Comprehensive CLASS - IX

Transcription

1 Comprehensive CLASS - IX

2 Comprehensive [For Class - IX] As Per New Continuous and Comprehensive [For Evaluation Class (CCE) - Scheme IX] given by Central Board of Secondary Education (CBSE) By J.B. Dixit Laxmi PubLications (P) Ltd (An ISO 9001:2008 Company) BENGALURU CHENNAI COCHIN GUWAHATI HYDERABAD JALANDHAR KOLKATA LUCKNOW MUMBAI RANCHI NEW DELHI BOSTON (USA) ACCRA (GHANA) NAIROBI (KENYA)

3 Comprehensive MATHEMATICS ACTIVITES AND PROJECTS Copyright by Laxmi Publications (P) Ltd. All rights reserved including those of translation into other languages. In accordance with the Copyright (Amendment) Act, 2012, 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. Any such act or scanning, uploading, and or electronic sharing of any part of this book without the permission of the publisher constitutes unlawful piracy and theft of the copyright holder s intellectual property. If you would like to use material from the book (other than for review purposes), prior written permission must be obtained from the publishers. Printed and bound in India Typeset at Sukuvisa Enterprises, Delhi New Edition ISBN Limits of Liability/Disclaimer of Warranty: The publisher and the author make no representation or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties. The advice, strategies, and activities contained herein may not be suitable for every situation. In performing activities adult supervision must be sought. Likewise, common sense and care are essential to the conduct of any and all activities, whether described in this book or otherwise. Neither the publisher nor the author shall be liable or assumes any responsibility for any injuries or damages arising herefrom. The fact that an organization or Website if referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers must be aware that the Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. All trademarks, logos or any other mark such as Vibgyor, USP, Amanda, Golden Bells, Firewall Media, Mercury, Trinity, Laxmi appearing in this work are trademarks and intellectual property owned by or licensed to Laxmi Publications, its subsidiaries or affiliates. Notwithstanding this disclaimer, all other names and marks mentioned in this work are the trade names, trademarks or service marks of their respective owners. PUBLISHED IN INDIA BY Laxmi Publications (P) Ltd. (An ISO 9001:2008 Company) 113, GOLDEN HOUSE, DARYAGANJ, NEW DELHI , INDIA Telephone : , Fax : , info@laxmipublications.com Branches & Bengaluru & Chennai , & Cochin , & Guwahati , & Hyderabad , & Jalandhar & Kolkata & Lucknow & Mumbai , & Ranchi C 7459/013/10 Printed at: IPP, Noida

4 Contents Activities term I Pages Activity 1: To Construct a Square-root Spiral 3 Activity 2: To Represent Some Irrational Numbers on the Number Line 6 Activity 3: Interpret Geometrically the Factors of a Quadratic Expression of the Type ax 2 + bx + c (where a = 1), Using Square Grids, Strips and Paper Slips 9 Activity 4: To Verify the Algebraic Identity: (a + b) 2 = a 2 + 2ab + b 2 13 Activity 5: To Verify the Algebraic Identity: (a b) 2 = a 2 2ab + b 2 16 Activity 6: To Verify the Algebraic Identity: a 2 b 2 = (a + b) (a b) 19 Activity 7: To Verify the Algebraic Identity: (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ca 21 Activity 8: To Verify the Algebraic Identity: (a + b) 3 = a 3 + b 3 + 3a 2 b + 3ab 2 24 Activity 9: To Verify the Algebraic Identity: (a b) 3 = a 3 b 3 3ab (a b) 27 Activity 10: To Verify the Algebraic Identity: a 3 + b 3 = (a + b) (a 2 ab + b 2 ) 29 Activity 11: To Verify the Algebraic Identity: a 3 b 3 = (a b) (a 2 + ab + b 2 ) 33 Activity 12: To Verify Experimentally that if Two Lines Intersect, Then (i) the vertically opposite angles are equal (ii) the sum of two adjacent angles is 180 (iii) the sum of all the four angles is Activity 13: To Verify that the Sum of the Angles of a Triangle is Activity 14: To Verify the Exterior Angle Property of a Triangle 40 Activity 15: To Verify Experimentally the Different Criteria for Congruency of Triangles Using Triangle Cut Outs 42 Activity 16: To Verify Experimentally that in a Triangle, the Longer Side has the Greater Angle Opposite to It 44 Activity 17: To Find a Hidden Picture by Plotting and Joining the Various Points with Given Coordinates in a Plane 47 term II Activity 1: To Verify Experimentally that the Sum of the Angles of a Quadrilateral is Activity 2: To Explore the Properties with Respect to Diagonals of the Following Quadrilaterals 53 a Parallelogram, a Square, a Rectangle, and a Rhombus

