6
Book A
Maths
Name:
Class:
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Section:
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Acknowledgements
Content
Production
Series Head
Creative Director
Peter Fernandes
Vinod Raj
Subject Matter Experts
Programme Manager
Uma Bharathi P,
Ravi Shankar J
Mohan KVK
Instructional Designers
Thapaswini Sathya Prathistha
Leena Johnsy,
Vikram Patil,
Mayura A
Editors
Arunashis Bhattacharjee,
Prableen Kaur,
Srimoyee Roy
Project Manager
Creative Managers
Renjith Kumar C, Sajesh S, Ganapathi Rao R
Graphic Designers
Sreelal K, Anoop Kumar P, Arun Kumar Muthalayil, Bharath Babu B, Heeral Desai,
Joseph Libin T J, Kanaka Rao K, Maria Devanesan A, Mohammed Shafeek Areekkaden,
Murali Mohan S, Nagaraju Tadepalli, Nikhil Rajan, Ramakrishna Ch, Thushal R,
Vipin Kanaran, Venkataramana Kokkirala,
Print Designers
Amol Gavasane, Jayavel M, Kiran Kumar Ieragaraju, Muralidhar Poola, Pradeep Kumar
Desapogu, Romel Lymon Budala, Srikanth Dara, Srinivasa Rao Dongala, Subbarao Anusuri,
Sudheer Jangam, Umashankar Akkinepalli, Venkatapathi Raju Rudraraju
The Next Books Series is an initiative of Next Education India Private Limited.
Next Education acknowledges the contribution of all the authors and reviewers in the creation of this book.
This book is printed on ECF card and ECF environment-friendly paper manufactured from
unconventional and other raw materials sourced from sustainable and identified sources.
Copyright © Next Education India Private Limited.
All rights reserved.
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, without prior written permission
of Next Education.
The authors and the publisher shall be neither liable nor responsible to any person or entity with respect to
any loss or damage arising from the information contained in the book or any associated material, whether
physical, electronic or mechanical.
Every effort has been made to trace the copyright holders and to obtain their permission for the use of
copyrighted material. The publisher apologises for any errors or omissions and would be grateful for
notification of any corrections that should be incorporated in future reprints or editions.
Maths 6 Book A
ISBN: 978-93-86292-41-4
Published 2017
NEIPL/NB/M-V4/LK16 : 1753
Published by Next Education India Private Limited
Sri Nilaya Cyber Spazio, Road No. 2, Banjara Hills, Hyderabad - 500034, Telangana, India.
www.NextEducation.in | [email protected]
00_G6_Maths_Book A_preface.indd 2
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Advisory Board
The NextBooksTM team is advised by a board of prominent educators. These professionals have, for decades,
been passionately involved in the education sector. With rich experience in their respective domains, the
board members are deeply involved in NextBooksTM production right from conceptualising the curricula to
final proofing.
Ms Prema Muralidhar, MA, MEd, MBA
has over 28 years of experience as a principal and a CEO. She has led various organisations and
chain schools, and has excelled in areas as diverse as teacher/student management initiatives,
administration, quality assurance, and training and development.
Dr Dheeraj Mehrotra, M Phil
is an author and an educational innovator. He has authored over 35 books on Computer
Science for ICSE/ISC/CBSE schools and has published over 800 papers. He received the
National Award for Best Teacher from the Hon’ble President of India in 2006.
Dr Sapna Agarwal, MA, MSc
has been a principal and a Master Trainer. She has conducted over 3000 hours of corporate training.
Ms Sunila Malhotra, MA, Dip. H. E.
has over 40 years of experience in the field of Education. She has been the principal of
three well-known schools. She has also been a teacher trainer and is an author of several
school books.
Ms Sunmita Shinde, MA, MEd
has served in premier educational institutions for a decade as a teacher and a teacher trainer.
She excels in the fields of copy-editing and material development (ELT). A renowned resource person
for English language training, she has conducted several workshops on CCE and experiential learning
for CBSE and ICSE schools.
