Mathematics K to 10

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Republic of the PhilippinesDepartment of Education

DepEd Complex, Meralco AvenuePasig City

K to 12 Curriculum Guide

MATHEMATICS

(Kindergarten to Grade 10)

January 31, 2012


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K to 12 Curriculum Guide - version as of 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 thinkingby Scriven and Paul (1987):

Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluatinginformation gathered from or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action.

On the other hand, we define problem solving in mathematics using Polyas (1945 & 1962) definition:

Mathematical problem solving is finding a way around a difficulty, around an obstacle, and finding a solution to a problem that is unknown.

These two goals are to be achieved with an organized and rigorous curriculum content, a well-defined set of high-level skills and processes, desirablevalues and attitudes, and appropriate tools, recognizing as well the different contexts of Filipino learners.

There are five content areas in the curriculum, as adopted from the framework prepared by thePhilippine Council of Mathematics Teacher Educators,Inc. and the Department of Science and Technology Science Education Institute(MATHTED & DOST-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, calculatorsand computers, Smartphones and tablet PCs, and the Internet.

We define context as a locale, situation or set of conditions of the Filipino learnerthat may influence his/her study and use of mathematics to developcritical thinking and problem solving skills. Contexts refer to beliefs, environment, language and culture that include traditions and practices, and learners priorknowledge and experiences.

The framework is supported by the following underlying learning principles and theories: experiential and situated learning, reflective learning,constructivism, cooperative learning and discovery and inquiry-based learning. The mathematics curriculum is grounded in these theories.


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Experiential learning as advocated by David Kolb is learning that occurs by making sense of direct everyday experiences. Experiential learning theorydefines learning as "the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of graspingand transforming experience" (Kolb, 1984, p. 41). Situated learning, theorized by Lave and Wenger, is learning in the same context on which concepts andtheories are applied.

Reflective learning refers to learning that is facilitated by reflective thinking. It is not enough that learners encounter real-life situations. Deeper learningoccurs when learners are able to think about their experiences and process these allowing them the opportunity to make sense and meaning of theirexperiences.

Constructivism is the theory that argues that knowledge is constructed when the learner is able to draw ideas from his/her own experiences andconnects 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 learners to learn by asking relevant questions and discovering new ideas. Discovery and inquiry-based learning(Bruner, 1961) support the idea that learners learn when they make use of personal experiences to discover facts, relationships and concepts.


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Figure 1. The Conceptual Framework of Mathematics Education


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LEARNING AREA STANDARD: The learner demonstrates understanding and appreciation of key concepts and principles of mathematics as

applied, using appropriate technology, in problem solving, communicating, reasoning, making connections,

representations, and decisions in real life.

KEY STAGE STANDARDS:

K 3 4 6 7 10At the end of Grade 3, the learnerdemonstrates understanding and appreciationof key concepts and skills involving wholenumbers up to ten thousand, fractions,measurement, simple geometric figures, pre-algebra concepts and data representation and

analysis as applied, using appropriatetechnology, in critical thinking, problemsolving, reasoning, communicating, makingconnections, representations and decisions inreal life.

At the end of Grade 6, the learner demonstratesunderstanding and appreciation of key conceptsand skills involving rational numbers,measurement, geometric figures, pre-algebraconcepts, simple probability and data analysis asapplied, using appropriate technology, in critical

thinking, problem solving, reasoning,communicating, making connections,representations and decisions in real life.

At the end of grade 10, the learner demonstratesunderstanding and appreciation of key conceptsand skills involving number sense, measurement,algebra, geometry, probability and statistics, andtrigonometry as applied, using appropriatetechnology, in critical thinking, problem solving,

communicating, reasoning, making connections,representations, and decisions in real life.


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GRADE LEVEL STANDARDS:

Grade Level Grade Level Standards

KThe learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 20, space andmeasurement, simple geometric figures, pre-algebra concepts and data collection as applied, using appropriate technology, in criticalthinking, problem solving, reasoning, communicating, making connections, representations and decision in real life.

Grade 1

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 100, fractions,measurement, simple geometric figures, pre-algebra concepts, data collection and representation as applied, using appropriatetechnology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in reallife.

Grade 2

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 1 000, fractions,

measurement and geometric figures, pre-algebra concepts, data collection, representation and analysis as applied, using appropriatetechnology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in reallife.

Grade 3

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 10 000, fractions,measurement, geometric figures, pre-algebra concepts, data collection, representation and analysis as applied, using appropriatetechnology, in critical thinking, problem solving, reasoning, communicating, making connections, representations and decision in reallife.

Grade 4

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 100 000,fractions, decimals including money, ratio, angles, plane figures like square, rectangle, and triangle, measurement (perimeter, area of

triangle, parallelogram and trapezoids, volume of cubes and rectangular prisms, pre-algebra concepts, data collection, representationand analysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.

Grade 5

The learner demonstrates understanding and appreciation of key concepts and skills involving whole numbers up to 10 000 000,fractions, decimals including money, ratio, percent, geometry (circles and five or more-sided polygons), measurement (circumference,area of circle, volume of cubes and rectangular prisms, temperature) ,pre-algebra concepts, data collection, representation andanalysis as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.


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Grade Level Grade Level Standards

Grade 6

The learner is expected to have mastered the concepts and operations on whole numbers; demonstrates understanding andappreciation of the key concepts and skills involving fractions, decimals including money, ratio and proportion, percent, rate, integers,geometry (spatial figures), measurement (surface area, volume, meter reading), pre-algebra concepts, data collection, representationand analysis, probability, expressions and equations as applied, using appropriate technology, in critical thinking, problem solving,reasoning, communicating, making connections, representations and decisions in real life.

Grade 7The learner demonstrates understanding of key concepts and principles of number sense, measurement, algebra, geometry,probability and statistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating,making connections, representations and decisions in real life.

Grade 8The learner demonstrates understanding of key concepts and principles of algebra, geometry, probability and statistics as applied,using appropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representationsand decisions in real life.

Grade 9The learner demonstrates understanding of key concepts and principles of algebra, geometry, and trigonometry as applied, usingappropriate technology, in critical thinking, problem solving, reasoning, communicating, making connections, representations anddecisions in real life.

Grade10The learner demonstrates understanding of key concepts and principles of number sense, algebra, geometry, probability andstatistics as applied, using appropriate technology, in critical thinking, problem solving, reasoning, communicating, makingconnections, representations and decisions in real life.


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KINDERGARTEN

Content Content Standards Performance Standards Learning Competencies

Numbers and Number Sense The learner

begins to understand setsand the relationship betweennumbers and quantities up to20.

The learner isable to

explore the concept of setsand elements of sets.

