CLASS
CBSE-i
WORKING
H
WIT
NUMBERS
CHAPTER
1
Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India
VI
UNIT-1
CBSE-i
WORKING
H
WIT
NUMBERS
1
CHAPTER
CLASS
VI
UNIT-1
Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India
The CBSE-International is grateful for permission to reproduce and/or
translate copyright material used in this publication.
The
acknowledgements have been included wherever appropriate and
sources from where the material has been taken duly mentioned. In
case anything has been missed out, the Board will be pleased to rectify
the error at the earliest possible opportunity.
All Rights of these documents are reserved. No part of this publication
may be reproduced, printed or transmitted in any form without the
prior permission of the CBSE-i. This material is meant for the use of
schools who are a part of the CBSE-International only.
Preface
The Curriculum initiated by Central Board of Secondary Education -International (CBSE-i) is a progressive step in making
the educational content and methodology more sensitive and responsive to the global needs. It signifies the emergence of a
fresh thought process in imparting a curriculum which would restore the independence of the learner to pursue the
learning process in harmony with the existing personal, social and cultural ethos.
The Central Board of Secondary Education has been providing support to the academic needs of the learners worldwide. It
has about 11500 schools affiliated to it and over 158 schools situated in more than 23 countries. The Board has always been
conscious of the varying needs of the learners in countries abroad and has been working towards contextualizing certain
elements of the learning process to the physical, geographical, social and cultural environment in which they are engaged.
The International Curriculum being designed by CBSE-i, has been visualized and developed with these requirements in
view.
The nucleus of the entire process of constructing the curricular structure is the learner. The objective of the curriculum is to
nurture the independence of the learner, given the fact that every learner is unique. The learner has to understand,
appreciate, protect and build on values, beliefs and traditional wisdom, make the necessary modifications, improvisations
and additions wherever and whenever necessary.
The recent scientific and technological advances have thrown open the gateways of knowledge at an astonishing pace. The
speed and methods of assimilating knowledge have put forth many challenges to the educators, forcing them to rethink
their approaches for knowledge processing by their learners. In this context, it has become imperative for them to
incorporate those skills which will enable the young learners to become 'life long learners'. The ability to stay current, to
upgrade skills with emerging technologies, to understand the nuances involved in change management and the relevant
life skills have to be a part of the learning domains of the global learners. The CBSE-i curriculum has taken cognizance of
these requirements.
The CBSE-i aims to carry forward the basic strength of the Indian system of education while promoting critical and
creative thinking skills, effective communication skills, interpersonal and collaborative skills along with information and
media skills. There is an inbuilt flexibility in the curriculum, as it provides a foundation and an extension curriculum, in all
subject areas to cater to the different pace of learners.
The CBSE has introduced the CBSE-i curriculum in schools affiliated to CBSE at the international level in 2010 and is now
introducing it to other affiliated schools who meet the requirements for introducing this curriculum. The focus of CBSE-i is
to ensure that the learner is stress-free and committed to active learning. The learner would be evaluated on a continuous
and comprehensive basis consequent to the mutual interactions between the teacher and the learner. There are some nonevaluative components in the curriculum which would be commented upon by the teachers and the school. The objective
of this part or the core of the curriculum is to scaffold the learning experiences and to relate tacit knowledge with formal
knowledge. This would involve trans-disciplinary linkages that would form the core of the learning process. Perspectives,
SEWA (Social Empowerment through Work and Action), Life Skills and Research would be the constituents of this 'Core'.
The Core skills are the most significant aspects of a learner's holistic growth and learning curve.
The International Curriculum has been designed keeping in view the foundations of the National Curricular Framework
(NCF 2005) NCERT and the experience gathered by the Board over the last seven decades in imparting effective learning to
millions of learners, many of whom are now global citizens.
The Board does not interpret this development as an alternative to other curricula existing at the international level, but as
an exercise in providing the much needed Indian leadership for global education at the school level. The International
Curriculum would evolve on its own, building on learning experiences inside the classroom over a period of time. The
Board while addressing the issues of empowerment with the help of the schools' administering this system strongly
recommends that practicing teachers become skillful learners on their own and also transfer their learning experiences to
their peers through the interactive platforms provided by the Board.
I profusely thank Shri G. Balasubramanian, former Director (Academics), CBSE, Ms. Abha Adams and her team and Dr.
