Single National Curriculum Mathematics

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PREFACEIt is a well-established fact that educational curriculum plays a key role in nation building.Having a uniform curriculum across the country is a long-standing aspiration of allsegments of the society and the present government has declared it as its priority.Development of the Single National Curriculum for Pre 1-5 is the fulfillment of the dreamof ‘One Nation, One Curriculum’.The decades old educational apartheid amongst the different streams of education in thecountry has not only kept the different educational institutions, educational quality,teachers and students divided, but has also perpetuated inequity in opportunities ofsocial and economic progress amongst the population. These systems or streams ofeducation in the country are creating disparities and different mindsets.In our beloved country, different systems of education cater to the educational needs ofchildren in the different classes of society. These include public sector schools, low costprivate schools and the well-endowed state of the art private schools. Alongside, acrossthe length and breadth of the country there are madrassahs which cater to theeducational needs of approximately three million children. These different educationalinstitutes follow completely different curricula, and resultantly we have graduates withcompletely different thinking and approach to life and livelihoods. These are precisely thedifferences that become stumbling blocks for nations aspiring to become great. A singlenational curriculum is therefore, an important step in the journey to building a strongnation.Development of the Single National Curriculum for grade Pre 1-5 has been completedunder a broad-based consultative process with the engagement of experts from allprovinces and areas. To achieve this goal, the experts of provincial and area curriculumauthorities, textbook boards, faculty from renowned universities, research organizations,teacher training institutes and assessment experts and representatives of minoritiesparticipated in the consultative process. For the first time ever, distinguished experts fromthe Ittehad Tanzeemat Ul Madaras Pakistan (ITMP) participated in the development of thecurriculum for grade Pre1-5 under an all-inclusive consultative year-long processamassing extensive inputs of more than four hundred experts.The key considerations in the development of SNC include: teachings from the Quran andSunnah; vision of Quaid-e-Azam Muhammad Ali Jinnah and Allama Iqbal; the Constitutionof Pakistan, national policies; international commitments, including SustainableDevelopment Goals (SDGs); latest trends in education; societal values; inclusive education;human rights and child protcetion; hygiene and sanitation; environment and climatechange; global citizenship; life skills based and civic education; respect for religious andcultural diversity; move away from rote learning; activities and project based learning; 21stcentury skills; use of information and communication technology; and the ever evolvingchallenges and trends of the new era.At the onset of the development of SNC, it was crucial to analyze and build upon itspredecessor national curriculum 2006 of Pakistan. In this regard, comparative studies ofthe 2006 curriculum were conducted vis-à-vis the curricula of Singapore and Cambridge

education. In parallel, standards for learners of Pakistan were compared with those ofSingapore, Malaysia and United Kingdom. Based on the findings and recommendations ofthese research activities, standards for the SNC were agreed upon. In order to ensure theinclusion of international trends in the SNC, a series of national level workshops andconferences were organized on the topics of Critical Thinking, Sustainable DevelopmentGoals (SDGs) and Life Skills Based Education (LSBE).The 2006 national curriculum was revised in the light of recommendations derived fromthe above-mentioned researches and conferences, under the careful supervision ofexperts. The draft of the SNC pre 1-5, hence prepared was shared with the provinces andareas for their review and feedback. For the first time in the history of curriculumdevelopment of Pakistan, experts from Gilgit-Baltistan and Federal GovernmentEducational Institutes (Cantts & Garrisons) participated in the consultative workshops.Moreover, the draft curriculum was also shared with the Cambridge University UK andInstitute for Educational Development, Karachi for expert inputs and value addition. Thedraft curriculum was then updated in the light of feedback received. As a next step anational conference was organized in which experts from all over the country participatedto conduct yet another thorough review of the updated curriculum draft. In an historicmoment, at the conclusion of the national conference, experts from different schools ofthought reached consensus and signed off on the Single National Curriculum for gradePre 1-5In addition to being aligned to modern international trends, the SNC has our national andcultural values at its core. This curriculum endeavors to build a nation that takes pride inits religious and national beliefs and values and at the same time inculcates respect forreligious and cultural diversity in the society and the world at large. It envisions thedevelopment of exemplary attitudes and behaviors in individuals who are capable ofdealing with the challenges of the 21st century.To enable implementation of the SNC in its true spirit, model textbooks, teacher trainingmodules and an assessment framework are being developed, which will ensure delivery ofeducation that is qualitatively superior and relevant to the children’s lives.It is of foremost import to thank all provinces and areas, public and private institutionsand experts, university faculty and researchers, experts from ITMP and representatives ofminorities for their relentless efforts and invaluable recommendations which enabled thedevelopment of the SNC grade Pre 1-5.

