedlearning (Bruner, 1961) support the idea that students learn when they make use of personal experiences to discover facts, relationships and concepts.
4. 4. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 4Figure 1. The Conceptual Framework of Mathematics Education
5. 5. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 5BRIEF COURSE DESCRIPTIONMathematics from K-10 is a skills subject. By itself, it is all about quantities, shapes and figures, functions, logic and reasoning. Mathematics is also atool 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. Itfocuses 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 geometricmodeling and proofs.Patterns and Algebra as a strand studies patterns, relationships and changes among shapes and quantities and includes the use of algebraicnotations 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 necessaryconcepts 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, thePhilippines.
6. 6. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 6LEARNING AREA STANDARD: The learner demonstrates understanding and appreciation of key concepts and principles of mathematicsas applied, using appropriate technology, in problem solving, communicating, reasoning, makingconnections, representations, and decisions in real life.KEY STAGE STANDARDS:K – 3 4 – 6 7 – 10At the end of Grade 3, the learner demonstratesunderstanding and appreciation of key conceptsand skills involving whole numbers up to tenthousand, fractions, measurement, simplegeometric figures, pre-algebra concepts anddata representation and analysis as applied,using appropriate technology, in critical thinking,problem solving, reasoning, communicating,making connections, representations anddecisions in real life.At the end of Grade 6, the learner demonstratesunderstanding and appreciation of key conceptsand skills involving rational numbers,measurement, geometric figures, pre-algebraconcepts, simple probability and data analysis asapplied, using appropriate technology, in criticalthinking, problem solving, reasoning,communicating, making connections,representations and decisions in real life.At the end of grade 10, the learnerdemonstrates understanding and appreciationof key concepts and skills involving numbersense, measurement, algebra, geometry,probability and statistics, and trigonometry asapplied, using appropriate technology, incritical thinking, problem solving,communicating, reasoning, makingconnections, representations, and decisions inreal life.
7. 7. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 7GRADE LEVEL STANDARDS:Grade Level Grade Level StandardsGrade 1The 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 appropriatetechnology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in reallife.Grade 2The 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 appropriatetechnology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in reallife.Grade 3The 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 appropriatetechnology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in reallife.Grade 4The 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 oftriangle, parallelogram and trapezoids, volume of cubes and rectangular prisms, pre-algebra concepts, data collection, representationand analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.Grade 5The 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 andanalysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.Grade 6The learner is expected to have mastered the concepts and operations on whole numbers; demonstrates understanding andappreciation 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, representationand 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.
8. 8. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 8Grade Level Grade Level StandardsGrade 7The 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 8The 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, representationsand decisions in real life.Grade 9The learner demonstrates understanding of key concepts and principles of algebra, geometry, and trigonometry as applied, usingappropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations anddecisions in real life.Grade10The learner demonstrates understanding of key concepts and principles of number sense, algebra, geometry, probability andstatistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.
9. 9. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 9GRADE 1Content Content Standards Performance Standards Learning CompetenciesNumbers and Number Sense The learner demonstratesunderstanding of… number notation and placevalue, cardinal and ordinalnumbers, and comparing andordering numbers up to 100.The learner is able to… explore the concept ofcardinal numbers up to 100and compare these numbersin various contexts.The learner… recognizes cardinal numbers from 0 to 100. counts and tells the number of objects in agiven set by ones and tens. identifies the number that is one more or oneless from a given number. composes and decomposes a given number. regroups sets of ones into sets of tens andsets 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 andviceversa. counts by 2’s, 5’s and 10’s through 100. reads and writes numbers up to 100 insymbols and in words. identifies the place value and finds the valueof a digit in a one- and two-digit numbers. renames numbers into tens and ones. compares numbers up to 100 using relationsymbols.
10. 10. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 10Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … arranges numbers up to 100 in increasingorder and vice versa. recognizes coins and bills up to P100 (pesosand centavos). explore the concept of ordinalnumbers. reads and writes ordinal numbers 1st, 2nd,3rd up to 10th. identifies the 1st, 2nd, 3rd up to the 10thobject in a given set from a given point ofreference. determines the position of an object using1st to 10th from a given point of reference. addition and subtraction up to100. illustrate addition andsubtraction of whole numbers. illustrates addition as putting together andsubtraction as taking away, comparing andadding up. illustrates the relationship of joining sets toaddition of whole numbers. illustrates that addition and subtraction areinverse operations. identifies and constructs equivalent numberexpressions using addition and subtractions. identifies and creates patterns to composeand decomposes numbers using addition.
12. 12. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 12Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … subtracts one to two-digit numbers withminuends up to 99 without regrouping. uses the expanded form to explainsubtraction with regrouping. subtracts one to two-digit numbers withminuends up to 99 with regrouping. mentally subtracts 1-digit numbers fromminuends up to 18 without regrouping. mentally subtracts a 1-digit number from 2-digit minuends without regrouping. solves word problems involving subtractionof whole numbers including money withminuends up to 99 with and withoutregrouping using appropriate problemsolving strategy. the concepts of halves andfourths and applies them individing a whole or setequally. visualize, model andrepresent the concept ofhalves and fourths usingwhole objects and sets. visualizes and identifies ½ and ¼ of a wholeobject. divides a whole into halves and fourths. divides the elements of a set of objects intotwo groups of equal quantities to showhalves of sets. divides the elements of a set of objects intofour groups of equal quantities to showfourths of sets.
13. 13. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 13Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner… given half of a region or a set, draws thewhole region or set.Geometry 2-D and 3-D shapes throughidentifying, classifying andconstructing figures using cut-outs and concrete models. explore the properties of 2-and 3-dimensional figures. identifies, names and describes the fourbasic shapes in 2- and 3-dimensionalobjects: square, rectangle, triangle andcircle. compares and classifies 2- and 3-dimensional figures according to commonattributes. model and represent 2- and3-dimensional objects. draws the four basic shapes. constructs three-dimensional objects usingmanipulative materials.Patterns and Algebra  simple patterns.  identify and create numberand attribute patterns. identifies and explains simple repeatingpatterns. makes patterns of shapes, colors andnumbers. complete number andattribute patterns. finds the missing number/digit in addition orsubtraction problems. finds and completes patterns of one or twoof the following attributes: Shape, Size,Color, Number, Orientation. determines the next term (figure/number) ina given sequence and give a reason.
14. 14. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 14Content Content Standards Performance Standards Learning CompetenciesMeasurement The learner demonstratesunderstanding of… the concepts of time andmeasures and comparesobjects using directcomparison and non-standardunits of length, mass andcapacity.The learner is able to… give different measures oftime.The learner … names and tells the number of days in aweek; months in a year in the right order. uses a calendar to determine a day ormonth. tells the time by an hour, half-hour andquarter-hour. estimate and compute formeasurements of length,mass and capacity. compares objects using the comparativewords: Short, shorter, shortest; Long, longer,longest; Tall, taller, tallest; High, higher,highest; 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 mass/weight measures. shows and finds capacity using non-standard unit.Statistics and Probability  organizing, representing andcomparing data usingpictographs without scalerepresentations andprobability, and exploresgames and activities. organize and interpret data.  collects and organizes data using tallies andtables. represents data using pictographs withoutusing a scale. reads and interprets a pictograph.