The learner

sorts and groups objects according to thefollowing attributes: color, shape, size andfunction.

matches elements of sets (both objects andpictures) using one-to-one correspondence.

recognizes sets of objects of up to 20elements.

compares two or more sets of objects of up

to 20 elements.

explore the concepts ofcounting numbers 1 to 20 and0.

compares quantities to determine which ismore than, less than or if quantities are thesame.

counts and tells how many objects there arein a given set.

recognizes and represents numbers of up to20.

recognizes and identifies numeral 0 to 20.

matches numbers to a set of objects 1 to 20and 0.

matches numbers0 to 10 and number words.

reads and writes numbers up to 20.


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recognizes coins and bills up to P20 (pesosand centavos).

begins to understand, todescribe simple addition andsubtraction, and to use themto solve problems.

explore the concept ofaddition and subtraction ofwhole numbers and recognizeaddition-like and subtraction-like situations.

recognizes the words put together, addto, plus, and in all that indicate the act ofadding whole numbers.

recognizes the words take away, minus,less, and are left that indicate the act ofsubtracting whole numbers.

represents the concept of addition bycombining elements of two sets.

represents the concept of subtraction bytaking away and comparing two sets.

recognizes situations that require additionand subtraction of whole numbers.

uses manipulative objects to explore theconcept of addition and subtraction withsums and differences between 0 and 10.

matches addition and subtractionexpressions with concrete representations.

estimate and compute forsums and differences andsolve addition and subtractionproblems.

adds and subtracts up to quantities of 10using concrete objects.

subtracts up to quantities of 10 usingconcrete objects.

uses concrete objects to determine answers


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to addition and subtraction problems.

solves number stories involving addition andsubtraction up to quantities of 10.

matches addition and subtractionexpressions with concrete representations.

writes addition and subtraction equations.

counts groups of equal quantity usingconcrete objects (beginning multiplication).

subtracts groups of equal quantity usingconcrete objects (beginning division).

begins to understand theconcept of dividing wholesinto equal parts.

explore the concept of halvesand fourths.

recognizes a half and a fourth as parts of awhole.

represents a half and a fourth by dividing awhole object into 2 and 4 equal parts,respectively.

Measurement begins to understand theconcept of time, length, massand capacity and the non-standard units to measure

them.

explore the concept of time. observes sunrise and sunset to tell the timeof the day (morning, noontime, evening).

tells the time of day when activities are being

done (e.g. morning).

tells the number of days in a week and themonths in a year.

identifies days of the week and months ofthe year.


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changes and describes rate of movement(going faster, going slower).

compares time intervals by determining

which activities take a longer or shorter time.

recognizes clock as a measure of time: hour,half-hour.

explain and represent theconcepts of location, positionand direction.

uses words that determine location:top/bottom, front/back, left-right.

tells if an object is near or far.

uses body movement exercises to show

understanding of positions and directions(top to bottom/bottom to top, left to right/rightto left).

uses drawings to show understanding ofenclosures and boundaries.

describe and compare theconcepts of length,mass/weight and capacity.

describes familiar objects according to theirlength, heaviness and amount of space theyoccupy.

compares objects based on their length,

mass/weight and capacity.

uses vocabulary of measurement.

estimate lengthmass/weight andcapacity.

uses non-standard units to estimate andmeasure the following attributes of familiarobjects: length, mass/weight and capacity.


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Geometry begins to identify the commonattributes of an object and thecommon 2- or 3-dimensionalobjects in the environment.

identify and describe thecolor, shape and size ofobjects.

identifies and describes the followingattributes: color, shape and size.

identifies objects based on the attributes of

color, shape and size.

describes objects according to the attributesof color, shape and size.

describes objects that are similar or differentbased on the attributes of color, shape andsize.

explore, visualize and modeltwo- and three-dimensional

shapes and figures.

explores the environment to observe,identify, describe, and compare 2- to 3-

dimensional objects.

identifies objects in the environment thathave a particular 2-dimensional and 3-dimensional shape.

describes and compares shapes, sizes, andpositions of 2- to 3-dimensional objects.

uses manipulatives to create 2- to 3-dimensional objects.

identifies objects that have the same shapeand size.

Patterns and Algebra begins to understand theconcept of a sequence.

explore the concept of asequence.

identifies a sequence of events according tohow they happen.

identifies the event before and after, thefirst and last and the next in reference to


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a given event.

arranges objects in a sequence according tosize: long, longer, longest; wide, wider,

widest; high, higher, highest, etc.

represent and communicatethe concept of a pattern andsequence.

extends a pattern or sequence of objects bycolor, shape and size.

creates a pattern and sequence of objectsby color, shape and size.

explore the concept of order,number patterns andsequences.

identifies the number that comes before,after or in-between.

arranges three numbers from least togreatest/greatest to least.

counts numbers up to 10 in correctsequence.

gives the number pairs for a given numberup to 10 (e.g. 3 is 1and 2, 5 is 2 and 3).

compares numbers up to 10.

writes numbers 1 to 10 in increasing and

decreasing order.

Statistics and Probability starts to make a graph orchart based on theinformation gathered.

use skills in collecting andorganizing information anddata.

collects data by observing and by askingquestions.

organizes data using charts and graphs.


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GRADE 1


Numbers and Number Sense The learner demonstrates

understanding of

number notation and placevalue, cardinal and ordinalnumbers, and comparing andordering numbers up to 100.

The learner is able to

explore the concept ofcardinal numbers up to 100and compare these numbersin various contexts.

The learner

recognizes cardinal numbers from 0 to 100.

counts and tells the number of objects in agiven set by ones and tens.

identifies the number that is one more or oneless from a given number.

composes and decomposes a given number.

regroups sets of ones into sets of tens andsets of tens into hundred using objects.

compares two sets using the expressionsfewer than, more than, and as many as.

orders sets from least to greatest and vice-versa.

counts by 2s, 5s and 10s through 100.

reads and writes numbers up to 100 insymbols and in words.

identifies the place value and finds the valueof a digit in a one- and two-digit numbers.

renames numbers into tens and ones.


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The learner demonstrates

understandingof

The learner is able to The learner

compares numbers up to 100 using relationsymbols.

arranges numbers up to 100 in increasingorder and vice versa.

recognizes coins and bills up to P100 (pesosand centavos).

explore the concept of ordinalnumbers.

reads and writes ordinal numbers 1st, 2nd,3rd up to 10th.

identifies the 1st, 2nd, 3rd up to the 10thobject in a given set from a given point of

reference.

determines the position of an object using1st to 10th from a given point of reference.

addition and subtraction up to100.

illustrate addition andsubtraction of whole numbers.

illustrates addition as putting together andsubtraction as taking away, comparing andadding up.

illustrates the relationship of joining sets to

addition of whole numbers.

illustrates that addition and subtraction areinverse operations.

identifies and constructs equivalent numberexpressions using addition and subtractions.

