# Republic of the Philippines Department of Education DepEd Complex, Meralco Avenue Pasig City. K to 12 Curriculum Guide MATHEMATICS

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1 Republic of the Philippines Department of Education DepEd Complex, Meralco Avenue Pasig City K to 12 Curriculum Guide MATHEMATICS (Grade 1 to Grade 10) January 31, 2012

2 CONCEPTUAL FRAMEWORK Mathematics is one subject that pervades life at any age, in any circumstance. Thus, its value goes beyond the classroom and the school. Mathematics as a school subject, therefore, must be learned comprehensively and with much depth. The twin goals of mathematics in the basic education levels, K-10 are Critical Thinking and Problem Solving. We adopt the definition of critical thinking by Scriven and Paul (1987): Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. On the other hand, we define Problem Solving in mathematics using Polya s (1945 & 1962) definition: Mathematical problem solving is finding a way around a difficulty, around an obstacle, and finding a solution to a problem that is unknown. These two goals are to be achieved with an organized and rigorous curriculum content, a well-defined set of high-level skills and processes, desirable values and attitudes, and appropriate tools, recognizing as well the different contexts of Filipino learners. There are five content areas in the curriculum, as adopted from the framework prepared by MATHTED & SEI (2010): Numbers and Number Sense, Measurement, Geometry, Patterns and Algebra, and Probability and Statistics. The specific skills and processes to be developed are: Knowing and Understanding; Estimating, Computing and Solving; Visualizing and Modelling; Representing and Communicating; Conjecturing, Reasoning, Proving and Decision-making, and: Applying and Connecting. The following values and attitudes are to be honed as well: Accuracy, Creativity, Objectivity, Perseverance, and Productivity. We recognize that the use of appropriate tools is needed in teaching mathematics. These include: manipulative objects, measuring devices, calculators and computers, Smartphones and tablet PCs, and the Internet. We define context as a locale, situation or set of conditions of Filipino learners that may influence their study and use of mathematics to develop critical thinking and problem solving skills. Contexts refer to beliefs, environment, language and culture that include traditions and practices, and learner s prior knowledge and experiences. *K to 12 Curriculum Guide version as of January 31,

3 The framework is supported by the following underlying learning principles and theories: Experiential and Situated Learning, Reflective Learning, Constructivism, Cooperative Learning and Discovery and Inquiry-based Learning. The mathematics curriculum is grounded in these theories. Experiential learning as advocated by David Kolb is learning that occurs by making sense of direct everyday experiences. Experiential learning theory defines learning as "the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of grasping and transforming experience" (Kolb, 1984, p. 41). Situated learning, theorized by Lave and Wenger, is learning in the same context on which concepts and theories are applied. Reflective learning refers to learning that is facilitated by reflective thinking. It is not enough that learners encounter real-life situations. Deeper learning occurs when learners are able to think about their experiences and process these allowing them the opportunity to make sense and meaning of their experiences. Constructivism is the theory that argues that knowledge is constructed when the learner is able to draw ideas from his own experiences and connects them to new ideas that are encountered. Cooperative Learning puts premium on active learning achieved by working with fellow learners as they all engage in a shared task. The mathematics curriculum allows for students to learn by asking relevant questions and discovering new ideas. Discovery and Inquiry-based learning (Bruner, 1961) support the idea that students learn when they make use of personal experiences to discover facts, relationships and concepts. *K to 12 Curriculum Guide version as of January 31,

4 Figure 1. The Conceptual Framework of Mathematics Education *K to 12 Curriculum Guide version as of January 31,

5 BRIEF COURSE DESCRIPTION Mathematics from K-10 is a skills subject. By itself, it is all about quantities, shapes and figures, functions, logic and reasoning. Mathematics is also a tool of science and a language complete with its own notations and symbols and grammar rules, with which concepts and ideas are effectively expressed. The contents of mathematics include Numbers and Number Sense, Measurement, Geometry, Patterns & Algebra and Statistics and Probability. Numbers and Number Sense as a strand includes concepts of numbers, properties, operations, estimation and their applications. Measurement as a strand includes the use of numbers and measures to describe, understand and compare mathematical and concrete objects. It focuses on attributes such as length, mass and weight, capacity, time, money and temperature among others, as well as applications involving perimeter, area, surface area, volume and angle measure. Geometry as a strand includes properties of two- and three-dimensional figures and their relationships, spatial visualization, reasoning and geometric modeling and proofs. Patterns and Algebra as a strand studies patterns, relationships and changes among shapes and quantities and includes the use of algebraic notations and symbols, equations and most importantly, functions, to represent and analyze relationships. Statistics and Probability as a strand is all about developing skills in collecting and organizing data using charts, tables and graphs, understanding, analyzing and interpreting data, dealing with uncertainty and making predictions and outcomes. The K to 10 Mathematics Curriculum provides a solid foundation for Mathematics at Grades 11 to 12. More importantly, it provides necessary concepts and life skills needed by Filipino learners as they proceed to the next stage in their life as learners and as citizens of our beloved country, the Philippines. *K to 12 Curriculum Guide version as of January 31,