15. 15. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 15Content Content Standards Performance Standards Learning CompetenciesThe learner is able to… make conjectures aboutgames and activities.The learner … identifies cause and effect relationships. predicts and records outcome ofexperiments and chance games.
16. 16. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 16GRADE 2Content Content Standards Performance Standards Learning CompetenciesNumbers and Number Sense The learner demonstratesunderstanding of… the relationships betweennumbers and place value ofwhole numbers up to 1000and of ordinal numbers up to20th.The learner is able to… explore the concepts ofnumbers up to 1000, readand write these numbers.The learner… visualizes and identifies numbers from 101through 1000. associates numbers with sets having 101 upto 500 objects and give the number ofobjects. associates numbers with sets having 501 upto 1000 objects and give the number ofobjects. counts and groups objects in ones, tens, andhundreds. reads and writes numbers from 101 through1000 in symbols and in words. counts numbers by 10s, 50s and 100s. reads and writes numbers through 1000 insymbols and in words. gives the place value of each digit in a three-digit number. writes three-digit numbers in expanded form. compares numbers using >, < and =. orders numbers up to 1000 from least togreatest and vice versa.
18. 18. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 18Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … analyzes and solves word problemsinvolving addition of whole numbersincluding money with sums up to 1000without and with regrouping. compute differences andsolve subtraction problemsinvolving numbers of up to1000. subtracts 2- to 3-digit numbers withminuends up to 999 without and withregrouping. mentally subtracts 1-digit numbers from 1 to2-digit numbers with minuends up to 50. mentally subtracts 3-digit by ones withoutregrouping. mentally subtracts 3-digit by tens withoutregrouping. mentally subtracts 3-digit by hundredswithout regrouping. analyzes and solves one-step wordproblems involving subtraction of wholenumbers including money with minuends upto1000 without and with regrouping. compute for sums anddifferences and solveproblems involving bothaddition and subtraction ofnumbers. performs order of operations involvingaddition and subtraction of small numbers. solves two-step word problems involvingaddition and subtraction of 2- to 3-digitnumbers including money using appropriateprocedures.
19. 19. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 19Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… explore and illustrate theconcept of multiplication ofwhole numbers.The learner … illustrates multiplication as repeated addition,arrays, counting by multiples, and equaljumps on the number line. writes a related equation for each type ofmultiplication: repeated addition, array,counting by multiples, and equal jumps onthe number line. illustrates the property of multiplication thatany number multiplied by one (1) is thesame number. illustrates the property of multiplication thatzero multiplied by any number is zero. illustrates the commutative property ofmultiplication. compute products of numbersinvolving 2, 3, 4, 5 and 10 andsolve problems involvingmultiplication of thesenumbers. constructs and fills up the multiplicationtables of 2, 3, 4, 5 and 10. multiplies mentally to fill up multiplicationtables of 2, 3, 4, 5 and 10. analyzes and solves one-step wordproblems involving multiplication of wholenumbers including money. analyzes and solves two-step word problemsinvolving multiplication of whole numbers aswell as addition and subtraction includingmoney.
20. 20. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 20Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… explore and model theconcept of division of wholenumbers.The learner … models and describes division situations inwhich sets are separated into equal parts. represents division as equal sharing,repeated subtraction, equal jumps on thenumber line, and formation of equal groupsof objects. writes a related equation for each type ofsituation: equal sharing, repeatedsubtraction, equal jumps on the number line,and formation of equal groups of objects. compute quotients ofnumbers found in themultiplication tables involving2, 3, 4, 5 and 10 and solveproblems involving division ofthese numbers. divides numbers found in the multiplicationtables of 2, 3, 4, 5, and 10. mentally divides numbers found in themultiplication tables of 2, 3, 4, 5 and 10. analyzes and solves one-step wordproblems involving division of numbersfound in the multiplication tables of 2, 3, 4, 5,and 10. unit fractions, proper fractionsand similar fractions, andidentification of money valuethrough 100. explore the concept of unitfractions and other fractionsless than 1 and comparethese fractions. visualizes and identifies unit fractions withdenominators 10 and below. reads and writes unit fractions. compares unit fractions using relationsymbols. orders unit fractions.
21. 21. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 21Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … visualizes and identifies other fractions lessthan 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 relationsymbols. orders similar fractions. apply number concepts onproblem situations involvingmoney. reads and writes money with value through100. counts and tells the value of a set of bills ora set of coins through 100 in peso ( coinsonly, bills only and coins and bills). counts and tells the value of a set of bills ora set of coins through 100 in centavo (coins). counts and tells the value of a set of bills ora set of coins through 100 in combinations ofpesos and centavos (Peso and centavocoins only, bills and centavo coins, coins andbills). reads and writes money in symbols and inwords through 100. compares values of different denominationsof coins and paper bills through 100 usingrelation symbols >, < and =.
22. 22. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 22Content Content Standards Performance Standards Learning CompetenciesGeometry The learner demonstratesunderstanding of… the basic properties ofgeometric shapes, simpletessellations and symmetry.The learner is able to… visualize and model half-circles and quarter circles aswell as other commonshapes.The learner … visualizes, identifies, classifies anddescribes half-circles and quarter circles. constructs squares, rectangles, triangle,circles, half-circles and quarter circles usingcut-outs and square grids. explore the concept ofsymmetry. identifies shapes/figures that show symmetryin a line. creates figures that show symmetry in a line. visualize, model andrepresent tessellations. recognizes shapes that can tessellate. tessellates a surface using triangles andsquares. explore the concept of lines,curves and surface on 3-dimensional objects. identifies straight lines and curves, flat andcurved surfaces in a 3-dimenional object. explains the differences between straightlines and curved lines, flat surfaces andcurved surfaces.Patterns and Algebra  patterns on numbers andgeometric objects. argue and justify patterns.  identifies and explains simple repeatingpatterns. determines the next term (figure/number) ina given sequence and give a reason.
23. 23. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 23Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… apply their understanding andstrategies in completingpatterns.The learner … finds and completes patterns according toone or two of the following attributes: shape,size, color, orientation.Measurement  the concept and application oftime and of using standardunits in measuring length,mass, area and capacity. compute for measures of timeand solve problems involvingtime. tells and writes the time in minutes includinga.m. and p.m. using analog and digitalclocks. finds the duration of time elapsed usingcalendar, analog and digital clocks. solves simple word problems involving time. identify and compare thestandard units centimeter andmeter. shows and uses the appropriate unit oflength to measure a particular object andtheir abbreviations cm and m. compares length in meters or centimeters. estimate and compute forlengths of objects and solveproblems involving lengthsusing centimeter and meter. measures objects using appropriatemeasuring tools in m or cm. estimates and measures length using meteror centimeter. solves simple word problems involvinglength. identify, use and compare thestandard units gram andkilogram. shows and uses the appropriate unit of massto measure a particular object or situationand their abbreviations g and kg. compares mass in grams or kilograms.