Ms Romaa Joshi, MA
has been the principal of four eminent schools and is now an academic consultant and
corporate trainer. She has been an examiner for Trinity College, London for several years.
Ms Poonamjit Kaur, MA, BEd
has been the founding principal of many reputed schools. An expert in education management, she
has in-depth knowledge of educational psychology, instructional skills and pedagogy. She constantly
tries to adapt and innovate to ensure that teaching and learning can be made interesting and fun.
We also acknowledge the feedback from more than 150,000 teachers and 7,00,000 students who have used
NextEducation products over the last 9 years.
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Preface
Maths is a curriculum series envisioned to make mathematics a meaningful and inspiring
experience for child. It is based on a paradigm that inspires a child to look around and
experience mathematics in his/her immediate environment and relate concepts to everyday
realities. Mathematics in this series is thus grounded in reality than in the abstract, and the
instructional design adopted focuses on developing a spirit of inquisitiveness and discovery.
This has been achieved through thematic treatment of content that uses story-based scenarios.
Besides this, the series also focuses on developing problem-solving abilities, logical reasoning
while catering to diverse learning styles, and multiple intelligences. The design of the series has
incorporated key recommendations made by the NCF, 2005.
The pedagogical elements in the series will sustain the interest of the learners and facilitate
in-depth understanding of the concepts in mathematics. The elements in the series inculcate
the requisite knowledge, skills, values and space for reflection and critical thinking among
children.
This series links the knowledge gained at school with a child’s out-of-school experiences.
This has been achieved by selecting contexts that are available in the child’s surroundings. The
story-based approach deals with the most challenging issues while introducing a concept.
This series espouses the Continuous and Comprehensive Evaluation (CCE) methodology and
enables the teacher to monitor each child’s progress. This series is supported by the following:
• Teacher Manuals, which offer pedagogical support in the form of activities, classroom
strategies, listening inputs and answer keys for all the exercises. Each activity in the
manuals encourages participatory learning and can be used as a tool for formative
assessment.
• Resource Kits, which contain manipulatives to help children experience abstract
concepts, facilitate meaningful learning.
• Digital content, which forms a part of the series, includes TeachNext, Next Education’s
award-winning digital learning solution, currently being used in over 7,000 schools
across India and abroad. TeachNext offers a creative and fascinating mix of digital
content, animation videos, quizzes, questions and answers, and tools like geographical
maps, pictures and clipart.
The exercises in this book are based on bloom’s taxonomy, and suitably graded from simple
to complex and from immediate to remote. Each module in the series facilitates a systematic
approach to real-life situations.
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Here is a description of the icons that are used in the book.
Jump Start: Sets the stage to introduce the concept in focus. This is done by
introducing tasks that help the child recapitulate the basics needed to understand
the concept.
Key terms: Every chapter introduces the child to new grade-appropriate words to
help improve vocabulary.
Why: This section defines the ‘Why’ or reason for learning the concept along with
its life application. It also states how the concept in linked to the other topics.
Remember: Provides a quick recap of concepts taught in previous units
and grades.
Discussion Box: In this section, the child is introduced to discussion prompts
to generate meaningful conversations on the topic.
Do It Yourself: This section introduces the child to open ended questions and
challenging puzzles for experiential learning.
Amazing Fact: This section introduces the child to interesting Fact around the
chapter they are learning.
Knowledge Nugget: Provides a snapshot of important definitions and
learning points.
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Let Us Try: This section introduces the child to exercises that ensure mastery
of the concepts learnt. The letters K, S, A in this section implies Knowledge, Skill
and Application based questions respectively.
Project Time: Gives an opportunity for children to solidify the topics learned by
applying Logical thinking and analytical skills.
Through these books, children will get an opportunity to apply the knowledge
gained, and effectively express their ideas and thoughts. They will also have
ample opportunity to engage with their peers, family members and others to help
develop their skills in mathematics.
We hope these books will positively, creatively and intellectually impact the lives of
the children.
