Mathematics

K to 12 Curriculum Guide MATHEMATICS Grade 1 to 10

Republic of the Philippines Department of Education DepEd Complex, Meralco Avenue Pasig CityK to 12 Curriculum Guide MATHEMATICS (Grade 1 to Grade 10) December 2013

K to 12 BASIC EDUCATION CURRICULUM Figure 1.The Conceptual Framework of Mathematics Education Page 2 of 109K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUM CONCEPTUAL FRAMEWORK Mathematics is one subject that pervades life at any age and in any circumstance. Thus, its value goes beyond the classroom and the school. Mathematicsas 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. Critical thinking, according to Scriven and Paul (1987) is the intellectually disciplined process of actively and skilfully 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, according to Polya (1945 & 1962), mathematical problem solving is finding a way around a difficulty, around an obstacle, and finding a solution to aproblem 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 andattitudes, and appropriate tools, taking into account 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 andcommunicating; 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 necessary in teaching mathematics. These include: manipulative objects, measuring devices, calculators andcomputers, smart phones and tablet PCs, and the Internet. We define context as a locale, situation, or set of conditions of Filipino learners that may influence their study and use of mathematics to develop critical thinking andproblem solving skills. Contexts refer to beliefs, environment, language and culture that include traditions and practices, as well as the learner’s prior knowledge andexperiences.K to 12 Mathematics Curriculum Guide December 2013 Page 3 of 109

K to 12 BASIC EDUCATION CURRICULUM The framework is supported by the following underlying learning principles and theories: Experie ntial 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 learningas \"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 in 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 whenlearners are able to think about their experiences and process these, allowing them the opportunity to make sense of and derive meaning from their experiences. Constructivism is the theory that argues that knowledge is constructed when the learner is able to draw ideas from his/her own experiences and connect them to newideas. 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 Learning 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 Curriculum Guide December 2013 Page 4 of 109

K to 12 BASIC EDUCATION CURRICULUMBRIEF 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 scienceand 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 include 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 onattributes such as length, mass and weight, capacity, time, money, and temperature, as well as applications involving perimeter, area, surface area, volume, and anglemeasure. Geometry as a strand includes properties of two- and three-dimensional figures and their relationships, spatial visualization, reasoning, and geometric modelling andproofs. Patterns and Algebra as a strand studies patterns, relationships, and changes among shapes and quantities. It includes the use of algebraic notations andsymbols, 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 andinterpreting data; dealing with uncertainty; and making predictions about outcomes. The K to 10 Mathematics Curriculum provides a solid foundation for Mathematics at Grades 11 to 12. More importantly, it pro vides necessary concepts and lifeskills needed by Filipino learners as they proceed to the next stage in their life as learners and as citizens of the Philippines.K to 12 Mathematics Curriculum Guide December 2013 Page 5 of 109

K to 12 BASIC EDUCATION CURRICULUMLEARNING AREA STANDARD: The learner demonstrates understanding and appreciation of key concepts and principles of mathematics as applied - using appropriatetechnology - in problem solving, critical thinking, communicating, reasoning, making connections, representations, and decisions in real life.KEY STAGE STANDARDS: 4–6 7 – 10 K–3At the end of Grade 3, the learner demonstrates At the end of Grade 6, the learner demonstrates At the end of grade 10, the learnerunderstanding and appreciation of key concepts and skills understanding and appreciation of key concepts and skills demonstrates understanding and appreciation of keyinvolving numbers and number sense (whole numbers up involving numbers and number sense (whole numbers, concepts and skills involving numbers and number senseto 10,000 and the four fundamental operations including number theory, fractions, decimals, ratio and proportion, (sets and real numbers); measurement (conversion ofmoney, ordinal numbers up to 100th, basic concepts of percent, and integers);measurement (time, speed, units); patterns and algebra (linear equations andfractions); measurement (time, length, mass, capacity, perimeter, circumference and area of plane figures, inequalities in one and two variables, linear functions,area of square and rectangle); geometry (2-dimensional volume and surface area of solid/space figures, systems of linear equations, and inequalities in twoand 3-dimensional objects, lines, symmetry, and temperature and meter reading); geometry (parallel and variables, exponents and radicals, quadratic equations,tessellation); patterns and algebra (continuous and perpendicular lines, angles, triangles, quadrilaterals, inequalities, functions, polynomials, and polynomialrepeating patterns and number sentences); statistics and polygons, circles, and solid figures); patterns and algebra equations and functions); geometry (polygons, axiomaticprobability (data collection and representation in tables, (continuous and repeating patterns, number sentences, structure of geometry, triangle congruence, inequalitypictographs and bar graphs and outcomes)as applied - sequences, and simple equations); statistics and and similarity, and basic trigonometry);statistics andusing appropriate technology - in critical thinking, probability (bar graphs, line graphs and pie graphs, probability (measures of central tendency, variability andproblem solving, reasoning, communicating, making simple experiment, and experimental probability) as position; combinatorics and probability) as applied - usingconnections, representations, and decisions in real life. applied -using appropriate technology - in critical thinking, appropriate technology - in critical thinking, problem problem solving, reasoning, communicating, making solving, communicating, reasoning, making connections, connections, representations, and decisions in real life. representations, and decisions in real life.K to 12 Mathematics Curriculum Guide December 2013 Page 6 of 109

K to 12 BASIC EDUCATION CURRICULUMGRADE LEVEL STANDARDS:GRADE LEVEL GRADE LEVEL STANDARDS K The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 20,GRADE 1 basic concepts on addition and subtraction); geometry (basic attributes of objects), patterns and algebra (basic concept of sequence and numberGRADE 2 pairs); measurement (time, location, non-standard measures of length, mass and capacity); and statistics and probability (data collection and tables)GRADE 3 as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations andGRADE 4 decisions in real life.GRADE 5 The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 100, ordinal numbers up to 10th, money up to PhP100, addition and subtraction of whole numbers, and fractions ½ and 1/4);geometry (2- and 3- dimensional objects); patterns and algebra (continuous and repeating patterns and number sentences); measurement (time, non-standard measures of length, mass, and capacity);and statistics and probability (tables, pictographs, and outcomes) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life. The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 1 000, ordinal numbers up to 20th, money up to PhP100, the four fundamental operations of whole numbers, and unit fractions); geometry (basic shapes, symmetry, and tessellations); patterns and algebra (continuous and repeating patterns and number sentences);measurement (time, length, mass, and capacity); and statistics and probability (tables, pictographs, and outcomes) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life. The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 10 000; ordinal numbers up to 100th; money up to PhP1 000;the four fundamental operations of whole numbers; proper and improper fractions; and similar, dissimilar, and equivalent fractions); geometry (lines, symmetry, and tessellations); patterns and algebra (continuous and repeating patterns and number sentences); measurement (conversion of time, length, mass and capacity, area of square and rectangle); and statistics and probability (tables, bar graphs, and outcomes) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life. The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 100 000, multiplication and division of whole numbers, order of operations, factors and multiples, addition and subtraction of fractions, and basic concepts of decimals including money); geometry (lines, angles, triangles, and quadrilaterals); patterns and algebra (continuous and repeating patterns and number sentences); measurement (time, perimeter, area, and volume); and statistics and probability (tables, bar graphs, and simple experiments) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life. The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 10 000 000, order of operations, factors and multiples, fractions and decimals including money, ratio and proportion, percent); geometry (polygons, circles, solid figures); patterns and algebra (sequence and number sentences); measurement (time, circumference, area, volume, and temperature); and statistics and probability (tables, line graphs and experimental probability) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.K to 12 Mathematics Curriculum Guide December 2013 Page 7 of 109

GRADE LEVEL K to 12 BASIC EDUCATION CURRICULUM GRADE 6 GRADE 7 GRADE LEVEL STANDARDS GRADE 8 GRADE 9 The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (divisibility, order of GRADE 10 operations, fractions and decimals including money, ratio and proportion, percent, integers); geometry (plane and solid figures); patterns and algebra (sequence, expression, and equation); measurement (rate, speed, area, surface area, volume, and meter reading); and statistics and probability (tables, pie graphs, and experimental and theoretical probability) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life. The learner demonstrates understanding of key concepts and principles of numbers and number sense (sets and real number system); measurement (conversion of units of measurement);patterns and algebra (algebraic expressions and properties of real numbers as applied in linear equations and inequalities in one variable); geometry (sides and angles of polygons); and statistics and probability (data collection and presentation, and measures of central tendency and variability) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life. The learner demonstrates understanding of key concepts and principles of patterns and algebra (factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables); geometry (axiomatic structure of geometry, triangle congruence, inequalities in a triangle, and parallel and perpendicular lines); and statistics and probability (probability of simple events) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life. The learner demonstrates understanding of key concepts and principles of patterns and algebra (quadratic equations and inequalities, quadratic functions, rational algebraic equations, variations, and radicals) and geometry (parallelograms and triangle similarities and basic concepts of trigonometry) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life. The learner demonstrates understanding of key concepts and principles of patterns and algebra (sequences, series, polynomials, polynomial equations, and polynomial functions); geometry (circles and coordinate geometry); and statistics and probability (combinatorics and probability, and measures of position) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.K to 12 Mathematics Curriculum Guide December 2013 Page 8 of 109

K to 12 BASIC EDUCATION CURRICULUMTime Allotment: Grade 1 2 3 4 5 6 7 8 9 10Daily 50 min 50 min 50 min 50 min 50 min 50 minWeekly 4 hours 4 hours 4 hours 4 hoursK to 12 Mathematics Curriculum Guide December 2013 Page 9 of 109