24. 24. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 24Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… estimate and compute for themass/weight of an object andsolve problems involvingmass/weight.The learner … measures objects using appropriatemeasuring units in g or kg. estimates and measures mass using gramor kilogram. solves simple word problems involvingmass. explore and illustrate theconcept of area. illustrates area as a measure of how muchsurface is covered or occupied by planefigure. shows the area of a given figure usingsquare tile units, i.e. number of square tilesneeded. estimate and compute for thearea of a plane figure. estimates the area of a given figure usingany shape. finds the area of a given figure using squaretile units i.e. number of square tiles needed. measure capacity.  shows and finds capacity using appropriatemeasuring tools, e.g. amount of liquidneeded.Statistics and Probability  pictographs with scalerepresentations and the ideaof likelihood. organize and interpret data.  collects and organizes data using tables andpictures. reads and interprets data in a givenpictograph.
25. 25. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 25Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… represent data using scales.The learner … forms scale representation of objects fromthe data collected. makes pictographs using scalerepresentation. make conjectures andeducated guesses about thelikelihood of events. makes a guess on whether an event is lesslikely, more likely, equally likely or unlikely tohappen based on facts.
26. 26. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 26GRADE 3Content Content Standards Performance Standards Learning CompetenciesNumbers and Number Sense The learner demonstratesunderstanding of… the concepts of wholenumbers up to 10000, ordinalnumbers up to 100th andRoman numerals up to M.The learner is able to… explore the concepts ofnumbers up to 10 000, count,read and write these numbersand identify ordinal numbersof up to 100th.The learner … reads and writes the numbers through 10000 in symbols and in words. identifies the place value and find the valueof a digit in 4- to 5-digit numbers. compares 4- to 5-digit numbers usingrelation symbols. orders 4- to 5-digit numbers in increasingorder and vice versa. rounds numbers to the nearest tens,hundreds and thousands. identifies ordinal numbers from 1st to 100th. read and write numbers usingRoman numerals up to M. reads and writes the value of romannumbers in Hindu-Arabic and vice versa I toL. reads and writes the value of romannumbers in Hindu-Arabic and vice versa L toC. reads and writes the value of Romannumbers in Hindu-Arabic and vice versa C toD. reads and writes the value of Roman
28. 28. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 28Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… estimate and compute fordifferences and solvesubtraction problemsinvolving numbers of up to 10000.The learner… subtracts 3-digit numbers from 3- to 4-digitnumbers without and with regrouping andwith and without zeros in the digits. subtracts 3- to 4-digit numbers from 4-digitnumbers without and with regrouping andwith and without zeros in the digits. estimates the difference of two numbers withthree to four digits by rounding. mentally subtracts without and withregrouping 2-digit and 1-digit numbers andexplain the strategies used. mentally subtracts without and withregrouping two 2-digit numbers and explainthe strategies used. mentally subtracts without and withregrouping 2-digit to 3-digit numbers frommultiples of hundreds and explain thestrategies used. solves one-step word problems involvingsubtraction of whole numbers includingmoney using appropriate problem solvingstrategies. solves two-step word problems involvingaddition and subtraction of whole numbersincluding money using appropriate problemsolving strategies.
29. 29. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 29Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… estimate and multiply 2- and3-digit numbers by 1-digit to2-digit numbers and solvemultiplication problemsinvolving these numbers.The learner … constructs and completes the multiplicationtables of 6, 7, 8 and 9. states basic multiplication facts for numbersup to 10. applies the commutative property ofmultiplication. multiplies 2-digit by 1-digit by using thedistributive property of multiplication. multiplies three 1-digit numbers by using theassociative property of multiplication. multiplies 2- to 3-digit numbers by 1-digitnumbers without or with regrouping. multiplies 2-digit numbers by 2-digit numberswithout regrouping. multiplies 2-digit numbers by 2-digit numberswith regrouping. multiplies 2- to 3-digit numbers by multiplesof 10 and 100. multiplies 1- to 2-digit numbers by 1000. estimates the product of 2- to 3-digitnumbers by 1- to 2-digit numbers byrounding.
30. 30. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 30Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … mentally multiplies 2-digit by 1-digit numberswithout regrouping involving products of upto 100. solves one-step word problems involvingmultiplication of whole numbers includingmoney using appropriate problem solvingstrategies. solves two-step word problems involvingmultiplication as well as addition andsubtraction including money usingappropriate problem solving strategies. explore the concepts offactors and multiples. states multiples of 1- to 2-digit numbers. differentiates prime and composite numbers. estimate and divide 3-digitnumbers by up to 2-digitnumbers and solve divisionproblems involving thesenumbers. divides numbers found in the multiplicationtables of 6, 7, 8, 9. states basic division facts of numbers up to10. divides 2- to 3-digit numbers by 1-digitnumbers without remainder. divides 2- to 3-digit numbers by 1-digitnumbers with remainder. divides 2-digit numbers by 2-digit numbers. divides numbers by 10 and 100.
31. 31. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 31Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … estimates the quotient of 2- to 3-digitnumbers by 1- to 2-digit numbers. mentally divides 2-digit numbers by 1-digitnumbers without remainder. solves one-step word problem involvingdivision of 2- to 4-digit numbers by 1- to 2-digit numbers including money usingappropriate problem solving strategies. solves word problems involving division andother fundamental operations, includingmoney, using appropriate problem solvingstrategies. the basic kinds of fractions,know how to simplify andorder them, and to apply toproblem solving moneythrough 100. explore the concepts ofdissimilar fractions, improperfractions and mixed numbers. visualizes and identifies fractions that areequal to one and greater than one. reads and writes fractions that are greaterthan one in symbols and in words. relates and changes improper fractions tomixed numbers and vice versa. visualizes and identifies dissimilar fractions. compares dissimilar fractions. arranges dissimilar fractions in increasing ordecreasing order.
32. 32. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 32Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner… recognizes and generates equivalentfractions of commonly used fractions. changes fractions to lowest forms. apply number concepts tosolve problems involvingmoney through 1000. reads and writes money in symbols through1000. compares values of the differentdenominations of coins and bills through1000. solves real-life problems involving moneythrough 1000.Geometry  the basic elements of angles,lines and rays. explore the concepts of point,line, line segment and ray. recognizes and draws a point, line, linesegment and ray. recognizes and draws perpendicular lines,parallel lines and intersecting lines. visualizes, identifies and draws congruentline segments. explore symmetry in planefigures and the environment. identifies and draws the line of symmetry ina given symmetrical figure. identifies and visualizes symmetry in theenvironment and in design. completes a symmetric figure with respect toa given line of symmetry.
33. 33. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 33Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … tessellates the plane using triangles,squares and other shapes that cantessellate.Patterns and Algebra  patterns of numbers,operations, geometric objectsand relationships. explore the concept of oddand even numbers. tells when a number is odd or even. finds the pattern using odd and evennumbers with objects, pictures and words. identify the rule for a patternand complete the numberpattern. determines the pattern of a given sequenceand state the rule. finds the missing number or digit in apattern.Measurement  the concept and application oftime (in minutes), length,mass, area and capacity. convert time measures fromone unit to another. converts time measure from seconds tominutes, minutes to hours, hours to day. converts time measure from days to weeksand months, and convert weeks, months andyears to days. finds the exact time between dates. solves word problems involving timemeasure. recognize, perform and useconversions of common units. converts common units of measure fromlarger unit to smaller unit and vice versa:meter and centimeter, kilogram and gram,liter and milliliter. solves word problems involving conversionsof common units of measure.