The learner


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The learner is able to identifies and creates patterns to composeand decomposes numbers using addition.

compute for sums and solveaddition problems.

adds two one-digit numbers with sums up to18 using the order and zero properties ofaddition.

adds two to three one-digit numbershorizontally and vertically with sums up to18.

adds three one-digit numbers having sumsup to 18 using the order and groupingproperties of addition.

uses expanded form to explain the meaningof addition with regrouping.

adds numbers with sums through 99 withoutor with regrouping.

mentally adds two to three 1-digit numberswith sums up to 18.

mentally adds a 2-digit number and 1-digitnumber with regrouping.

solves one-step word problems involvingaddition of whole numbers including moneywith sums up to 99 using appropriateproblem solving strategy.

The learner demonstrates The learner is able to Thelearner


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understanding of compute for differences andsolve subtraction problems.

subtracts one-digit numbers with minuendsthrough 18 (basic facts).

subtracts one to two-digit numbers with

minuends up to 99 without regrouping.

uses the expanded form to explainsubtraction with regrouping.

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

mentally subtracts 1-digit numbers fromminuends up to 18 without regrouping.

mentally subtracts a 1-digit number from 2-digit minuends without regrouping.

solves word problems involving subtractionof whole numbers including money withminuends up to 99 with and withoutregrouping using appropriate problemsolving strategy.

the concepts of halves andfourths and applies them in

dividing a whole or setequally.


understanding of

visualize, model andrepresent the concept of

halves and fourths usingwhole objects and sets.


visualizes and identifies and of a wholeobject.

divides a whole into halves and fourths.

divides the elements of a set of objects intotwo groups of equal quantities to showhalves of sets.

The learner

divides the elements of a set of objects into

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four groups of equal quantities to showfourths of sets.

given half of a region or a set, draws thewhole region or set.

Geometry 2-D and 3-D shapes throughidentifying, classifying andconstructing figures using cut-outs and concrete models.

explore the properties of 2-and 3-dimensional figures.

identifies, names and describes the fourbasic shapes in 2- and 3-dimensionalobjects: square, rectangle, triangle andcircle.

compares and classifies 2- and 3-dimensional figures according to commonattributes.

model and represent 2- and3-dimensional objects

draws the four basic shapes.

constructs three-dimensional objects usingmanipulative materials.

Patterns and Algebra simple patterns. identify and create numberand attribute patterns.

identifies and explains simple repeatingpatterns.

makes patterns of shapes, colors andnumbers.

complete number andattribute patterns.

finds the missing number/digit in addition orsubtraction problems.

finds and completes patterns of one or twoof the following attributes: Shape, Size,Color, Number, Orientation.

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understanding of


determines the next term (figure/number) ina given sequence and give a reason.

Measurement the concepts of time andmeasures and comparesobjects using directcomparison and non-standardunits of length, mass andcapacity.

give different measures oftime.

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

uses a calendar to determine a day ormonth.

tells the time by an hour, half-hour andquarter-hour.

estimate and compute formeasurements of length,mass and capacity

compares objects using the comparativewords: Short, shorter, shortest; Long, longer,longest; Tall, taller, tallest; High, higher,highest; Heavy, heavier, heaviest; Light,lighter, lightest.

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

estimates and measures mass using non-standard units of mass/weight measures.

shows and finds capacity using non-standard unit.

Statistics and Probability organizing, representing andcomparing data usingpictographs without scalerepresentations andprobability, and exploresgames and activities.

organize and interpret data. collects and organizes data using tallies andtables.

represents data using pictographs withoutusing a scale.

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reads and interprets a pictograph.

make conjectures aboutgames and activities.

identifies cause and effect relationships.

predicts and records outcome ofexperiments and chance games.

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GRADE 2


Numbers and Number Sense The learner demonstratesunderstanding of

the relationships betweennumbers and place value ofwhole numbers up to 1000and of ordinal numbers up to20th.


explore the concepts ofnumbers up to 1000, readand write these numbers.

The learner

visualizes and identifies numbers from 101through 1000.

associates numbers with sets having 101 upto 500 objects and give the number ofobjects.

associates numbers with sets having 501 upto 1000 objects and give the number ofobjects.

counts and groups objects in ones, tens, andhundreds.

reads and writes numbers from 101 through1000 in symbols and in words.

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

reads and writes numbers through 1000 insymbols and in words.

gives the place value of each digit in a three-

digit number.

writes three-digit numbers in expanded form.

compares numbers using >, < and =.

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

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identify ordinal numbersthrough 20th.

visualizes and identifies the 1st through the20th object of a given set from a given pointof reference.

reads and writes ordinal numbers from 1stthrough the 20th.

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

the concept of the fouroperations of whole numbersand the identity and zeroproperties of multiplication.

compute sums and solveaddition problems involvingnumbers of up to 1000.

adds numbers with sums up to 1000 withoutand with regrouping: 2 digit and 3-digit.

adds numbers with sums up to 1000 withoutand with regrouping: 3 digit and 3-digit.

uses the following properties of addition incomputing for sums of up to 1000:zero/identity property of addition,commutative property of addition,associative property of addition.

mentally adds 1- to 2-digit numbers withsums up to 50.

mentally adds 3-digit numbers by ones (up

to 9).

mentally adds 3-digit numbers by tens(multiples of 10 up to 90).

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

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analyzes and solves word problemsinvolving addition of whole numbersincluding money with sums up to 1000without and with regrouping.

compute differences andsolve subtraction problemsinvolving numbers of up to1000.

subtracts 2- to 3-digit numbers withminuends up to 999 without and withregrouping.

mentally subtracts 1-digit numbers from 1 to2-digit numbers with minuends up to 50.

mentally subtracts 3-digit by ones withoutregrouping.

mentally subtracts 3-digit by tens without

regrouping.

mentally subtracts 3-digit by hundredswithout regrouping.

analyzes and solves one-step wordproblems involving subtraction of wholenumbers including money with minuends upto1000 without and with regrouping.

compute for sums and

differences and solveproblems involving bothaddition and subtraction ofnumbers.

performs order of operations involving

addition and subtraction of small numbers.

solves two-step word problems involvingaddition and subtraction of 2- to 3-digitnumbers including money using appropriateprocedures.

explore and illustrate the illustrates multiplication as repeated addition,

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concept of multiplication ofwhole numbers.

arrays, counting by multiples, and equaljumps on the number line.

writes a related equation for each type of

multiplication: repeated addition, array,counting by multiples, and equal jumps onthe number line.

illustrates the property of multiplication thatany number multiplied by one (1) is thesame number.

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

illustrates the commutative property of

multiplication.

compute products of numbersinvolving 2, 3, 4, 5 and 10 andsolve problems involvingmultiplication of thesenumbers.

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

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

analyzes and solves one-step wordproblems involving multiplication of wholenumbers including money.

analyzes and solves two-step word problemsinvolving multiplication of whole numbers aswell as addition and subtraction includingmoney.

explore and model theconcept of division of whole

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

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numbers.

represents division as equal sharing,repeated subtraction, equal jumps on thenumber line, and formation of equal groups

of objects.

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

compute quotients ofnumbers found in themultiplication tables involving2, 3, 4, 5 and 10 and solveproblems involving division of

these numbers.