K to 12 BASIC EDUCATION CURRICULUM GRADE 1CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... M1NS-Ia-1.1  BEAM LG Gr.1 Module 2-Grade 1- FIRST QUARTER The learner... M1NS-Ib-2.1 Sets of Whole Numbers M1NS-Ib-3Numbers and demonstrates 1. is able to recognize, 1. visualizes and represents numbers  Lesson Guide in Elem. represent, and order from 0 to 100 using a variety of M1NS-Ic-4 Math Grade 1 p. 70Number understanding of whole whole numbers up to materials. M1NS- Id-5Sense numbers up to 100, 100 and money up to M1NS-Id- 6  Lesson Guide in Elem. PhP100 in various 2. counts the number of objects in a given M1NS-Ie-7 Math Grade 1 pp. 49, 54, ordinal numbers up to forms and contexts. set by ones and tens. 73, 84 10th, money up to PhP100 M1NS-Ie-8.1 2. is able to recognize, 3. identifies the number that is one more  BEAM LG Gr.1 Module 2- and fractions ½ and 1/4. and represent ordinal or one less from a given number. M1NS-If-9.1 Reading and Writing of numbers up to 10th, Whole Numbers in various forms and 4. composes and decomposes a given contexts. number. e.g. 5 is 5 and 0, 4 and 1, 3  BEAM LG Gr.1 Module 2- and 2, 2 and 3, 1 and 4, 0 and 5. Sets of Whole Numbers 5. regroups sets of ones into sets of tens  BEAM LG Gr.1 Module 2- and sets of tens into hundreds using Sets of Whole Numbers objects.  Lesson Guide in Elem. 6. visualizes, represents, and compares Math Grade 1 p. 40 two sets using the expressions “less than,” “more than,” and “as many as.”  BEAM LG Gr.1 Module 2- Reading and Writing of 7. visualizes, represents, and orders sets Whole Numbers from least to greatest and vice versa.  Lesson Guide in Elem. 8. visualizes and counts by 2s, 5s and 10s Math Grade 1 pp. 76, 79, through 100. 82 9. reads and writes numbers up to 100 in  BEAM LG Gr.1 Module 2- symbols and in words. Reading and Writing of Whole NumbersK to 12 Mathematics Curriculum Guide December 2013  Lesson Guide in Elem. Math Grade 1 pp. 90, 94 Page 10 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M1NS-Ig-10.1  BEAM LG Gr.1 Module 2- The learner... The learner... M1NS-Ig-11 Reading and Writing of M1NS-Ih-12.1 Whole Numbers 10. visualizes and gives the place value and M1NS-Ih-13.1 value of a digit in one- and two-digit M1NS-Ii-16.1  Lesson Guide in Elem. numbers. M1NS-Ii-17.1 Math Grade 1 p. 88 M1NS-Ij-19.1 11. renames numbers into tens and ones.  Lesson Guide in Elem. M1NS-IIa-23 Math Grade 1 p. 97 12. visualizes, represents, and compares M1NS-IIa-26.1 numbers up to 100 using relation  Lesson Guide in Elem. symbols. M1NS-IIa-28.1a Math Grade 1 p.67 13. visualizes, represents, and orders  Lesson Guide in Elem. numbers up to 100 in increasing or Math Grade 1 p. 58 decreasing order.  BEAM LG Gr.1 Module 2- 14. identifies the 1st , 2nd, 3rd, up to 10th Reading and Writing of object in a given set from a given point Whole Numbers of reference.  Lesson Guide in Elem. 15. reads and writes ordinal numbers: 1st, Math Grade 1 p. 104 2nd, 3rd up to 10th.  BEAM LG Gr.1 Module 2- 16. recognizes and compares coins and Reading and Writing of bills up to PhP100 and their notations. Whole NumbersGrade 1- SECOND QUARTER  Lesson Guide in Elem. Math Grade 1 p. 109Numbers and demonstrates is able to apply 17. illustrates addition as “puttingNumber understanding of addition and together or combining or joining sets”  Lesson Guide in Elem.Sense addition and Math Grade 1 p. 123 subtraction of whole subtraction of whole numbers up to 100  BEAM LG Gr.1 Module 4- including money numbers up to 100 18. visualizes and adds two one-digit Addition including money in mathematical numbers with sums up to 18 using the  Lesson Guide in Elem. order and zero properties of addition. Math Grade 1 pp. 135, 137 problems and real- life situations. 19. adds two one-digit numbers using appropriate mental techniques e.g. adding doubles and/or near-doubles.K to 12 Mathematics Curriculum Guide December 2013 Page 11 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS M1NS-IIb-26.2  BEAM LG Gr.1 Module 4- The learner... The learner... The learner... Addition M1NS-IIb-27.1 20. visualizes and adds three one-digit M1NS-IIc-27.2  Lesson Guide in Elem. numbers using the grouping property M1NS-IIc-27.3 Math Grade 1 p. 141 of addition. M1NS-IId-28.1b M1NS-IId-28.2  BEAM LG Gr.1 Module 4- 21. visualizes and adds two to three one- Addition digit numbers horizontally and M1NS-IIe-29.1 vertically.  Lesson Guide in Elem. M1NS-IIe-30.1 Math Grade 1 p. 144 22. uses expanded form to explain the M1NS-IIf-24 meaning of addition with regrouping. M1NS-IIf-25  BEAM LG Gr.1 Module 4- Addition 23. visualizes and adds numbers with M1NS-IIg-32.1 sums through 99 without or with  Lesson Guide in Elem. regrouping. Math Grade 1 pp. 149, 152 24. adds mentally two to three one- digit  Lesson Guide in Elem. numbers with sums up to 18 using Math Grade 1 p. 147 appropriate strategies.  BEAM LG Gr.1 Module 5- 25. adds mentally two-digit numbers and Application of Addition one-digit numbers with regrouping using appropriate strategies.  Lesson Guide in Elem. Math Grade 1 p. 169 26. visualizes and solves one-step routine and non-routine problems involving  BEAM LG Gr.1 Module 6- addition of whole numbers including Subtraction money with sums up to 99 using appropriate problem solving  BEAM LG Gr.1 Module 6- strategies. Subtraction 27. creates situations involving addition of  Lesson Guide in Elem. whole numbers including money . Math Grade 1 p. 190 Page 12 of 109 28. illustrates subtraction as “taking away” or “comparing” elements of sets. 29. illustrates that addition and subtraction are inverse operations. 30. visualizes, represents, and subtracts one-digit numbers with minuends through 18 (basic facts)K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS M1NS-IIg-32.2 M1NS-IIh-32.3  BEAM LG Gr.1 Module 6- The learner... The learner... The learner... M1NS-IIh-32.4 Subtraction M1NS-IIi-33.1 31. visualizes, represents, and subtracts  Lesson Guide in Elem. one- to two-digit numbers with M1NS-IIi-34.1 Math Grade 1 p. 194 minuends up to 99 without regrouping. M1NS-IIj-35.1  BEAM LG Gr.1 Module 6- M1NS-IIIa-37 Subtraction 32. uses the expanded form to explain M1NS-IIIa-48 subtraction with regrouping.  Lesson Guide in Elem. Math Grade 1 p. 197 33. visualizes, represents, and subtracts one- to two-digit numbers with  BEAM LG Gr.1 Module 6- minuends up to 99 with regrouping. Subtraction 34. subtracts mentally one-digit numbers  Lesson Guide in Elem. from two-digit minuends without Math Grade 1 p. 209 regrouping using appropriate strategies.  BEAM LG Gr.1 Module 7- Application of Subtraction 35. visualizes, represents, and solves routine and non-routine problems  Lesson Guide in Elem. involving subtraction of whole Math Grade 1 p. 235 numbers including money with minuends up to 99 with and without Page 13 of 109 regrouping using appropriate problem solving strategies and tools.Grade 1- THIRD QUARTER 36. creates situations involving subtraction of whole number including money. 37. counts groups of equal quantity using concrete objects up to 50 and writes an equivalent expression. e.g. 2 groups of 5 38. visualizes, represents, and separates objects into groups of equal quantity using concrete objects up to 50. e.g. 10 grouped by 5sK to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS M1NS-IIIb-72.1  Lesson Guide in Elem. The learner... The learner... The learner... M1NS-IIIc-73 Math Grade 1 pp. 239, M1NS-IIIc-74.1 242Numbers and demonstrates is able to recognize, 39. visualizes and identifies ½ and ¼ of M1NS-IIId-74.2Number understanding of represent, and a whole object. M1NS-IIId-75  BEAM LG Gr.1 Module 8-Sense fractions ½ and 1/4. compare fractions ½ Fractions and 1/4 in various 40. visualizes, represents, and divides a M1GE-IIIe-1 forms and contexts. whole into halves and fourths.  Lesson Guide in Elem. M1GE-IIIe-2 Math Grade 1 pp. 246, 41. visualizes, and divides the elements 249 of sets into two groups of equal quantities to show halves.  BEAM LG Gr.1 Module 8- Fractions 42. visualizes, represents, and divides the elements of sets into four groups  Lesson Guide in Elem. of equal quantities to show fourths Math Grade 1 p. 254Geometry demonstrates is able to describe, 43. visualizes and draws the whole  BEAM LG Gr.1 Module 8- understanding of 2- compare, and region or set given its ½ and/or ¼ Fractions dimensional and 3- construct 2- dimensional figures. dimensional and 3- 44. identifies, names, and describes the  Lesson Guide in Elem. dimensional objects four basic shapes (square, rectangle, Math Grade 1 p. 258 triangle and circle) in 2-dimensional (flat/plane) and 3-dimensional (solid)  BEAM LG Gr.1 Module 8- objects. Fractions 45. compares and classifies 2-  BEAM LG Gr.2 Module - dimensional (flat/plane) and 3- Shapes dimensional (solid) figures according to common attributes. 46. draws the four basic shapes. M1GE-IIIf-3 47. constructs three dimensional objects M1GE-IIIf-4 (solid) using manipulative materials.K to 12 Mathematics Curriculum Guide December 2013 Page 14 of 109