34. 34. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 34Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… explore the concept of areaand find areas of squares andrectangles using cm2and m2.The learner … estimates the area of a square and rectangleusing non-standard units. finds the area of a square in cm2and m2. finds the area of a rectangle in cm2and m2. solves word problems involving areas ofsquares and rectangles. measure capacity usingmilliliter and liter. finds the capacity of a container usingmilliliter/liter. solves word problems involving capacitymeasure.Statistics and Probability  tables, bar graphs andprobability. organize and interpret datapresented in tables and bargraphs. collects and organizes data in a table. reads and interprets a table. constructs a bar graph. reads and interprets a bar graph. make simple predictions ofevents. tells whether an event is most likely tohappen, equally likely to happen or unlikelyto happen based on facts.
35. 35. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 35GRADE 4Content Content Standards Performance Standards Learning CompetenciesNumbers and Number Sense The learner demonstratesunderstanding of… number notation and placevalue of numbers up to100000, and of factors andmultiples of numbers up to100, and of the greatestcommon factor and leastcommon multiple.The learner is able to… read, write, compare andarrange numbers through 100000 and round off numbers tothe nearest thousands andten thousands.The learner… reads and writes numbers through hundredthousands in symbols and in words. identifies numbers up to 100 000. gives the place value of each digit in a six-digit number. reads and writes numbers up to hundredthousands in symbols and in words. compares numbers up to hundredthousands. arranges numbers up to hundred thousands. investigate the concepts offactors and multiples. identifies factors of a given number up to100. identifies the multiples of a given number upto 100. makes conjectures about common factors ofnumbers. find the greatest commonfactor and the least commonmultiple of given numbers. differentiates prime numbers from compositenumbers. finds the prime factors of a number.
36. 36. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 36Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … writes a given number as a product of itsprime factors. gives the common factors and the greatestcommon factor (GCF) of two numbers usingthe following methods: listing, factor tree. gives the common multiples and leastcommon multiple (LCM) of two numbers:listing, factor tree, continuous division. finds the GCF and LCM of 2 given numbers. multiplication, division andMDAS of whole numbers. estimate and multiply 3-digitnumbers and solvemultiplication problemsinvolving these numbers. multiplies numbers up to 3-digit numbers byup to 2-digit numbers without regrouping andwith zero in any of the factors. multiplies numbers up to 3-digit numbers byup to 2-digit numbers with regrouping andwith zero in any of the factors. estimates the products of three to four digitsby two to three-digit numbers. mentally multiplies two-digit numbers withproducts up to 200 and explain thestrategies used. analyzes and solves word problemsinvolving multiplication of whole numbersincluding money using appropriate problemsolving strategies.
37. 37. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 37Content Content Standards Performance Standards Learning CompetenciesThe learner is able to… The learner … analyzes and solves two-step word problemsinvolving multiplication and addition orsubtraction using appropriate problemsolving strategies. creates and solves word problems involvingmultiplication and any of the two operationsinvolving whole numbers and money. estimate and divide 3- to 4-digit numbers by 1- to 2- digitnumbers and solve divisionproblems involving thesenumbers. divides 3- to 4-digit numbers by 1- to 2- digitnumbers without remainder. divides 3- to 4-digit numbers by 1- to 2- digitnumbers with remainder. divides 3- to 4-digit numbers by 1- to 2- digitnumbers with zeros in the middle orcontinuous zeros in the dividend. divides 3- to 4-digit numbers by multiples of10 and 100 or by 1000. estimates the quotient of 3- to 4-digitdividends by 1- to 2- digit divisors byrounding up or rounding down dividends ordivisors. mentally divides 2- to 3-digit numbers by 1-digit numbers without remainder and explainthe strategies used.
38. 38. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 38Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … analyzes and solves one-step wordproblems involving division of 3- to 4-digitnumbers by 1- to 2- digit numbers includingmoney using appropriate problem solvingstrategies. analyzes and solves 2- to 3-step wordproblems involving division and any one ortwo of the other fundamental operationsincluding money using appropriate problemsolving strategies. creates and solves 1- to 2- step wordproblems involving multiplication and anyother operations involving whole numbersand money. perform series of operationsfollowing the MDAS rule. interprets and explains MDAS correctly. performs a series of two or more operations. a fraction as part of a set ofobjects, as a number, asdivision, and of the differentkinds of fractions and appliesthem in real-life situations. identify fractions on a numberline and investigate fractionsas part of a set of objects. illustrates fractions using regions, sets andthe number line. divides sets of objects into smaller sets ofequal amounts to recognize and identifyfractional parts of a set. compare and arrange similarand dissimilar fractions. identifies similar and dissimilar fractions froma given set of fractions. compares and arranges similar fractionsfrom least to greatest and vice versa.
39. 39. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 39Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … compares and arranges dissimilar fractionsfrom least to greatest and vice versa. convert improper fractions tomixed numbers and viceversa. identifies proper fraction/ improperfraction/mixed numbers from a given set offractions including those with denominatorsof 10 and 100. changes improper fraction to mixed numbersand vice versa. converts one (1) to a fraction and vice versa. operation of fractions.  add and subtract fractionsand solve problems involvingaddition and subtraction offractions. visualizes and adds similar fractions. visualizes and subtracts similar fractions. visualizes and subtracts a fraction from awhole number. adds and subtracts dissimilar fractions. solves word problems involving addition andsubtraction of fractions using appropriateproblem solving strategies.Geometry  parallel and perpendicularlines, measures of angles,symmetry, plane figures up to4 sides, and 2-Drepresentation of a 3-D solid. investigate the concepts ofparallel and perpendicularlines and angles. describes and illustrates different angles(right, acute and obtuse) using models. draws perpendicular and parallel lines usinga ruler and set squares.
40. 40. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 40Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner is able to… identifies parts of an angle and name anglesusing notation such as ABC , x , and 2in plane figures. draws a given angle using a protractor. describes and illustrates parallel andperpendicular lines. identifies parallel and perpendicular linesand use these terms to describe geometricfigures. describe various plane figuresup to four sides and discusstheir properties. uses concrete objects/ models toexplore/describe plane figures according totheir attributes/properties of triangles andquadrilaterals. identifies and describes the different kinds oftriangles: acute, right, obtuse, scalene,isosceles, equilateral, equiangular. identifies and describes the different kinds ofquadrilaterals: square, rectangle,parallelogram, trapezoid, rhombus. explore symmetry in planefigures and the environment. identifies and visualizes symmetry in theenvironment and in design. completes a symmetric figure with respect toa given line of symmetry.
