Mathematics Syllabus: Grade 1 – 7

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Republic of ZambiaMinistry of Education, Science, Vocational Training and EarlyEducationMathematics Syllabus(Grades 1-7)Published by the Curriculum development CentreP O Box 50092LusakaJuly 2013

COPYRIGHT Curriculum Development Centre, 2013All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic,mechanical, photocopying, recording or otherwise without prior written permission of the Publisher.Mathematics Grades 1-7i

VISIONQuality, lifelong education for all which is accessible, inclusive and relevant to individual, national and global needs and value systems.Mathematics Grades 1-7ii

TABLE OF CONTENTSCOPYRIGHT . iVISION . iiPREFACE. ivACKNOWLEDGEMENT . vINTRODUCTION. viRationale. viSuggested Teaching Methodology . viiAssessment . viiTime and period allocation. viiiGeneral Outcome. viiiGRADE 1. 1GRADE 2. 5GRADE 3. 11GRADE 4. 16GRADE 5. 21GRADE 6. 27GRADE 7. 33APPENDIXGrades 1- 7 Topic Sequence . 34Mathematics Grades 1-7iii

PREFACEThe syllabus was produced as a result of the Curriculum review process carried out by the Ministry of Education, Science, Vocational Trainingand Early Education under the auspices of the Curriculum Development Centre (CDC). The curriculum reform process started way back in1999 when the Ministry of Education commissioned five (5) curriculum studies which were conducted by the University of Zambia. Thesestudies were followed by a review of the lower and middle basic and primary teacher education curriculum. In 2005 the upper basic educationNational survey was conducted and information from learners, parents, teachers, school managers, educational administrators, tertiaryinstitutions traditional leaders civic leaders and various stakeholders in education was collected to help design a relevant curriculum.The recommendations provided by various stakeholders during the Upper Basic Education National survey of 2005 and National symposiumon curriculum held in June 2009 guided the review process.The review was necessitated by the need to provide an education system that would not only incorporate latest social, economic, technologicaland political developments but also equip learners with vital knowledge, skills and values that are necessary to contribute to the attainment ofVision 2030.The syllabus has been reviewed in line with the Outcome Based Education principles which seek to link education to real life experiences thatgive learners skills to access, criticize analyze and practically apply knowledge that help them gain life skills. Its competences and generaloutcomes are the expected outcomes to be attained by the learners through the acquisition of knowledge, skills, techniques and values whichare very important for the total development of the individual and the nation as a whole.Effective implementation of Outcome Based Education requires that the following principles be observed: clarity of focus, Reflectivedesigning, setting high expectations for all learners and appropriate opportunities.It is my sincere hope that this Outcome Based syllabus will greatly improve the quality of education provided at Grade 8 and 9 level as definedand recommended in various policy documents including Educating Our Future 1996 and the Zambia Education Curriculum Framework 2013.Chishimba Nkosha (Mr.)Permanent Secretary,MINISTRY OF EDUCATION, SCIENCE, VOCATIONAL TRAINING AND EARLY EDUCATIONMathematics Grades 1-7iv

ACKNOWLEDGEMENTThe syllabus presented here is a result of broad-based consultation involving several stakeholders within and outside the education system.Many individuals, institutions and organizations were consulted to gather their views on the existing syllabus and to accord them anopportunity to make suggestions for the new syllabus. The Ministry of Education wishes to express heartfelt gratitude to all those whoparticipated for their valuable contributions, which resulted in the development of this syllabus.The Curriculum Development Centre worked closely with other sister departments and institutions to create this document. We sincerely thankthe Directorate of Teacher Education and Specialized Services, the Directorate of Planning and Information, the Directorate of HumanResource and Administration, the Directorate of Open and Distance Education ,the Examinations Council of Zambia, the University ofZambia, schools and other institutions too numerous to mention, for their steadfast support.We pay special tribute to co-operating partners especially JICA in conjunction with Hiroshima University and UNICEF for rendering financialand technical support in the production of the syllabus.C.N.M Sakala (Mrs.)Director-Standard and CurriculumMINISTRY OF EDUCATION, SCIENCE, VOCATIONAL TRAINING AND EARLY EDUCATIONMathematics Grades 1-7v

