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The CBSE-International is grateful for permission to reproduce and/or translate copyright material used in this publication. The acknowledgements have been included wherever appropriate and sources from where the material has been taken duly mentioned. In case anything has been missed out, the Board will be pleased to rectify the error at the earliest possible opportunity. All Rights of these documents are reserved. No part of this publication may be reproduced, printed or transmitted in any form without the prior permission of the CBSE-i. This material is meant for the use of schools who are a part of the CBSE-International only.
PREFACE The Curriculum initiated by Central Board of Secondary Education -International (CBSE-i) is a progressive step in making the educational content and methodology more sensitive and responsive to the global needs. It signifies the emergence of a fresh thought process in imparting a curriculum which would restore the independence of the learner to pursue the learning process in harmony with the existing personal, social and cultural ethos. The Central Board of Secondary Education has been providing support to the academic needs of the learners worldwide. It has about 11500 schools affiliated to it and over 158 schools situated in more than 23 countries. The Board has always been conscious of the varying needs of the learners in countries abroad and has been working towards contextualizing certain elements of the learning process to the physical, geographical, social and cultural environment in which they are engaged. The International Curriculum being designed by CBSE-i, has been visualized and developed with these requirements in view. The nucleus of the entire process of constructing the curricular structure is the learner. The objective of the curriculum is to nurture the independence of the learner, given the fact that every learner is unique. The learner has to understand, appreciate, protect and build on values, beliefs and traditional wisdom, make the necessary modifications, improvisations and additions wherever and whenever necessary. The recent scientific and technological advances have thrown open the gateways of knowledge at an astonishing pace. The speed and methods of assimilating knowledge have put forth many challenges to the educators, forcing them to rethink their approaches for knowledge processing by their learners. In this context, it has become imperative for them to incorporate those skills which will enable the young learners to become 'life long learners'. The ability to stay current, to upgrade skills with emerging technologies, to understand the nuances involved in change management and the relevant life skills have to be a part of the learning domains of the global learners. The CBSE-i curriculum has taken cognizance of these requirements. The CBSE-i aims to carry forward the basic strength of the Indian system of education while promoting critical and creative thinking skills, effective communication skills, interpersonal and collaborative skills along with information and media skills. There is an inbuilt flexibility in the curriculum, as it provides a foundation and an extension curriculum, in all subject areas to cater to the different pace of learners. The CBSE has introduced the CBSE-i curriculum in schools affiliated to CBSE at the international level in 2010 and is now introducing it to other affiliated schools who meet the requirements for introducing this curriculum. The focus of CBSE-i is to ensure that the learner is stress-free and committed to active learning. The learner would be evaluated on a continuous and comprehensive basis consequent to the mutual interactions between the teacher and the learner. There are some nonevaluative components in the curriculum which would be commented upon by the teachers and the school. The objective of this part or the core of the curriculum is to scaffold the learning experiences and to relate tacit knowledge with formal knowledge. This would involve trans-disciplinary linkages that would form the core of the learning process. Perspectives, SEWA (Social Empowerment through Work and Action), Life Skills and Research would be the constituents of this '<strong>Core</strong>'. The <strong>Core</strong> skills are the most significant aspects of a learner's holistic growth and learning curve. The International Curriculum has been designed keeping in view the foundations of the National Curricular Framework (NCF 2005) NCERT and the experience gathered by the Board over the last seven decades in imparting effective learning to millions of learners, many of whom are now global citizens. The Board does not interpret this development as an alternative to other curricula existing at the international level, but as an exercise in providing the much needed Indian leadership for global education at the school level. The International Curriculum would evolve on its own, building on learning experiences inside the classroom over a period of time. The Board while addressing the issues of empowerment with the help of the schools' administering this system strongly recommends that practicing teachers become skillful learners on their own and also transfer their learning experiences to their peers through the interactive platforms provided by the Board. I profusely thank Shri G. Balasubramanian, former Director (Academics), CBSE, Ms. Abha Adams and her team and Dr. Sadhana Parashar, Head (Innovations and Research) CBSE along with other Education Officers involved in the development and implementation of this material. The CBSE-i website has already started enabling all stakeholders to participate in this initiative through the discussion forums provided on the portal. Any further suggestions are welcome. Vineet Joshi Chairman