41. 41. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 41Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… explore different geometricsolids.The learner is able to… visualizes and describes geometric solids. makes models of different geometric solids:cube, prism, cylinder.Patterns and Algebra  patterns and numbersentences. describe the rule in a patternin order to complete thepattern. searches for a pattern given a set of objectsor figures. determines the next object or term or figurefrom a given pattern. complete number sentences.  finds the missing value in a numbersentence involving one of the fouroperations of whole numbers.Measurement  measures of perimeter andarea of squares, rectangles,triangles, parallelograms andtrapezoids, and their relatedfigures, and volume ofrectangular prism. find the perimeter of a planefigure and solve problemsinvolving perimeter. describes and illustrates the perimeter of agiven figure. finds the perimeter of triangles, squares,rectangles, parallelograms and trapezoids. solves word problems involving perimeter ofsquares and rectangles, triangles,parallelograms and trapezoids. find the area of a plane figureand solve problems involvingarea. estimates the area of an irregular planefigure made up of squares and rectanglesusing non-standard units. derives inductively the formulas for the areaof squares and rectangles.
42. 42. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 42Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner is able to… finds the area of a figure made up of squaresand rectangles using cm2and m2. estimates the area of triangles,parallelograms and trapezoids using non-standard units. derives inductively the formulas for the areaof triangles, parallelograms and trapezoids. finds the area of triangles, parallelogramsand trapezoids using cm2and m2. solves word problems involving the area of afigure made up of squares and rectangles. solves word problems involving the area of atriangle, parallelogram and trapezoid. explore the concept of volumeof a solid and solve problemsinvolving the volume of asolid. visualizes and builds rectangular prismsusing unit cubes. derives inductively the formula for thevolume of rectangular prisms. finds the volume of a rectangular prism usingcubic units. solves word problems involving the volumeof a rectangular prism.
43. 43. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 43Content Content Standards Performance Standards Learning CompetenciesStatistics and Probability The learner demonstratesunderstanding of… tables, bar graphs andprobability.The learner is able to… solve problems involving datapresented in bar graphs andtables.The learner is able to… organizes data in tables. constructs bar graphs and organize datausing bar graphs. reads and interprets data presented in tablesand bar graphs. solves problems using data presented in bargraphs and tables. make simple predictions ofevents based on datarecords. gathers and records favorable outcomesfrom an activity with different results (e.g.,rolling a die, drawing a card, tossing coins,etc.). analyzes the chance of a result usingspinners.
44. 44. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 44GRADE 5Content Content Standards Performance Standards Learning CompetenciesNumbers and Number Sense The learner demonstrates… understanding of numbernotation and place value ofnumbers up to 10 million andof some number theoryconcepts.The learner is able to… read and write large wholenumbers and round off wholenumbers to the nearestthousands and millions.The learner… visualizes and represents whole numbers upto 10 000 000. reads and writes whole numbers up to 10000 000. rounds off whole numbers to the nearestthousands and millions. find the greatest commonfactor and the least commonmultiple of given numbers. writes a given number as a product of itsprime factors. gives the common factors and the greatestcommon factor (GCF) of two numbers usingthe following methods: listing, factor tree,continuous division. gives the common multiples and leastcommon multiple (LCM) of two numbers:listing, factor tree, continuous division. finds the GCF and LCM of 2 given numbers. apply divisibility rules for 2, 3,4, 5, 6, 8, 9, 10, 11 and 12 ondifferent contexts. uses divisibility rules for 2, 5 and 10 to findcommon factors of numbers. uses divisibility rules for 3, 6 and 9 to findcommon factors. uses divisibility rules for 4, 8, 11 and 12 tofind common factors.
45. 45. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 45Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… The learner … solves problems involving factors, multiplesand divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10,11 and 12. mastery of concepts andoperations/series ofoperations (PMDAS) of wholenumbers. simplify a series of operationson whole numbers and solveproblems involving these. states, explains and interprets the PMDASor GMDAS rule. simplifies a series of operations on wholenumbers involving more than two operationsusing the PMDAS or GMDAS rule. analyzes and solves problems involvingseries of operations. the ability to perform the fourfundamental operations onsimilar and dissimilarfractions. perform the four fundamentaloperations on fractions andmixed numbers and solverelated problems. represents the four operations on dissimilarfractions and mixed numbers using concreteand pictorial models. estimates sums, differences, products andquotients of fractions and mixed numbers. adds fractions and mixed numbers withoutand with regrouping. subtracts fractions and mixed numberswithout and with regrouping. multiplies fractions and mixed numbers. finds a fractional part of a whole number orof a fraction. mentally multiplies fractional units.
46. 46. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 46Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… The learner … divides fractions and mixed numbers. simplifies fractions and mixed numbers totheir lowest terms. solves problems involving addition,subtraction, multiplication and division offractions and mixed numbers using theappropriate strategies. understanding of the conceptof decimals, and addition andsubtraction of decimals up tohundredths. investigate the relationshipbetween fractions anddecimal numbers. uses models to illustrate fractions as divisionof two numbers. visualizes decimal numbers using modelslike blocks, grid, number line and money. visualizes decimal numbers usingmodels/pictures to show the relationship tofractions. reads and writes common fractions indecimal form through thousandths. renames decimal numbers to fractions withdenominators of 10, 100, 1000,10000. explore, know andunderstand the concept andvalue of a decimal number. gives the place value of each digit of a givendecimal through thousandths. reads and writes decimal numbers throughthousandths.
47. 47. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 47Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… The learner … rounds decimals to the nearest tenths andhundredths. compares and arranges decimal numbersfrom least to greatest and vice versa. add and subtract decimalnumbers with values throughthousandths and solveproblems involving these. estimates the sum or difference of decimalnumbers. adds and subtracts decimals throughthousandths without and with regrouping. adds and subtracts mixed decimals withoutand with regrouping. analyzes and solves word problems,including money problems, involving additionand subtraction of decimal numbers. multiply decimal numbers ofvalues up to the hundredthsand solve problems involvingthese numbers. represents multiplication of decimal numbersusing pictorial models. estimates the products of decimal numbers. multiplies decimal numbers by multiples of10 and 100. multiplies decimal numbers of values up tohundredths. multiplies mixed decimals with tenths andhundredths by whole numbers.
48. 48. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 48Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… The learner … multiplies mixed decimals by mixed decimalswith tenths and hundredths. multiplies decimals mentally by 0.1, 0.01, 10and 100. analyzes and solves word problemsinvolving multiplication of decimals includingmoney. divide decimal numbers ofvalues up to the hundredthsand solve problems involvingthese numbers. represents division of decimal numbersusing pictorial models. estimates the quotients of decimal numbers. divides decimal numbers of values up to thehundredths. divides decimal numbers by whole numbers. analyzes and solves problems of varioustypes using whole numbers, fractions anddecimals. understanding on the use ofratio, proportion and percent. manipulate ratios and solveproblems involving ratios andproportions visualizes the ratio of two given sets ofobjects. expresses the ratio of two numbers usingeither the colon (:) or a fraction. expresses one value as a fraction of anothergiven their ratio and vice versa.
49. 49. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 49Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… The learner … finds how many times one value is as largeas another given their ratio and vice versa. identifies and writes equivalent ratios. expresses ratios in their simplest forms. finds the missing term in a pair of equivalentratios. defines and describes a proportion. recognizes when two quantities are in directproportion. solves problems involving ratio and directproportion. know and understand theconcept of percent and tosolve problems involvingpercents. uses models to illustrate the concept ofpercent and its relationship to fractions,ratios and decimal numbers. gives the relationship among fractions, ratiosand percents, between percent and adecimal number, among fractions, ratios,decimal numbers and percents. defines the following: percentage, rate orpercent, base. identifies the base percentage and rate in aproblem.