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

mentally divides numbers found in themultiplication tables of 2, 3, 4, 5 and 10.

analyzes and solves one-step wordproblems involving division of numbersfound in the multiplication tables of 2, 3, 4, 5,and 10.

unit fractions, proper fractionsand similar fractions, andidentification of money valuethrough 100.

explore the concept of unitfractions and other fractionsless than 1 and comparethese fractions.

visualizes and identifies unit fractions withdenominators 10 and below.

reads and writes unit fractions.

compares unit fractions using relationsymbols.

orders unit fractions.

visualizes and identifies other fractions lessthan one with denominators 10 and below.

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

reads and writes similar fractions.

compares similar fractions using relationsymbols.

orders similar fractions.

apply number concepts onproblem situations involvingmoney.

reads and writes money with value through100.

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

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

counts and tells the value of a set of bills ora set of coins through 100 in combinations ofpesos and centavos (Peso and centavocoins only, bills and centavo coins, coins andbills).

reads and writes money in symbols and in

words through 100.

compares values of different denominationsof coins and paper bills through 100 usingrelation symbols >, < and =.

Geometry the basic properties ofgeometric shapes, simple

visualize and model half-circles and quarter circles as

visualizes, identifies, classifies anddescribes half-circles and quarter circles.

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tessellations and symmetry. well as other commonshapes. constructs squares, rectangles, triangle,

circles, half-circles and quarter circles usingcut-outs and square grids.

explore the concept ofsymmetry.

identifies shapes/figures that show symmetryin a line.

creates figures that show symmetry in a line.

visualize, model andrepresent tessellations.

recognizes shapes that can tessellate.

tessellates a surface using triangles andsquares.

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

identifies straight lines and curves, flat andcurved surfaces in a 3-dimenional object.

explains the differences between straightlines and curved lines, flat surfaces andcurved surfaces.

Patterns and Algebra patterns on numbers andgeometric objects.

argue and justify patterns. identifies and explains simple repeatingpatterns.

determines the next term (figure/number) ina given sequence and give a reason.

apply their understanding andstrategies in completingpatterns.

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

Measurement the concept and application oftime and of using standardunits in measuring length,

compute for measures of timeand solve problems involvingtime.

tells and writes the time in minutes includinga.m. and p.m. using analog and digitalclocks.

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mass, area and capacity.

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

solves simple word problems involving time.

identify and compare thestandard units centimeter andmeter.

shows and uses the appropriate unit oflength to measure a particular object andtheir abbreviations cm and m.

compares length in meters or centimeters.

estimate and compute forlengths of objects and solveproblems involving lengthsusing centimeter and meter.

measures objects using appropriatemeasuring tools in m or cm.

estimates and measures length using meter

or centimeter.

solves simple word problems involvinglength.

identify, use and compare thestandard units gram andkilogram.

shows and uses the appropriate unit of massto measure a particular object or situationand their abbreviations g and kg.

compares mass in grams or kilograms.

estimate and compute for themass/weight of an object andsolve problems involvingmass/weight.

measures objects using appropriatemeasuring units in g or kg.

estimates and measures mass using gramor kilogram.

solves simple word problems involvingmass.

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explore and illustrate theconcept of area.

illustrates area as a measure of how muchsurface is covered or occupied by planefigure.

shows the area of a given figure usingsquare tile units, i.e. number of square tilesneeded.

estimate and compute for thearea of a plane figure.

estimates the area of a given figure usingany shape.

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

measure capacity. shows and finds capacity using appropriate

measuring tools, e.g. amount of liquidneeded.

Statistics and Probability pictographs with scalerepresentations and the ideaof likelihood.

organize and interpret data. collects and organizes data using tables andpictures.

reads and interprets data in a givenpictograph.

represent data using scales. forms scale representation of objects fromthe data collected.

makes pictographs using scalerepresentation.

make conjectures andeducated guesses about thelikelihood of events.

makes a guess on whether an event is lesslikely, more likely, equally likely or unlikely tohappen based on facts.

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GRADE 3



understanding of

the concepts of wholenumbers up to 10000, ordinalnumbers up to 100th andRoman numerals up to M.


explore the concepts ofnumbers up to 10 000, count,read and write these numbersand identify ordinal numbersof up to 100th.

reads and writes the numbers through 10

000 in symbols and in words.

identifies the place value and find the valueof a digit in 4- to 5-digit numbers.

compares 4- to 5-digit numbers usingrelation symbols.

orders 4- to 5-digit numbers in increasingorder and vice versa.

rounds numbers to the nearest tens,

hundreds and thousands.

identifies ordinal numbers from 1st to 100th.

read and write numbers usingRoman numerals up to M.

reads and writes the value of romannumbers in Hindu-Arabic and vice versa I toL.

reads and writes the value of romannumbers in Hindu-Arabic and vice versa L toC.

reads and writes the value of Romannumbers in Hindu-Arabic and vice versa C toD.

reads and writes the value of Romannumbers in Hindu-Arabic and vice versa D toM.

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the four operations of wholenumbers and of the conceptof identity, commutative,associative and distributiveproperties of addition andmultiplication.

use properties of addition toestimate and compute forsums and solve additionproblems involving numbersof up to 10 000.

illustrates the properties of addition(commutative, associative, identity).

adds 3- to 4 -digit numbers up to threeaddends with sums up to 10 000 withoutregrouping.

adds 3- to 4 -digit numbers up to threeaddends with sums up to 10 000 withregrouping.

estimates the sum of 3- to 4-digit addendsby rounding.

mentally adds without or with regrouping 2-

digit and 1-digit numbers and explain thestrategies used.

mentally adds without or with regrouping two2-digit numbers and explain the strategiesused.

mentally adds without or with regrouping 2-digit and 3-digit multiples of hundreds andexplain the strategies used.

solves word problems involving addition ofwhole numbers with sums up to 10 000including money using appropriate problemsolving strategy.

estimate and compute fordifferences and solvesubtraction problems

subtracts 3-digit numbers from 3- to 4-digitnumbers without and with regrouping andwith and without zeros in the digits.