6 LEARNING AREA STANDARD: understanding and appreciation of key concepts and principles of mathematics as applied, using appropriate technology, in problem solving, communicating, reasoning, making connections, representations, and decisions in real life. KEY STAGE STANDARDS: K At the end of Grade 3, the learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to ten thousand, fractions, measurement, simple geometric figures, pre-algebra concepts and data representation and analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. At the end of Grade 6, the learner demonstrates understanding and appreciation of key concepts and skills involving rational numbers, measurement, geometric figures, pre-algebra concepts, simple probability and data analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. At the end of grade 10, the learner demonstrates understanding and appreciation of key concepts and skills involving number sense, measurement, algebra, geometry, probability and statistics, and trigonometry as applied, using appropriate technology, in critical thinking, problem solving, communicating, reasoning, making connections, representations, and decisions in real life. *K to 12 Curriculum Guide version as of January 31,

7 GRADE LEVEL STANDARDS: Grade Level Grade 1 Grade Level Standards understanding and appreciation of key concepts and skills involving whole numbers up to 100, fractions, measurement, simple geometric figures, pre-algebra concepts, data collection and representation as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in real life. Grade 2 understanding and appreciation of key concepts and skills involving whole numbers up to 1 000, fractions, measurement and geometric figures, pre-algebra concepts, data collection, representation and analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in real life. Grade 3 Grade 4 Grade 5 Grade 6 understanding and appreciation of key concepts and skills involving whole numbers up to , fractions, measurement, geometric figures, pre-algebra concepts, data collection, representation and analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in real life. understanding and appreciation of key concepts and skills involving whole numbers up to , fractions, decimals including money, ratio, angles, plane figures like square, rectangle, and triangle, measurement (perimeter, area of triangle, parallelogram and trapezoids, volume of cubes and rectangular prisms, pre-algebra concepts, data collection, representation and analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. understanding and appreciation of key concepts and skills involving whole numbers up to , fractions, decimals including money, ratio, percent, geometry (circles and five or more-sided polygons), measurement (circumference, area of circle, volume of cubes and rectangular prisms, temperature),pre-algebra concepts, data collection, representation and analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. The learner is expected to have mastered the concepts and operations on whole numbers; demonstrates understanding and appreciation of the key concepts and skills involving fractions, decimals including money, ratio and proportion, percent, rate, integers, geometry (spatial figures), measurement (surface area, volume, meter reading), pre-algebra concepts, data collection, representation and analysis, probability, expressions and equations as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. *K to 12 Curriculum Guide version as of January 31,

8 Grade Level Grade Level Standards Grade 7 understanding of key concepts and principles of number sense, measurement, algebra, geometry, probability and statistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. Grade 8 understanding of key concepts and principles of algebra, geometry, probability and statistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. Grade 9 understanding of key concepts and principles of algebra, geometry, and trigonometry as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. Grade10 understanding of key concepts and principles of number sense, algebra, geometry, probability and statistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life. *K to 12 Curriculum Guide version as of January 31,

9 GRADE 1 Numbers and Number Sense The learner number notation and place value, cardinal and ordinal numbers, and comparing and ordering numbers up to 100. explore the concept of cardinal numbers up to 100 and compare these numbers in various contexts. recognizes cardinal numbers from 0 to 100. counts and tells the number of objects in a given set by ones and tens. identifies the number that is one more or one less from a given number. composes and decomposes a given number. regroups sets of ones into sets of tens and sets of tens into hundred using objects. compares two sets using the expressions fewer than, more than, and as many as. orders sets from least to greatest and viceversa. counts by 2 s, 5 s and 10 s through 100. reads and writes numbers up to 100 in symbols and in words. identifies the place value and finds the value of a digit in a one- and two-digit numbers. renames numbers into tens and ones. compares numbers up to 100 using relation symbols. *K to 12 Curriculum Guide version as of January 31,