INTRODUCTIONThis syllabus has been prepared and produced against the background of the need to set high standards for mathematics education andactualize the country’s vision from ECCDE through to Teacher Education. It is a culmination of reviews of existing materials and policiesfrom a number of countries both in Africa and beyond with progressive mathematics education. It also draws from studies, research and thecountry’s policy documents and aspirations.The following are the underlying principles for the revised Junior Secondary school mathematics syllabus: Equity Orderly and logical progression Varied teaching methodology with subjective learning as the keystone Integration of knowledge, skills and valuesThese syllabus guidelines have been defined at two levels namely the content and process domains. The content domain is defined accordingto six themes namely; Numbers & Calculations, Algebra, Geometry, Measures, Probability & Statistics and Relations. The processdomain on the other hand is defined according to three categories of knowledge, skills and values. These two domains constitute the generaloutcomes of the Mathematics course.RationaleMathematics is an important subject on the Zambian School curriculum. It is featured as one of the core subjects in all the options for both theacademic as well as the practical career pathways.Mathematics enhances the learners’ understanding of the world around and prepares them for further education. It also plays a key role as atool for learning other subjects and learning areas. The subject fosters the development and improvement of learners’ intellectual competencein logical reasoning, spatial visualization, analysis and abstract thought. When learners have acquired enough knowledge in mathematics theydevelop reasoning, thinking and problem solving skills. Mathematics is also important in science and technology subjects which are vital forthe development of the country. It therefore equips the learner to live in the age of Science and technology and enable them contribute tosocial, economic development of the country.Mathematics can also be an interesting subject when learners appreciate basic concepts and insights that will equip them to pursuemathematics education at higher levels.Mathematics Grades 1-7vi

Suggested Teaching MethodologyThis Syllabus for Primary schools aims at enabling learners acquire mathematical knowledge, values and skills for the further study of thesubject at the Junior Secondary level as well as apply it in their daily lives. It is for this reason that teachers should focus on encouragingcommunication of mathematical ideas among learners, emphasise problem solving and application to real life situations besides cultivatinginterest in the subjects.The mathematical concepts and principles presented in this syllabus aim to encourage learners to think logically and critically and makeconnections between topics and with other subjects. To achieve this, teachers should put emphasis on teaching the subject in a manner wherelearners communicate their mathematical ideas as well as misconceptions. This approach will enhance learners’ understanding andappreciation of mathematical concepts and ideas as they construct their own knowledge. Teachers will also need to refocus their teachingapproaches and continuously sharpen their pedagogical skills in line with contemporary approaches in the teaching of the subject.Further, since Mathematics is a discipline with hierarchical concepts and skills, teachers should present it in a systematic manner. In the designof the syllabus, effort has been made to sequence the topics across the entire course of study. Successful interpretation and implementation ofthis syllabus however requires flexibility on the part of teachers in order for them to arrange the content in an easy to understand progressionso as to improve mathematics education in the country.AssessmentAssessment is an important diagnostic tool in the teaching and learning process used to determine whether teaching and learning have takenplace or not. It requires well defined rubrics to facilitate a fair and consistent assessment of learner’s work as well as clearly definedperformance targets at key stages and during the process of teaching and learning.Classroom based continuous assessment must form an integral part of the implementation of this syllabus. This is in view of the value that thisadds to the modification of instruction delivery thereby contributing to best practices by the teacher. In order to attain this, teachers are urgedto employ various techniques of assessment according to the topics and themes at various levels. These methods may include learnerobservation, projects, tests, portfolios and projects among others.For terminal assessment, the Examinations Council will provide guidelines on the objectives to be assessed in at specific levels both forselection and certification.Mathematics Grades 1-7vii

Time and period allocationTime allocation for this syllabus is at two levels; the Lower Primary (Grades 1 – 4) and the Upper Primary (Grades 5 – 7) levels. The Lower Primary Level will require at least 3 hours (Six-30 minutes periods) per week to complete.The Upper Primary Level on the other hand will require at least 4 hours (Six-40 minute periods) per week to complete.General Outcome1. To foster the development and improvement of learners’ intellectual competence in logical reasoning, spatial visualization, analysisand abstract thought.2. To equip the learner to live in the age of Science and technology and enable them contribute to social, economic development of thecountryMathematics Grades 1-7viii

General Outcomes Develop numeracy and arithmetic operations skills. Enrich learners’ understanding of mathematicalconcepts on Numbers, shapes and diagrams.Key Competences at Grade 1 Level Sort objects with respect to colour, size and shape . Identify digits from0-9. Count given objects up to 20. Read and write numbers sequentially from 1-100. Identify and tell the meaning of addition and subtraction signs. Recognise denominations of Zambian money (Coins and notes) Identify circles, rectangles and triangles .GRADE 1TOPICSPECIFIC 2SETSMathematics Grades 1-7Recognise, count, read andwrite numbers from 1 to 100(including the meaning ofzero).Interpret numbers using ten asa unit.Order numbers in terms ofmagnitude.Count in tens up to ten tens(100).1.2.1 Sort objects according to size,colour and shape.1.2.2 Match sets into one-to-onecorrespondence.CONTENTKNOWLEDGESKILLS Comparing number of objects by Identification ofmaking one-to-one correspondence.numerals. The meaning of zero. Communicationthrough writing Counting from 1 to 100 (Useand counting.concrete objects and mathsongs/games/rhymes, ICT as well). Comparison ofnumber. Reading and writing numbers from 1magnitude andto 100.ordering them. Interpreting numbers using ten as aunit (i.e. 12 is 10 and 2, 13 is 10 and Representation ofnumbers with 103 etc).as a unit. Recognizing that one number ismore or less than the other. Counting numbers in tens up to 100. Sorting objects according to size Classification ofcolour and shape.objects. Matching sets of objects into one-to- Comparison ofone correspondence.objects in realVALUES Awareness ofnumeration system. Team work throughcooperative learning. Interest in thenumbers and theirorder. Curiosity to explorenature. Appreciation oforder in nature.1