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involving numbers of up to 10000. subtracts 3- to 4-digit numbers from 4-digit

numbers without and with regrouping andwith and without zeros in the digits.

estimates the difference of two numbers withthree to four digits by rounding.

mentally subtracts without and withregrouping 2-digit and 1-digit numbers andexplain the strategies used.

mentally subtracts without and withregrouping two 2-digit numbers and explainthe strategies used.

mentally subtracts without and withregrouping 2-digit to 3-digit numbers frommultiples of hundreds and explain thestrategies used.

solves one-step word problems involvingsubtraction of whole numbers includingmoney using appropriate problem solvingstrategies.

solves two-step word problems involvingaddition and subtraction of whole numbersincluding money using appropriate problemsolving strategies.

estimate and multiply 2- and3-digit numbers by 1-digit to2-digit numbers and solvemultiplication problems

constructs and completes the multiplicationtables of 6, 7, 8 and 9.

states basic multiplication facts for numbers

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involving these numbers. up to 10.

applies the commutative property ofmultiplication.

multiplies 2-digit by 1-digit by using thedistributive property of multiplication.

multiplies three 1-digit numbers by using theassociative property of multiplication.

multiplies 2- to 3-digit numbers by 1-digitnumbers without or with regrouping.

multiplies 2-digit numbers by 2-digit numberswithout regrouping.

multiplies 2-digit numbers by 2-digit numberswith regrouping.

multiplies 2- to 3-digit numbers by multiplesof 10 and 100.

multiplies 1- to 2-digit numbers by 1000.

estimates the product of 2- to 3-digitnumbers by 1- to 2-digit numbers byrounding.

mentally multiplies 2-digit by 1-digit numberswithout regrouping involving products of upto 100.

solves one-step word problems involvingmultiplication of whole numbers including

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money using appropriate problem solvingstrategies.

solves two-step word problems involvingmultiplication as well as addition andsubtraction including money usingappropriate problem solving strategies.

explore the concepts offactors and multiples.

states multiples of 1- to 2-digit numbers.

differentiates prime and composite numbers.

estimate and divide 3-digitnumbers by up to 2-digitnumbers and solve divisionproblems involving these

numbers.

divides numbers found in the multiplicationtables of 6, 7, 8, 9.

states basic division facts of numbers up to

10.

divides 2- to 3-digit numbers by 1-digitnumbers without remainder.

divides 2- to 3-digit numbers by 1-digitnumbers with remainder.

divides 2-digit numbers by 2-digit numbers.

divides numbers by 10 and 100.

estimates the quotient of 2- to 3-digitnumbers by 1- to 2-digit numbers.

mentally divides 2-digit numbers by 1-digitnumbers without remainder.

solves one-step word problem involving

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division of 2- to 4-digit numbers by 1- to 2-digit numbers including money usingappropriate problem solving strategies.

solves word problems involving division andother fundamental operations, includingmoney, using appropriate problem solvingstrategies.

the basic kinds of fractions,know how to simplify andorder them, and to apply toproblem solving moneythrough 100.

explore the concepts ofdissimilar fractions, improperfractions and mixed numbers.

visualizes and identifies fractions that areequal to one and greater than one.

reads and writes fractions that are greaterthan one in symbols and in words.

relates and changes improper fractions to

mixed numbers and vice versa.

visualizes and identifies dissimilar fractions.

compares dissimilar fractions.

arranges dissimilar fractions in increasing ordecreasing order.

recognizes and generates equivalentfractions of commonly used fractions.

changes fractions to lowest forms.

apply number concepts tosolve problems involvingmoney through 1000.

reads and writes money in symbols through1000.

compares values of the differentdenominations of coins and bills through

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1000.

solves real-life problems involving moneythrough 1000.

Geometry the basic elements of angles,lines and rays.

explore the concepts of point,line, line segment and ray.

recognizes and draws a point, line, linesegment and ray.

recognizes and draws perpendicular lines,parallel lines and intersecting lines.

visualizes, identifies and draws congruentline segments.

explore symmetry in planefigures and the environment.

identifies and draws the line of symmetry ina given symmetrical figure.

identifies and visualizes symmetry in theenvironment and in design.

completes a symmetric figure with respect toa given line of symmetry.

tessellates the plane using triangles,squares and other shapes that cantessellate.

Patterns and Algebra patterns of numbers,operations, geometric objectsand relationships.

explore the concept of oddand even numbers.

tells when a number is odd or even.

finds the pattern using odd and evennumbers with objects, pictures and words.

identify the rule for a patternand complete the numberpattern.

determines the pattern of a given sequenceand state the rule.

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finds the missing number or digit in apattern.

Measurement the concept and application oftime (in minutes), length,mass, area and capacity.

convert time measures fromone unit to another.

converts time measure from seconds tominutes, minutes to hours, hours to day.

converts time measure from days to weeksand months, and convert weeks, months andyears to days.

finds the exact time between dates.

solves word problems involving timemeasure.

recognize, perform and use

conversions of common units.

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 conversionsof common units of measure.

explore the concept of areaand find areas of squares andrectangles using cm2 and m2.

estimates the area of a square and rectangleusing non-standard units.

finds the area of a square in cm2 and m2.

finds the area of a rectangle in cm2 and m2.

solves word problems involving areas ofsquares and rectangles.

measure capacity usingmilliliter and liter.

finds the capacity of a container usingmilliliter/liter.

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solves word problems involving capacitymeasure.

Statistics and Probability tables, bar graphs andprobability.

organize and interpret datapresented in tables and bargraphs.

collects and organizes data in a table.

reads and interprets a table.

constructs a bar graph.

reads and interprets a bar graph.

make simple predictions ofevents.

tells whether an event is most likely tohappen, equally likely to happen or unlikelyto happen based on facts.

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GRADE 4


Numbers and Number Sense The learner demonstratesunderstanding of

number notation and placevalue of numbers up to100000, and of factors andmultiples of numbers up to100, and of the greatestcommon factor and leastcommon multiple.


read, write, compare andarrange numbers through 100000 and round off numbers tothe nearest thousands andten thousands.

The learner

reads and writes numbers through hundredthousands in symbols and in words.

identifies numbers up to 100 000.

gives the place value of each digit in a six-digit number.

reads and writes numbers up to hundredthousands in symbols and in words.

compares numbers up to hundred

thousands.

arranges numbers up to hundred thousands.

investigate the concepts offactors and multiples.

identifies factors of a given number up to100.

identifies the multiples of a given number upto 100.

makes conjectures about common factors ofnumbers.

find the greatest commonfactor and the least commonmultiple of given numbers.

differentiates prime numbers from compositenumbers.

finds the prime factors of a number.

writes a given number as a product of its

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prime factors.

gives the common factors and the greatestcommon factor (GCF) of two numbers usingthe following methods: listing, factor tree.

gives the common multiples and leastcommon multiple (LCM) of two numbers:listing, factor tree, continuous division.

finds the GCF and LCM of 2 given numbers.

multiplication, division andMDAS of whole numbers.

estimate and multiply 3-digitnumbers and solvemultiplication problemsinvolving these numbers.

multiplies numbers up to 3-digit numbers byup to 2-digit numbers without regrouping andwith zero in any of the factors.

multiplies numbers up to 3-digit numbers byup to 2-digit numbers with regrouping andwith zero in any of the factors.

estimates the products of three to four digitsby two to three-digit numbers.

mentally multiplies two-digit numbers withproducts up to 200 and explain thestrategies used.

analyzes and solves word problems

involving multiplication of whole numbersincluding money using appropriate problemsolving strategies.

analyzes and solves two-step word problemsinvolving multiplication and addition orsubtraction using appropriate problem

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solving strategies.

creates and solves word problems involvingmultiplication and any of the two operationsinvolving whole numbers and money.