K to 12 BASIC EDUCATION CURRICULUM CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS M1AL-IIIg-1Patterns and  Lesson Guide in Elem.Algebra The learner... The learner... The learner... M1AL-IIIg-2 Math Grade 1 p. 184 M1AL-IIIh-8 demonstrates is able to apply 48. determines the missing term/s in a M1AL-IIIi-9  Lesson Guide in Elem. understanding of knowledge of given continuous pattern using M1AL-IIIj-10 Math Grade 1 pp. 39 – 41; continuous and continuous and one attribute (letters/ 57 – 63 repeating patterns and repeating patterns numbers/events). mathematical and number Page 15 of 109 sentences. sentences in various e.g. situations. A,B,C,D,__ 2,3,__5,6,7 __,Wed, Thur, Fri Aa, Bb, Cb, __,___ 49. determines the missing term/s in a given repeating pattern using one attribute(letters, numbers, colors, figures, sizes, etc.). e.g. A,B,C,A,B,C,A,__ _ 50. constructs equivalent number expression using addition and subtraction. e.g. 6 + 5 = 12 - 1 51. identifies and creates patterns to compose and decompose using addition. e.g. 7 = 0 + 7, 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1, 7 + 0 52. visualizes and finds the missing number in an addition or subtraction sentence using a variety of ways e.g. n+2=5 5–n=3K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner...Grade 1- FOURTH QUARTERMeasurement demonstrates is able to apply  BEAM LG Gr.1 Module 5- understanding of time knowledge of time and Measurement: Time and non-standard non-standard 53. tells the days in a week; months in a M1ME-IVa-1 Measure units of length, mass measures of length, year in the right order. M1ME-IVa-2 and capacity. M1ME-IVb-3  Lesson Guide in Elem. mass, and capacity in 54. determines the day or the month using Math Grade 1 pp. 262, mathematical a calendar. 267 problems and real-life situations  Lesson Guide in Elem. Math Grade 1 pp. 270, 55. tells and writes time by hour, half-hour 274, 281 and quarter-hour using analog clock. 56. solves problems involving time (days in M1ME-IVb-4  BEAM LG Gr.1 Module 10- a week, months in a year, hour, half- M1ME-IVc-19 Linear Measure hour, and quarter-hour) M1ME-IVd-20 M1ME-IVe-21  Lesson Guide in Elem. 57. compares objects using comparative M1ME-IVf-22 Math Grade 1 p. 284 words: short, shorter, shortest; long, longer, longest; heavy, heavier,  BEAM LG Gr.1 Module 11- heaviest; light, lighter, lightest. Mass Measure 58. estimates and measures length using  Lesson Guide in Elem. non- standard units of linear measures. Math Grade 1 p. 292 59. estimates and measures mass using  Lesson Guide in Elem. non-standard units of mass measure. Math Grade 1 p. 298 60. estimates and measures capacity using non-standard unit.K to 12 Mathematics Curriculum Guide December 2013 Page 16 of 109

K to 12 BASIC EDUCATION CURRICULUM CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS M1SP-IVg-1.1Statistics and The learner... M1SP-IVg-2.1Probability The learner... The learner... demonstrates M1SP-IVh-3.1 understanding of is able to create and 61. collects data on one variable through pictographs without interpret simple simple interview. M1SP-IVh-4.1 scales and outcomes representations of data M1SP-IVi-7.1 of an event using the (tables and pictographs 62. sorts, classifies, and organizes data in M1SP-IVj-8.1 terms likely and without scales) and tabular form and presents this into a unlikely to happen. describe outcomes of pictograph without scales. familiar events using the terms likely and 63. infers and interprets data presented in unlikely to happen. a pictograph without scales. e.g. finding out from the title what the pictograph is all about, comparing which has the least or greatest … 64. solves routine and non-routine problems using data presented in pictograph without scales. 65. tells whether an event is likely or unlikely to happen. 66. describe events in real-life situations using the phrases “ likely” or “unlikely to happen”. e.g. Tomorrow it will rain.K to 12 Mathematics Curriculum Guide December 2013 Page 17 of 109