Sadhana Parashar, Head (Innovations and Research) CBSE along with other Education Officers involved in the
development and implementation of this material.
The CBSE-i website has already started enabling all stakeholders to participate in this initiative through the discussion
forums provided on the portal. Any further suggestions are welcome.
Vineet Joshi
Chairman
Acknowledgements
Advisory
Shri Vineet Joshi, Chairman, CBSE
Shri Shashi Bhushan, Director(Academic), CBSE
Ideators
Ms. Aditi Misra
Ms. Amita Mishra
Ms. Anita Sharma
Ms. Anita Makkar
Dr. Anju Srivastava
Dr. Indu Khetarpal
Ms. Vandana Kumar
Ms. Anju Chauhan
Ms. Deepti Verma
Ms. Ritu Batra
Conceptual Framework
Shri G. Balasubramanian, Former Director (Acad), CBSE
Ms. Abha Adams, Consultant, Step-by-Step School, Noida
Dr. Sadhana Parashar, Head (I & R),CBSE
Ms. Anuradha Sen
Ms. Jaishree Srivastava
Ms. Archana Sagar
Dr. Kamla Menon
Ms. Geeta Varshney
Dr. Meena Dhami
Ms. Guneet Ohri
Ms. Neelima Sharma
Dr. Indu Khetrapal
Dr. N. K. Sehgal
Material Production Group: Classes I-V
Ms. Rupa Chakravarty
Ms. Anita Makkar
Ms. Anuradha Mathur
Ms. Kalpana Mattoo
Ms. Savinder Kaur Rooprai
Ms. Monika Thakur
Ms. Seema Choudhary
Mr. Bijo Thomas
Ms. Kalyani Voleti
Dr. Rajesh Hassija
Ms. Rupa Chakravarty
Ms. Sarita Manuja
Ms. Seema Rawat
Dr. Uma Chaudhry
Ms. Nandita Mathur
Ms. Seema Chowdhary
Ms. Ruba Chakarvarty
Ms. Mahua Bhattacharya
Material Production Groups: Classes VI-VIII
Mathematics :
Ms. Seema Rawat
Ms. N. Vidya
Ms. Mamta Goyal
Ms. Chhavi Raheja
Political Science:
Ms. Kanu Chopra
Ms. Shilpi Anand
English :
Ms. Rachna Pandit
Ms. Neha Sharma
Ms. Sonia Jain
Ms. Dipinder Kaur
Ms. Sarita Ahuja
Science :
Dr. Meena Dhami
Mr. Saroj Kumar
Ms. Rashmi Ramsinghaney
Ms. Seema kapoor
Ms. Priyanka Sen
Dr. Kavita Khanna
Ms. Keya Gupta
English :
Ms. Sarita Manuja
Ms. Renu Anand
Ms. Gayatri Khanna
Ms. P. Rajeshwary
Ms. Neha Sharma
Ms. Sarabjit Kaur
Ms. Ruchika Sachdev
Geography:
Ms. Deepa Kapoor
Ms. Bharti Dave
Ms. Bhagirathi
Ms. Archana Sagar
Ms. Manjari Rattan
Mathematics :
Dr. K.P. Chinda
Mr. J.C. Nijhawan
Ms. Rashmi Kathuria
Ms. Reemu Verma
Science :
Ms. Charu Maini
Ms. S. Anjum
Ms. Meenambika Menon
Ms. Novita Chopra
Ms. Neeta Rastogi
Ms. Pooja Sareen
Political Science:
Ms. Sharmila Bakshi
Ms. Srelekha Mukherjee
Economics:
Ms. Mridula Pant
Mr. Pankaj Bhanwani
Ms. Ambica Gulati
Geography:
Ms. Suparna Sharma
Ms. Leela Grewal
History :
Ms. Leeza Dutta
Ms. Kalpana Pant
Material Production Groups: Classes IX-X
Dr. Sadhana Parashar,
Head (I and R)
Shri R. P. Sharma, Consultant
Ms. Seema Lakra, S O
History :
Ms. Jayshree Srivastava
Ms. M. Bose
Ms. A. Venkatachalam
Ms. Smita Bhattacharya
Coordinators:
Ms. Sugandh Sharma,
Dr. Srijata Das,
Dr. Rashmi Sethi,
E O (Com)
E O (Maths)
E O (Science)
Ms. Ritu Narang, RO (Innovation) Ms. Sindhu Saxena, R O (Tech) Shri Al Hilal Ahmed, AEO
Ms. Preeti Hans, Proof Reader
CONTENT
Preface
Acknowledgment
1. Syllabus
2. Scope Document
3. Activity - Skill Matrix
4. Teacher support Material
Warm up Activity W1
Activity 1- Importance of Mathematics
Activity 2 - word puzzle
Activity 3 - Cross word
Warm up Activity W2
Activity 1- Sudoku
Pre Content Worksheet P1
Activity 1- hands on activity (forming a number)
Pre Content Worksheet P2
Activity 1- Practice worksheet
Content Worksheet C1 - Understanding numbers
Activity 1
Activity 2
Content Worksheet C2.1 - Compare and Order
Activity 1
Activity 2
Activity 3
Activity 4
Content Worksheet C2.2 -Practice
Activity 1
Activity 2
Activity 3