estimate and divide 3- to 4-digit numbers by 1- to 2- digitnumbers and solve divisionproblems involving thesenumbers.

divides 3- to 4-digit numbers by 1- to 2- digitnumbers without remainder.

divides 3- to 4-digit numbers by 1- to 2- digitnumbers with remainder.

divides 3- to 4-digit numbers by 1- to 2- digitnumbers with zeros in the middle orcontinuous zeros in the dividend.

divides 3- to 4-digit numbers by multiples of10 and 100 or by 1000.

estimates the quotient of 3- to 4-digitdividends by 1- to 2- digit divisors byrounding up or rounding down dividends ordivisors.

mentally divides 2- to 3-digit numbers by 1-digit numbers without remainder and explainthe strategies used.

analyzes and solves one-step wordproblems involving division of 3- to 4-digitnumbers by 1- to 2- digit numbers includingmoney using appropriate problem solvingstrategies.

analyzes and solves 2- to 3-step word

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problems involving division and any one ortwo of the other fundamental operationsincluding money using appropriate problemsolving strategies.

creates and solves 1- to 2- step wordproblems involving multiplication and anyother operations involving whole numbersand money.

perform series of operationsfollowing the MDAS rule.

interprets and explains MDAS correctly.

performs a series of two or more operations.

a fraction as part of a set ofobjects, as a number, as

division, and of the differentkinds of fractions and appliesthem in real-life situations.

identify fractions on a numberline and investigate fractions

as part of a set of objects.

illustrates fractions using regions, sets andthe number line.

divides sets of objects into smaller sets ofequal amounts to recognize and identifyfractional parts of a set.

compare and arrange similarand dissimilar fractions.

identifies similar and dissimilar fractions froma given set of fractions.

compares and arranges similar fractionsfrom least to greatest and vice versa.

compares and arranges dissimilar fractions

from least to greatest and vice versa.

convert improper fractions tomixed numbers and viceversa.

identifies proper fraction/ improperfraction/mixed numbers from a given set offractions including those with denominatorsof 10 and 100.

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changes improper fraction to mixed numbersand vice versa.

converts one (1) to a fraction and vice versa.

operation of fractions. add and subtract fractionsand solve problems involvingaddition and subtraction offractions.

visualizes and adds similar fractions.

visualizes and subtracts similar fractions.

visualizes and subtracts a fraction from awhole number.

adds and subtracts dissimilar fractions.

solves word problems involving addition andsubtraction of fractions using appropriate

problem solving strategies.

Geometry parallel and perpendicularlines, measures of angles,symmetry, plane figures up to4 sides, and 2-Drepresentation of a 3-D solid.

investigate the concepts ofparallel and perpendicularlines and angles.

describes and illustrates different angles(right, acute and obtuse) using models.

draws perpendicular and parallel lines usinga ruler and set squares.

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 andperpendicular lines.

identifies parallel and perpendicular linesand use these terms to describe geometric

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figures.

describe various plane figuresup to four sides and discusstheir properties.

uses concrete objects/ models toexplore/describe plane figures according totheir attributes/properties of triangles and

quadrilaterals.

identifies and describes the different kinds oftriangles: acute, right, obtuse, scalene,isosceles, equilateral, equiangular.

identifies and describes the different kinds ofquadrilaterals: square, rectangle,parallelogram, trapezoid, rhombus.

explore symmetry in plane

figures and the environment.

identifies and visualizes symmetry in the

environment and in design.

completes a symmetric figure with respect toa given line of symmetry.

explore different geometricsolids.

visualizes and describes geometric solids.

makes models of different geometric solids:cube, prism, cylinder.

Patterns and Algebra patterns and numbersentences.

describe the rule in a patternin order to complete thepattern.

searches for a pattern given a set of objectsor figures.

determines the next object or term or figurefrom a given pattern.

complete number sentences. finds the missing value in a numbersentence involving one of the fouroperations of whole numbers.

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Measurement measures of perimeter andarea of squares, rectangles,triangles, parallelograms andtrapezoids, and their related

figures, and volume ofrectangular prism.

find the perimeter of a planefigure and solve problemsinvolving perimeter.

describes and illustrates the perimeter of agiven figure.

finds the perimeter of triangles, squares,

rectangles, parallelograms and trapezoids.

solves word problems involving perimeter ofsquares and rectangles, triangles,parallelograms and trapezoids.

find the area of a plane figureand solve problems involvingarea.

estimates the area of an irregular planefigure made up of squares and rectanglesusing non-standard units.

derives inductively the formulas for the area

of squares and rectangles.

finds the area of a figure made up of squaresand rectangles using cm2 and m2.

estimates the area of triangles,parallelograms and trapezoids using non-standard units.

derives inductively the formulas for the areaof triangles, parallelograms and trapezoids.

finds the area of triangles, parallelogramsand trapezoids using cm2 and m2.

solves word problems involving the area of afigure made up of squares and rectangles.

solves word problems involving the area of a

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triangle, parallelogram and trapezoid.

explore the concept of volumeof a solid and solve problemsinvolving the volume of a

solid.

visualizes and builds rectangular prismsusing unit cubes.

derives inductively the formula for thevolume of rectangular prisms.

finds the volume of a rectangular prism usingcubic units.

solves word problems involving the volumeof a rectangular prism.

Statistics and Probability tables, bar graphs andprobability.

solve problems involving datapresented in bar graphs and

tables.

organizes data in tables.

constructs bar graphs and organize datausing bar graphs.

reads and interprets data presented in tablesand bar graphs.

solves problems using data presented in bar

graphs and tables.

make simple predictions ofevents based on data

records.

gathers and records favorable outcomesfrom an activity with different results (e.g.,

rolling a die, drawing a card, tossing coins,etc.).

analyzes the chance of a result usingspinners.

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GRADE 5



understanding of number

notation and place value ofnumbers up to 10 million andof some number theoryconcepts.


read and write large whole

numbers and round off wholenumbers to the nearestthousands and millions.

The learner

visualizes and represents whole numbers up

to 10 000 000.

reads and writes whole numbers up to 10000 000.

rounds off whole numbers to the nearestthousands and millions.

find the greatest commonfactor and the least commonmultiple of given numbers.

writes a given number as a product of itsprime factors.

gives the common factors and the greatestcommon factor (GCF) of two numbers usingthe following methods: listing, factor tree,continuous division.

gives the common multiples and leastcommon multiple (LCM) of two numbers:listing, factor tree, continuous division.

finds the GCF and LCM of 2 given numbers.

apply divisibility rules for 2, 3,

4, 5, 6, 8, 9, 10, 11 and 12 ondifferent contexts.

uses divisibility rules for 2, 5 and 10 to find

common factors of numbers.

uses divisibility rules for 3, 6 and 9 to findcommon factors.

uses divisibility rules for 4, 8, 11 and 12 tofind common factors.