K to 12 BASIC EDUCATION CURRICULUM GRADE 2CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... M2NS-Ia-1.2  BEAM LG Gr. 2 Module 1-Grade 2- FIRST QUARTER The learner... M2NS-Ib-2.2 Whole Numbers M2NS-Ib-10.2Numbers and 1. visualizes and represents numbers M2NS-Ib-8.2  Lesson Guide in Elem.Number M2NS-Ic-9.2 Math Grade 2 p. 1Sense 1. demonstrates 1. is able to recognize, from 0-1000 with emphasis on M2NS-Ic-14 understanding of represent, compare, M2NS-Id-12.2  BEAM LG Gr. 2 Module 1- whole numbers up numbers 101 – 1 000 using a variety of M2NS-Id-13.2 Whole Numbers to 1000, ordinal and order whole materials. numbers up to 20th, numbers up to 1000,  Lesson Guide in Elem. and money up to 2. groups objects in ones, tens, and Math Grade 2 p.12 PhP100. ordinal numbers up to hundreds. 20th, and money up  BEAM LG Gr. 2 Module 1- 2. demonstrates to PhP100 in various Whole Numbers understanding of forms and contexts. 3. gives the place value and finds addition of whole the value of a digit in three-digit  Lesson Guide in Elem. numbers up to Math Grade 2 p.24 1000 including 2. is able to recognize numbers. money.  BEAM LG Gr. 2 Module 1- and represent ordinal Whole Numbers numbers up to 20th in various forms and 4. visualizes and counts numbers by  Lesson Guide in Elem. contexts. 10s, 50s, and 100s. Math Grade 2 p.15 3. is able to apply 5. reads and writes numbers up to  BEAM LG Gr. 2 Module 1- 1 000 in symbols and in words. Whole Numbers addition of whole 6. visualizes and writes three-digit  Lesson Guide in Elem. numbers up to 1000 numbers in expanded form. Math Grade 2 p.18 including money in  BEAM LG Gr. 2 Module 1- mathematical Whole Numbers problems and real-life  Lesson Guide in Elem. situations. Math Grade 2 p.21 7. visualizes and compares numbers up to 1 000 using relation symbols. 8. visualizes and orders numbers up to 1 000 in increasing or decreasing order.K to 12 Mathematics Curriculum Guide December 2013 Page 18 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner... 9. identifies the 1st through the M2NS-Ie-16.2  BEAM LG Gr. 2 Module 2- 20th with the emphasis on 11th M2NS-Ie-17.2 Presenting Whole to 20th object in a given set from M2NS-Ie-18 Numbers a given point of reference. M2NS-If-20.1  Lesson Guide in Elem. 10. reads and writes ordinal numbers M2NS-If-21 Math Grade 2 p.28 from 1st through the 20th.  BEAM LG Gr. 2 Module 1- 11. identifies and uses the pattern of Whole Numbers naming ordinal numbers from 1st to the 20th.  BEAM LG Gr. 2 Module 1- Whole Numbers 12. reads and writes money in symbols and in words through  Lesson Guide in Elem. PhP100. Math Grade 2 p.40 13. counts the value of a set of bills  BEAM LG Gr. 1 Module 1- or a set of coins through PhP100 Reading and Writing (peso-coins only; centavo-coins Whole Numbers only; peso-bills only and combined peso-coins and peso-  Lesson Guide in Elem. bills). Math Grade 2 p.42 14. compares values of different  BEAM LG Gr. 2 Module 3- denominations of coins and Money paper bills through PhP100 using relation symbols. M2NS-If-22.1  BEAM LG Gr. 2 Module 3- M2NS-Ig-26.3 Money 15. illustrates the properties of addition (commutative,  Lesson Guide in Elem. associative, identity) and applies Math Grade 2 p.50 each in appropriate and relevant situations.  BEAM LG Gr. 2 Module 4- AdditionK to 12 Mathematics Curriculum Guide December 2013  Lesson Guide in Elem. Math Grade4 p.24  DLP Gr. 4 Modules 9, 10, 11; Gr. 5 Module 2 Page 19 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner... 16. visualizes, represents, and adds M2NS-Ig-27.4  BEAM LG Gr. 2 Module 4- 2-digit by 3-digit numbers with M2NS-Ih-27.5 Addition sums up to 1000 without and M2NS-Ih-28.3 with regrouping .  Lesson Guide in Elem. Math Grade 2 p.59 17. visualizes, represents, and adds 3-digit by 3-digit numbers with  BEAM LG Gr. 2 Module 4- sums up to 1000 without and Addition with regrouping.  Lesson Guide in Elem. 18. adds mentally 1- to 2-digit Math Grade 2 p.59 numbers with sums up to 50 using appropriate strategies.  BEAM LG Gr. 2 Module 4- Addition  Lesson Guide in Elem. Math Grade 2 p.83 19. adds mentally 3-digit numbers M2NS-Ii-28.4 and 1-digit numbers using appropriate strategies. 20. adds mentally three -digit M2NS-Ii-28.5 numbers and tens (multiples of 10 up to 90) using appropriate strategies. 21. adds mentally 3-digit numbers M2NS-Ii-28.6 and hundreds (multiples of 100 up to 900) using appropriate M2NS-Ij-29.2  BEAM LG Gr. 2 Module – strategies. Application of Addition 22. solves routine and non-routine  Lesson Guide in Elem. problems involving addition of Math Grade 2 p.87 whole numbers including money with sums up to 1000 using M2NS-Ij-30.2 appropriate problem solving strategies and tools. 23. creates problems involving addition of whole numbers including money.K to 12 Mathematics Curriculum Guide December 2013 Page 20 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner...Grade 2- SECOND QUARTERNumbers and demonstrates is able to apply subtraction 24. visualizes, represents, and M2NS-IIa-32.5  BEAM LG Gr. 2 Module 6-Number understanding of and multiplication of whole subtracts 2- to 3-digit numbers M2NS-IIb-33.2 SubtractionSense subtraction and numbers up to 1000 with minuends up to 999 without multiplication of whole including money in and with regrouping.  Lesson Guide in Elem. numbers up to 1000 mathematical problems and Math Grade 2 p.105 including money. real-life situations. 25. subtracts mentally 1-digit numbers from 1- to 3-digit  BEAM LG Gr. 2 Module 6- numbers without regrouping Subtraction using appropriate strategies.  LessonGuide in Elem. 26. subtracts mentally 3-digit Math Grade 2 p.123 numbers by tens and by hundreds without regrouping M2NS-IIb-33.3 using appropriate strategies. M2NS-IIc-34.2  BEAM LG Gr. 2 Module – 27. solves routine and non-routine Application of Subtraction problems involving subtraction of whole numbers including money  Lesson Guide in Elem. with minuends up to 1000 using Math Grade 2 p.126 appropriate problem solving strategies and tools. M2NS-IId-35.2 28. creates problems involving M2NS-IId-34.3 subtraction of whole numbers including money. 29. performs orders of operations involving addition and subtractions of small numbers. 30. solves multi-step routine and M2NS-IIe-34.4  BEAM LG Gr. 2 Module 8- non-routine problems involving Application of Addition addition and subtraction of 2- to and Subtraction 3-digit numbers including money using appropriate problem solving strategies and tools.K to 12 Mathematics Curriculum Guide December 2013 Page 21 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner... 31. creates word problems involving M2NS-IIe-35.3 addition and subtraction of whole numbers including money.  Lesson Guide in Elem. Math Grade 2 p.140 32. illustrates multiplication as repeated addition using M2NS-IIf-38 32.1 groups of equal quantities 32.2 arrays 32.3 counting by multiples 32.4 equal jumps on the number line 33. writes a related equation for each  Lesson Guide in Elem. type of multiplication: repeated Math Grade 2 p.148 addition, array, counting by multiples, and equal jumps on M2NS-IIf-39 the number line. M2NS-IIg-40.1  Lesson Guide in Elem. 34. illustrates the property of Math Grade 2 p.157 multiplication that any number multiplied by one (1) is the same M2NS-IIg-40.2  Lesson Guide in Elem. number. Math Grade 2 p.160 35. illustrates the property of  DLP Gr. 4 Module 27 multiplication that zero multiplied by any number is zero. 36. illustrates the commutative M2NS-IIg-40.3 property of multiplication. M2NS-IIh-41.1  BEAM LG Gr. 2 Module - 37. visualizes multiplication of numbers 1 to 10 by 2,3,4,5 Multiplication and10. 38. multiplies mentally 2,3,4,5 and 10 M2NS-IIi-42.1  BEAM LG Gr. 2 Module – using appropriate strategies. Multiplication  Lesson Guide in Elem. Math Grade 2 p.166K to 12 Mathematics Curriculum Guide December 2013 Page 22 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner... 39. solves routine and non-routine M2NS-IIi-45.1  BEAM LG Gr. 2 Module – problems involving multiplication M2NS-IIj-45.2 Multiplication of whole numbers including money using appropriate problem  Lesson Guide in Elem. solving strategies and tools. Math Grade 2 p.169 40. solves routine and non-routine  Lesson Guide in Elem. problems involving multiplication Math Grade 2 p.177 and addition or subtraction of whole numbers including money using appropriate problem solving strategies and tools. 41. creates problems involving M2NS-IIj-46.1 multiplication only and multiplication with addition or subtraction of whole numbers including money with reasonable answers.Grade 2- THIRD QUARTERNumbers and 1. demonstrates 1. is able to apply 42. visualizes and represents division as M2NS-IIIa-49  BEAM LG Gr. 2 ModuleNumber understanding of division of whole equal sharing, repeated subtraction, 11– Application of DivisionSense division of whole numbers up to 1000 equal jumps on the number line and numbers up to 1000 including money in using formation of equal groups of  Lesson Guide in Elem. including money. mathematical objects Math Grade 2 p.181 problems and real-life situations. 43. creates and writes a related  DLP Gr. 3 Module 24 equation for each type of 2. demonstrates 2. is able to recognize situation: equal sharing, repeated M2NS-IIIa-50 understanding of unit and represent unit subtraction, equal jumps on the fractions. fractions in various number line, and formation of forms and contexts. equal groups of objects. M2NS-IIIb-51.1  BEAM LG Gr. 2 Module 44. visualizes division of numbers up 11– Application of Division to 100 by 2,3,4,5, and 10 (multiplication table of 2, 3, 4, 5 and 10).K to 12 Mathematics Curriculum Guide December 2013 Page 23 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner... 45. divides mentally numbers by M2NS-IIIb-52.1 2,3,4,5 and 10 using appropriate strategies (multiplication table of 2, 3, 4, 5 and 10). 46. illustrates that multiplication and M2NS-IIIc-53  DLP Gr. 3 Module 28 division are inverse operations.  Lesson Guide in Elem. 47. solves routine and non-routine Math Grade 2 p.206 problems involving division of numbers by 2,3,4,5 and 10 and  BEAM LG Gr. 2 Module with any of the other operations 11– Application of Division of whole numbers including money using appropriate M2NS-IIIc-56.1 problem solving strategies and tools. M2NS-IIIc-57.1 48. creates word problems involving M2NS-IIId-72.2  BEAM LG Gr. 2 Module 13 division of whole numbers – Fractions including money. M2NS-IIId-76.1 M2NS-IIIe-77.1  Lesson Guide in Elem. 49. visualizes, represents and Math Grade 2 p.231 identifies unit fractions with denominators of 10 and below.  Lesson Guide in Elem. Math Grade 2 p.240 50. reads and writes unit fractions.  Lesson Guide in Elem. 51. compares unit fractions using Math Grade 2 p.245 relation symbols. M2NS-IIIe-78.1 52. arranges unit fractions in increasing or decreasing order. 53. identifies other fractions less than  DLP Gr. 3 Module 35 one with denominators 10 and below. M2NS-IIIe-79.1K to 12 Mathematics Curriculum Guide December 2013 Page 24 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALSGeometry STANDARDS The learner... The learner... The learner... 54. visualizes similar fractions M2NS-IIIf-72.3 (using group of objects and number line). M2NS-IIIf-76.2  DLP Gr. 3 Module 36 M2NS-IIIf-77.2 55. reads and writes similar  Lesson Guide in Elem. fractions. M2NS-IIIf-78.2 Math Grade 4 p.205 56. compares similar fractions  MISOSA Module Gr. 4 – using relation symbols. Ordering Similar Fractions 57. arranges similar fractions in increasing or decreasing order. demonstrates is able to recognize and 58. visualizes, identifies, classifies M2GE-IIIg-5 understanding of straight construct straight and and describes half circles and and curved lines, flat curved lines, flat and quarter circles. M2GE-IIIg-6 and curved surfaces, curved surfaces, basic basic shapes, symmetry shapes and create simple 59. constructs squares, rectangles,  BEAM LG Gr. 2 Module in a line, and designs that show triangles, circles, half-circles, Geometry – Tessellations tessellations using symmetry in a line and and quarter circles using cut- triangles and squares. tessellation using outs and square grids.  Lesson Guide in Elem. triangles and squares. Math Grade 2 p.266 60. identifies shapes/figures that M2GE-IIIh-7.1 show symmetry in a line. 61. identifies and draws the line M2GE-IIIh-7.4a of symmetry in a given symmetrical figure. M2GE-IIIh-7.2 62. creates figures that show M2GE-IIIh-8.1  Lesson Guide in Elem. symmetry in a line. M2GE-IIIi-8.2 Math Grade 2 p.263 63. recognizes shapes that can tessellate. 64. tessellates a surface using triangles and squares.K to 12 Mathematics Curriculum Guide December 2013 Page 25 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner... 65. identifies straight lines and M2GE-IIIi-9 curves, flat and curved surfaces in a 3-dimensional M2GE-IIIi-10 object. This is not reflected in the performance standards. 66. explains the differences between straight lines and curved lines, flat surfaces and curved surfaces. This is not reflected in the performance standards.Patterns and demonstrates is able to apply 67. determines the missing term/s inAlgebra understanding of knowledge of a given continuous pattern using continuous patterns using continuous patterns two attributes (any two of the two attributes and using two attributes following: figures, numbers, M2AL-IIIj-3 mathematical sentences and number sentences colors, sizes, and orientations, involving multiplication involving multiplication etc.) and division of whole and division using 2, 3, numbers using 2, 3, 4, 5 4, 5 and 10 only in e.g. and 10 only. various situations. 1, A, 2,B,3,C,__,__ 1 , 2 , 3 , 4 __ 68. visualizes and finds the missing M2AL-IIIj-11 value in a number sentence involving multiplication or division of whole numbers using 2, 3, 4, 5 and 10 only. e.g. 5 x __ = 30 30 ÷ __ = 6K to 12 Mathematics Curriculum Guide December 2013 Page 26 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner...Grade 2- FOURTH QUARTERMeasurement demonstrates is able to apply knowledge 69. tells and writes time in minutes M2ME-IVa-5  BEAM LG Gr. 2 Module 9 – understanding of time, of time, standard measures including a.m. and p.m. using M2ME-IVa-6 Time Measure standard measures of of length, weight, and analog and digital clocks. M2ME-IVa-7 length, mass and capacity capacity, and area using  Lesson Guide in Elem. and area using square-tile square-tile units in 70. visualizes and finds the elapsed Math Grade 2 p.285 units. mathematical problems and time in days. real-life situations.  BEAM LG Gr. 2 Module 9 – 71. visualizes, represents, and solves Time Measure problems involving time (minutes including a.m. and p.m. and  Lesson Guide in Elem. elapsed time in days). Math Grade 2 p.304 72. shows and uses the appropriate M2ME-IVb-23 unit of length and their abbreviation cm and m to M2ME-IVb-24  Lesson Guide in Elem. measure a particular object. M2ME-IVb-25 Math Grade 2 p.309 M2ME-IVc-26 73. compares length in meters or M2ME-IVc-27  Lesson Guide in Elem. centimeters. Math Grade 2 p.312 74. measures objects using M2ME-IVd-28 appropriate measuring tools in m or cm. M2ME-IVd-29  BEAM LG Gr. 2 Module 18 M2ME-IVd-30 – Mass and Capacity 75. estimates and measures length using meter or centimeter.  BEAM LG Gr. 2 Module 18 – Mass and Capacity 76. solves routine and non-routine problems involving length.  Lesson Guide in Elem. Math Grade 2 p.317 77. shows and uses the appropriate unit of weight and their Page 27 of 109 abbreviations g and kg to measure a particular object. 78. compares mass in grams or kilograms. 79. measures objects using appropriate measuring units in g or kg.K to 12 Mathematics Curriculum Guide December 2013