50. 50. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 50Content Content Standards Performance Standards Learning Competencies finds the percentage in a given problem. analyzes and solves problems involvingpercents.Geometry The learner demonstrates… understanding of polygons upto 10 sides, congruence andsimilarities of polygons andcircle and its parts.The learner is able to… explore polygons with up to10 sides.The learner… describes, models and draws polygons. names polygons with 5 or more sides. describes and compares properties ofpolygons. represents congruent polygons usingmodels. identifies and describes congruent polygons. represents similar polygons using models. identifies and describes similar polygons. finds the missing dimension in a pair ofsimilar polygons. explore circles.  visualizes and describes a circle. identifies and defines the terms related to acircle. draws circles with different radii using acompass.
51. 51. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 51Content Content Standards Performance Standards Learning CompetenciesPatterns and Algebra The learner demonstrates… understanding of simpleequations.The learner is able to… solve for the unknown valuesin simple equations involvingone or more operations onwhole numbers and fractions.The learner … uses models to illustrate mathematicalsentences. determines the patterns in completingmathematical sentences. uses patterns to solve for the unknown insimple equations involving one or moreoperation on whole numbers and fractions.Measurement  understanding onmeasurement in metric unitsto approximate measure andto compute for thecircumference, area, volumeand temperature. describe the circumference ofa circle, measure and use it tosolve problems. the measureof circumference, area of acircle, volume of a cube and arectangular prism andtemperature. represents and describes the circumferenceof a circle. uses a model to estimate the circumferenceof a circle. derives a formula for finding thecircumference of a circle. finds the circumference of the given circleusing the formula/s derived. solves problems involving circumference. convert units of measure forarea and volume and selectappropriate units and tools forconsistency and accuracy. estimates and uses appropriate units ofmeasure for area. converts sq cm to sq m and vice versa. names the appropriate unit of measure usedfor measuring area for accuracy. estimates and uses appropriate units ofmeasure for volume.
52. 52. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 52Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… The learner … converts one cubic unit of measure to alarger or smaller unit. names the appropriate unit of measure usedfor measuring the volume of a cube and arectangular prism for accuracy. describe the area of a circle,measure and use it to solveproblems. represents and describes the area of acircle. uses a model to find the area of a circle. derives a formula for finding the area of acircle. finds the area of a circle using the formula/sderived. solves problems involving area of circleusing appropriate formulas and procedures. describe the volume of a cubeand a rectangular prism,measure and use it to solveproblems. describes the volume of cube and arectangular prism. derives a formula for finding the volume ofcube and a rectangular prism. solves problems involving volume of a cubeand rectangular prism using appropriateformulas and procedures.
53. 53. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 53Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… describe temperature,measure and use it to solveproblems.The learner … describes and estimates the temperatureinside and outside of the classroom. identifies the parts of a thermometer. reads a thermometer. measures temperature using the degreeCelsius. solves problems involving temperature.Probability and Data Analysis  understanding to record,arrange, present, andinterpret data using tables,line graphs and probability. construct, read and interpret aline graph and itscorresponding table of dataand solve problems involvingdata from a table and a linegraph. reads and interprets data presented in a linegraph and in its corresponding table of data. constructs a line graph using thecorresponding table of data. describes and estimates the average valueof a set of data. finds the average value of a set of data thatincludes whole numbers, fractions anddecimal numbers. solves problems involving line graphs andthe average of a set of data. make simple predictions ofevents based on a probabilityexperiment. describes a probability experiment. performs a probability experiment and recordresults by listing.
54. 54. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 54Content Content Standards Performance Standards Learning Competencies analyzes data obtained from chance usingexperiments involving letter cards (A to Z)and number cards (0 to 20).
55. 55. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 55GRADE 6Content Content Standards Performance Standards Learning CompetenciesNumbers and Number Sense The learner demonstrates… understanding of the conceptof integers, exponents, baseand scientific notation.The learner is able to… explore the concept ofintegers and compareintegers with whole numbers,fractions and decimalnumbers.The learner… describes the set of integers. identifies real-life situations that make use ofintegers. represents integers on the number line. compares integers with other numbers suchas whole numbers, fractions and decimals. compares and arranges integers from leastto greatest and vice versa. use the notation andcomputation of positive wholenumber powers to find valuesof numbers. defines and describes the exponent and thebase in a number expressed in exponentialnotation. gives the value of numbers expressed inexponential notation. expresses positive whole numbers inexpanded notation using exponentialnotation and vice versa. finds and compares the value of thenumbers expressed in either the expandedor exponential notation. reads and writes numbers up to trillions inscientific notation.
56. 56. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 56Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… The learner… determines the value of a number expressedin scientific notation. perform the four basicoperations on integers describes and interprets the basic operationson integers using materials such as algebratiles, counters, chips and cards. states the rules for addition, subtraction,multiplication and division of integers. performs the basic operations on integers. solves problems involving basic operationson integers. perform a series of operationsfollowing the GEMDAS ruleand solve problems involvinga series of operations onwhole numbers. interprets and explains the GEMDAS rule. performs two or more different operations onwhole numbers with or without exponentsand grouping symbols. solves problems involving a series ofoperations on whole numbers. mastery of the operations offractions and decimals. add and subtract fractionsand decimal numbers andsolve problems involvingthese numbers. estimates sums and differences of fractionsand decimals in simple or mixed forms. rounds decimals through thousandths. adds and subtracts fractions in simple mixedforms without or with regrouping.
57. 57. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 57Content Content Standards Performance Standards Learning CompetenciesThe learner is able to… The learner … adds and subtracts decimals and mixeddecimals through ten thousandths without orwith regrouping. solves problems involving addition andsubtraction of fractions and decimals insimple or mixed forms without and withregrouping. multiply fractions and decimalnumbers and solve problemsinvolving multiplication offractions and decimalnumbers. illustrates multiplication of fractions anddecimals using models. estimates products of whole numbers,fractions and decimals. multiplies fractions in simple and mixedforms. shows that multiplying a fraction by itsreciprocal is equal to 1. multiplies decimals and mixed decimalsthrough thousandths without and withregrouping and with “0” difficulty. solves problems involving addition,subtraction, and multiplication of numbers inmixed forms. divide fractions and decimalnumbers and solve problemsinvolving division of fractionsand decimal numbers. illustrates division of fractions and decimalsusing models.
58. 58. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 58Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… The learner… estimates quotients of whole numbers,fractions and decimals and determine thereasonableness of results (add this to allother competencies involving estimation). divides fractions and decimal numbers insimple and mixed forms. divides whole numbers (two to five-digitdividends) by decimals (one to two- digitdivisors). divides mixed decimals by whole numbers. divides whole numbers by decimals andmixed decimals. divides mixed decimals by mixed decimals. divides decimals by 10, 100, 1,000 mentally. divides decimals by 0.1, 0.01, 0.001mentally. differentiates between terminating andrepeating from non-terminating decimalquotients. solves problems involving division offractions and decimals in mixed formsincluding money. solves word problems involving alloperations on fractions.
