GANITA MANJARI
Textbook of Mathematics for
GRADE
9
Part I
,0904 – G anita M anjari
ISBN 978-93-5729-603-8
Textbook of Mathematics for Grade 9 (Part I)
First Edition ALL RIGHTS RESERVED
April 2026 Chaitra 1948 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 the prior permission of the publisher.
PD 2000T BS This book is sold subject to the condition that it shall not, by
way of trade, be lent, re-sold, hired out or otherwise disposed
of without the publisher’s consent, in any form of binding or
© National Council of Educational cover other than that in which it is published.
Research and Training, 2026 The correct price of this publication is the price printed on
this page, Any revised price indicated by a rubber stamp or
by a sticker or by any other means is incorrect and should
be unacceptable.
OFFICES OF THE PUBLICATION
DIVISION, NCERT
NCERT Campus
Sri Aurobindo Marg
New Delhi 110 016 Phone : 011-26562708
108, 100 Feet Road
Hosdakere Halli Extension
Banashankari III Stage
Bengaluru 560 085 Phone : 080-26725740
Navjivan Trust Building
P.O. Navjivan
Ahmedabad 380 014 Phone : 079-27541446
CWC Campus
Opp. Dhankal Bus Stop
Panihati
Kolkata 700 114 Phone : 033-25530454
115.00
CWC Complex
Maligaon
Guwahati 781 021 Phone : 0361-2674869
Publication Team
Head, Publication : M.V. Srinivasan
Division
Chief Editor : Bijnan Sutar
Chief Business Manager : Amitabh Kumar
Chief Production Officer : Deepak Jaiswal
Printed on 80 GSM paper with NCERT (In charge)
watermark Assistant Production : Prakash Veer Singh
Officer
Published at the Publication Cover
Division by the Secretary, National Akshita
Council of Educational Research
Layout
and Training, Sri Aurobindo Marg,
Bhuvan Enterprises
New Delhi 110016 and printed at
Krown Printers, B-20/1 (GF, FF, Illustrations
Akshita, Bhuvan Enterprises, and Ritika B
SF, Fourth Floor), Okhla Indl. Area,
Phase-2, New Delhi-110020
, Foreword
The National Education Policy (NEP) 2020 envisions an education system
that is firmly rooted in India’s cultural and intellectual wisdom, values, and
ethical traditions. The rich intellectual heritage simultaneously enables
learners to engage meaningfully with the complexities and possibilities of
a rapidly changing world. The National Curriculum Framework for School
Education (NCF-SE) 2023 provides concrete expression to this vision by laying
out a coherent curricular pathway across various stages of schooling that
nurtures critical thinking, creativity and sensitivity, along with the values and
dispositions that are needed for responsible citizenship in an interconnected
global society.
Learners have progressed through the Foundational, Preparatory and
Middle Stages, where their inherent potential has been nurtured holistically.
Now, they enter the Secondary Stage with enhanced capacity for reflection,
reasoning, enquiry, and self-expression. Spanning across Grades 9 to 12.
It marks a crucial period in the intellectual and personal growth of the students.
It prepares them to engage with abstract ideas, complex social realities, ethical
dilemmas and the expanding universe of knowledge, while deepening their
understanding of the self and the world around them.
The NCF-SE 2023 recommends that the curriculum for Grades 9–10 equips
students with the skills that are needed to grow as they advance in their lives.
Students can use these skills for reasoning, argumentation, and effective
communication. It endeavours to enhance their analytical and descriptive
capabilities to prepare them for the challenges and opportunities that await
them. A diverse curriculum, covering ten subjects: three languages — including
at least two languages native to India — Science, Mathematics, Social Sciences,
Arts Education, Physical Education and Well-being, Individuals in Society/
Environmental Education, Skill Education, and AI and Computational Thinking,
promotes their holistic development.
As per NCF-SE 2023, the Secondary Stage focuses on further developing
students’ ability to justify claims and arguments through logical reasoning.
At this stage, students are expected to be comfortable working with abstractions
and core techniques of Mathematics and Computational Thinking, such as
mathematical modelling and algorithm development for problem-solving. They
also need to strengthen key mathematical skills, including problem-solving,
visualisation, optimisation, representation, and communication, thereby
building essential capacities in Mathematics and Computational Thinking.