10 The learner arranges numbers up to 100 in increasing order and vice versa. recognizes coins and bills up to P100 (pesos and centavos). explore the concept of ordinal numbers. reads and writes ordinal numbers 1st, 2nd, 3rd up to 10th. identifies the 1st, 2nd, 3rd up to the 10th object in a given set from a given point of reference. determines the position of an object using 1st to 10th from a given point of reference. addition and subtraction up to 100. illustrate addition and subtraction of whole numbers. illustrates addition as putting together and subtraction as taking away, comparing and adding up. illustrates the relationship of joining sets to addition of whole numbers. illustrates that addition and subtraction are inverse operations. identifies and constructs equivalent number expressions using addition and subtractions. identifies and creates patterns to compose and decomposes numbers using addition. *K to 12 Curriculum Guide version as of January 31,

12 The learner subtracts one to two-digit numbers with minuends up to 99 without regrouping. uses the expanded form to explain subtraction with regrouping. subtracts one to two-digit numbers with minuends up to 99 with regrouping. mentally subtracts 1-digit numbers from minuends up to 18 without regrouping. mentally subtracts a 1-digit number from 2- digit minuends without regrouping. solves word problems involving subtraction of whole numbers including money with minuends up to 99 with and without regrouping using appropriate problem solving strategy. the concepts of halves and fourths and applies them in dividing a whole or set equally. visualize, model and represent the concept of halves and fourths using whole objects and sets. visualizes and identifies ½ and ¼ of a whole object. divides a whole into halves and fourths. divides the elements of a set of objects into two groups of equal quantities to show halves of sets. divides the elements of a set of objects into four groups of equal quantities to show fourths of sets. *K to 12 Curriculum Guide version as of January 31,

13 The learner given half of a region or a set, draws the whole region or set. Geometry 2-D and 3-D shapes through identifying, classifying and constructing figures using cutouts and concrete models. explore the properties of 2- and 3-dimensional figures. identifies, names and describes the four basic shapes in 2- and 3-dimensional objects: square, rectangle, triangle and circle. compares and classifies 2- and 3- dimensional figures according to common attributes. model and represent 2- and 3-dimensional objects. draws the four basic shapes. constructs three-dimensional objects using manipulative materials. Patterns and Algebra simple patterns. identify and create number and attribute patterns. identifies and explains simple repeating patterns. makes patterns of shapes, colors and numbers. complete number and attribute patterns. finds the missing number/digit in addition or subtraction problems. finds and completes patterns of one or two of the following attributes: Shape, Size, Color, Number, Orientation. determines the next term (figure/number) in a given sequence and give a reason. *K to 12 Curriculum Guide version as of January 31,

14 Measurement the concepts of time and measures and compares objects using direct comparison and non-standard units of length, mass and capacity. give different measures of time. The learner names and tells the number of days in a week; months in a year in the right order. uses a calendar to determine a day or month. tells the time by an hour, half-hour and quarter-hour. estimate and compute for measurements of length, mass and capacity. compares objects using the comparative words: Short, shorter, shortest; Long, longer, longest; Tall, taller, tallest; High, higher, highest; Heavy, heavier, heaviest; Light, lighter, lightest. estimates and measures length using nonstandard units of linear measures. estimates and measures mass using nonstandard units of mass/weight measures. shows and finds capacity using nonstandard unit. Statistics and Probability organizing, representing and comparing data using pictographs without scale representations and probability, and explores games and activities. organize and interpret data. collects and organizes data using tallies and tables. represents data using pictographs without using a scale. reads and interprets a pictograph. *K to 12 Curriculum Guide version as of January 31,

15 The learner make conjectures about games and activities. identifies cause and effect relationships. predicts and records outcome of experiments and chance games. *K to 12 Curriculum Guide version as of January 31,

16 GRADE 2 Numbers and Number Sense the relationships between numbers and place value of whole numbers up to 1000 and of ordinal numbers up to 20th. explore the concepts of numbers up to 1000, read and write these numbers. The learner visualizes and identifies numbers from 101 through associates numbers with sets having 101 up to 500 objects and give the number of objects. associates numbers with sets having 501 up to 1000 objects and give the number of objects. counts and groups objects in ones, tens, and hundreds. reads and writes numbers from 101 through 1000 in symbols and in words. counts numbers by 10s, 50s and 100s. reads and writes numbers through 1000 in symbols and in words. gives the place value of each digit in a threedigit number. writes three-digit numbers in expanded form. compares numbers using >, < and =. orders numbers up to 1000 from least to greatest and vice versa. *K to 12 Curriculum Guide version as of January 31,

