VIII maths EM Covers - Telangana

1 SCERT TELANGANACHILDREN! THESE DIINSTRUCTIONS FOR For each and every conceptual understanding, a real life context with appropriateillustrations are given in the textbook. Try to understand the concept through keenreading of context along with observation of illustration. While understanding the concepts through activities, some doubts may those doubts by through discussion with your friends and teachers,understand the mathematical concepts without any doubts. ''Do this/Do these" exercises are given to test yourself, how far the concept hasbeen understood. If you are facing any difficulty in solving problems in theseexercises, you can clarify them by discussing with your teacher. The problems given in "Try this/try these", can be solved by reasoning, thinkingcreatively and extensively.

2 When you face difficulty in solving these problems,you can take the help of your friends and teachers. The activities or discussion points given "Think & disicuss" have been given forextensive understanding of the concept by thinking critically. These activities shouldbe solved by discussions with your fellow students and teachers. Different typs of problems with different concepts discussed in the chapter aregiven in an "Exercise" given at the end of the concept/chapter. Try to solve theseproblems by yourself at home or leisure time in school. The purpose of "Do this"/do these", and "Try this/try these" exercises is to solveproblems in the presence of teacher only in the class itself. Where ever the "project works" are given in the textbook, you should conductthem in groups.

3 But the reports of project works should be submitted individually. Try to solve the problems given as homework on the day itself. Clarify yourdoubts and make corrections also on the day itself by discussions with yourteachers. Try to collect more problems or make new problems on the concepts learnt andshow them to your teachers and fellow students. Try to collect more puzzles, games and interesting things related to mathematicalconcepts and share with your friends and teachers. Do not confine mathematical conceptual understanding to only classroom. But,try to relate them with your suroundings outside the classroom. Student must solve problems, give reasons and make proofs, be able tocommunicate mathematically, connect concepts to understand more concepts &solve problems and able to represent in mathematics learning.

4 Whenever you face difficulty in achieving above competencies/skills/standards,you may take the help of your TELANGANAFree Distribution by Government 2018-19 MATHEMATICSCLASS - VIIITEXTBOOK DEVELOPMENT & PUBLISHING COMMITTEE Chief Production Officer: Sri. A. Satyanarayana Reddy,Director, SCERT, Chief Sudhakar,Director, Govt. Text Book Press, Incharge:Dr. Nannuru Upender Reddy,Prof. & Head, Curriculum & Text Book Department,SCERT, byThe Government of Telangana , HyderabadRespect the LawGrow by Education Get the Rights Behave Humbly(i)Chairperson for Position Paper and mathematics Curriculum and Textbook DevelopmentProf. ,Department of mathematics and Statistics,Hyderabad Central University, HyderabadChief AdvisorsSri. Chukka RamaiahDr. Scholar in MathematicsEducational Advisor, Vidya Bhavan SocietyTelangana, , RajasthanSCERT Telangana Government of Telangana , Published 2013 New Impressions 2014, 2015, 2016, 2017, 2018 All rights part of this publication may be reproduced,stored in a retrieval system, or transmitted, in anyform or by any means without the prior permission inwriting of the publisher, nor be otherwise circulatedin any form of binding or cover other than that inwhich it is published and without a similar conditionincluding this condition being imposed on the sub-sequent copy right holder of this book is the Directorof School Education, Hyderabad.

5 Telangana This Book has been printed on 70 SS MaplithoTitle Page 200 White Art CardPrinted in Indiaat the Telangana Govt. Text Book Press,Mint Compound, Hyderabad, distribution by Government 2018-19(ii)SCERT TELANGANAFree Distribution by Government 2018-19 Text Book Development CommitteeWritersSri. Tata Venkata Rama KumarSri. Gottumukkala , ZPPHS, Mulumudi, Nellore , Mpl. High School, Kaspa, Soma Prasad BabuSri. Sunder ReddyPGT. APTWRS, Chandrashekarapuram, NelloreSA, ZPHS,Thakkasila, Alampur Mandal Mahabubnagar Komanduri Murali SrinivasSri. Abbaraju School of Excellence, , MPUPS,Chamallamudi, Guntur Padala Suresh KumarSri. G. Anantha ReddySA,GHS, Vijayanagar Colony, Headmaster, Ranga Reddy Ganapati SharmaSri.