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Contents
1. Knowing Numbers
Forming Numbers........................................................................ 3
Comparing and Ordering Numbers........................................ 10
Estimation of Numbers............................................................. 15
Roman Numerals....................................................................... 20
Using Brackets ........................................................................... 24
2. Whole Numbers
Natural Numbers........................................................................ 29
Whole Numbers......................................................................... 31
Number Line............................................................................... 33
Addition on a Number Line..................................................... 36
Subtraction on a Number Line ................................................ 39
Multiplication on a Number Line............................................ 41
Properties of Whole Numbers.................................................. 43
Patterns in Whole Numbers..................................................... 49
3. Playing with Numbers
Factors and Multiples................................................................ 54
Prime and Composite Numbers .............................................. 61
Rules and Tests for Divisibility................................................. 64
Prime Factors and Prime Factorisation................................... 69
Common Factors and Common Multiples............................. 72
4. Basic Geometrical Ideas
Points, Lines, Line Segments and Rays................................... 80
Curves.......................................................................................... 84
Polygons...................................................................................... 87
Angle, Triangle and Quadrilateral........................................... 90
Circles.......................................................................................... 95
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5. Understanding Elementary Shapes
Measuring Line Segments.......................................................102
Turns and Angles.....................................................................105
Triangles....................................................................................111
Quadrilaterals...........................................................................116
Three-Dimensional Shapes.....................................................120
6.Integers
Deciding the Sign.....................................................................126
Representation of Integers on the Number Line..................130
Absolute Value of Integers......................................................134
Ordering of Integers................................................................136
Addition of Integers.................................................................139
Subtraction of Integers............................................................146
7.Fractions
Fractions....................................................................................154
00_G6_Maths_Book A_preface.indd 8
Equivalent Fractions................................................................161
Comparing and Ordering of Fractions.................................166
Addition and Subtraction of Fractions..................................170
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1
Knowing Numbers
Numbers play an important role in our lives. They are used to count objects and money,
find the distance between two locations, measure temperature, population, etc. Numbers also
help compare a group of objects and arrange them in order.
Knowing Numbers
01_Maths_Grade6_Book A_Knowing Numbers.indd 1
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Jump Start
1. Write the place value and face value of the digit highlighted in red in the numbers given
below.
(a) 48,129
(b) 47,200
(c) 376 (d) 12,451 (e) 18,478
2. Compare each pair of numbers using ‘<’, ‘>’ or ‘=’.
(a) 9874 (c) 14,273 (e) 1,472 3120
14,273
(b) 98,123 (d) 7,147 98,236
3,072
2,071
Now, tick what you already know.
I can:
ü
Write the place value and the face value of a digit in a given number.
Compare numbers.
In this unit, you will learn to:
• Form numbers using digits
• Identify the greatest and the smallest number in a set of given
numbers
• Write a number in its standard form and expanded form
• Write the number name for a numeral
• Find the predecessor and the successor of a number
• Read and write numbers in the Indian and the international system
of numeration
• Compare and order numbers
• Round off and estimate numbers
• Check the accuracy of estimated numbers
• Write the Roman numeral equivalent of the given Hindu-Arabic
numeral and vice versa
• Understand the use of brackets
Key terms
•
•
•
•
•
•
•
•
•
Numeral
Standard form
Expanded form
Predecessor
Successor
Ascending
Descending
Roman Numerals
Brackets
2
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Forming Numbers
Why
In the decimal system, we use the digits 0–9 to write numbers. For example, time in a digital
clock, and the odometer of a car that shows the distance travelled. Different numbers can be
formed by arranging digits in different orders.
Maya visits the bank with her father. Her father wants to withdraw some money from his account.
He submits a cheque and collects a token bearing the number 547. They wait for their turn to be
called to the cash counter.
When the display board shows
the number 457, Maya walks
towards the cash counter.
Is it Maya’s turn to collect cash?
Are the numbers 547 and 457
the same?