18 The learner analyzes and solves word problems involving addition of whole numbers including money with sums up to 1000 without and with regrouping. compute differences and solve subtraction problems involving numbers of up to subtracts 2- to 3-digit numbers with minuends up to 999 without and with regrouping. mentally subtracts 1-digit numbers from 1 to 2-digit numbers with minuends up to 50. mentally subtracts 3-digit by ones without regrouping. mentally subtracts 3-digit by tens without regrouping. mentally subtracts 3-digit by hundreds without regrouping. analyzes and solves one-step word problems involving subtraction of whole numbers including money with minuends up to1000 without and with regrouping. compute for sums and differences and solve problems involving both addition and subtraction of numbers. performs order of operations involving addition and subtraction of small numbers. solves two-step word problems involving addition and subtraction of 2- to 3-digit numbers including money using appropriate procedures. *K to 12 Curriculum Guide version as of January 31,

19 explore and illustrate the concept of multiplication of whole numbers. The learner illustrates multiplication as repeated addition, arrays, counting by multiples, and equal jumps on the number line. writes a related equation for each type of multiplication: repeated addition, array, counting by multiples, and equal jumps on the number line. illustrates the property of multiplication that any number multiplied by one (1) is the same number. illustrates the property of multiplication that zero multiplied by any number is zero. illustrates the commutative property of multiplication. compute products of numbers involving 2, 3, 4, 5 and 10 and solve problems involving multiplication of these numbers. constructs and fills up the multiplication tables of 2, 3, 4, 5 and 10. multiplies mentally to fill up multiplication tables of 2, 3, 4, 5 and 10. analyzes and solves one-step word problems involving multiplication of whole numbers including money. analyzes and solves two-step word problems involving multiplication of whole numbers as well as addition and subtraction including money. *K to 12 Curriculum Guide version as of January 31,

20 explore and model the concept of division of whole numbers. The learner models and describes division situations in which sets are separated into equal parts. represents division as equal sharing, repeated subtraction, equal jumps on the number line, and formation of equal groups of objects. writes a related equation for each type of situation: equal sharing, repeated subtraction, equal jumps on the number line, and formation of equal groups of objects. compute quotients of numbers found in the multiplication tables involving 2, 3, 4, 5 and 10 and solve problems involving division of these numbers. divides numbers found in the multiplication tables of 2, 3, 4, 5, and 10. mentally divides numbers found in the multiplication tables of 2, 3, 4, 5 and 10. analyzes and solves one-step word problems involving division of numbers found in the multiplication tables of 2, 3, 4, 5, and 10. unit fractions, proper fractions and similar fractions, and identification of money value through 100. explore the concept of unit fractions and other fractions less than 1 and compare these fractions. visualizes and identifies unit fractions with denominators 10 and below. reads and writes unit fractions. compares unit fractions using relation symbols. orders unit fractions. *K to 12 Curriculum Guide version as of January 31,

21 The learner visualizes and identifies other fractions less than one with denominators 10 and below. visualizes and identifies similar fractions (using group of objects and number line). reads and writes similar fractions. apply number concepts on problem situations involving money. compares similar fractions using relation symbols. orders similar fractions. reads and writes money with value through 100. counts and tells the value of a set of bills or a set of coins through 100 in peso ( coins only, bills only and coins and bills). counts and tells the value of a set of bills or a set of coins through 100 in centavo (coins). counts and tells the value of a set of bills or a set of coins through 100 in combinations of pesos and centavos (Peso and centavo coins only, bills and centavo coins, coins and bills). reads and writes money in symbols and in words through 100. compares values of different denominations of coins and paper bills through 100 using relation symbols >, < and =. *K to 12 Curriculum Guide version as of January 31,

22 Geometry The learner the basic properties of geometric shapes, simple tessellations and symmetry. visualize and model halfcircles and quarter circles as well as other common shapes. visualizes, identifies, classifies and describes half-circles and quarter circles. constructs squares, rectangles, triangle, circles, half-circles and quarter circles using cut-outs and square grids. explore the concept of symmetry. identifies shapes/figures that show symmetry in a line. creates figures that show symmetry in a line. visualize, model and represent tessellations. recognizes shapes that can tessellate. tessellates a surface using triangles and squares. explore the concept of lines, curves and surface on 3- dimensional objects. identifies straight lines and curves, flat and curved surfaces in a 3-dimenional object. explains the differences between straight lines and curved lines, flat surfaces and curved surfaces. Patterns and Algebra patterns on numbers and geometric objects. argue and justify patterns. identifies and explains simple repeating patterns. determines the next term (figure/number) in a given sequence and give a reason. *K to 12 Curriculum Guide version as of January 31,