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner... 80. estimates and measures mass M2ME-IVe-31  BEAM LG Gr. 2 Module 18 using gram or kilogram. – Mass and Capacity  Lesson Guide in Elem. Math Grade 2 p.323 81. solves routine and non-routine M2ME-IVe-32 problems involving mass. 82. measures objects using M2ME-IVf-33 appropriate measuring tools in mL or L. 83. creates problems involving M2ME-IVf-34 length, mass and capacity. M2ME-IVg-35  BEAM LG Gr. 2 Module 12 84. illustrates area as a measure of – Area how much surface is covered or occupied by a plane figure. M2ME-IVg-36 85. finds the area of a given figure M2ME-IVh-37 using square-tile units i.e. number of square-tiles needed. 86. estimates the area of a given figure using any shape. 87. solves routine and non-routine M2ME-IVh-38 problems involving any figure using square tiles.K to 12 Mathematics Curriculum Guide December 2013 Page 28 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner... The learner...Statistics and deepens understanding of is able to create and 88. collects data on one variable M2SP-IVh-1.2Probability interpret simple using a questionnaire. pictographs without and representations of data with scales and outcomes (tables and pictographs 89. sorts, classifies, and organizes M2SP-IVi-2.2 without and with scales) data in tabular form and of an event using the and describe outcomes of presents this into a pictograph familiar events using the without and with scales. terms likely, equally likely terms likely, equally likely and unlikely to happen. and unlikely to happen. 90. infers and interprets data presented in a pictograph without and with scales. M2SP-IVi-3.2  BEAM LG Gr. 3 Module 15 – Pictograph 91. solves routine and non-routine M2SP-IVi-4.2 problems using data presented in M2SP-IVj-7.2 a pictograph without and with M2SP-IVj-8.2 scales. 92. tells whether an event is likely, equally likely, unlikely to happen. 93. describe events in real-life situations using the phrases “ likely to happen” or “unlikely to happen” or “equally likely to happen”.K to 12 Mathematics Curriculum Guide December 2013 Page 29 of 109