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solves problems involving factors, multiplesand divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10,11 and 12.

mastery of concepts andoperations/series ofoperations (PMDAS) of wholenumbers.

simplify a series of operationson whole numbers and solveproblems involving these.

states, explains and interprets the PMDASor GMDAS rule.

simplifies a series of operations on wholenumbers involving more than two operationsusing the PMDAS or GMDAS rule.

analyzes and solves problems involvingseries of operations.

the ability to perform the four

fundamental operations onsimilar and dissimilarfractions.

perform the four fundamental

operations on fractions andmixed numbers and solverelated problems.

represents the four operations on dissimilar

fractions and mixed numbers using concreteand pictorial models.

estimates sums, differences, products andquotients of fractions and mixed numbers.

adds fractions and mixed numbers withoutand with regrouping.

subtracts fractions and mixed numberswithout and with regrouping.

multiplies fractions and mixed numbers.

finds a fractional part of a whole number orof a fraction.

mentally multiplies fractional units.

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divides fractions and mixed numbers.

simplifies fractions and mixed numbers totheir lowest terms.

solves problems involving addition,subtraction, multiplication and division offractions and mixed numbers using theappropriate strategies.

understanding of the conceptof decimals, and addition andsubtraction of decimals up tohundredths.

investigate the relationshipbetween fractions anddecimal numbers.

uses models to illustrate fractions as divisionof two numbers.

visualizes decimal numbers using modelslike blocks, grid, number line and money.

visualizes decimal numbers usingmodels/pictures to show the relationship tofractions.

reads and writes common fractions indecimal form through thousandths.

renames decimal numbers to fractions withdenominators of 10, 100, 1000,10000.

explore, know andunderstand the concept and

value of a decimal number.

gives the place value of each digit of a givendecimal through thousandths.

reads and writes decimal numbers throughthousandths.

rounds decimals to the nearest tenths andhundredths.

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compares and arranges decimal numbersfrom least to greatest and vice versa.

add and subtract decimalnumbers with values through

thousandths and solveproblems involving these.

estimates the sum or difference of decimalnumbers.

adds and subtracts decimals throughthousandths without and with regrouping.

adds and subtracts mixed decimals withoutand with regrouping.

analyzes and solves word problems,including money problems, involving additionand subtraction of decimal numbers.

multiply decimal numbers ofvalues up to the hundredthsand solve problems involvingthese numbers.

represents multiplication of decimal numbersusing pictorial models.

estimates the products of decimal numbers.

multiplies decimal numbers by multiples of10 and 100.

multiplies decimal numbers of values up tohundredths.

multiplies mixed decimals with tenths and

hundredths by whole numbers.

multiplies mixed decimals by mixed decimalswith tenths and hundredths.

multiplies decimals mentally by 0.1, 0.01, 10and 100.

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analyzes and solves word problemsinvolving multiplication of decimals includingmoney.

divide decimal numbers ofvalues up to the hundredthsand solve problems involvingthese numbers.

represents division of decimal numbersusing pictorial models.

estimates the quotients of decimal numbers.

divides decimal numbers of values up to thehundredths.

divides decimal numbers by whole numbers.

analyzes and solves problems of various

types using whole numbers, fractions anddecimals.

understanding on the use ofratio, proportion and percent.

manipulate ratios and solveproblems involving ratios andproportions

visualizes the ratio of two given sets ofobjects.

expresses the ratio of two numbers usingeither the colon (:) or a fraction.

expresses one value as a fraction of anothergiven their ratio and vice versa.

finds how many times one value is as largeas another given their ratio and vice versa.

identifies and writes equivalent ratios.

expresses ratios in their simplest forms.


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describes and compares properties ofpolygons.

represents congruent polygons usingmodels.

identifies and describes congruent polygons.

represents similar polygons using models.

identifies and describes similar polygons.

finds the missing dimension in a pair ofsimilar polygons.

explore circles. visualizes and describes a circle.

identifies and defines the terms related to acircle.

draws circles with different radii using acompass.

Patterns and Algebra understanding of simpleequations.

solve for the unknown valuesin simple equations involvingone or more operations onwhole numbers and fractions.

uses models to illustrate mathematicalsentences.

determines the patterns in completingmathematical sentences.

uses patterns to solve for the unknown insimple equations involving one or moreoperation on whole numbers and fractions.

Measurement understanding onmeasurement in metric units

describe the circumference ofa circle, measure and use it to

represents and describes the circumferenceof a circle.

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to approximate measure andto compute for thecircumference, area, volumeand temperature.

solve problems. the measureof circumference, area of acircle, volume of a cube and arectangular prism andtemperature.

uses a model to estimate the circumferenceof a circle.

derives a formula for finding the

circumference of a circle.

finds the circumference of the given circleusing the formula/s derived.

solves problems involving circumference.

convert units of measure forarea and volume and selectappropriate units and tools forconsistency and accuracy.

estimates and uses appropriate units ofmeasure for area.

converts sq cm to sq m and vice versa.

names the appropriate unit of measure usedfor measuring area for accuracy.

estimates and uses appropriate units ofmeasure for volume.

converts one cubic unit of measure to alarger or smaller unit.

names the appropriate unit of measure usedfor measuring the volume of a cube and a

rectangular prism for accuracy.

describe the area of a circle,measure and use it to solveproblems.

represents and describes the area of acircle.

uses a model to find the area of a circle.

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derives a formula for finding the area of acircle.

finds the area of a circle using the formula/sderived.

solves problems involving area of circleusing appropriate formulas and procedures.

describe the volume of a cubeand a rectangular prism,measure and use it to solveproblems.

describes the volume of cube and arectangular prism.

derives a formula for finding the volume ofcube and a rectangular prism.

solves problems involving volume of a cubeand rectangular prism using appropriateformulas and procedures.

describe temperature,measure and use it to solveproblems.

describes and estimates the temperatureinside and outside of the classroom.

identifies the parts of a thermometer.

reads a thermometer.

measures temperature using the degreeCelsius.

solves problems involving temperature.

Probability and Data Analysis understanding to record,arrange, present, andinterpret data using tables,line graphs and probability.

construct, read and interpret aline graph and itscorresponding table of dataand solve problems involving

reads and interprets data presented in a linegraph and in its corresponding table of data.

constructs a line graph using the

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data from a table and a linegraph.

corresponding table of data.

describes and estimates the average valueof a set of data.

finds the average value of a set of data thatincludes whole numbers, fractions anddecimal numbers.

solves problems involving line graphs andthe average of a set of data.

make simple predictions ofevents based on a probabilityexperiment.

describes a probability experiment.

performs a probability experiment and recordresults by listing.

analyzes data obtained from chance usingexperiments involving letter cards (A to Z)and number cards (0 to 20).

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understanding of the concept

of integers, exponents, baseand scientific notation.


explore the concept of

integers and compareintegers with whole numbers,fractions and decimalnumbers.