23 apply their understanding and strategies in completing patterns. The learner finds and completes patterns according to one or two of the following attributes: shape, size, color, orientation. Measurement the concept and application of time and of using standard units in measuring length, mass, area and capacity. compute for measures of time and solve problems involving time. tells and writes the time in minutes including a.m. and p.m. using analog and digital clocks. finds the duration of time elapsed using calendar, analog and digital clocks. solves simple word problems involving time. identify and compare the standard units centimeter and meter. shows and uses the appropriate unit of length to measure a particular object and their abbreviations cm and m. compares length in meters or centimeters. estimate and compute for lengths of objects and solve problems involving lengths using centimeter and meter. measures objects using appropriate measuring tools in m or cm. estimates and measures length using meter or centimeter. solves simple word problems involving length. identify, use and compare the standard units gram and kilogram. shows and uses the appropriate unit of mass to measure a particular object or situation and their abbreviations g and kg. compares mass in grams or kilograms. *K to 12 Curriculum Guide version as of January 31,

24 estimate and compute for the mass/weight of an object and solve problems involving mass/weight. The learner measures objects using appropriate measuring units in g or kg. estimates and measures mass using gram or kilogram. solves simple word problems involving mass. explore and illustrate the concept of area. illustrates area as a measure of how much surface is covered or occupied by plane figure. shows the area of a given figure using square tile units, i.e. number of square tiles needed. estimate and compute for the area of a plane figure. estimates the area of a given figure using any shape. finds the area of a given figure using square tile units i.e. number of square tiles needed. measure capacity. shows and finds capacity using appropriate measuring tools, e.g. amount of liquid needed. Statistics and Probability pictographs with scale representations and the idea of likelihood. organize and interpret data. collects and organizes data using tables and pictures. reads and interprets data in a given pictograph. *K to 12 Curriculum Guide version as of January 31,

25 represent data using scales. The learner forms scale representation of objects from the data collected. makes pictographs using scale representation. make conjectures and educated guesses about the likelihood of events. makes a guess on whether an event is less likely, more likely, equally likely or unlikely to happen based on facts. *K to 12 Curriculum Guide version as of January 31,

26 GRADE 3 Numbers and Number Sense The learner the concepts of whole numbers up to 10000, ordinal numbers up to 100th and Roman numerals up to M. explore the concepts of numbers up to , count, read and write these numbers and identify ordinal numbers of up to 100th. reads and writes the numbers through in symbols and in words. identifies the place value and find the value of a digit in 4- to 5-digit numbers. compares 4- to 5-digit numbers using relation symbols. orders 4- to 5-digit numbers in increasing order and vice versa. rounds numbers to the nearest tens, hundreds and thousands. identifies ordinal numbers from 1st to 100th. read and write numbers using Roman numerals up to M. reads and writes the value of roman numbers in Hindu-Arabic and vice versa I to L. reads and writes the value of roman numbers in Hindu-Arabic and vice versa L to C. reads and writes the value of Roman numbers in Hindu-Arabic and vice versa C to D. reads and writes the value of Roman *K to 12 Curriculum Guide version as of January 31,

28 estimate and compute for differences and solve subtraction problems involving numbers of up to The learner subtracts 3-digit numbers from 3- to 4-digit numbers without and with regrouping and with and without zeros in the digits. subtracts 3- to 4-digit numbers from 4-digit numbers without and with regrouping and with and without zeros in the digits. estimates the difference of two numbers with three to four digits by rounding. mentally subtracts without and with regrouping 2-digit and 1-digit numbers and explain the strategies used. mentally subtracts without and with regrouping two 2-digit numbers and explain the strategies used. mentally subtracts without and with regrouping 2-digit to 3-digit numbers from multiples of hundreds and explain the strategies used. solves one-step word problems involving subtraction of whole numbers including money using appropriate problem solving strategies. solves two-step word problems involving addition and subtraction of whole numbers including money using appropriate problem solving strategies. *K to 12 Curriculum Guide version as of January 31,