K to 12 BASIC EDUCATION CURRICULUM GRADE 3CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS The learner... The learner...Grade 3- FIRST QUARTER The learner...Numbers and 1. demonstrates 1. is able to recognize, 1. visualizes numbers up to 10 000 with M3NS-Ia-1.3  Lesson Guide in Elem.Number understanding of represent, compare, emphasis on numbers 1001 - 10000. Math 3 pp. 1 – 14Sense whole numbers up and order whole to 10 000, ordinal numbers up to 10 2. gives the place value and value of a  BEAM LG Gr. 3 Module 1.1 numbers up to 000, and money up digit in 4- to 5-digit numbers. 100th, and money up to PhP1000 in – Whole Numbers to PhP1000. various forms and 3. reads and writes numbers up to 10 contexts. 000 in symbols and in words. M3NS-Ia-10.3  Lesson Guide in Elem. 2. demonstrates M3NS-Ia-9.3 Math 3 pp. 15 – 17 understanding of 2. is able to recognize 4. rounds numbers to the nearest ten, M3NS-Ib-15.1 addition and and represent, hundred and thousand.. M3NS-Ib-12.3  BEAM LG Gr. 3 Module 1.1 subtraction of whole ordinal numbers up M3NS-Ib-13.3 – Whole Numbers numbers including to 100th in various money forms and contexts.  MTB-MLE Group – Teacher’s Guide 3. is able to apply addition and  Lesson Guide in Elem. subtraction of whole Math 3 pp. 18 - 27 numbers including money in  BEAM LG Gr. 3 Module 1.1 mathematical – Whole Numbers problems and real- life situations.  MTB-MLE Group – Teacher’s Guide 5. compares numbers up to 10 000 using relation symbols.  Lesson Guide in Elem. Math 3 pp. 37 – 40 6. orders 4- to 5-digit numbers in increasing or decreasing order.  BEAM LG Gr. 3 Module 1.2 – Whole Numbers  DLP Gr. 4 Module 5  MTB-MLE Group – Teacher’s Guide  BEAM LG Gr. 3 Module 1.1 – Whole Numbers  MTB-MLE Group – Teacher’s Guide  MTB-MLE Group – Teacher’s GuideK to 12 Mathematics Curriculum Guide December 2013 Page 30 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M3NS-Ic-16.3 M3NS-Ic-19.2  MTB-MLE Group – The learner... The learner... M3NS-Ic-20.2 Teacher’s Guide 7. identifies ordinal numbers from 1st to M3NS-Id-22.2  Lesson Guide in Elem. 100th with emphasis on the 21st to M3NS-Id-27.6 Math 3 pp.49 – 51 100th object in a given set from a M3NS-Ie-31 given point of reference. M3NS-Ie-28.7  BEAM LG Gr. 3 Module 1.3 – Whole Numbers 8. recognizes coins and bills up to PhP1 000.  DLP Gr. 3 Module 8, Gr. 4 Module 48 9. reads and writes money in symbols and in words through PhP1 000 in pesos  MTB-MLE Group – and centavos. Teacher’s Guide 10. compares values of the different  Lesson Guide in Elem. denominations of coins and bills Math 3 pp.52 – 56 through PhP1 000 using relation symbols.  BEAM LG Gr. 3 Module 1.3 – Whole Numbers 11. adds 3- to 4-digit numbers up to three addends with sums up to 10 000  MTB-MLE Group – without and with regrouping. Teacher’s Guide 12. estimates the sum of 3- to 4-digit  Lesson Guide in Elem. addends with reasonable results. Math 3 pp.70 – 80 13. adds mentally 2-digit and 1-digit  DLP Gr. 3 Module 12, 13 numbers without or with regrouping  MTB-MLE Group – using appropriate strategies. Teacher’s GuideK to 12 Mathematics Curriculum Guide December 2013  LG in Elem. Math 3 pp.81 – 84  DLP Gr. 3 Module 14  MTB-MLE Group – Teacher’s Guide  Lesson Guide in Elem. Math 3 pp.85 – 90  DLP Gr. 3 Module 15  MTB-MLE Group – Teacher’s Guide Page 31 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS The learner... The learner... 14. adds mentally 2- to 3-digit numbers M3NS-Ie-28.8  LG in Elem. Math 4 pp.35 with multiples of hundreds using M3NS-If-29.3 – 36 appropriate strategies.  MTB-MLE Group – 15. solves routine and non-routine Teacher’s Guide problems involving addition of whole  Lesson Guide in Elem. numbers with sums up to 10 000 Math 3 pp.95 – 99 including money using appropriate  DLP Gr. 3 Module 16 problem solving strategies and tools.  MTB-MLE Group – Teacher’s Guide 16. creates problems involving addition of M3NS-If-30.3 whole numbers including money. M3NS-Ig-32.6 M3NS-Ih-36 17. subtracts 3-to 4-digit numbers from 3- M3NS-Ih-33.5  Lesson Guide in Elem. to 4-digit numbers without and with M3NS-Ii-33.6 Math 3 pp.100 – 144 regrouping.  BEAM LG Gr. 3 Module 1 – 18. estimates the difference of two Subtraction numbers with three to four digits with reasonable results.  DLP Gr. 3 Module 17, 18  MTB-MLE Group – 19. subtracts mentally 1- to 2 – digits numbers without and with regrouping Teacher’s Guide using appropriate strategies.  Lesson Guide in Elem. 20. subtracts mentally 2- to 3 – digits Math 3 pp.145 – 148 numbers with multiples of hundreds without and with regrouping using  BEAM LG Gr. 3 Module 1 – appropriate strategies. Subtraction  MTB-MLE Group – Teacher’s Guide  Lesson Guide in Elem. Math 3 pp.149 – 154  BEAM LG Gr. 3 Module 1 – Subtraction  MTB-MLE Group – Teacher’s Guide  MTB-MLE Group – Teacher’s GuideK to 12 Mathematics Curriculum Guide December 2013 Page 32 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M3NS-Ii-34.5  Lesson Guide in Elem. The learner... The learner... Math 3 pp.155 – 169 M3NS-Ij-35.4 21. solves routine and non-routine M3NS-IIa-41.2  BEAM LG Gr. 3 Module 2 – M3NS-IIa-41.3 Application of Subtraction, problems involving subtraction without M3NS-IIb-40.4 Module 3 – Application of or with addition of whole numbers M3NS-IIb-40.5 Addition and Subtraction including money using appropriate  DLP Gr. 3 Module 19, Gr. problem solving strategies and tools. 4 Module 19 22. creates problems involving addition  MTB-MLE Group – and/or subtraction of whole numbers Teacher’s Guide including money.  BEAM LG Gr.2 Module –Grade 3- SECOND QUARTER MultiplicationNumbers and demonstrates is able to apply 23. visualizes multiplication of numbers 1  MTB-MLE Group –Number understanding of multiplication and division of to 10 by 6,7,8 and 9. Teacher’s GuideSense multiplication and division whole numbers including of whole numbers including money in mathematical 24. visualizes and states basic  MTB-MLE Group – money. problems and real-life multiplication facts for numbers up to Teacher’s Guide situations 10.  Lesson Guide in Elem. 25. applies the commutative property of Math 3 pp.170 – 174 multiplication.  DLP Gr. 5 Module 3 26. multiplies 2-digit by 1-digit numbers  MTB-MLE Group – using the distributive property of multiplication. Teacher’s Guide  DLP Gr. 4 Module 29  MTB-MLE Group – Teacher’s GuideK to 12 Mathematics Curriculum Guide December 2013 Page 33 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M3NS-IIb-40.6 M3NS-IIc-43.1  DLP Gr. 4 Module 26, Gr. The learner... The learner... M3NS-IIc-43.2 5 Module 3 M3NS-IIc-43.3 27. multiplies three 1-digit numbers using M3NS-IId-43.4  MTB-MLE Group – the associative property of M3NS-IId-43.5 Teacher’s Guide multiplication. M3NS-IId-44.1 M3NS-IIe-42.2  Lesson Guide in Elem. 28. multiplies 2- to 3-digit numbers by 1- Math 3 pp.185 – 193 digit numbers without or with M3NS-IIe-45.3 regrouping.  MTB-MLE Group – Teacher’s Guide 29. multiplies 2-digit numbers by 2-digit numbers without regrouping.  MTB-MLE Group – Teacher’s Guide 30. multiplies 2-digit number by 2-digit numbers with regrouping.  MTB-MLE Group – Teacher’s Guide 31. multiplies 2- to 3-digit numbers by multiples of 10 and 100.  Lesson Guide in Elem. Math 3 pp.194 – 203 32. multiplies 1- to 2-digit numbers by 1 000.  MTB-MLE Group – Teacher’s Guide 33. estimates the product of 2- to 3-digit numbers and 1- to 2-digit numbers  MTB-MLE Group – with reasonable results . Teacher’s Guide 34. multiplies mentally 2-digit by 1-digit  MTB-MLE Group – numbers without regrouping with Teacher’s Guide products of up to 100.  Lesson Guide in Elem. 35. solves routine and non-routine Math 3 pp.212 – 215 problems involving multiplication without or with addition and  MTB-MLE Group – subtraction of whole numbers including Teacher’s Guide money using appropriate problem solving strategies and tools.  Lesson Guide in Elem. Math 3 pp.216 – 222  MTB-MLE Group – Teacher’s GuideK to 12 Mathematics Curriculum Guide December 2013 Page 34 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M3NS-IIf-46.2 M3NS-IIf-47  MTB-MLE Group – The learner... The learner... M3NS-IIg-51.2 Teacher’s Guide M3NS-IIg-51.3 36. creates problems involving M3NS-IIh-54.1  BEAM LG Gr.2 Module 11 multiplication or with addition or – Division subtraction of whole numbers including M3NS-IIh-54.2 money. M3NS-IIi-55.1  MTB-MLE Group – M3NS-IIi-52.2 Teacher’s Guide 37. visualizes and states the multiples of 1- to 2-digit numbers.  BEAM LG Gr.2 Module 11 – Division 38. visualizes division of numbers up to 100 by 6,7,8,and 9 (multiplication table  MTB-MLE Group – of 6, 7, 8, and 9). Teacher’s Guide 39. visualizes and states basic division facts  Lesson Guide in Elem. of numbers up to 10. Math 3 pp.229 – 236 40. divides 2- to 3-digit numbers by 1- to  DLP Gr. 3 Module 29 2- digit numbers without and with  MTB-MLE Group – remainder. Teacher’s Guide 41. divides 2-3 digit numbers by 10 and  Lesson Guide in Elem. 100 without or with remainder. Math 3 pp.270 – 275 42. estimates the quotient of 2- to 3- digit  BEAM LG Gr.3 Module – numbers by 1- to 2- digit numbers. Application of Division 43. divides mentally 2-digit numbers by 1-  DLP Gr. 3 Module 32 digit numbers without remainder using  MTB-MLE Group – appropriate strategies. Teacher’s GuideK to 12 Mathematics Curriculum Guide December 2013  MTB-MLE Group – Teacher’s Guide  Lesson Guide in Elem. Math 3 pp.276 – 280  DLP Gr. 3 Module 39  MTB-MLE Group – Teacher’s Guide Page 35 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M3NS-IIj-56.2 M3NS-IIj-57.2  Lesson Guide in Elem. The learner... The learner... Math 3 pp.281 – 292 M3NS-IIIa-63 44. solves routine and non-routine  BEAM LG Gr.2 Module 11 problems involving division of 2- to 4- M3NS-IIIa-72.4 – Division, Gr.3 Module – digit numbers by 1- to 2-digit numbers M3NS-IIIb-76.3 Application of Division without or with any of the other M3NS-IIIb-72.5 operations of whole numbers including M3NS-IIIc-72.6  MTB-MLE Group – money using appropriate problem Teacher’s Guide solving strategies and tools.  Lesson Guide in Elem. 45. creates problems involving division or Math 3 pp.44 – 48, Gr. 5 with any of the other operations of p. 27 whole numbers including money.  DLP Gr. 3 Module 7Grade 3- THIRD QUARTER  BEAM LG Gr.3 Module 1.2  MTB-MLE Group –Numbers and demonstrates is able to recognize and 46. identifies odd and even numbers.Number understanding of represent proper and Teacher’s GuideSense proper and improper, improper, similar and  Lesson Guide in Elem. similar and dissimilar dissimilar and equivalent and equivalent fractions in various forms Math 3 pp.305 – 311 fractions. and contexts.  DLP Gr. 3 Module 37  MTB-MLE Group – 47. visualizes and represents fractions that are equal to one and greater than one. Teacher’s Guide  BEAM LG Gr.3 Module 1- 48. reads and writes fractions that are equal to one and greater than one in Identify and Order symbols and in words. Fractions  MTB-MLE Group – 49. represents fractions using regions, sets, Teacher’s Guide and the number line.  Lesson Guide in Elem. Math 4 p.188 50. visualizes and represents dissimilar  BEAM LG Gr.6 Module 22 fractions.  DLP Gr. 4 Module 58, 59  Lesson Guide in Elem.K to 12 Mathematics Curriculum Guide December 2013 Math 4 p.197  MTB-MLE Group – Teacher’s Guide Page 36 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS The learner... The learner... 51. visualizes, represents, and compares M3NS-IIId-77.3  MISOSA Module Gr.6 – dissimilar fractions. M3NS-IIId-78.3 Comparing Fractions 52. visualizes, represents, and arranges M3NS-IIIe-72.7  MTB-MLE Group – dissimilar fractions in increasing or M3GE-IIIe-11 Teacher’s Guide decreasing order. M3GE-IIIf-12.1 M3GE-IIIf-13  BEAM LG Gr.5 Module 2, 53. visualizes and generates equivalent Gr.6 Module 29 fractions.  MISOSA Gr. 5 Module –Geometry demonstrates is able to recognize and 54. recognizes and draws a point, line, line Ordering Dissimilar understanding of lines, represent lines in real segment and ray. Fractions symmetrical designs, and objects and designs or tessellation using square, drawings, complete 55. recognizes and draws parallel,  MTB-MLE Group – triangle and other shapes symmetrical designs, and intersecting and perpendicular lines. Teacher’s Guide that can tessellate. create patterns of designs  Lesson Guide in Elem. using square, triangle and Math 5 p.63 other shapes that can tessellate.  BEAM LG Gr.5 Module 2  MISOSA Gr. 5 and 6 56. visualizes, identifies and draws congruent line segments. Modules – Equal/Equivalent Fractions  MTB-MLE Group – Teacher’s Guide  MTB-MLE Group – Teacher’s Guide  Lesson Guide in Elem. Math 3 pp.330 – 337  DLP Gr. 3 Module 42  BEAM LG Gr.3 Module 7 – Line and Line Segment  MTB-MLE Group – Teacher’s Guide  Lesson Guide in Elem. Math 3 pp.338 – 344  DLP Gr. 3 Module 43  BEAM LG Gr.3 Module 7 – Line and Line Segment  MTB-MLE Group – Teacher’s GuideK to 12 Mathematics Curriculum Guide December 2013 Page 37 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS The learner... The learner... 57. identifies and visualizes symmetry in M3GE-IIIg-7.3  DLP Gr. 3 Module 44 the environment and in design. M3GE-IIIg-7.4  BEAM LG Gr.3 Module 7 – 58. identifies and draws the line of Line and Line Segment symmetry in a given symmetrical  MTB-MLE Group – figure. Teacher’s Guide  MTB-MLE Group – Teacher’s Guide 59. completes a symmetric figure with M3GE-IIIh-7.5  Lesson Guide in Elem. respect to a given line of symmetry. M3GE-IIIh-8.3 Math 3 pp.357 – 362Patterns and demonstrates is able to apply knowledge 60. tessellates the plane using triangles,  BEAM LG Gr.3 Module 7 –Algebra understanding of of continuous and repeating squares and other shapes that can Line and Line Segment continuous and repeating patterns and number tessellate. patterns and mathematical sentences involving  MTB-MLE Group – sentences involving multiplication or division of 61. determines the missing term/s in a Teacher’s Guide multiplication and division whole numbers in various given combination of continuous and repeating pattern.  Lesson Guide in Elem. of whole numbers. situations. Math 3 pp.345 – 356 e.g.  MTB-MLE Group – 4A,5B, 6A,7B,__ Teacher’s Guide 1 2 3 4 ___  MTB-MLE Group – Teacher’s Guide M3AL-IIIi-4 62. finds the missing value in a number M3AL-IIIj-12 sentence involving multiplication or division of whole numbers. e.g. n x 7 = 56 56 ÷ n = 8K to 12 Mathematics Curriculum Guide December 2013 Page 38 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS STANDARDS M3ME-IVa-8 M3ME-IVa-9  Lesson Guide in Elem. The learner... The learner... The learner... M3ME-IVb-10 Math 3 pp.368 – 372Grade 3- FOURTH QUARTER M3ME-IVb-39 M3ME-IVc-40  MTB-MLE Group –Measurement demonstrates is able to apply knowledge 63. visualizes, and represents, and M3ME-IVc-41 Teacher’s Guide understanding of of conversion of time, converts time measure from seconds conversion of time, linear, linear, mass and capacity to minutes, minutes to hours, and  Lesson Guide in Elem. mass and capacity measures and area of hours to a day and vice versa. Math 3 pp.363 – 367 measures and area of square and rectangle rectangle and square in 64. visualizes, and represents, and  BEAM LG Gr.2 Module 9- mathematical problems and converts time measure Time Measure, Gr. 3 real-life situations 64.1 days to week, month and year Module 8 and vice versa 64.2 weeks to months and year and  MTB-MLE Group – vice versa Teacher’s Guide 64.3 months to year and vice versa.  Lesson Guide in Elem. 65. visualizes, and represents, and solves Math 3 pp.376 – 379 problems involving conversion of time measure.  BEAM LG Gr.3 Module 8  MTB-MLE Group – 66. visualizes, and represents, and converts common units of measure Teacher’s Guide from larger to smaller unit and vice  DLP Gr. 3 Module 45 versa: meter and centimeter, kilogram  BEAM LG Gr.3 Module 1 and gram, liter and milliliter.  MTB-MLE Group – 67. visualizes, and represents, and solves Teacher’s Guide routine and non-routine problems involving conversions of common  BEAM LG Gr.3 Module 2 – units of measure. Capacity 68. visualizes, and represents, and finds  the capacity of a container using milliliter and liter.  Lesson Guide in Elem. Math 3 pp.406 – 409K to 12 Mathematics Curriculum Guide December 2013  BEAM LG Gr.2 Module 18 – Mass and Capacity, Gr.3 Module 1-Capacity  MTB-MLE Group – Teacher’s Guide Page 39 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M3ME-IVd-42  Lesson Guide in Elem. The learner... The learner... M3ME-IVd-43 Math 3 pp.413 – 416 M3ME-IVe-44 69. visualizes, and represents, and solves M3ME-IVe-45  MTB-MLE Group – routine and non-routine problems Teacher’s Guide involving capacity measure. M3ME-IVf-46 M3ME-IVf-47  70. visualizes, and represents, and M3SP-IVg-1.3  MTB-MLE Group – measures area using appropriate unit. M3SP-IVg-2.3 Teacher’s Guide 71. derives the formula for the area of a M3SP-IVh-3.3  Lesson Guide in Elem. rectangle and a square. Math 3 pp.388 - 397 72. visualizes, and represents, and finds  BEAM LG Gr.3 Module 9 – the area of a rectangle and square in sq.cm and sq. m. Area  MTB-MLE Group – 73. solves routine and non-routine problems involving areas of squares Teacher’s Guide and rectangles.  Lesson Guide in Elem.Statistics and demonstrates is able to create and 74. creates problems involving area of Math 3 pp.398 – 405Probability understanding of bar interpret simple rectangle and square.  BEAM LG Gr.3 Module 9 – graphs and outcomes of representations of data 75. collects data on one variable using Area an event using the terms (tables and single bar existing records.  MTB-MLE Group – sure, likely, equally likely, graphs) and describe 76. sorts, classifies, and organizes data in Teacher’s Guide tabular form and presents this into a unlikely, and impossible to outcomes of familiar events vertical or horizontal bar graph.  MTB-MLE Group – happen. using the terms sure, likely, Teacher’s Guide 77. infers and interprets data presented in equally likely, unlikely, and different kinds of bar graphs  Lesson Guide in Elem. impossible to happen. (vertical/ horizontal). Math 3 pp.430 – 433K to 12 Mathematics Curriculum Guide December 2013  BEAM LG Gr.4 Module 15 – Bar Graphs  MTB-MLE Group – Teacher’s Guide  Lesson Guide in Elem. Math 3 p.426  DLP Gr. 4 Module 88, 89  BEAM LG Gr.4 Module 15 – Bar Graphs  MTB-MLE Group – Teacher’s Guide Page 40 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner... STANDARDS M3SP-IVh-4.3 M3SP-IVi-7.3  MTB-MLE Group – The learner... The learner... M3SP-IVj-8.3 Teacher’s Guide 78. solves routine and non-routine problems using data presented in a single-bar graph. 79. tells whether an event is sure, likely, equally likely, unlikely, and impossible to happen. 80. describes events in real-life situations using the phrases “sure to happen,“ likely to happen”, “equally likely to happen”, “unlikely to happen”, and “impossible to happen”.K to 12 Mathematics Curriculum Guide December 2013 Page 41 of 109