TABLE OF CONTENTSChapter 01: Introduction061.1 The Single National Curriculum Mathematics (I -V) 2020:071.2. Aims of Mathematics Curriculum071.3. Mathematics Curriculum Content Strands and Standards081.4 The Mathematics Curriculum Standards and Benchmarks10Chapter 02: Progression Grid14Chapter 03: Curriculum for Mathematics Grade I33Chapter 04: Curriculum for Mathematics Grade II39Chapter 05: Curriculum for Mathematics Grade III46Chapter 06: Curriculum for Mathematics Grade IV52Chapter 07: Curriculum for Mathematics Grade V60Chapter 08: Teaching Strategies68Role of a Teacher71Classroom Planning for Mathematics72Chapter 09: Assessment in Mathematics74Mathematics Curriculum Grade Wise Tables;77UNIT WISE WEIGHTAGES --- GRADE- I77UNIT WISE WEIGHTAGES --- GRADE- II77UNIT WISE WEIGHTAGES --- GRADE- III77UNIT WISE WEIGHTAGES --- GRADE- IV78UNIT WISE WEIGHTAGES --- GRADE- V78Cognitive Domains / Skills79Table of Specification for Grade – IV81Number and Operations distribution unit wise in Grade – IV81Paper Pattern for Assessment:82

TABLE OF CONTENTSChapter 10: Teaching and Learning Resources83The Textbook84Guidelines for Textbook Authors84Textbook Style and Structure85The Teacher’s Manual86The Workbook86Mathematics Laboratory87The Web-based Resources89The Reference Book Resources89Curriculum Review Committee for Mathematics (I-V)90


CHAPTER1.1 THE SINGLE NATIONAL CURRICULUM MATHEMATICS (I -V) 2020:The Single National Mathematics Curriculum 2020 has been designed in the perspectiveof modern trends in Mathematics and emerging requirements of society in terms ofNational Integrity and Social Cohesion.The main aim of the Single National Mathematics Curriculum 2020 is to developmathematical literacy, induce logical thinking, reasoning and solve real life situationsamong students. Overall this curriculum provides a framework that encompassesexpectations and provides guidance for meaningful learning of Mathematics at primarylevel. This document helps teachers to design, implement, and analyse instructions, andassessment methods in order to accomplish the overall goal of the curriculum. The entirecurriculum is divided into four strands, Numbers and Operations, Algebra, Measurementsand Geometry and Data Handling, all underpinned in Reasoning and Logical thinkingwhich serves as a cross cutting strand. This Curriculum is based on standards,benchmarks and also features a progression grid to show the progression ofMathematical concepts across the grades. Students’ learning outcomes are matched withthe contents and are aligned with the benchmarks and the standards. The learningoutcomes emphasize on the development of knowledge and conceptual understandingthrough application and reasoning skills. This curriculum also emphasizes on Values topromote student’s spiritual, moral, social and cultural development through mathematics.This curriculum (I-V) stimulates the logical cognition of students and encourages them tosolve real life mathematical situations. In grades VI-VIII, students will be provided with themathematical tools for justifying conclusions and to identify the relationship betweendifferent mathematical concepts in everyday situations. In grades IX-XII, students willadditionally develop the ability to use Mathematics in other fields of study.1.2 AIMS OF MATHEMATICS CURRICULUMThe basic aims of mathematics curriculum from grade I-V are as follow: Instill Mathematical skills for everyday use.Strengthen basic mathematical skills to set the foundation for higher levelmathematics.Develop the ability to think in a logical manner to analyze diverse situations.Develop a sense of appreciation and enjoy learning mathematics.Develop a long lasting understanding of the concepts through Concrete, Pictorialand Abstract (CPA) approach by Jerome Bruner.Engage in investigations and enquiries to develop skills in mathematical reasoning,processing information, making connections to real life situations and makingjudgments.07