29 estimate and multiply 2- and 3-digit numbers by 1-digit to 2-digit numbers and solve multiplication problems involving these numbers. The learner constructs and completes the multiplication tables of 6, 7, 8 and 9. states basic multiplication facts for numbers up to 10. applies the commutative property of multiplication. multiplies 2-digit by 1-digit by using the distributive property of multiplication. multiplies three 1-digit numbers by using the associative property of multiplication. multiplies 2- to 3-digit numbers by 1-digit numbers without or with regrouping. multiplies 2-digit numbers by 2-digit numbers without regrouping. multiplies 2-digit numbers by 2-digit numbers with regrouping. multiplies 2- to 3-digit numbers by multiples of 10 and 100. multiplies 1- to 2-digit numbers by estimates the product of 2- to 3-digit numbers by 1- to 2-digit numbers by rounding. *K to 12 Curriculum Guide version as of January 31,

30 The learner mentally multiplies 2-digit by 1-digit numbers without regrouping involving products of up to 100. solves one-step word problems involving multiplication of whole numbers including money using appropriate problem solving strategies. solves two-step word problems involving multiplication as well as addition and subtraction including money using appropriate problem solving strategies. explore the concepts of factors and multiples. states multiples of 1- to 2-digit numbers. differentiates prime and composite numbers. estimate and divide 3-digit numbers by up to 2-digit numbers and solve division problems involving these numbers. divides numbers found in the multiplication tables of 6, 7, 8, 9. states basic division facts of numbers up to 10. divides 2- to 3-digit numbers by 1-digit numbers without remainder. divides 2- to 3-digit numbers by 1-digit numbers with remainder. divides 2-digit numbers by 2-digit numbers. divides numbers by 10 and 100. *K to 12 Curriculum Guide version as of January 31,

31 The learner estimates the quotient of 2- to 3-digit numbers by 1- to 2-digit numbers. mentally divides 2-digit numbers by 1-digit numbers without remainder. solves one-step word problem involving division of 2- to 4-digit numbers by 1- to 2- digit numbers including money using appropriate problem solving strategies. solves word problems involving division and other fundamental operations, including money, using appropriate problem solving strategies. the basic kinds of fractions, know how to simplify and order them, and to apply to problem solving money through 100. explore the concepts of dissimilar fractions, improper fractions and mixed numbers. visualizes and identifies fractions that are equal to one and greater than one. reads and writes fractions that are greater than one in symbols and in words. relates and changes improper fractions to mixed numbers and vice versa. visualizes and identifies dissimilar fractions. compares dissimilar fractions. arranges dissimilar fractions in increasing or decreasing order. *K to 12 Curriculum Guide version as of January 31,

32 The learner recognizes and generates equivalent fractions of commonly used fractions. changes fractions to lowest forms. apply number concepts to solve problems involving money through reads and writes money in symbols through compares values of the different denominations of coins and bills through solves real-life problems involving money through 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, line segment and ray. recognizes and draws perpendicular lines, parallel lines and intersecting lines. visualizes, identifies and draws congruent line segments. explore symmetry in plane figures and the environment. identifies and draws the line of symmetry in a given symmetrical figure. identifies and visualizes symmetry in the environment and in design. completes a symmetric figure with respect to a given line of symmetry. *K to 12 Curriculum Guide version as of January 31,

33 Patterns and Algebra patterns of numbers, operations, geometric objects and relationships. explore the concept of odd and even numbers. The learner tessellates the plane using triangles, squares and other shapes that can tessellate. tells when a number is odd or even. finds the pattern using odd and even numbers with objects, pictures and words. identify the rule for a pattern and complete the number pattern. determines the pattern of a given sequence and state the rule. finds the missing number or digit in a pattern. Measurement the concept and application of time (in minutes), length, mass, area and capacity. convert time measures from one unit to another. converts time measure from seconds to minutes, minutes to hours, hours to day. converts time measure from days to weeks and months, and convert weeks, months and years to days. finds the exact time between dates. recognize, perform and use conversions of common units. solves word problems involving time measure. converts common units of measure from larger unit to smaller unit and vice versa: meter and centimeter, kilogram and gram, liter and milliliter. solves word problems involving conversions of common units of measure. *K to 12 Curriculum Guide version as of January 31,

34 explore the concept of area and find areas of squares and rectangles using cm 2 and m 2. The learner estimates the area of a square and rectangle using non-standard units. finds the area of a square in cm 2 and m 2. finds the area of a rectangle in cm 2 and m 2. solves word problems involving areas of squares and rectangles. measure capacity using milliliter and liter. finds the capacity of a container using milliliter/liter. solves word problems involving capacity measure. Statistics and Probability tables, bar graphs and probability. organize and interpret data presented in tables and bar graphs. 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 of events. tells whether an event is most likely to happen, equally likely to happen or unlikely to happen based on facts. *K to 12 Curriculum Guide version as of January 31,

