Comprehensive
CLASS - IX
Comprehensive
[For Class - IX]
[For Class - IX]
As Per New Continuous and Comprehensive
Evaluation (CCE) Scheme
given by
Central Board of Secondary Education (CBSE)
By
J.B. Dixit
Laxmi PubLications (P) Ltd
(An ISO 9001:2008 Company)
BENGALURU
JALANDHAR
●
●
CHENNAI
KOLKATA
BOSTON (USA)
●
●
COCHIN
LUCKNOW
●
●
●
GUWAHATI
MUMBAI
ACCRA (GHANA)
●
●
●
HYDERABAD
RANCHI
NAIROBI (KENYA)
●
NEW DELHI
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 978-81-318-0809-2
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.
Branches
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 - 110002, INDIA
Telephone : 91-11-4353 2500, 4353 2501
Fax : 91-11-2325 2572, 4353 2528
www.laxmipublications.com [email protected]
&
Bengaluru
080-26 75 69 30
&
Chennai
044-24 34 47 26,
24 35 95 07
&
Cochin
0484-237 70 04,
405 13 03
&
Guwahati
0361-254 36 69,
251 38 81
&
Hyderabad
040-27 55 53 83,
27 55 53 93
&
Jalandhar
0181-222 12 72
&
Kolkata
033-22 27 43 84
&
Lucknow
0522-220 99 16
&
Mumbai
022-24 91 54 15,
&
Ranchi
0651-220 44 64
C—7459/013/10
Printed at: IPP, Noida
24 92 78 69
Contents
Pages
Activities
term–I
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
ax2 + bx + c (where a = 1), Using Square Grids, Strips and Paper Slips
9
Activity 4: To Verify the Algebraic Identity: (a + b)2 = a2 + 2ab + b213
Activity 5: To Verify the Algebraic Identity: (a – b)2 = a2 – 2ab + b216
Activity 6: To Verify the Algebraic Identity: a2 – b2 = (a + b) (a – b)
19
Activity 7: To Verify the Algebraic Identity: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
21
Activity 8: To Verify the Algebraic Identity: (a + b)3 = a3 + b3 + 3a2b + 3ab2
24
b)
27
Activity 10: To Verify the Algebraic Identity: a3 + b3 = (a + b) (a2 – ab + b2)
29
Activity 11: To Verify the Algebraic Identity: a3 – b3 = (a – b) (a2 + ab + b2)
33
Activity 9: To Verify the Algebraic Identity: (a –
b)3
=
a3
–
b3
– 3ab (a –
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 360°
36
Activity 13: To Verify that the Sum of the Angles of a Triangle is 180°
38
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 360°
50
Activity 2: To Explore the Properties with Respect to Diagonals of the Following Quadrilaterals—
a Parallelogram, a Square, a Rectangle, and a Rhombus
53
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: 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
Activity 6: 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
Activity 7: 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: 105
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.
Project 5: Surveys and Graph
107
Project 6: An Intersecting Game with the Help of Coordinate Geometry
109
Project Work Assignment
111
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
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.
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.
Index – Activities and Projects
S. No.
1.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
2.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
3.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
4.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
5.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
6.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
7.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
8.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
9.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
10.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
Activities and Projects (First Term)
Date
Page No.
S. No.
11.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
12.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
13.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
14.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
15.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
16.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
17.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
18.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
19.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
20.
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
_____________________________________________________________________ ____________
Activities and Projects (First Term)
Date
Page No.