Let us place the numbers
in a place value chart
and compare.
Write down both the numbers in
the following place value chart.
H
T
O
457 = 547
True or False?
From the place value chart, we see that 547 and 457 are two different numbers formed of the same
set of digits. Though the digits at their units places are the same, the digits at the hundreds and the
tens places are different.
Write down the number names of the two numbers.
457 =
547 =
The value of a digit is dependent on its place value in the number.
Knowing Numbers
01_Maths_Grade6_Book A_Knowing Numbers.indd 3
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Can you form all the other possible numbers apart from 457 and 547 using the digits 4, 5 and 7?
The place value table given below will help you. One is shown as an example.
H
T
O
7
4
5
Now, identify the greatest and the smallest number among the numbers
formed using the digits 4, 5 and 7.
The greatest number is
.
The smallest number is
.
We know that the face value and place value of a digit in a number dictate
the value represented by that digit. For example, the place value of 5 in ‘457’
is 50, while that in ‘547’ it is 500, although its face value remains the same in
both, that is 5.
We can see from the table above that to form the largest possible number using the digits 4, 5
and 7, the digits from the hundreds place to the ones place are arranged in descending order.
Similarly, the smallest number is formed by arranging the digits from hundreds to ones place in
ascending order.
In the table below, form different numbers using the digits 0, 1, 2, 3 and 8. One has been done
for you.
TTh
Th
H
T
O
8
3
2
1
0
Can a number start with the digit 0?
The greatest five digit number formed by the digits 0, 1, 2, 3
.
and 8 is
The smallest five digit number formed by the digits 0, 1, 2, 3
and 8 is
.
Maya’s father wants to withdraw `9,875 from the bank. He asks
Maya to find out the denominations in which they can collect
the cash.
To find the denominations in which `9875 can be collected, we write
the amount in a place value chart.
Th
H
T
O
9
8
7
5
Look at the table and fill in the blanks with the number of notes of respective denomination.
In 9,875, there are ______ thousands, _________ hundreds, _______ tens and _____ ones.
Hence, the number name of 9,875 is
.
4
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The number 9,875 can be written as 9 × 1000 + 8 × 100 + 7 × 10 + 5 × 1.
Recall that this is the expanded form of 9,875. The expanded form of a number is the sum of the
products of the place values and the digits.
Now, consider the number 27,673.
The expanded form of 27,673 is 2 × 10,000 + 7 × 1,000 + 6 × 100 + 7 × 10 + 3 × 1.
Now, write the expanded form of:
(a) 8,456
.
(b) 19,712
.
Successor and Predecessor
Maya wants to write the largest four-digit number possible. She writes the greatest four-digit
number as 9,999. She wonders what its successor would be.
To find the successor, we simply add 1 to 9,999.
Hence, the successor of 9,999 is 9,999 + 1 = 10,000.
We can infer that 10,000 is the smallest five-digit number.
∴ Greatest four-digit number + 1 = Smallest five-digit number.
The numeral form, also called the standard form, is the most used form of a number.
Now, observe the following statements.
99,999 + 1 = 1,00,000
9,99,999 + 1 = 10,00,000
We can generalise the above as:
Greatest five-digit number + 1 = Smallest six-digit number
Greatest six-digit number + 1 = Smallest seven-digit number, and so on.
The predecessor of a number is one less than the number (number –1).
The successor of a number is one more than the number (number +1).
The successor of 1,23,505 is
Knowing Numbers
01_Maths_Grade6_Book A_Knowing Numbers.indd 5
. The predecessor of 1,23,505 is
.
5
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Systems of Numeration
There are two systems of numeration to read and write large numbers.
Indian System of Numeration
Indian System of Numeration
What is the number name of 1,00,000?
Place value
The Indian system of numeration uses
periods to understand numbers, namely
ones, thousands, lakhs, crores, etc. The
commas are placed according to these
periods.
To find the number name of the given
numeral:
Number
Ones (O)
1
Tens (T)
10
Hundreds (H)
Thousands
Step 1: Arrange the numeral in a place value chart.