35 GRADE 4 Numbers and Number Sense The learner number notation and place value of numbers up to , and of factors and multiples of numbers up to 100, and of the greatest common factor and least common multiple. read, write, compare and arrange numbers through and round off numbers to the nearest thousands and ten thousands. reads and writes numbers through hundred thousands in symbols and in words. identifies numbers up to gives the place value of each digit in a sixdigit number. reads and writes numbers up to hundred thousands in symbols and in words. compares numbers up to hundred thousands. arranges numbers up to hundred thousands. investigate the concepts of factors and multiples. identifies factors of a given number up to 100. identifies the multiples of a given number up to 100. makes conjectures about common factors of numbers. find the greatest common factor and the least common multiple of given numbers. differentiates prime numbers from composite numbers. finds the prime factors of a number. *K to 12 Curriculum Guide version as of January 31,

36 The learner writes a given number as a product of its prime factors. gives the common factors and the greatest common factor (GCF) of two numbers using the following methods: listing, factor tree. gives the common multiples and least common multiple (LCM) of two numbers: listing, factor tree, continuous division. finds the GCF and LCM of 2 given numbers. multiplication, division and MDAS of whole numbers. estimate and multiply 3-digit numbers and solve multiplication problems involving these numbers. multiplies numbers up to 3-digit numbers by up to 2-digit numbers without regrouping and with zero in any of the factors. multiplies numbers up to 3-digit numbers by up to 2-digit numbers with regrouping and with zero in any of the factors. estimates the products of three to four digits by two to three-digit numbers. mentally multiplies two-digit numbers with products up to 200 and explain the strategies used. analyzes and solves word problems involving multiplication of whole numbers including money using appropriate problem solving strategies. *K to 12 Curriculum Guide version as of January 31,

37 The learner estimate and divide 3- to 4- digit numbers by 1- to 2- digit numbers and solve division problems involving these numbers. analyzes and solves two-step word problems involving multiplication and addition or subtraction using appropriate problem solving strategies. creates and solves word problems involving multiplication and any of the two operations involving whole numbers and money. divides 3- to 4-digit numbers by 1- to 2- digit numbers without remainder. divides 3- to 4-digit numbers by 1- to 2- digit numbers with remainder. divides 3- to 4-digit numbers by 1- to 2- digit numbers with zeros in the middle or continuous zeros in the dividend. divides 3- to 4-digit numbers by multiples of 10 and 100 or by estimates the quotient of 3- to 4-digit dividends by 1- to 2- digit divisors by rounding up or rounding down dividends or divisors. mentally divides 2- to 3-digit numbers by 1- digit numbers without remainder and explain the strategies used. *K to 12 Curriculum Guide version as of January 31,

38 The learner analyzes and solves one-step word problems involving division of 3- to 4-digit numbers by 1- to 2- digit numbers including money using appropriate problem solving strategies. analyzes and solves 2- to 3-step word problems involving division and any one or two of the other fundamental operations including money using appropriate problem solving strategies. creates and solves 1- to 2- step word problems involving multiplication and any other operations involving whole numbers and money. perform series of operations following the MDAS rule. interprets and explains MDAS correctly. performs a series of two or more operations. a fraction as part of a set of objects, as a number, as division, and of the different kinds of fractions and applies them in real-life situations. identify fractions on a number line and investigate fractions as part of a set of objects. illustrates fractions using regions, sets and the number line. divides sets of objects into smaller sets of equal amounts to recognize and identify fractional parts of a set. compare and arrange similar and dissimilar fractions. identifies similar and dissimilar fractions from a given set of fractions. compares and arranges similar fractions from least to greatest and vice versa. *K to 12 Curriculum Guide version as of January 31,