Engagement with puzzles, word problems, and optimisation tasks helps
nurture values and dispositiouns, such as perseverance, curiosity, confidence,
rigour and honesty.
The Grade 9 Mathematics textbook, Ganita Manjari (Part I), carries forward
the vision of NEP 2020 and NCF-SE 2023 by promoting mathematical thinking,
problem-solving skills, and intuition among students. Mathematical thinking
involves systematic and logical approaches to interpreting the world. This
, textbook aims to develop students’ ability in formulating well-defined problems
that can be addressed through mathematical reasoning — an essential aspect of
learning Mathematics. It also fosters mathematical intuition, enabling students
to develop a sense of what is likely to be true in Mathematics, which is a key
goal of school education.
This textbook marks an important transition from the Middle to the
Secondary Stage of Mathematics. While building on students’ prior experiences,
it introduces greater conceptual depth, formal reasoning, and the foundations
of proof. Through real-life examples and collaborative learning experiences, it
enhances creativity, logical reasoning, and decision-making skills. This textbook
also highlights the rich history of Mathematics in India, spanning thousands of
years. By learning about mathematical developments in India and across the
world, students can develop a deeper sense of cultural rootedness. The content
attempts to integrate mathematics with other subject areas such as science,
social science and with cross-cutting themes like environmental education,
value education and inclusive education. Additionally, the inclusion of
QR codes integrates technology, providing access to a variety of learning
resources.
The National Council of Educational Research and Training acknowledges
the contributions of the Textbook Development Team, subject experts,
pedagogues, practising teachers, reviewers, and all others who have supported
the development of this textbook. We hope Ganita Manjari inspires learners
to think critically, communicate with confidence, and engage thoughtfully in
society and the global community. We also warmly welcome suggestions and
feedback from all its users for further improvement in the subsequent editions.
Dinesh Prasad Saklani
Director
New Delhi National Council of Educational
April, 2026 Research and Training
iv
Textbook of Mathematics for
GRADE
9
Part I
,0904 – G anita M anjari
ISBN 978-93-5729-603-8
Textbook of Mathematics for Grade 9 (Part I)
First Edition ALL RIGHTS RESERVED
April 2026 Chaitra 1948 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 the prior permission of the publisher.
PD 2000T BS This book is sold subject to the condition that it shall not, by
way of trade, be lent, re-sold, hired out or otherwise disposed
of without the publisher’s consent, in any form of binding or
© National Council of Educational cover other than that in which it is published.
Research and Training, 2026 The correct price of this publication is the price printed on
this page, Any revised price indicated by a rubber stamp or
by a sticker or by any other means is incorrect and should
be unacceptable.
OFFICES OF THE PUBLICATION
DIVISION, NCERT
NCERT Campus
Sri Aurobindo Marg
New Delhi 110 016 Phone : 011-26562708
108, 100 Feet Road
Hosdakere Halli Extension
Banashankari III Stage
Bengaluru 560 085 Phone : 080-26725740
Navjivan Trust Building
P.O. Navjivan
Ahmedabad 380 014 Phone : 079-27541446
CWC Campus
Opp. Dhankal Bus Stop
Panihati
Kolkata 700 114 Phone : 033-25530454
115.00
CWC Complex
Maligaon
Guwahati 781 021 Phone : 0361-2674869
Publication Team
Head, Publication : M.V. Srinivasan
Division
Chief Editor : Bijnan Sutar
Chief Business Manager : Amitabh Kumar
Chief Production Officer : Deepak Jaiswal
Printed on 80 GSM paper with NCERT (In charge)
watermark Assistant Production : Prakash Veer Singh
Officer
Published at the Publication Cover
Division by the Secretary, National Akshita
Council of Educational Research
Layout
and Training, Sri Aurobindo Marg,
Bhuvan Enterprises
New Delhi 110016 and printed at
Krown Printers, B-20/1 (GF, FF, Illustrations
Akshita, Bhuvan Enterprises, and Ritika B
SF, Fourth Floor), Okhla Indl. Area,
Phase-2, New Delhi-110020
, Foreword
The National Education Policy (NEP) 2020 envisions an education system
that is firmly rooted in India’s cultural and intellectual wisdom, values, and
ethical traditions. The rich intellectual heritage simultaneously enables
learners to engage meaningfully with the complexities and possibilities of
a rapidly changing world. The National Curriculum Framework for School
Education (NCF-SE) 2023 provides concrete expression to this vision by laying
out a coherent curricular pathway across various stages of schooling that
nurtures critical thinking, creativity and sensitivity, along with the values and
dispositions that are needed for responsible citizenship in an interconnected
global society.