This curriculum document includes details of pedagogical approaches are designed tohelp mathematics teachers achieve the overall aims of this curriculum. For example,among others, Real Life Situations and Number Stories are two of the strategies toachieve the aims of this curriculum. These approaches engage students in analyzingsituations and applying mathematical knowledge to solve related real-life situations.Moreover, students get opportunities construct similar situations and number stories andhence get intellectually inspired and engaged with mathematical content. MentalMathematics and inquiry approach are equally important strategies especially fordeveloping number sense, forming predictions, justifying arguments with evidence anddrawing conclusions. Thus, this curriculum focuses on principles, patterns and systems sothat students can apply their growing mathematical knowledge and develop a holisticunderstanding of the subject.This document also includes assessment guidelines to ensure meaningful relationshipand alignment between curriculum learning outcomes, instructional design andassessment methods. Specific formative assessment strategies are suggested that lead toimprovement of students learning. An effective learning-outcomes-oriented qualityassurance system, which is based on constant monitoring and effective feedback loop, isrecommended.Print materials, particularly the textbooks, have to play a key role towards providingquality education at all levels. Although there are many factors that contribute towardsthe overall learning of the child; yet, the importance of textbook as a reservoir ofinformation/knowledge cannot be ignored. In addition to the textbook, teaching andlearning resources include teacher’s manual, workbook, and a range ofweb-based/electronic resources. Suggested activities, web links, and reference books areadded to help the users of the Single National Curriculum for Mathematics (I-V) 2020.Mathematics teachers are therefore expected to: shift from dispensing information to plan investigative tasks.create cooperative and collaborative learning assessment tasks.draw valid inference about students.use this information to improve their own teaching practices.1.3 MATHEMATICS CURRICULUM CONTENT STRANDS AND STANDARDSThe curriculum for Mathematics is comprised of the following four strands. The strandsare intentionally kept broad to allow flexibility to the teachers to adapt their teachingstyles in accordance with their students.These strands include Numbers and Operations, Algebra, Geometry and Measurementand Data Handling. All of this content is underpinned by reasoning and logical thinking.All standards, benchmarks and students’ learning outcomes are built around thesestrands.Number andOperationsReasoning andlogical thinkingAlgebraGeometry andMeasurementData Handling08

Key Learning Strands1. NUMBERS AND OPERATIONSStandards 2. ALGEBRA 3. GEOMETRY AND MEASUREMENT 4. DATA HANDLING Identify numbers, ways of representingnumbers, comparing numbers and effects ofnumber operations.compute fluently with fractions, decimalsand percentagesexamine real life situations by identifyingmathematicallyvalidargumentsanddrawing conclusion to enhance theirmathematical thinkinganalyze number patterns;known facts, properties and relationships toanalyze mathematical situations,examine real life situations by identifyingmathematicallyvalidargumentsanddrawing conclusion to enhance theirmathematical thinkingidentify measurable attributes of objects,construct angles and two-dimensionalfigures;analyze characteristics and properties ofgeometric shapes and develop argumentsabout their geometric relationshipsexamine real life situations by identifying,mathematicallyvalidargumentsanddrawing conclusion to enhance theirmathematical thinkingcollect, organize, analyze, display andinterpret data/ informationexamine real life situations by identifyingmathematicallyvalidargumentsanddrawing conclusion to enhance theirmathematical thinking09