TOPICSPECIFIC UTCOMES1.2.3 Place sets in order accordingto their cardinal numbers.1.2.4 Assign numerals 0 to 10 toelements in a set.1.2.5 Use cardinal and ordinalnumbers in everyday life.1.3 ADDITION1. SUBTRACTION1. Grades 1-7Add whole numbers withsums up to 100.Complete addition of numbersentences.Apply addition to real life upto 100.Subtract whole numbers up to100.Develop the concept of zeroas a difference.Completesubtractionofnumber sentences.Apply addition to real life upto 100.Carry out shopping activitiesinvolving money.CONTENTKNOWLEDGESKILLSlife. Ordering sets according to their Identification ofcardinal and ordinal numbers.various criteria Counting the number of elements infor sortinga set (i.e. assign numerals 0 to 10 toobjects.elements in a set). Application ofgroups in real life. Meaning of addition. Addition of singleand double digit Adding single digit numbers upnumbers using theto10.concept of 10 as a Adding single digit numbers up tounit.18 horizontally (with carrying using Identification ofthe concept of ten as unit e.g. 8 5the additionas 8 2 3).sign/symbol. Adding numbers in 10s up to100 Application of(e.g. 20 10).addition to Adding numbers horizontally upmoney.to100 (without carrying). Applying addition to real life (ForMoney, DO NOT USE NGWEE ASA FRACTION OF KWACHA ATTHIS STAGE). Meaning of subtraction. Subtraction ofsingle and double Subtracting single digit numbers updigit numbersto10.using the concept Subtracting two digit numbers up toof 10 as a unit.18 by single digit number giving a Identification ofsingle digit difference (e.g. 18 – 9,the subtraction17-9, 17-8,. . . 12- 3, 12-2, 11-2),sign/symbol.horizontally (with borrowing usingthe concept of ten as unit e.g. 12-3 Application ofas 12-2-1or 10-3 2).subtraction toVALUES Team work throughcollaborativelearning. Awareness of themeaning of addition. Accuracy incomputations. Awareness of themeaning ofsubtraction. Accuracy incomputations. Team work throughthe shoppingactivity.2

TOPICSPECIFIC UTCOMES1.5 NUMBERPATTERNS1.5.1Identify number patternsinvolving addition andsubtraction up to 100.1.6 PLANESHAPES1.6.1Recognise squares, circles,rectangles and triangles.Trace outline of squares,circles, rectangles andtriangles.Make pictures using shapes ofsquares, rectangle circles andtriangles. Grades 1-7CONTENTKNOWLEDGESKILLSmoney. Subtracting numbers in 10s upto100 (e.g. 90 - 30). Relatingsubtraction to Subtracting numbers horizontally 100 (without borrowing). Developing the concept of zero. Relationship of subtraction toaddition (e.g. 36 – 12 24 or 24 12 36). Apply subtraction to real life up to100. Carrying out shopping activitiesinvolving money up to K100. (DONOT USE NGWEE AS AFRACTION OF KWACHA ATTHIS STAGE). Identifying number patterns Identification ofinvolving addition and subtractionnumber patterns.up to 100. Orderingnumbers. Recognizing squares, circles, Recognition ofsquares, circles,rectangles and triangles.rectangles and Tracing outlines of Shapes usingtriangles.concrete three dimensional shapes todraw squares, circles, rectangles andtriangles. Making pictures using shapes ofsquares, circles, rectangles andtriangles.VALUES Awareness in thearrangement ofnumbers. Appreciation ofbasic shapes. Creativity incombining basicshapes to makepictures.3

CONTENTKNOWLEDGESKILLSIdentify times of the day. Identifying the times of the day Ordering days ofTell days of the week.using activities (morning, midday,the week andName months of the yearafternoon, evening, night).months of theCompare lengths of different Days of the week.year.objects. Comparing Months of the year.lengths of different Non standard measurements e.g.objects.strides, feet, strings, heights such asheights of learners.TOPICSPECIFIC UTCOMES1. Grades 1-7VALUES Awareness of timesof the day andmonths of the year. Curiosity ofcomparing lengths

the Directorate of Teacher Education and Specialized Services, the Directorate of Planning and Information, the Directorate of Human . These syllabus guidelines have been defined at two levels namely the content and process domains. The content domain is defined according . General Outcomes Key Competences at Grade 1 Level