K to 12 BASIC EDUCATION CURRICULUM GRADE 4CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner…Grade 4- FIRST QUARTER The learner… 1. visualizes numbers up to 100 000 withNumbers and 1. demonstrates 1. is able to recognize and emphasis on numbers 10 001 – M4NS-Ia-1.4  BEAM LG Gr.3 Module 1.1Number understanding of represent whole 100 000. – Whole NumbersSense whole numbers up to numbers up to 100,000 100,000. in various forms and 2. gives the place value and value of a M4NS-Ia-10.4 contexts. digit in numbers up to 100 000. 2. demonstrates M4NS-Ia-9.4  BEAM LG Gr.3 Module 1.1 understanding of 2. is able to apply 3. reads and writes numbers up to – Whole Numbers multiplication and multiplication and hundred thousand in symbols and in division of whole division of whole words. M4NS-Ib-5.2  BEAM LG Gr.3 Module 1.1 numbers including numbers including M4NS-Ib-12.4 – Whole Numbers money. money in mathematical 4. rounds numbers to the nearest problems and real-life thousand and ten thousand.  DLP Gr. 4 Module 6 situations. 5. compares numbers up to 100 000 using relation symbols. M4NS-Ib-13.4 6. orders numbers up to 100 000 in M4NS-Ic-43.7  BEAM LG Gr.3 Module 1- increasing or decreasing order. M4NS-Ic-44.2 Multiplication M4NS-Id-42.3 7. multiplies numbers up to 3-digit M4NS-Id-45.4  DLP Gr. 3 Module 20, 22, numbers by up to 2-digit numbers Gr. 5 Module 6 without or with regrouping.  BEAM LG Gr.3 Module 1- 8. estimates the products of 3- to 4-digit Multiplication numbers by 2- to 3- digit numbers with reasonable results.  DLP Gr. 3 Module 21 9. multiplies mentally 2-digit by 1-to 2-  BEAM LG Gr.3 Module 1- digit numbers with products up to 200 Multiplication, Gr. 4 – and explains the strategies used. Module 4 – Multiplication 10. solves routine and non-routine  DLP Gr. 4 Module 31 problems involving multiplication of  BEAM LG Gr.3 Module 1- whole numbers including money using appropriate problem solving strategies Multiplication & Module on and tools. Problem Solving, Gr. 4 Module 4 – MultiplicationK to 12 Mathematics Curriculum Guide December 2013  DLP Gr. 4 Module 34 Page 42 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 11. solves multi-step routine and non- M4NS-Ie-45.5  BEAM LG Gr.4 Module 4- routine problems involving Multiplication multiplication and addition or subtraction using appropriate problem  DLP Gr. 4 Module 35 solving strategies and tools. 12. creates problems(with reasonable M4NS-Ie-46.3 answers) involving multiplication or with addition or subtraction of whole numbers including money. 13. divides 3- to 4-digit numbers by 1-to 2- M4NS-If-54.3  BEAM LG Gr.3 Module on digit numbers without and with M4NS-If-54.4 Division remainder. M4NS-Ig-55.2 M4NS-Ig-52.3  DLP Gr. 3 Module 26, 27, 14. divides 3- to 4-digit numbers by tens or 30, 33, 34, Gr. 4 Module hundreds or by 1 000 without and with M4NS-Ih-56.3 41, Gr. 5 Module 7 remainder. M4NS-Ih-56.4  MISOSA Module Gr. 4 – 15. estimates the quotient of 3- to 4-digit Division of Whole Numbers dividends by 1- to 2-digit divisors with by 10, 100 and 1000 reasonable results.  MISOSA Module Gr.4 – 16. divides mentally 2- to 3-digit numbers Estimating Quotients by 1-digit numbers without remainder using appropriate strategies.  BEAM LG Gr.3 Module on Division, Gr. 4 Module 5 - 17. solves routine and non-routine Division problems involving division of 3- to 4- digit numbers by 1- to 2-digit numbers  BEAM LG Gr.3 Module on including money using appropriate Division, Gr. 4 Module 5 – problem solving strategies and tools. Division 18. solves multi-step routine and non-  MISOSA Module Gr. 4 – One-Step Word Problems routine problems involving division and involving Division any of the other operations of whole BEAM LG Gr. 4 Module 5 – numbers including money using Division  DLP Gr. 6 Module 3 appropriate problem solving strategies  MISOSA Module Gr. 4 – and tools. Two- to Three-Step Word Problems involving DivisionK to 12 Mathematics Curriculum Guide December 2013 Page 43 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M4NS-Ii-57.3 M4NS-Ii-61.1 The learner… The learner… 19. creates problems involving division without or with any other operations of whole numbers including money, with reasonable answers 20. represents and explains Multiplication, Division, Addition, Subtraction (MDAS) correctly. 21. performs a series of two or more M4NS-Ij-62.1 operations.Grade 4- SECOND QUARTERNumbers and 1. demonstrates 1. is able to apply 22. identifies factors of a given number up M4NS-IIa-64Number understanding of knowledge of to 100.Sense factors and factors and multiples and multiples, and 23. identifies the multiples of a given addition and addition and number up to 100. M4NS-IIa-65 subtraction of subtraction of fractions. fractions in 24. differentiates prime from composite M4NS-IIb-66  BEAM LG Gr.5 Module 1 – mathematical numbers. M4NS-IIb-67 Subsets of Whole 2. demonstrates problems and real- M4NS-IIc-68.1 Numbers, Gr. 6 Number understanding of life situations. Theory improper fractions and mixed numbers 2. is able to  Lesson Guide in Elem. Math Gr. 5 p. 30 recognize and MISOSA Gr. 5 Module –Prime represent improper and Composite Numbers fractions and mixed numbers in various 25. writes a given number as a product of  BEAM LG Gr.5 Module 1 – forms and contexts. its prime factors. Subsets of Whole Numbers 26. finds the common factors and the  DLP Gr. 5 Module 10 greatest common factor (GCF) of two  MISOSA Gr. 5 Module – numbers using the following methods: listing, prime factorization, and Prime Factors of a Number continuous division.  BEAM LG Gr.5 Module 1 – Subsets of Whole Numbers  Lesson Guide in Elem. Math Gr. 5 p.33K to 12 Mathematics Curriculum Guide December 2013 Page 44 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 27. finds the common multiples and least M4NS-IIc-69.1  Lesson Guide in Elem. common multiple (LCM) of two Math Gr. 5 p.44 numbers using the following methods: listing, prime factorization, and  MISOSA Gr. 5 Module – continuous division. Least Common Multiple 28. solves real-life problems involving GCF M4NS-IId-70.1 and LCM of 2 given numbers . M4NS-IId-71.1 29. creates problems with reasonable answers involving GCF and LCM of 2 given numbers. 30. identifies proper fractions, improper M4NS-IIe-79.2  BEAM LG Gr.4 Module 8 – fractions, and mixed numbers. M4NS-IIe-80 Fractions M4NS-IIe-81 31. changes improper fraction to mixed M4NS-IIf-82.1  DLP Gr. 4 Module 57 numbers and vice versa.  Lesson Guide in Elem. 32. changes fractions to lowest forms. Math Gr. 4 p.192 33. visualizes addition and subtraction of  BEAM LG Gr.4 Module 8 – similar fractions. Fractions  DLP Gr. 4 Module 61, Gr. 6 Module 26  Lesson Guide in Elem. Math Gr. 4 p.209, Gr. 6 p. 170  MISOSA Module Gr. 4 – Improper to Mixed Numbers  BEAM LG Gr.3 Module 2 – Fractions; Gr. 6 Module 7  Lesson Guide in Elem. Math Gr. 6 p.166  BEAM LG Gr.4 Module 9 – Addition and Subtraction of Fractions  Lesson Guide in Elem. Math Gr. 4 p. 209, Gr. 5 p.124K to 12 Mathematics Curriculum Guide December 2013 Page 45 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 34. visualizes subtraction of a fraction M4NS-IIf-82.2  BEAM LG Gr.4 Module 9 – from a whole number. M4NS-IIg-82.3 Addition and Subtraction of Fractions 35. visualizes addition and subtraction of M4NS-IIg-83 dissimilar fractions.  BEAM LG Gr.5 Module 3 – Addition of Fractions 36. performs addition and subtraction of similar and dissimilar fractions.  Lesson Guide in Elem. Math Gr. 5 p. 83, 124  MISOSA Gr. 5 Module – Visualization of Dissimilar Fractions  BEAM LG Gr.4 Module 9 – Addition and Subtraction of Fractions  DLP Gr. 4 Module 63, 64, 65, 66, Gr. 5 Module 14, 15, 18, 20, 21  Lesson Guide in Elem. Math Gr. 4 217, 235, Gr. 5 p.79, 90, 94, 128 – 136  MISOSA Module Gr.4 – Addition of Similar Fractions, Fractions and Whole Numbers, Subtraction of Similar Fractions  MISOSA Module Gr.5 – Addition of Dissimilar Fractions  MISOSA Module Gr.6 – Subtraction of Dissimilar Fractions in Simple FormsK to 12 Mathematics Curriculum Guide December 2013 Page 46 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS M4NS-IIh-87.1 M4NS-IIh-88.1  BEAM LG Gr.4 Module 9 – The learner… The learner… Addition and Subtraction of Fractions, Grade 5 Module 37. solves routine and non-routine 4 problems involving addition and/or subtraction of fractions using  DLP Gr. 4 Module 67, 68, appropriate problem solving strategies Gr. 5 Module 17 and tools.  Lesson Guide in Elem. 38. creates problems(with reasonable Math Gr. 4 p. 242, 246 answers) involving addition and/or subtraction of fractions. 39. visualizes decimal numbers using M4NS-IIi-99  BEAM LG Gr.4 Module 7 – models like blocks, grids, number lines Decimals and money to show the relationship to fractions.  DLP Gr. 6 Module 4 40. renames decimal numbers to M4NS-IIi-100  BEAM LG Gr.4 Module 7 – fractions, and fractions whose M4NS-IIi-101.1 Decimals; Gr. 4 Module 8 – denominators are factors of 10 and 100 to decimals. Fractions  DLP Gr. 4 Module 44, Gr. 6 41. gives the place value and the value of a digit of a given decimal number Module 23 through hundredths.  Lesson Guide in Elem. Math Gr. 5 p.231, Gr. 6 p. 159  MISOSA Module Gr. 4 – Common Fractions as Decimals  MISOSA Module Gr.5 – Renaming Fractions in Decimal Form  BEAM LG Gr.4 Module 7 – Decimals  MISOSA Module Gr. 4 – Place Value of DecimalsK to 12 Mathematics Curriculum Guide December 2013 Page 47 of 109