1.4 THE MATHEMATICS CURRICULUM STANDARDS AND BENCHMARKSThe Standards for Mathematics are further sub-divided into the following Benchmarks forGrade Level-I-V:StandardsNUMBERS ANDOPERATIONS Identify numbers,ways of representingnumbers, comparingnumbers and effectsof operations invarious situations.compute fluently withfractions, decimalsand percentages.examine real lifesituations byidentifyingmathematically validarguments anddrawing conclusion toenhancemathematicalthinking.Benchmarks Grade-(I-III) Benchmarks Grade-(IV-V)The students will be able to:The students will be able to: 10identify, read and writewhole numbers up to10,000read and write Romannumbers up to 20identify anddifferentiate even andodd numbers up to 99arrange, comparenumbers up to 3-digitsusing symbols ( , or )identify and recogniseplace values up to5-digit numbersrepresent and identifythe given number onnumber lineround off a number tothe nearest 10 and 100add, subtract numbersup to 4-digitsdevelop multiplicationtables up to 10multiply number up to2-digits with 1-digitnumberrecognise and use ofdivision symbol, divideup to 2-digit numbersby 1-digit numbersolve real life situationsinvolving addition,subtraction,multiplication anddivisionround off a number tothe nearest 10 and 100recognise fractions anddifferent forms offractions with the helpof objects and figures read and write wholenumbers up to1,000,000 (1-million) innumerals and wordsadd and subtractnumbers of differentcomplexity and ofarbitrary sizemultiply and dividenumbers, up to 6-digits,by 2- or 3-digitnumbers and by 10,100and 1000solve real life situationsinvolving operations ofaddition, subtraction,multiplication anddivisionrecognise anddifferentiate betweenfactors and multiples oftwo or three 2-digitnumbersfind highest commonfactor (HCF) and leastcommon multiple (LCM)of two, three or fournumbers, up to 2-digitssolve real life situationsinvolving HCF and LCMrecognise and comparelike and unlike fractionsarrange, convert andsimplify fractionsadd, subtract, multiplyand divide fractionssolve real life situationsinvolving addition,subtraction,multiplication anddivision of fractions

StandardsBenchmarks Grade-(I-III) Benchmarks Grade-(IV-V) express and matchfractions in figures andcompare fractions withsame denominatorsusing symbols , or identify and writeequivalent fractions fora given fractionadd and subtract twofractions with samedenominators ALGEBRA analyze numberpatterns;known facts,properties andrelationships toanalyze mathematicalsituations,examine real lifesituations byidentifyingmathematically validarguments anddrawing conclusion toenhancemathematicalthinking develop the concept ofequality using additionand subtraction ofnumbersidentify and completegeometrical patternson square gridaccording to attributeslike shape, size andorientation. apply unitary methodfor solving real lifesituationsidentify and recognizedecimal numbersconvert decimalnumbers into fractionsand vice versaadd and subtractnumbers up to 3decimal placesmultiply and dividedecimal numbers withwhole numbersround off decimalnumbers up tospecified number ofdecimal placessolve real life situationsinvolving decimalnumbers (up to 3decimal places)convert percentage tofraction and to decimaland vice versadevelop the concept ofequality using addition,subtraction,multiplication anddivision of numbers.identify and describerepeating pattern usingrelationship betweenconsecutive terms andgenerate numberpatterns11

StandardsGEOMETRY ANDMEASUREMENT identify measurableattributes of objects,construct angles andtwo-dimensionalfigures;analyzecharacteristics andproperties ofgeometric shapes anddevelop argumentsabout their geometricrelationshipsexamine real lifesituations byidentifying,mathematically validarguments anddrawing conclusion toenhancemathematicalthinkingBenchmarks Grade-(I-III) Benchmarks Grade-(IV-V) 12use language tocompare heights/lengths, masses andcapacity of differentobjectsread, recognize and useunits of length(kilometer, meter andcentimeter), mass(kilogram and gram)and capacity (liter andmilliliter) and time(minute and second).add and subtract inunits of length, mass,capacity and time forsolving real lifesituationsuse solar and Islamiccalendar to find aparticular dates/ day.recognize and identifytwo- andthree-dimensionalfiguresdetermine perimeter ofsquare, rectangle andtriangleidentify anddifferentiate straightline and curved line.identify and drawpoints, lines, linesegments, and rays.identify and describesymmetrical shapes convert standard unitsof length, mass,capacity and timesolve the real-lifesituations involvingaddition andsubtraction of units ofdistance/ length, mass,capacity and timedistinguish parallel andnon-parallel lines.identify, classify andconstruct differenttypes of anglesdescribe and classify2-D figures and 3-Dgeometrical objectsdetermine perimeterand area of square andrectangledescribe and completesymmetric figures withrespect to given line ofsymmetry and point ofrotation.