Lakhs
Step 2: Identify the number name according to the periods of the place value chart.
Crores
100
Thousands (Th)
1,000
Ten Thousands (TTh)
Lakhs (L)
10,000
1,00,000
Ten Lakhs (TL)
10,00,000
Crores (C)
1,00,00,000
Ten Crores (TC)
10,00,00,000
We can write the number 1,00,000 in the place value chart as:
Lakh
Thousands
Ones
L
TTh
Th
H
T
O
1
0
0
0
0
0
Thus, the name of the number 1,00,000 is one lakh. Now, consider the following place value chart.
Lakh
Thousands
Ones
L
TTh
Th
H
T
O
4
5
3
8
5
2
The name of 4,53,852 is four lakh fifty three
thousand eight hundred fifty two. The expanded
form of the number is 4 × 1,00,000 +
5 × 10,000 + 3 × 1,000 + 8 × 100 + 5 × 10 + 2 × 1.
Similarly, the number 76,05,439 can be written down in the place value chart as shown below:
Lakhs
Thousands
Ones
TL
L
TTh
Th
H
T
O
7
6
0
5
4
3
9
The number name of 76,05,439 is seventy six lakh five thousand four hundred and thirty nine.
6
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The expanded form of the number is
7 × 10,00,000 + 6 × 1,00,000 + 0 × 10,000 + 5 × 1,000 + 4 × 100 + 3 × 10 + 9 × 1.
For the number 96,50,53,002, the place value chart is:
Crores
Lakhs
Thousands
Ones
TC
C
TL
L
TTh
Th
H
T
O
9
6
5
0
5
3
0
0
2
The name of 96,50,53,002 is ninety six crore fifty lakh fifty three thousand two.
The expanded form of the number is 9 × 10,00,00,000 + 6 × 1,00,00,000 + 5 × 10,00,000 + 0 ×
1,00,000 + 5 × 10,000 + 3 × 1,000 + 0 × 100 + 0 × 10 + 2 × 1.
Now, complete the following table using the Indian system of numeration.
Standard Form
Number Name
Expanded Form
8 × 10,000 + 1 × 100 + 2 × 10 + 8 × 1
25,42,032
Forty six crore sixty nine
International System of Numeration
The international system of numeration
also uses periods for reading large numbers.
The periods used in this system are ones,
thousands, millions, and so on. Note that the
expanded form of numbers is independent of
the system of numeration used.
Place value
1
Tens (T)
10
Hundreds (H)
Thousands Ten Thousands (TTh)
Hundred Thousands
(HTh)
Ones
HTh
TTh
Th
H
T
O
4
5
3
8
5
2
Number
Ones (O)
Thousands (Th)
Now, consider the following table for the
number 4,53,852.
Thousands
International System of Numeration
Million (M)
Millions
100
1,000
10,000
100,000
1,000,000
Ten Million (TM)
10,000,000
Hundred Million
(HM)
100,000,000
In the international system of numeration, the number name 453,852 is four hundred fifty three
thousand eight hundred fifty two.
Knowing Numbers
01_Maths_Grade6_Book A_Knowing Numbers.indd 7
7
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Similarly, the number name of 7,605,439 is seven million six hundred five thousand four hundred
thirty nine in the international system of numeration.
Millions
Thousands
Ones
M
HTh
TTh
Th
H
T
O
7
6
0
5
4
3
9
Now, complete the following table using the international system of numeration.
Number
Number Name
Expanded Form
Five million fifty thousand
4 × 100,000,000 + 5 × 10,000,000 +
7 × 1,000 + 9 × 100 + 5
909,501,107
Explain one way to count and write large numbers easily.
Do It Yourself
In the adjoining figure,
rearrange only two
matchsticks to form the
greatest possible number.
Amazing Fact
The name of the popular search engine
‘Google’ comes from a misspelling
of the word ‘googol’ which is a very
large number. Googol is equal to one
followed by one hundred zeros.