39 The learner compares and arranges dissimilar fractions from least to greatest and vice versa. convert improper fractions to mixed numbers and vice versa. identifies proper fraction/ improper fraction/mixed numbers from a given set of fractions including those with denominators of 10 and 100. changes improper fraction to mixed numbers and vice versa. converts one (1) to a fraction and vice versa. operation of fractions. add and subtract fractions and solve problems involving addition and subtraction of fractions. visualizes and adds similar fractions. visualizes and subtracts similar fractions. visualizes and subtracts a fraction from a whole number. adds and subtracts dissimilar fractions. solves word problems involving addition and subtraction of fractions using appropriate problem solving strategies. Geometry parallel and perpendicular lines, measures of angles, symmetry, plane figures up to 4 sides, and 2-D representation of a 3-D solid. investigate the concepts of parallel and perpendicular lines and angles. describes and illustrates different angles (right, acute and obtuse) using models. draws perpendicular and parallel lines using a ruler and set squares. *K to 12 Curriculum Guide version as of January 31,

40 identifies parts of an angle and name angles using notation such as ABC, x, and 2 in plane figures. draws a given angle using a protractor. describes and illustrates parallel and perpendicular lines. identifies parallel and perpendicular lines and use these terms to describe geometric figures. describe various plane figures up to four sides and discuss their properties. uses concrete objects/ models to explore/describe plane figures according to their attributes/properties of triangles and quadrilaterals. identifies and describes the different kinds of triangles: acute, right, obtuse, scalene, isosceles, equilateral, equiangular. identifies and describes the different kinds of quadrilaterals: square, rectangle, parallelogram, trapezoid, rhombus. explore symmetry in plane figures and the environment. identifies and visualizes symmetry in the environment and in design. completes a symmetric figure with respect to a given line of symmetry. *K to 12 Curriculum Guide version as of January 31,

41 explore different geometric solids. visualizes and describes geometric solids. makes models of different geometric solids: cube, prism, cylinder. Patterns and Algebra patterns and number sentences. describe the rule in a pattern in order to complete the pattern. searches for a pattern given a set of objects or figures. determines the next object or term or figure from a given pattern. complete number sentences. finds the missing value in a number sentence involving one of the four operations of whole numbers. Measurement measures of perimeter and area of squares, rectangles, triangles, parallelograms and trapezoids, and their related figures, and volume of rectangular prism. find the perimeter of a plane figure and solve problems involving perimeter. describes and illustrates the perimeter of a given figure. finds the perimeter of triangles, squares, rectangles, parallelograms and trapezoids. solves word problems involving perimeter of squares and rectangles, triangles, parallelograms and trapezoids. find the area of a plane figure and solve problems involving area. estimates the area of an irregular plane figure made up of squares and rectangles using non-standard units. derives inductively the formulas for the area of squares and rectangles. *K to 12 Curriculum Guide version as of January 31,

42 finds the area of a figure made up of squares and rectangles using cm 2 and m 2. estimates the area of triangles, parallelograms and trapezoids using nonstandard units. derives inductively the formulas for the area of triangles, parallelograms and trapezoids. finds the area of triangles, parallelograms and trapezoids using cm 2 and m 2. solves word problems involving the area of a figure made up of squares and rectangles. solves word problems involving the area of a triangle, parallelogram and trapezoid. explore the concept of volume of a solid and solve problems involving the volume of a solid. visualizes and builds rectangular prisms using unit cubes. derives inductively the formula for the volume of rectangular prisms. finds the volume of a rectangular prism using cubic units. solves word problems involving the volume of a rectangular prism. *K to 12 Curriculum Guide version as of January 31,

43 Statistics and Probability tables, bar graphs and probability. solve problems involving data presented in bar graphs and tables. organizes data in tables. constructs bar graphs and organize data using bar graphs. reads and interprets data presented in tables and bar graphs. solves problems using data presented in bar graphs and tables. make simple predictions of events based on data records. gathers and records favorable outcomes from an activity with different results (e.g., rolling a die, drawing a card, tossing coins, etc.). analyzes the chance of a result using spinners. *K to 12 Curriculum Guide version as of January 31,

44 GRADE 5 Numbers and Number Sense The learner understanding of number notation and place value of numbers up to 10 million and of some number theory concepts. read and write large whole numbers and round off whole numbers to the nearest thousands and millions. visualizes and represents whole numbers up to reads and writes whole numbers up to rounds off whole numbers to the nearest thousands and millions. find the greatest common factor and the least common multiple of given numbers. writes a given number as a product of its prime factors. gives the common factors and the greatest common factor (GCF) of two numbers using the following methods: listing, factor tree, continuous division. gives the common multiples and least common 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 on different contexts. uses divisibility rules for 2, 5 and 10 to find common factors of numbers. uses divisibility rules for 3, 6 and 9 to find common factors. uses divisibility rules for 4, 8, 11 and 12 to find common factors. *K to 12 Curriculum Guide version as of January 31,

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