K to 12 BASIC EDUCATION CURRICULUMCONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDS The learner… The learner… 42. reads and writes decimal numbers M4NS-IIj-102.1  BEAM LG Gr.4 Module 7 – through hundredths. M4NS-IIj-103.1 Decimals M4NS-IIj-104.1 43. rounds decimal numbers to the nearest  DLP Gr. 4 Module 45 whole number and tenth.  BEAM LG Gr.4 Module 7 - 44. compares and arranges decimal Decimals numbers.Grade 4- THIRD QUARTERGeometry demonstrates is able to construct and 45. describes and illustrates parallel, M4GE-IIIa-12.2 understanding of the describe parallel and intersecting, and perpendicular lines. concepts of parallel and perpendicular lines, angles, M4GE-IIIa-12.3 perpendicular lines, triangles, and quadrilaterals 46. draws perpendicular and parallel lines angles, triangles, and in designs, drawings and using a ruler and a set square. quadrilaterals. models.  BEAM LG Gr.4 Module 11 47. describes and illustrates different M4GE-IIIb-14 – Angles and Plane Figures angles (right, acute, and obtuse) using M4GE-IIIb-15 models.  DLP Gr. 4 Module 76, 77, 78, 79 48. describes the attributes/properties of triangles and quadrilaterals using  Lesson Guide in Elem. concrete objects or models. Math Gr. 4 p.287, 290, 293  MISOSA Module Gr. 4 – Congruent Angles  BEAM LG Gr.4 Module 11 – Angles and Plane Figures  DLP Gr. 4 Module 81 49. identifies and describes triangles M4GE-IIIc-16  BEAM LG Gr.4 Module 11 according to sides and angles. M4GE-IIIc-17 – Angles and Plane Figures 50. identifies and describes the different  DLP Gr. 3 Module 41, Gr. 4 kinds of quadrilaterals: square, Module 73 rectangle, parallelogram, trapezoid, and rhombus.  Lesson Guide in Elem. Math Gr. 4 p.298  BEAM LG Gr.4 Module 11 – Angles and Plane FiguresK to 12 Mathematics Curriculum Guide December 2013 Page 48 of 109

K to 12 BASIC EDUCATION CURRICULUM CONTENT CONTENT STANDARDS PERFORMANCE LEARNING COMPETENCY CODE LEARNING MATERIALS The learner… STANDARDSPatternsand The learner… The learner…Algebra 51. relates triangles to quadrilaterals M4GE-IIId-18.1 M4GE-IIId-18.2 52. relates one quadrilateral to another demonstrates is able to identify the quadrilateral (e.g. square to understanding of concepts missing element in a rhombus). of continuous and pattern and number 53. determines the missing term/s in a repeating patterns and sentence. sequence of numbers (e.g. odd numbers, even numbers, multiples of number sentences. a number, factors of a number, etc.) e.g. M4AL-IIIe-5 3,6,9,__ 4,8,12,16,__ (e.g. odd numbers, even numbers, multiples of a number, factors of a number, etc.)Measurement demonstrates is able to apply the 1 2 3 4 5 6 7 ____ M4AL-IIIe-13 54. finds the missing number in an understanding of the concepts of time, M4ME-IIIf-11 concept of time, perimeter, area, and equation involving properties of M4ME-IIIf-12 operations. (e.g. (4+__ ) + 8 = 4 + M4ME-IIIg-13 perimeter, area, and volume to mathematical ( 5 + __) M4ME-IIIg-48 volume. problems and real-life M4ME-IIIh-49 55. finds the elapsed time in minutes and M4ME-IIIh-50 situations. seconds. 56. estimates the duration of time in  DLP Gr. 4 Module 84 minutes.  BEAM LG Gr.4 Module 18 57. solves problems involving elapsed time. – Perimeter Page 49 of 109 58. visualizes the perimeter of any given plane figure in different situations. 59. measures the perimeter of any given figure using appropriate tools. 60. derives the formula for perimeter of any given figure.K to 12 Mathematics Curriculum Guide December 2013