Learners have progressed through the Foundational, Preparatory and
Middle Stages, where their inherent potential has been nurtured holistically.
Now, they enter the Secondary Stage with enhanced capacity for reflection,
reasoning, enquiry, and self-expression. Spanning across Grades 9 to 12.
It marks a crucial period in the intellectual and personal growth of the students.
It prepares them to engage with abstract ideas, complex social realities, ethical
dilemmas and the expanding universe of knowledge, while deepening their
understanding of the self and the world around them.
The NCF-SE 2023 recommends that the curriculum for Grades 9–10 equips
students with the skills that are needed to grow as they advance in their lives.
Students can use these skills for reasoning, argumentation, and effective
communication. It endeavours to enhance their analytical and descriptive
capabilities to prepare them for the challenges and opportunities that await
them. A diverse curriculum, covering ten subjects: three languages — including
at least two languages native to India — Science, Mathematics, Social Sciences,
Arts Education, Physical Education and Well-being, Individuals in Society/
Environmental Education, Skill Education, and AI and Computational Thinking,
promotes their holistic development.
As per NCF-SE 2023, the Secondary Stage focuses on further developing
students’ ability to justify claims and arguments through logical reasoning.
At this stage, students are expected to be comfortable working with abstractions
and core techniques of Mathematics and Computational Thinking, such as
mathematical modelling and algorithm development for problem-solving. They
also need to strengthen key mathematical skills, including problem-solving,
visualisation, optimisation, representation, and communication, thereby
building essential capacities in Mathematics and Computational Thinking.
Engagement with puzzles, word problems, and optimisation tasks helps
nurture values and dispositiouns, such as perseverance, curiosity, confidence,
rigour and honesty.
The Grade 9 Mathematics textbook, Ganita Manjari (Part I), carries forward
the vision of NEP 2020 and NCF-SE 2023 by promoting mathematical thinking,
problem-solving skills, and intuition among students. Mathematical thinking
involves systematic and logical approaches to interpreting the world. This
, textbook aims to develop students’ ability in formulating well-defined problems
that can be addressed through mathematical reasoning — an essential aspect of
learning Mathematics. It also fosters mathematical intuition, enabling students
to develop a sense of what is likely to be true in Mathematics, which is a key
goal of school education.
This textbook marks an important transition from the Middle to the
Secondary Stage of Mathematics. While building on students’ prior experiences,
it introduces greater conceptual depth, formal reasoning, and the foundations
of proof. Through real-life examples and collaborative learning experiences, it
enhances creativity, logical reasoning, and decision-making skills. This textbook
also highlights the rich history of Mathematics in India, spanning thousands of
years. By learning about mathematical developments in India and across the
world, students can develop a deeper sense of cultural rootedness. The content
attempts to integrate mathematics with other subject areas such as science,
social science and with cross-cutting themes like environmental education,
value education and inclusive education. Additionally, the inclusion of
QR codes integrates technology, providing access to a variety of learning
resources.
The National Council of Educational Research and Training acknowledges
the contributions of the Textbook Development Team, subject experts,
pedagogues, practising teachers, reviewers, and all others who have supported
the development of this textbook. We hope Ganita Manjari inspires learners
to think critically, communicate with confidence, and engage thoughtfully in
society and the global community. We also warmly welcome suggestions and
feedback from all its users for further improvement in the subsequent editions.
Dinesh Prasad Saklani
Director
New Delhi National Council of Educational
April, 2026 Research and Training
iv