59. 59. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 59Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… The learner … analyzes and solves problems of varioustypes-mathematical tasks, word problems,contextual questions and real-world settingsusing whole numbers, fractions anddecimals. understanding of ratio andproportion and percent. use ratio and proportion in avariety of ways and solveproblems in different contexts. defines and illustrates the meaning of ratioand proportion using concrete or pictorialmodels. forms ratios and sets up proportions forgroups of objects or numbers. tells whether two ratios make a proportion. finds a missing term in a proportion. sets up a proportion for a given situation. solves problems involving direct proportion,partitive proportion, inverse proportion indifferent contexts such as distance-rate-time. use percent in a variety ofways and solve problems indifferent contexts. defines and illustrates percent. determines the percentage, rate and base ina given problem. computes common percentage problemsmentally: percent of increase or decrease,discounts and sales, value-added tax andservice charge.
60. 60. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 60Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… The learner is able to… The learner … solves problems involving finding thepercentage, rate and base: commission,sales, taxes and simple interest.Geometry  understanding of angles ingeometric figures usingvarious properties, attributesof spatial figures, 2-Drepresentation of a 3-D solidand identification of nets ofcube, prism and pyramid. find unknown angle measuresin geometrical figures. describes the properties of angles on astraight line, angles at a point and verticallyopposite angles. determines the sum of the angles in atriangle and a quadrilateral. finds unknown angles using angle propertiesin geometrical figures such as a square,rectangle, parallelogram, rhombus, trapezoidand triangle. explore spatial figures.  identifies the different spatial figures. illustrates the different spatial figures usingvarious concrete and pictorial models. visualizes and describes the different spatialfigures: cube, prism, cylinder, sphere,pyramid, cone, etc. identifies the nets of the following spatialfigures: cube, prism, cylinder, pyramid andcone.Measurement  understanding ofcircumference and area of acircle, perimeter and area offigures related to square, solve problems involvingfinding areas of compositefigures. finds the area of composite figures formedby any two or more of the following: triangle,square, rectangle, circle and semi-circle.
61. 61. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 61Content Content Standards Performance Standards Learning Competenciesrectangle, triangle and circle,surface area and volume ofrectangular prisms andcapacity.The learner is able to… The learner … solves word problem involving area ofcomposite figures formed by any two ormore of the following: triangle, square,rectangle, circle and semi-circle. explore the concept ofsurface area and find thesurface area of geometricsolids. identifies the faces of a geometric solid. visualizes and describes surface area andname the unit of measure used formeasuring the surface area of solids. derives a formula for finding the surface areaof cubes, prisms and cylinders. finds the surface area of cubes, prisms andcylinders. solves word problems involvingmeasurement of surface area. find the volume of solids andsolve problems related to this. describes the meaning of the volume of asolid. determines the relationship between thevolume of a rectangular prism and of apyramid and between a cylinder and a cone. obtains formulas for finding the volumes ofcylinders, pyramids and cones. finds the volume of a cylinder, pyramid or acone. solves problems involving volumes of solids.
62. 62. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 62Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates… understanding of electric andwater consumption, time, rateand speed.The learner is able to… read and interpret meterreadings.The learner… reads and interprets electric and water meterreadings. solves problems involving electric and waterconsumptions. measure time in a variety ofways and solve problemsinvolving time, rate andspeed. estimates the duration of time in secondsand minutes. measures time using a 12-hour and a 24-hour clock. converts measures of time from a 12-hour toa 24-hour clock and vice versa. calculates time in the different world timezones. calculates speed, distance and time. solves problems involving average rate andspeed.Statistics and Probability  understanding to record,arrange, present and interpretdata using tables and circlegraphs and understands themeaning of probability. construct and interpret circlegraphs. reads and interprets data presented in acircle graph. constructs a circle graph based on a table ofdata. makes inferences and hypotheses on datapresented in a circle graph.
63. 63. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 63Content Content Standards Performance Standards Learning CompetenciesThe learner demonstrates The learner is able to… make simple predictions ofevents based on experiments.The learner … describes the meaning of probability such as“50% chance of rain” and “one in a millionchance of winning.” quantifies the phrases “most likely tohappen” and “unlikely to happen.” performs experiments and record outcomes. makes listings and diagrams of outcomesand tell the number of favorable outcomesand chances using these listings anddiagrams. makes simple predictions of events basedon the results of experiments.Patterns and Algebra  understanding of constants,variables and algebraicexpressions in one variable. explore the meaning ofnumerical expressions andequations. differentiates between an expression and anequation and differentiate the two. gives a verbal translation of an equation andan expression using real-life contexts andvice versa. solves problems involving different types ofnumerical expressions and equations suchas 7 + 9 = _____ + 6. use a letter or symbol torepresent a quantity in asimple algebraic expressionand simplify an algebraicexpression. replaces a quantity in a numerical equationor expression with a letter or symbol andwrite the equation or expression in differentforms.
64. 64. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 64Content Content Standards Performance Standards Learning CompetenciesThe learner is able to… The learner … writes an algebraic expression involving onlyone letter or symbol. describes the uses of a letter or symbol in analgebraic expression: placeholder, patterngeneralizer, unknown, value (e.g.  ) andlabel. defines a variable in an algebraicexpression. simplifies algebraic expressions in onevariable. evaluates algebraic expressions involvingone variable. represents quantities in real-life situationusing algebraic expressions. use a variable to generate apattern in a series. identifies the pattern in a given series ofobjects and numbers. determines the quantity to be represented bya letter or a symbol in a pattern. writes the algebraic expression thatrepresents the pattern in a given series ofobjects or numbers. determines the next object or number in agiven series using the algebraic expressionfor the pattern.
65. 65. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 65GRADE 7Content Content Standards Performance Standards Learning CompetenciesNumbers and Number Sense The learner demonstratesunderstanding of… the key concepts of sets, thereal number system,estimation / approximation ofa square of a number and themeasures of quantities, andthe applications of realnumbers to measurements.The learner is able to… explore set concepts and setoperations.The learner… describes and illustrates well-defined sets,subsets, universal set and the null set. defines and describes the union andintersection of sets and the complement of aset. uses Venn Diagrams to represent sets,subsets and set operations. solves problems involving sets. apply various procedures andmanipulations on the differentsubsets of the set of realnumbers. describes and illustrates the absolute valueof a number on a number line as thedistance of the number from 0. performs fundamental operations onintegers: addition, subtraction, multiplication,division. states and illustrates the different propertiesof the operations on integers (commutative,associative, distributive, identity, inverse). defines and illustrates rational numbers andarrange them on a number line.
66. 66. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 66Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … expresses rational numbers (both repeatingand terminating/non-repeating and non-terminating) from fraction form to decimalform and vice versa. performs operations on rational numbersand illustrate their properties. describes principal roots and tells whetherthey are rational or irrational. determines between what two integers thesquare root of a number is. estimates the square root of a number to thenearest tenth. illustrates and graphs irrational numbers(square roots) on a number line with andwithout appropriate technology. describes, represents and compares thedifferent subsets of real numbers. finds the union, intersection and complementof the set of real numbers and its subsets. arranges real numbers in increasing ordecreasing order. determines the significant digits in a givensituation.