StandardsDATA HANDLING collect, organize,analyze, display andinterpret data/informationexamine real lifesituations byidentifyingmathematically validarguments anddrawing conclusion toenhancemathematicalthinkingBenchmarks Grade-(I-III) Benchmarks Grade-(IV-V) read, interpret andrepresent data usingCarroll diagram, picturegraph and tally charts read and interpret bargraphs, line graphs andpie chartsrepresent real lifesituations using piechartfind an average of givenquantities in the datadraw and read simplebar graphs both inhorizontal and verticalformsolve real life situationsusing simple bar graphs13


CHAPTERPROGRESSIONGRIDThe Progression Grid serves as a guide indicating how competencies at a particulardevelopmental level are to be attained in order to meet the standards. They provideindicators of expectations from students at completion of each grade (I-V). TheProgression Grid lists all the SLOs in parallel and shows the gradual development oflearning objectives from one grade to another to bridge the gaps between the grades.Concept of Whole NumbersGrade I identify numbers1–9identify 0 as anumberread and writenumbers up to 9 innumerals and inwordscount objects up to9 and represent innumbersmatch thenumbers 0–9 withobjectscount backwardfrom 9identify 10 as a2-digit numberread and writenumbers up to 99count forward andbackward up to 99count in tens andrecognise 100 as athree-digit numberidentify and writemissing numbersin a sequence from1 to 100count and writethe number ofobjects in a givenset.identify theposition of objectsusing ordinalnumbers such asfirst, second tenth, includingrepresentations 1st,2nd 10th throughpicturesGrade II write ordinalnumbersfrom first totwentiethwritenumbers1–100 inwordsreadnumbers upto 999writenumbers upto 999 asnumeralsGrade III read Romannumbers upto 20write Romannumbers upto 20recogniseeven and oddnumbers upto 99 within agivensequencedifferentiateeven and oddnumberswithin a givensequenceread andwrite givennumbers upto 10,000 (tenthousand) innumerals andwords.Grade IV readnumbers upto 100,000(one hundredthousand).writenumbers upto 100,000(one hundredthousand)writenumbers inwords up to100,000 (onehundredthousandrecognizeprime andcompositenumbers upto 100Grade V read numbersup to1,000,000(one million)in numeralsand wordswritenumbers upto 1,000,000(one million)in numeralsand words15

Compare and Order NumbersGrade I arrangenumbers inascending anddescendingorder up to 9identify whichnumber(up to 9) comes before/aftera givennumber, between twogivennumberscompare andorder thenumbers oneand two-digitnumbersorder numbersfrom 0 to 99 inascending anddescendingorderidentify whichnumber(up to 99) comes before/aftera givennumber. between twogivennumbersidentify andwrite missingnumbers in asequence from1 to 100compare two ormore groups ofobjects in termsof numbersmatch objectshaving one toonecorrespondenceidentify thenumber ofobjects in twogroups to show‘more than’ or‘less than’16Grade II compare2 - digitnumbers with3 - digitnumbers(hundreds,tens and ones)compare3 - digitnumbers with3 - digitnumbers(hundreds,tens and ones)countbackward tensteps downfrom any givennumberarrangenumbers up to999, written inmixed formand inascending ordescendingordercount andwrite in 10s(e.g.10,20,30,.)count andwrite in 100s(e.g.100,200,300,.)identify thesmallest/largest number in agiven set ofnumbersGrade III compare twonumbers up to3 - digitnumbers usingsymbols “ ”,“ ”, or “ ”write the givenset ofnumbers inascending anddescendingorder (up to3 - digitnumbers)Grade IV compare andorder numbersup to 6 - digitGrade V