6 M. RamanjaneyuluSA,GHS, Zamisthanpur, Manikeshwar Nagar, , Govt , Vikarabad, Duggaraju VenuSri. M. Rama CharySA,UPS, Allawada, Chevella Mandal, ,Govt , Vikarabad, P. Anthony ReddyDr. A. ,St. Peter s High School, , , Government CTE, WarangalSri D. ManoharDr. Poondla RameshSA, ZPHS, Brahmanpally, Tadwai (Mandal) Nizamabad , Government lASE, NelloreEditorsProf. Ramacharyulu (Retd.)Dr. S Suresh Babu Prof. V. Shiva Ramaprasad (Retd.)National Institute of Technology,Professor, Dept. of Statistics,Dept. of mathematics , , HyderabadOsmania University, HyderabadDr. MurthySri A. PadmanabhamSri. K Brahmaiah(Retd.)(Retd.)(Retd.)Reader in of MathematicsProf., SCERT,Rajah College, BobbiliMaharani College, PeddapuramHyderabadCo-ordinatorsSri Kakulavaram Rajender ReddySri RayaluSCERT, HyderabadLecturer, IASE, Masab Tank, HyderabadAcademic Support Group Members Sri Inder Mohan Sri Yashwanth Kumar DaveSri Hanif Paliwal Sri Asish ChordiaVidyabhawan Society Resource Centre, Udaipur Sri Sharan Gopal Kum M.

7 ArchanaSri P. ChiranjeeviDepartment of mathematics and Statistics, University of HyderabadIllustrations and Design TeamSri Prasanth Soni Sri Sk. Shakeer AhmadSri S. M. IkramVidyabhawan Society Resource Centre, UdaipurCover Page DesigningSri. K. Sudhakara Chary, HM, UPS Neelikurthy, , Dist. Warangal(iii)SCERT Telangana (iv)ForewordEducation is a process of human enlightenment and empowerment. Recognizing theenormous potential of education, all progressive societies have committed to theUniversalization of Elementary Education with an explicit aim of providing quality educationto all. As the next step, universalization of Secondary Education has gained secondary stage marks the beginning of the transition from functional mathematicsstudied upto the upper primary stage to the study of mathematics as a discipline.

8 The logicalproofs of propositions, theorems etc. are introduced at this stage. Apart from being a specificsubject, it is to be treated as a concomitant to every subject involving analysis as am confident that the children in our state of Andhra Pradesh learn to enjoy mathematics ,make mathematics a part of their life experience, pose and solve meaningful problems,understand the basic structure of mathematics by reading this text teachers, to understand and absorb critical issues on curricular and pedagogicperspectives duly focusing on learning rather than of marks, is the need of the hour. Alsocoping with a mixed class room environment is essentially required for effective transaction ofcurriculum in teaching learning process. Nurturing class room culture to inculcate positiveinterest among children with difference in opinions and presumptions of life style, to infuse lifein to knowledge is a thrust in the teaching afore said vision of mathematics teaching presented in State Curriculum Framework (SCF -2011) has been elaborated in its mathematics position paper which also clearlylays down the academic standards of mathematics teaching in the state.

9 The text books makean attempt to concretize all the State Council for Education Research and Training Telangana appreciates the hardwork of the text book development committee and several teachers from all over the statewho have contributed to the development of this text book at different levels. I am thankful tothe District Educational Officers, Mandal Educational Officers and head teachers for makingthis mission possible. I also thank the institutions and organizations which have given theirtime in the development of this text book. I am grateful to the office of the Commissioner andDirector of School Education, ( ) and Vidya Bhawan Society, Udaipur, Rajasthan forextending co-operation in developing this text book. In the endeavor to continuously improvethe quality of our work, we welcome your comments and suggestions in this : HyderabadDirectorDate : 03 December 2012 SCERT, HyderabadSCERT TELANGANAFree Distribution by Government 2018-19(v)PrefaceThe Government of Telangana has decided to revise the curriculum of all the subjectsbased on State Curriculum Frame work (SCF - 2011) which recommends that childrens lifeat schools must be linked to their life outside the school.

10 Right to Education (RTE - 2009)perceives that every child who enters the school should acquire the necessary skills prescribedat each level upto the age of 14 years. The introduction of syllabus based on NationalCurriculum Frame Work - 2005 is every much necessary especially in mathematics andSciences at secondary level with a national perspective to prepare our students with a strongbase of mathematics and strength of a nation lies in its commitment and capacity to prepare its people tomeet the needs, aspirations and requirements of a progressive technological syllabus in mathematics for three stages primary, upper primary and secondaryis based on structural and spiral approaches. The teachers of secondary school Mathematicshave to study the syllabus of classes 8 to 10 with this background to widen and deepen theunderstanding and application of concepts learnt by pupils in primary and upper syllabus is based on the structural approach, laying emphasis on the discovery andunderstanding of basic mathematical concepts and generalisations.