5 Activity 3: To Verify that the Straight Line Joining Mid-points of any Two Sides of a Triangle is Parallel to the Third Side and is Equal to Half of it 56 Activity 4: To Find the Formula for the Area of a Trapezium Experimentally 59 Activity 5: Activity 6: Activity 7: To Verify that: (a) Area of Parallelograms on the Same Base and between Same Parallels are Equal (b) Area of Triangles on the Same Base and between Same Parallels are Equal 61 To Verify that the Ratio of the Areas of a Parallelogram and a Triangle on the Same Base and between the Same Parallels is 2 : 1 64 To Verify that the Angle Subtended by an Arc at the Centre of Circle is Double the Angle it Subtends at any Point on the Remaining Part of the Circle 67 Activity 8: To Verify that the Angles in the Same Segment of a Circle are Equal 70 Activity 9: To Verify that the Opposite Angles of a Cyclic Quadrilateral are Supplementary 73 Activity 10: To Form a Cuboid and Find the Formula for its Surface Area Experimentally 75 Activity 11: To Form a Cone from a Sector of a Circle and to Find the Formula for its Curved Surface Area 78 Activity 12: To Find the Surface Area of a Right Circular Cylinder, Experimentally 81 Activity 13: To Find the Relationship Among the Volumes of a Right Circular Cone, a Hemisphere and a Right Circular Cylinder of Equal Radii and Equal Heights 85 Activity 14: To Obtain the Formula for the Surface Area of a Sphere 88 Activity 15: To Draw Histograms for Classes of Equal Widths and Varying Widths 91 Activity 16: To Find Experimental Probability of Unit s Digits of Telephone Numbers Listed on a Page Selected at Random of a Telephone Directory 95 Activity 17: To Find Experimental Probability of Each Outcome of a Die when it is Thrown a Large Number of Times 98 projects Project 1: Observing Intersecting Patterns in Cricket Match 102 Project 2: Design a Crossword Puzzle with Mathematical Terms 102 Project 3: A Measuring Task 104 Project 4: Project in History of Mathematics: The Students can Choose Several Topics from History of Mathematics, for doing a Project. For Instance, the Topic can be about an Indian Mathematician or to the Concept of Zero in Various Ancient Civilizations. 105 Project 5: Surveys and Graph 107 Project 6: An Intersecting Game with the Help of Coordinate Geometry 109 Project Work Assignment 111

6 preface Mathematics laboratory is a place where students can learn and explore mathematical concepts and verify mathematical facts and results (theorems and formulae) through a variety of activities and projects using easily available non-costly materials. These activities and projects can be carried out by teachers and students to explore, to learn and to create interest of students in the subject and develop positive attitude towards the subject. The primary purpose of this laboratory manual is to engage the secondary school teachers in mathematical activities and projects that will enhance their conceptual knowledge, introduce them to important manipulatives, and model the kind of mathematical learning experiences they will be expected to provide for their students. The aim of this manual is to develop a complete understanding of the subject. The CBSE and other state boards, strongly assert that students learn mathematics well only when they construct their own mathematical thinking. Information can be transmitted from one person to another but mathematical understanding and knowledge come from within the learner as that individual explores, discovers, and makes connections. This manual is a part of Formative Assessment in CCE (Continuous and Comprehensive Evaluation) scheme and covers all the aspects of a student s development. The termwise syllabus for laboratory activities and projects will necessarily be accessed through formative assessments. This book contains activities and projects to actively engage students in mathematical explorations. It provides the teachers an opportunity to examine and learn Mathematics in a meaningful way. It provides the instructor with the resources to make student s mathematical activity the focus of attention. Misprints/mistakes have been removed and some important questions have been included in Viva-Voce as per the requirement to familiarise students with the latest trend. The author is very thankful to all those who have helped in preparation of this book, especially Mr. Sunil Bajaj (Head of Mathematics Department SCERT, Gurgaon, Haryana) and Mr. Virender Rathee (Little Angles Sr. Sec. School, Sonipat, Haryana). Wish you a grand success in your examination, and a very bright future in the field of Mathematics. Valuable and constructive suggestions are always most welcome. AUTHOR

7 Mathematics Laboratory Reasons for Mathematical Activities and Projects It is well known that effective teachers have a good understanding of the Mathematics they teach and are skillful in choosing and using a variety of appropriate instructional techniques. The importance of using manipulatives in Mathematics teaching and learning is well documented and amply illustrated in this book. The activities and projects allow students to think deeply about how manipulatives and visual models help to understand the mathematical concepts. Students experience Mathematics directly by using models that embody concepts and promote mathematical thinking. This book represents the belief that: l Prospective teachers who learn Mathematics through appropriate use of manipulatives, models and diagrams are more likely to develop a solid conceptual basis and a deeper understanding of the Mathematics they will teach. l Prospective teachers who learn Mathematics by being actively involved in doing Mathematics will be more likely to teach in the same manner. l Prospective teachers who use manipulatives effectively in their learning will experience how manipulatives assist understanding and be more likely to use them effectively in their teaching. l Becoming familiar with manipulatives and models in structured activities and projects will help prepare prospective teachers to develop similar lessons for their students. l Tactile and visual approaches provide mental images that, for some students, can be easily retained to provide understanding for symbolic representations. l Computers provide an aid for study materials.

8 Salient features The salient features of this lab manual are: 1. It motivates the unmotivated. 2. As per new CCE (Continuous and Comprehensive Evaluation) scheme given by CBSE and has been divided termwise. 3. It provides instructors with activities and projects to actively engage students in mathematical explorations When the teachers engage in these activities and projects, they enhance their mathematical knowledge, become familiar with manipulatives, and model the kind of math learning experiences they will one day provide for their students. 4. It provides active learning each of the activity and project sets use physical materials or visual models to provide a content for increased understanding and retention. Students are able to grasp and intercept concepts more easily and in an active manner. Models and visuals help students to better understand the material. 5. It provides cooperative learning each of the activity and project sets are designed so that they can be completed by students individually or in small groups. Students learn to communicate about Mathematics, and how to work together to solve problems. 6. It provides individual reflections the framework of student s activity set encourages students to describe patterns, discuss their thinking and thought processes, as well as write explanations of their reasoning. Develops critical thinking skills and the ability to communicate about Mathematics. 7. The DVD contains a lot of activities to enhance the overall mathematical development of students.

9 Index Activities and Projects S. No. Activities and Projects (First Term) Date Page No

10 S. No. Activities and Projects (First Term) Date Page No

11 Comprehensive Mathematics Activities And Projects Class 9th 40% OFF Publisher : Laxmi Publications ISBN : Author : J. B. Dixit Type the URL : Get this ebook