The learner

describes the set of integers.

identifies real-life situations that make use ofintegers.

represents integers on the number line.

compares integers with other numbers suchas whole numbers, fractions and decimals.

compares and arranges integers from leastto greatest and vice versa.

use the notation andcomputation of positive wholenumber powers to find valuesof numbers.

defines and describes the exponent and thebase in a number expressed in exponentialnotation.

gives the value of numbers expressed inexponential notation.

expresses positive whole numbers inexpanded notation using exponentialnotation and vice versa.

finds and compares the value of thenumbers expressed in either the expandedor exponential notation.

reads and writes numbers up to trillions inscientific notation.

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determines the value of a number expressedin scientific notation.

perform the four basicoperations on integers

describes and interprets the basic operationson integers using materials such as algebra

tiles, counters, chips and cards.

states the rules for addition, subtraction,multiplication and division of integers.

performs the basic operations on integers.

solves problems involving basic operationson integers.

perform a series of operationsfollowing the GEMDAS ruleand solve problems involvinga series of operations onwhole numbers.

interprets and explains the GEMDAS rule.

performs two or more different operations onwhole numbers with or without exponentsand grouping symbols.

solves problems involving a series ofoperations on whole numbers.

mastery of the operations offractions and decimals.

add and subtract fractionsand decimal numbers andsolve problems involvingthese numbers.

estimates sums and differences of fractionsand decimals in simple or mixed forms.

rounds decimals through thousandths.

adds and subtracts fractions in simple mixedforms without or with regrouping.

adds and subtracts decimals and mixeddecimals through ten thousandths without orwith regrouping.

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s s g p s

solves problems involving addition andsubtraction of fractions and decimals insimple or mixed forms without and withregrouping.

multiply fractions and decimalnumbers and solve problemsinvolving multiplication offractions and decimalnumbers.

illustrates multiplication of fractions anddecimals using models.

estimates products of whole numbers,fractions and decimals.

multiplies fractions in simple and mixedforms.

shows that multiplying a fraction by itsreciprocal is equal to 1.

multiplies decimals and mixed decimalsthrough thousandths without and withregrouping and with 0 difficulty.

solves problems involving addition,subtraction, and multiplication of numbers inmixed forms.

divide fractions and decimalnumbers and solve problems

involving division of fractionsand decimal numbers.

illustrates division of fractions and decimalsusing models.

estimates quotients of whole numbers,fractions and decimals and determine thereasonableness of results (add this to allother competencies involving estimation).

divides fractions and decimal numbers in

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g p

simple and mixed forms.

divides whole numbers (two to five-digitdividends) by decimals (one to two- digitdivisors).

divides mixed decimals by whole numbers.

divides whole numbers by decimals andmixed decimals.

divides mixed decimals by mixed decimals.

divides decimals by 10, 100, 1,000 mentally.

divides decimals by 0.1, 0.01, 0.001mentally.

differentiates between terminating andrepeating from non-terminating decimalquotients.

solves problems involving division offractions and decimals in mixed formsincluding money.

solves word problems involving alloperations on fractions.

analyzes and solves problems of varioustypes-mathematical tasks, word problems,contextual questions and real-world settingsusing whole numbers, fractions anddecimals.

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understanding of ratio andproportion and percent.

use ratio and proportion in avariety of ways and solveproblems in different contexts.

defines and illustrates the meaning of ratioand proportion using concrete or pictorialmodels.

forms ratios and sets up proportions for

groups of objects or numbers.

tells whether two ratios make a proportion.

finds a missing term in a proportion.

sets up a proportion for a given situation.

solves problems involving direct proportion,partitive proportion, inverse proportion indifferent contexts such as distance-rate-time.

use percent in a variety ofways and solve problems indifferent contexts.

defines and illustrates percent.

determines the percentage, rate and base ina given problem.

computes common percentage problemsmentally: percent of increase or decrease,discounts and sales, value-added tax andservice charge.

solves problems involving finding the

percentage, rate and base: commission,sales, taxes and simple interest.

Geometry understanding of angles ingeometric figures usingvarious properties, attributesof spatial figures, 2-D

find unknown angle measuresin geometrical figures.

describes the properties of angles on astraight line, angles at a point and verticallyopposite angles.

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representation of a 3-D solidand identification of nets ofcube, prism and pyramid.

determines the sum of the angles in atriangle and a quadrilateral.

finds unknown angles using angle propertiesin geometrical figures such as a square,

rectangle, parallelogram, rhombus, trapezoidand triangle.

explore spatial figures. identifies the different spatial figures.

illustrates the different spatial figures usingvarious concrete and pictorial models.

visualizes and describes the different spatialfigures: cube, prism, cylinder, sphere,pyramid, cone, etc.

identifies the nets of the following spatialfigures: cube, prism, cylinder, pyramid andcone.

Measurement understanding ofcircumference and area of acircle, perimeter and area offigures related to square,rectangle, triangle and circle,surface area and volume ofrectangular prisms and

capacity.

solve problems involvingfinding areas of compositefigures.

finds the area of composite figures formedby any two or more of the following: triangle,square, rectangle, circle and semi-circle.

solves word problem involving area ofcomposite figures formed by any two ormore of the following: triangle, square,

rectangle, circle and semi-circle.

explore the concept ofsurface area and find thesurface area of geometricsolids.

identifies the faces of a geometric solid.

visualizes and describes surface area andname the unit of measure used for

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measuring the surface area of solids.

derives a formula for finding the surface areaof cubes, prisms and cylinders.

finds the surface area of cubes, prisms andcylinders.

solves word problems involvingmeasurement of surface area.

find the volume of solids andsolve problems related to this.

describes the meaning of the volume of asolid.

determines the relationship between thevolume of a rectangular prism and of apyramid and between a cylinder and a cone.

obtains formulas for finding the volumes ofcylinders, pyramids and cones.

finds the volume of a cylinder, pyramid or acone.

solves problems involving volumes of solids.

understanding of electric andwater consumption, time, rate

and speed.

read and interpret meterreadings.

reads and interprets electric and water meterreadings.

solves problems involving electric and waterconsumptions.

measure time in a variety ofways and solve problemsinvolving time, rate and

estimates the duration of time in secondsand minutes.

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speed. measures time using a 12-hour and a 24-hour clock.

converts measures of time from a 12-hour toa 24-hour clock and vice versa.

calculates time in the different world timezones.

calculates speed, distance and time.

solves problems involving average rate andspeed.

Statistics and Probability understanding to record,arrange, present and interpretdata using tables and circle

graphs and understands themeaning of probability.

construct and interpret circlegraphs.

reads and interprets data presented in acircle graph.

constructs a circle graph based on a table ofdata.

makes inferences and hypotheses on datapresented in a circle graph.

make simple predictions ofevents based on experiments.

describes the meaning of probability such as50% chance of rain and one in a millionchance of winning.

quantifies the phrases most likely to

happen and unlikely to happen.

performs experiments and record outcomes.

makes listings and diagrams of outcomesand tell the number of favorable outcomesand chances using these listings and

K TO 12 MATHEMATIC

Documents

Mathematics K to 10