Page 1: CBSE-i CLASS IX UNIT-1 MATHEMATICS
Page 5 and 6: CONTENTs PREFACE ACKNOWLEDGEMENTS 1
Page 7 and 8: ♦ SW8 : Content Worksheet CW4 93
Page 9 and 10: SCOPE DOCUMENT Key concepts: 1. Rat
Page 11 and 12: Perspective: Use the square root va
Page 13 and 14: TEACHER’S NOTE The teaching of Ma
Page 15 and 16: 24. To determine the sum of a ratio
Page 17 and 18: project and students can observe va
Page 19 and 20: ACTIVITY 1: WARM UP (W1) Recalling
Page 21 and 22: ACTIVITY 3: PRE CONTENT (P1) Useful
Page 23 and 24: Description: ACTIVITY 5: CONTENT (C
Page 25 and 26: ACTIVITY 7: CONTENT (CW3) Successiv
Page 27 and 28: ACTIVITY 8: CONTENT (CW4) Irrationa
Page 29 and 30: Specific Objectives ACTIVITY 9: CON
Page 31 and 32: ACTIVITY 11: CONTENT (CW7) Real Num
Page 33 and 34: Parameters for assessment: Students
Page 35 and 36: ACTIVITY 18-: POST CONTENT (PCW4) A
Page 37 and 38: Parameter Mastered Developing Needs
Page 39 and 40: Parameter 5 4 3 2 1 i i Able to sim
Page 41 and 42: NUMBER SYSTEM AND NUMBER SENSE ♦
Page 43 and 44: Think!! What will happen if we mult
Page 45 and 46: ♦ Representation of rational numb
Page 47 and 48: ♦ Decimal Expansion of Rational N
Page 49 and 50: Here, the remainder is not coming a
Page 51 and 52: 30 28 20 14 60 56 40 35 50 49 Here,
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Subtracting (1) From (2), we get 99
Page 55 and 56:
Introduction to Irrational Numbers
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B P -1 0 A 1 3 4 5 6 2 This shows t
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l Introduction to real numbers Taki
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1 1 Some other irrational numbers b
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Thus it can be concluded that Diffe
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Consider the quotients (rational) 3
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We can also rationalize the denomin
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which is given to be equal to a + b
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i i i i i i i i i i i i i i i Betwe
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STUDENT'S WORKSHEET 1 (SW1) Warm Up
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SELF ASSESSMENT RUBRIC -1 WARM UP (
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SELF ASSESSMENT RUBRIC 2 - WARM UP
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3. You are the teacher. Mark the fo
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Match the following numbers in colu
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STUDENT'S WORKSHEET 4 (SW4) Pre Con
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3. Am I right, if I say that 2 is a
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STUDENT'S WORKSHEET 6 (SW6) Content
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(vi) Which of the following represe
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SELF ASSESSMENT RUBRIC - 6 CONTENT
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And then 2.75 lies between 2.7 and
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7. Visualise the value of π upto 5
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Name of student………………
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4. The approximate value of is 22/7
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Section 3: Activity:-Locating irrat
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Diagram Working Space Justification
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Am I right if I say 2.5666666010010
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Meena: Yes, it is so easy. It can b
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STUDENT'S WORKSHEET 10 (SW10) Conte
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Solution: ________________ (Rationa
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Student's Worksheet 14 (SW14) Conte
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Down 1. decimal representation of r
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Post Content (PCW3) Oral assessment
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124
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126 Solution
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SUGGESTED USEFUL EXTRA READINGS Typ
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