Knowledge Nugget
•
•
•
•
•
We can form many different numbers with the same set of digits by just changing their
place values.
The number name of a number is the number written in words.
A number written in numerals is called the standard form of the number. This is the most
used form to represent a number.
The expanded form of a number is written as the sum of the place values of its digits.
The number obtained by adding 1 to a given number is the successor of the number, and the
number obtained by subtracting 1 from a given number is the predecessor of the number.
8
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Let Us Try 1.1
K1. Fill in the blanks.
(a) The successor of 4,261 is
.
(b) The predecessor of 2,467 is
.
(c) The greatest three-digit number is
(d) The name of the number 6,756 is
.
.
K2. Fill in the following blanks.
(a) The place value of 6 in the numeral 5,256 is
(b) The face value of 3 in the numeral 12,53,125 is
.
.
(c) Rewrite 2645978 in its standard form using the Indian system of numeration
.
(d) As per the Indian system of numeration, the place value to the left of lakhs is .
K3. Write the number name of 12350005 using both the numeration systems.
K4. Find the place value of 8 in the number circled in the cheque below.
S1. Complete the following table using the Indian system of numeration.
Number
Number Name
Expanded Form
3,24,657
23,17,894
S2. Complete the following table using the international system of numeration.
Predecessor
Number
Successor
3,245,678
5,646,780
Knowing Numbers
01_Maths_Grade6_Book A_Knowing Numbers.indd 9
65,478,941
9
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S3. Form all possible three-digit numbers using the digits 5, 8 and 9.
S4. Write the given number name in the standard form: Three hundred seven million one
hundred nine thousand nine hundred ninety seven.
A1. Find the sum of the place values of 4 and 9 in the number 2,46,57,890.
A2. Jagan bought a new house for `3,465,700. Find the difference between the place values of 6
and 5 in the given amount.
A3. Rajni bought a piece of land for `9,99,999. Her brother constructed a building on the plot for
`10,00,001. How much money did the two of them spend in total? Write the amount using
the international system of numeration.
10
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6
Book B
Maths
Name:
Class:
00_G6_Maths_Book B_preface.indd 1
Section:
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Acknowledgements
Content
Production
Series Head
Creative Director
Peter Fernandes
Vinod Raj
Subject Matter Experts
Programme Manager
Uma Bharathi P,
Ravi Shankar J
Mohan KVK
Instructional Designers
Thapaswini Sathya Prathistha
Leena Johnsy,
Vikram Patil,
Mayura A
Editors
Arunashis Bhattacharjee,
Prableen Kaur,
Srimoyee Roy
Project Manager
Creative Managers
Renjith Kumar C, Sajesh S, Ganapathi Rao R
Graphic Designers
Sreelal K, Anoop Kumar P, Arun Kumar Muthalayil, Bharath Babu B, Heeral Desai,
Joseph Libin T J, Kanaka Rao K, Maria Devanesan A, Mohammed Shafeek Areekkaden,
Murali Mohan S, Nagaraju Tadepalli, Nikhil Rajan, Ramakrishna Ch, Thushal R,
Vipin Kanaran, Venkataramana Kokkirala,
Print Designers
Amol Gavasane, Jayavel M, Kiran Kumar Ieragaraju, Muralidhar Poola, Pradeep Kumar
Desapogu, Romel Lymon Budala, Srikanth Dara, Srinivasa Rao Dongala, Subbarao Anusuri,
Sudheer Jangam, Umashankar Akkinepalli, Venkatapathi Raju Rudraraju
The Next Books Series is an initiative of Next Education India Private Limited.
Next Education acknowledges the contribution of all the authors and reviewers in the creation of this book.
This book is printed on ECF card and ECF environment-friendly paper manufactured from
unconventional and other raw materials sourced from sustainable and identified sources.
Copyright © Next Education India Private Limited.
All rights reserved.
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, without prior written permission
of Next Education.