Place Value of NumbersGrade I Grade IIrecognise the place values of a2 - digit number(tens and ones)Identify theplace value of the specific digitin 2 - digitnumbersdecompose a number up to99 to identifythe value of anumber in ten’sand one’s placeGrade IIIrecognise that1,000 is onemore than 999and the first4 - digitnumberrecognise theplace value ofa 3 - digitnumbersidentify theplace value ofa specific digitin a 3 - digitnumbers identify theplace valuesup to 5 - digitnumbersrepresent agiven numberon numberline up to2 - digitnumbersidentify thevalue of anumber onnumber lineup to 2 - digitnumbersGrade VGrade IV identify placevalues up to6 - digitnumbersAddition of NumbersGrade I comparenumbers from1 to 20 toidentify ‘howmuch more’one is than theother number.recognise anduse symbols ofaddition ‘ ’and equality ‘ ’add two,1 - digitnumbers (sumup to 9)add a 2 - digitnumbers with1 - digitnumberadd a 2 - digitnumber to 10sadd two,2 - digitnumbersrecognise theuse of symbolto representan unknownsuch as 4 7(includequestions thatsum up to 20)add numbers(up to 20)using mentalcalculations Grade II add 1-digitnumbers with1 - digitnumbersadd 1-digitnumbers with2 - digitnumbers withcarryingadd 2 - digitnumbers with2 - digitnumbers withcarryingsolve real lifenumberstoriesinvolvingaddition of2 - digitnumbers withcarryingadd numbersup to 50 usingmentalcalculationsadd 3 - digitnumbers with1 - digitnumberswithoutcarryingGrade III add numbersup to 4 - digitwith andwithoutcarryingadd numbersup to 100using mentalcalculationstrategiessolve real lifenumberstoriesinvolvingadditionGrade IV add numbersup to 5 - digitnumberssolve real lifenumberstoriesinvolvingaddition up toto 5 - digitnumbersGrade V add numbersup to 6 - digitnumberssolve real lifesituationsinvolvingaddition up to6 - digitnumbers17

Addition of NumbersGrade I constructadditionequationsfrom givenpictures ornumberstories.identifyPakistanicurrency coins(Rs 1, 2, 5 and10)identifyPakistanicurrency notes(Rs 10, 20, 50and 100)match a groupof coins/notesto anequivalentgroup ofdifferentdenominationsadd andsubtractmoney usingthe prices ofobjects(transactionsfor exampletoys)recognizemoney change(up to Rs100)to itsequivalent’sdenominationsdetermine ifenough moneyis available tomake apurchase up toRs100add differentcombinationsof coins/notes(to make sumup to Rs100)18Grade II add 3-digitnumbers with2-digitnumberswithoutcarryingadd 3-digitnumbers with3-digitnumberswithoutcarryingsolve real lifenumberstoriesinvolvingaddition of3-digitnumberswithoutcarryingadd 3-digitnumberswith1-digitnumbers withcarrying oftens andhundredsadd 3-digitnumbers with2-digitnumbers withcarrying oftens andhundredsadd 3-digitnumbers with3-digitnumbers withcarrying oftens andhundredssolve real lifenumberstoriesinvolvingaddition of3-digitnumbers withcarrying oftens andhundredsGrade IIIGrade IVGrade V

