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2 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 Goswami Associates, 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 7581/013/10 Printed at: IPP, Noida

3 Contents ACTIVITIES (Term I) Pages Activity 1: To Find the HCF of Two Numbers Experimentally Based on Euclid Division Lemma 3 Activity 2: Activity 3: To Draw the Graph of a Quadratic Polynomial and Observe: (i) The shape of the curve when the coefficient of x 2 is positive (ii) The shape of the curve when the coefficient of x 2 is negative (iii) Its number of zeroes 6 To Verify the Conditions for Consistency/Inconsistency for a Pair of Linear Equations in Two Variables by Graphical Method 10 Activity 4: To Draw a System of Similar Squares, Using Two Intersecting Strips with Nails 15 Activity 5: To Draw a System of Similar Triangles, Using Y Shaped Strips with Nails 19 Activity 6: To Verify Basic Proportionality Theorem (Thales Theorem) 23 Activity 7: To Establish the Criteria for Similarity of Two Triangles 26 Activity 8: To Find the Relationship between Areas and Sides of Similar Triangles 32 Activity 9: To Verify Experimentally that the Ratio of the Areas of Two Similar Triangles is Equal to the Ratio of the Squares of Their Corresponding Sides 35 Activity 10: To Verify Pythagoras Theorem 39 Activity 11: To Verify Pythagoras Theorem by Bhaskara Method 42 Activity 12: To Draw a Cumulative Frequency Curve (or an Ogive) of Less Than Type 45 Activity 13: To Draw a Cumulative Frequency Curve (or an Ogive) of More Than Type 48 ACTIVITIES (Term II) Activity 1: To Obtain the Solution of a Quadratic Equation (x 2 + 4x = 60) by Completing the Square Geometrically 52 Activity 2: To Identify Arithmetic Progressions in Some Given Lists of Numbers (Patterns) 55 Activity 3: To Find the Sum of First n Natural Numbers 58 Activity 4: To Find the Sum of First n Odd Natural Numbers 61

4 Activity 5: To Find the Sum of First n Even Natural Numbers 63 Activity 6: To Establish a Formula for the Sum of First n Terms of an Arithmetic Progression 65 Activity 7: To Verify Experimentally that the Tangent at any Point to a Circle is Perpendicular to the Radius Through that Point 68 Activity 8: To Find the Number of Tangents From a Point to the Circle 71 Activity 9: To Verify that Lengths of Tangents to a Circle from Some External Point are Equal 73 Activity 10: To Draw a Quadrilateral Similar to a Given Quadrilateral as Per Given Scale Factor (Less Than 1) 77 Activity 11: To Find the Height of a Building Using a Clinometer 81 Activity 12: To Determine Experimental Probability of 1, 2, 3, 4, 5 or 6 by Throwing a Die 500 Times and Compare Them with Their Theoretical Probabilities 85 Activity 13: To Determine Experimental Probability of a Head (or a Tail) by Tossing a Coin 1000 Times and Compare it with its Theoretical Probability 89 Activity 14: To Verify the Distance Formula by Graphical Method 92 Activity 15: To Verify Section Formula by Graphical Method 94 Activity 16: To Verify the Formula for the Area of a Triangle by Graphical Method 97 Activity 17: To Obtain Formula for Area of a Circle Experimentally 100 Activity 18: To Obtain Formula for the Surface Area of a Circus Tent 103 Activity 19: To Form a Frustum of a Cone and Obtain the Formulae for the Surface Area and the Volume of a Frustum of a Cone 108 PROJECTS Project 1: Efficiency in Packing 114 Project 2: Geometry in Daily Life 116 Project 3: Experiment on Probability 117 Project 4: Displacement and Rotation of a Geometrical Figure 119 Project 5: Frequency of Letters / Words in a Language Text 120 Project 6: Golden Rectangle and Golden Ratio 123 Project Work Assignment 128

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

5 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 Angels Sr. Sec. School, Sonepat, 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

6 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: 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. Prospective teachers who learn Mathematics by being actively involved in doing mathematics will be more likely to teach in the same manner. 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. Becoming familiar with manipulatives and models in structured activities and projects will help prepare prospective teachers to develop similar lessons for their students. Tactile and visual approaches provide mental images that, for some students, can be easily retained to provide understanding for symbolic representations. Computers provide an aid for study materials.

7 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

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11 Comprehensive Activities Mathematics and Project Class 10th New % OFF Publisher : Laxmi Publications ISBN : Author : J.B.Dixit Type the URL : Get this ebook

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