The authors and the publisher shall be neither liable nor responsible to any person or entity with respect to
any loss or damage arising from the information contained in the book or any associated material, whether
physical, electronic or mechanical.
Every effort has been made to trace the copyright holders and to obtain their permission for the use of
copyrighted material. The publisher apologises for any errors or omissions and would be grateful for
notification of any corrections that should be incorporated in future reprints or editions.
Maths 6 Book B
ISBN: 978-93-86292-42-1
Published 2017
NEIPL/NB/M-V4/LK16 : 1753
Published by Next Education India Private Limited
Sri Nilaya Cyber Spazio, Road No. 2, Banjara Hills, Hyderabad - 500034, Telangana, India.
www.NextEducation.in | [email protected]
00_G6_Maths_Book B_preface.indd 2
16-12-2016 12:50:13
Advisory Board
The NextBooksTM team is advised by a board of prominent educators. These professionals have, for decades,
been passionately involved in the education sector. With rich experience in their respective domains, the
board members are deeply involved in NextBooksTM production right from conceptualising the curricula to
final proofing.
Ms Prema Muralidhar, MA, MEd, MBA
has over 28 years of experience as a principal and a CEO. She has led various organisations and
chain schools, and has excelled in areas as diverse as teacher/student management initiatives,
administration, quality assurance, and training and development.
Dr Dheeraj Mehrotra, M Phil
is an author and an educational innovator. He has authored over 35 books on Computer
Science for ICSE/ISC/CBSE schools and has published over 800 papers. He received the
National Award for Best Teacher from the Hon’ble President of India in 2006.
Dr Sapna Agarwal, MA, MSc
has been a principal and a Master Trainer. She has conducted over 3000 hours of corporate training.
Ms Sunila Malhotra, MA, Dip. H. E.
has over 40 years of experience in the field of Education. She has been the principal of
three well-known schools. She has also been a teacher trainer and is an author of several
school books.
Ms Sunmita Shinde, MA, MEd
has served in premier educational institutions for a decade as a teacher and a teacher trainer.
She excels in the fields of copy-editing and material development (ELT). A renowned resource person
for English language training, she has conducted several workshops on CCE and experiential learning
for CBSE and ICSE schools.
Ms Romaa Joshi, MA
has been the principal of four eminent schools and is now an academic consultant and
corporate trainer. She has been an examiner for Trinity College, London for several years.
Ms Poonamjit Kaur, MA, BEd
has been the founding principal of many reputed schools. An expert in education management, she
has in-depth knowledge of educational psychology, instructional skills and pedagogy. She constantly
tries to adapt and innovate to ensure that teaching and learning can be made interesting and fun.
We also acknowledge the feedback from more than 150,000 teachers and 7,00,000 students who have used
NextEducation products over the last 9 years.
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Preface
Maths is a curriculum series envisioned to make mathematics a meaningful and inspiring
experience for child. It is based on a paradigm that inspires a child to look around and
experience mathematics in his/her immediate environment and relate concepts to everyday
realities. Mathematics in this series is thus grounded in reality than in the abstract, and the
instructional design adopted focuses on developing a spirit of inquisitiveness and discovery.
This has been achieved through thematic treatment of content that uses story-based scenarios.
Besides this, the series also focuses on developing problem-solving abilities, logical reasoning
while catering to diverse learning styles, and multiple intelligences. The design of the series has
incorporated key recommendations made by the NCF, 2005.
The pedagogical elements in the series will sustain the interest of the learners and facilitate
in-depth understanding of the concepts in mathematics. The elements in the series inculcate
the requisite knowledge, skills, values and space for reflection and critical thinking among
children.
This series links the knowledge gained at school with a child’s out-of-school experiences.
This has been achieved by selecting contexts that are available in the child’s surroundings. The
story-based approach deals with the most challenging issues while introducing a concept.
This series espouses the Continuous and Comprehensive Evaluation (CCE) methodology and
enables the teacher to monitor each child’s progress. This series is supported by the following:
• Teacher Manuals, which offer pedagogical support in the form of activities, classroom
strategies, listening inputs and answer keys for all the exercises. Each activity in the
manuals encourages participatory learning and can be used as a tool for formative
assessment.