Subtraction of NumbersGrade I comparenumbers from1- 20 and find‘how many oneis less than theother?recognisesubtraction asa differenceand take away,(use thesymbol ‘-’)subtract1 - digitnumbers from1 - digitnumbers(which resultsin positive)subtract1 - digitnumbers from2 - digitnumberssubtract tensfrom 2 - digitnumberssubtract2 - digitnumbers from2 - digitnumbers(which resultsin positive)recognise theuse of symbolsto representan unknownsuch as 9- 7subtractnumbers (upto 20) esfrom givenpictures ornumberstoriesGrade II subtract1 - digitnumbers from2 - digitnumbers withborrowingsubtract2 - digitnumbers from2 - digitnumbers withborrowingsubtractnumbers up to50 usingmentalcalculationssolve real lifenumberstories ofsubtractionwithborrowingsubtract1 - digitnumbers from3 - digitnumberswithoutborrowingsubtract2 - digitnumbers from3 - digitnumberwithoutborrowingsubtract3 - digitnumbers from3 - digitnumberswithoutborrowingsolve real lifenumberstories ofsubtractionwithoutborrowingsubtract1 - digitnumbers from3 - digitnumbers withborrowingsubtract2 - digitnumbers from3 - digitnumbers withborrowingGrade III subtract up to4 - digitnumbers withand withoutborrowingsubtractnumbers up to100 usingmentalcalculationssolve real lifenumberstoriesinvolvingsubtractionGrade VGrade IV subtract up to5 - digitnumbers withand withoutborrowingsolve real lifesituationsinvolvingsubtraction ofup to 5 - digitnumbers subtract up to6 - digitnumberssolve real lifesituationsinvolvingsubtraction ofup to 6 - digitnumbers19

Subtraction of NumbersGrade IGrade II Grade IIIGrade IVGrade Vsubtract3 - digitnumbers from3 - digitnumbers withborrowingsolve real lifenumberstories ofsubtraction upto 3 - digitnumbers withborrowinganalyze on ofaddition andsubtractionwithcarrying/borrowing in mixedform.Multiplication of NumbersGrade IGrade II 20recognisemultiplicationas repeatedaddition (forexample2 2 2 6 isequivalent to 3times 2 whichis 3 x 2 6) andusemultiplicationsymbol “ ”completenumbersequences insteps of 2,3,4,5and 10 (forexample insteps of 2 thesequence isexpressed as2,4, 6 )Grade III developmultiplicationtables for 6, 7,8, and 9multiply2 - digitnumbers by1 - digitnumbersmultiply anumber by 0and 1apply mentalmathematicalstrategies tomultiply1 - digitnumbers to1 - digitnumberssolve real lifesituationsinvolvingmultiplicationof 2 - digitnumbers by1 - digitnumbersGrade IV multiply up to4 - digitnumbers by upto 2 - digitnumberssolve real lifesituationsinvolvingmultiplicationof up to4 - digitnumbers by upto 2 - digitnumbersGrade V multiply up to5 - digitnumbers by10, 100, and1000multiply up to5 - digitnumber, by anumber up to3 - digitsolve real lifesituationsinvolvingmultiplicationof up to5 - digitnumbers, by aup to 3 - digitnumbers

Multiplication of NumbersGrade IGrade II Grade IIIGrade IVGrade VGrade IVGrade Vdevelopmultiplicationtables of 2,3,4,5 and 10 till themultiplicationof 10x10multiplynumbers withinmultiplicationtablewrite numbersentence formultiplicationfrom thepictures suchas2 [] ̇ 6solve numberstories onmultiplicationup to 1-digitDivision of NumbersGrade IGrade II recognize and use divisionsymbol “ ”recognizedivision assuccessive subtractiondivide numberswithin themultiplicationtables withremainder zerosolve numberstories involvingdivision up to1 - digitnumberssolve real lifesituations(using Pakistanicurrency aswell) involvingaddition,subtraction,multiplication,and division.give reasonsfor choosingthe correctoperationGrade IIIdivide 2 - digitnumbers by a1 - digitnumbers (withzero remainder)apply mentalmathematicalstrategies todivide1 - digitnumber by a1 - digitnumbersolve real lifesituationsinvolvingdivision of2 - digitnumbers by a1 - digitnumbers divide numbersup to 4 - digitby numbers upto 2 - digitsolve real lifesituationsinvolvingdivision ofnumbers up to4 - digit bynumbers up to2 - digitsolve real lifesituations usingappropriateoperations ofadditi

1.1 The Single National Curriculum Mathematics (I -V) 2020: 1.2. Aims of Mathematics Curriculum 1.3. Mathematics Curriculum Content Strands and Standards 1.4 The Mathematics Curriculum Standards and Benchmarks Chapter 02: Progression Grid Chapter 03: Curriculum for Mathematics Grade I Chapter 04: Curriculum for Mathematics Grade II

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