67. 67. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 67Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … writes very large or very small numbers inscientific notation. describes and represents real-life situationswhich involve integers, rational numbers,square roots of a rational numbers andirrational numbers. solves problems involving real numbers.Measurement  the different types ofmeasures. extend concepts ofmeasurements to includedifferent types of measuresand all the subsets of the setof real numbers to solvemeasurement problems. describes what it means to measure. describes the development of measurementfrom the primitive to the present internationalsystem of units. estimates or approximates the measures ofquantities particularly length, weight/mass,volume, time, angle and temperature. uses appropriate instruments to measurequantities such as length, weight/mass,volume, time, angle and temperature. converts measurements from one unit toanother for each type of measurementincluding the English system. solves problems involving measurementssuch as perimeter, area, weight, time,speed, temperature, volume/capacity andutilities usage (meter reading).
68. 68. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 68Content Content Standards Performance Standards Learning CompetenciesAlgebra The learner demonstratesunderstanding of… the key concepts of algebraicexpressions as applied insolving problems.The learner is able to… simplify and evaluatealgebraic expressions in oneor more variables.The learner … translates verbal phrases to mathematicalphrases and vice versa. differentiates between constants andvariables in a given algebraic expression. evaluates algebraic expressions for givenvalues of the variables. explore the concept of andmanipulate polynomials. gives examples of polynomials, monomial,binomial, trinomial. identifies the base, coefficient, terms andexponents in a given polynomial. defines and interprets the meaning of anwhere 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 asum and difference of two terms; (c) squareof a binomial; (d) cube of a binomial; (e)product of a binomial and a trinomial.
69. 69. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 69Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … finds algebraically the (a) product of twobinomials; (b) product of a sum anddifference of two terms; (c) square of abinomial; (d) cube of a binomial; (e) productof a binomial and a trinomial. solve equations andinequalities. differentiates between mathematicalexpressions and mathematical equations. translates English sentences tomathematical sentences and vice versa. differentiates between equations andinequalities. defines and illustrates the meaning ofabsolute value. finds the solution of an equation or inequalityinvolving one variable, including one thatinvolves absolute value (a) from a givenreplacement; (b) intuitively by guess andcheck; (c) by algebraic procedures (applyingthe properties of equalities and inequalities);(d) graphing. solves problems that use equations andinequalities.
70. 70. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 70Content Content Standards Performance Standards Learning CompetenciesGeometry The learner demonstratesunderstanding of… the key concepts of geometryof shapes and sizes,geometric construction andthe application ofmeasurements in geometricfigures.The learner is able to… analyze and investigate in amore formal environment thebasic concepts in geometry.The learner … represents a point, line and plane usingconcrete and pictorial models. defines, identifies and names the subsets ofa line. illustrates, names, identifies and defines thedifferent kinds of angles. derives relationships of geometric figuresusing measurements and by inductivereasoning: supplementary angles,complementary angles, equal angles,adjacent angles, linear pairs, perpendicularlines and parallel lines. derives relationships between vertical anglesand among angles formed by parallel linescut by a transversal using measurement andby inductive reasoning. analyze and investigate thedifferent kinds of triangles,quadrilaterals, convexpolygons and circles. uses a compass and straightedge to bisectline segments and angles and constructperpendiculars and parallels. classifies triangles according to their anglesand according to their sides. illustrates, names and identifies differentkinds of triangles and define the termsassociated with a triangle.
71. 71. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 71Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … derives relationships among the sides andangles of a triangle using measurement andinductive reasoning. illustrates, names and identifies the differentkinds of quadrilaterals. derives relationships among the angles andamong the sides of a quadrilateral usingmeasurement and inductive reasoning. defines and illustrates convex polygons. derives the relationship of exterior andinterior angles of any convex polygon usingmeasurement and inductive reasoning. illustrates a circle and defines the termsrelated to it: radius, diameter, center, arc andcentral angle.Statistics and Probability  the key concepts, uses andimportance of statistics andprobability, datacollection/gathering and thedifferent forms of datarepresentation. engage in statisticalinvestigations. explains the basic concepts, uses andimportance of Statistics. poses questions and problems that may beanswered using Statistics. collects or gathers statistical data andorganizes the data in a frequency tableaccording to some systematicconsiderations.
72. 72. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 72Content Content Standards Performance Standards Learning CompetenciesThe learner is able to… The learner … uses appropriate graphs to representorganized data: pie chart, bar graph, linegraph and a histogram. finds the mean, median and mode ofstatistical data. describes the data using information fromthe mean, median and mode. analyzes, interprets accurately and drawsconclusions from graphic and tabularpresentations of statistical data.
73. 73. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 73GRADE 8Content Content Standards Performance Standards Learning CompetenciesAlgebra The learner demonstratesunderstanding of… special products and factorsof polynomials and operationsrational expressions.The learner is able to… recognize special productsand factor polynomials.The learner… identifies polynomials which are specialproducts: polynomials with commonmonomial factors, trinomials that areproducts of two binomials, trinomials that aresquares of a binomial, and products of thesum and difference of two terms (e.g.x2 y2,x3 y3). finds special products and factors of certainpolynomials: product of two binomials,product of sum and difference of two terms,square of a binomial, cube of a binomial, andproduct of the special case of multiplying abinomial and a trinomial. factors completely different types ofpolynomials (polynomials with commonmonomial factors, a difference of twosquares, sum and difference of two cubes,perfect square trinomial, general trinomials)using special formulas, grouping and othertechniques. solves problems involving polynomials andtheir products and factors. perform operations on rationalexpressions. defines and illustrates rational expressions. simplifies rational expressions.
74. 74. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 74Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner… multiplies and divides rational expressions. adds and subtracts rational expressions. simplifies complex fractions. solves problems involving rationalexpressions. manipulate algebraicexpressions with integralexponents. defines and interprets zero and negativeexponents. evaluates algebraic expressions involvingintegral exponents. simplifies algebraic expressions involvingintegral exponents. linear functions and theirgraphs. explore the rectangularcoordinate system. describes the rectangular coordinate systemand its uses. defines and illustrates the coordinate axes,the origin and a point on the coordinateplane. describes and plots positions on thecoordinate plane using coordinate axes. explore the concept of arelations and a function. defines and illustrates a relation and afunction. determines if a given relation is a functionusing a table of ordered pairs, graphs andequations.
75. 75. K TO 12 MATHEMATICS*K to 12 Curriculum Guide – version as of January 31, 2012 75Content Content Standards Performance Standards Learning CompetenciesThe learner demonstratesunderstanding of…The learner is able to… The learner … differentiates between dependent andindependent variables. defines and describes the domain and rangeof a function. explore the linear function, itsequation and graph. defines and describes a linear function usingits points, equation and graph. finds the domain and range of a linearfunction. defines and illustrates the meaning of slopeof a line. finds the slope of a line given two points, atable of values or list of ordered pairs, itsequation and graph. writes the linear equationAx  By  C in theformy  mx b and vice versa. graphs a linear equation given (a) any twopoints; (b) the x- and y-intercepts; (c) theslope and a point on the line. characterizes the graph of a linear equationin terms of its intercept and slope. finds the equation of a line given (a) twopoints; (b) the slope and a point; (c) theslope and its intercept.