• Resource Kits, which contain manipulatives to help children experience abstract
concepts, facilitate meaningful learning.
• Digital content, which forms a part of the series, includes TeachNext, Next Education’s
award-winning digital learning solution, currently being used in over 7,000 schools
across India and abroad. TeachNext offers a creative and fascinating mix of digital
content, animation videos, quizzes, questions and answers, and tools like geographical
maps, pictures and clipart.
The exercises in this book are based on bloom’s taxonomy, and suitably graded from simple
to complex and from immediate to remote. Each module in the series facilitates a systematic
approach to real-life situations.
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Here is a description of the icons that are used in the book.
Jump Start: Sets the stage to introduce the concept in focus. This is done by
introducing tasks that help the child recapitulate the basics needed to understand
the concept.
Key terms: Every chapter introduces the child to new grade-appropriate words to
help improve vocabulary.
Why: This section defines the ‘Why’ or reason for learning the concept along with
its life application. It also states how the concept in linked to the other topics.
Remember: Provides a quick recap of concepts taught in previous units
and grades.
Discussion Box: In this section, the child is introduced to discussion prompts
to generate meaningful conversations on the topic.
Do It Yourself: This section introduces the child to open ended questions and
challenging puzzles for experiential learning.
Amazing Fact: This section introduces the child to interesting Fact around the
chapter they are learning.
Knowledge Nugget: Provides a snapshot of important definitions and
learning points.
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Let Us Try: This section introduces the child to exercises that ensure mastery
of the concepts learnt. The letters K, S, A in this section implies Knowledge, Skill
and Application based questions respectively.
Project Time: Gives an opportunity for children to solidify the topics learned by
applying Logical thinking and analytical skills.
Through these books, children will get an opportunity to apply the knowledge
gained, and effectively express their ideas and thoughts. They will also have
ample opportunity to engage with their peers, family members and others to help
develop their skills in mathematics.
We hope these books will positively, creatively and intellectually impact the lives of
the children.
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Contents
8.Decimals
Decimal Numbers........................................................................ 3
Place Value of Decimals.............................................................. 7
Comparing and Ordering Decimals........................................ 12
Adding Decimals........................................................................ 17
Subtracting Decimals ................................................................ 21
Conversion of Decimals to Fractions...................................... 23
Conversion of Fractions to Decimals...................................... 25
9. Data Handling
Collecting Data........................................................................... 31
Organising Data ........................................................................ 34
Pictograph................................................................................... 41
Graphical Representation of Data............................................ 46
10. Perimeter and Area
Perimeter..................................................................................... 57
Perimeter of a Triangle.............................................................. 66
Perimeter of a Circle.................................................................. 71
Area of Squares and Rectangles .............................................. 74
Area of a Right-angled Triangle............................................... 79
11.Algebra
Variables...................................................................................... 83
Variables in a Formula............................................................... 88
Power........................................................................................... 91
Algebraic Expressions................................................................ 94
Formation of an Algebraic Expression.................................... 99
Value of an Algebraic Expression...........................................103
Equations...................................................................................105
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Solution of an Equation...........................................................109
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12. Ratio and Proportion
Ratio of Numbers.....................................................................115
Equivalent Ratios.....................................................................121
Comparison of Ratios..............................................................124
Proportion.................................................................................127
Mean Proportion......................................................................132
Unitary Method........................................................................134
13. Line Symmetry
Measuring Line Segments.......................................................141
Making Symmetrical Figures..................................................144
Figures with Two Lines of Symmetry....................................148
Figures with Multiple Lines of Symmetry.............................151
Reflection and Symmetry........................................................154
14. Practical Geometry
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Construction of Lines..............................................................161
Construction of Perpendicular Lines....................................167
Construction of Angles...........................................................173
Construction of Special Angles..............................................179
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