Content Worksheet C3.1 - Place value systems
Activity 1
Activity 2
Activity 3
Activity 4
Content Worksheet C3.2 - Practice
Activity 1
1
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5
6
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Activity 2
Activity 3
Content Worksheet C4.1 - Four Operations of Mathematics
Activity 1
Activity 2
Activity 3
Content Worksheet C4.2 - Practice
Activity 1
Activity 2
Activity 3
Content Worksheet C4.3 - Practice
Activity 1
Activity 2
Activity 3
Activity 4
Activity 5
Content Worksheet C5 - DMAS
Activity 1
Activity 2
Activity 3
Content Worksheet C6 - Estimation
Activity 1
Activity 2
Content Worksheet C7 - Roman Numerals
Activity 1
Activity 2
Post Content Worksheet PS1
Post Content Worksheet PS2
Assessment Rubric
Student's support material
Student content
Student's worksheet 1
Student's worksheet 2
Student's worksheet 3
Student's worksheet 4
Student's worksheet 5
Student's worksheet 6
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Student's worksheet 7
Student's worksheet 8
Student's worksheet 9
Student's worksheet 10
Student's worksheet 11
Student's worksheet 12
Student's worksheet 13
Student's worksheet 14
Student's worksheet 15
Student's worksheet 16
Student's worksheet 17
Student's worksheet 18
Student's worksheet 19
Student's worksheet 20
Student's worksheet 21
Student's worksheet 22
Student's worksheet 23
Student's worksheet 24
Student's worksheet 25
Student's worksheet 26
Student's worksheet 27
Student's worksheet 28
Student's worksheet 29
Student's worksheet 30
Student's worksheet 31
Student's worksheet 32
Student's worksheet 33
Student's worksheet 34
Student's worksheet 35
Student's worksheet 36
Suggested videos/ links/ PPT's
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Syllabus
Unit 1 - Working with numbers
Working with Numbers
Recall of content learnt in class V,
Comprehending and understanding
numbers, Comparing and ordering of
numbers, Representing more than 4 digit
numbers in Indian and International place
value system, Extending the four basic
operations to large numbers, Word problems
related to real situations (based on the four
operations), Order of operations, Estimation
and Roman numerals.
SCOPE DOCUMENT
WORKING WITH NUMBERS
Prerequisite : Knowledge of numbers, big and small, concept of addition, subtraction and
multiplication
Concepts:
1.
Comprehending and understanding numbers
2.
Comparing and ordering of numbers
3.
Representing more than 4 digit numbers in Indian and International place value
system
4.
Extending the four basic operations to large numbers
5.
Word problems related to real situations (based on the four operations)
6.
Order of operations
7.
Estimation
8.
Roman numerals
MATHEMATICS UNIT - 1
1
Learning objectives
Foundation
At the end of the chapter student will be able to:
Demonstrate knowledge of representing numbers.
J
Explore the importance of place value.
J
Read and write numbers (more than 5 digits) in the Indian and the international
J
system.
Compare numbers and order them in ascending and descending order applying
J
knowledge of place value.
Perform the four basic operations of arithmetic extending his/her knowledge of
J
the four basic operations, and compute fluently with and without using
manipulative.
Make reasonable estimates.
J
Apply the knowledge acquired to word problems and real life situations.
J
Research about Roman numerals and use them.
J
Know and appreciate the purpose in real life situations of knowledge of
J
mathematics and how they have been represented down the ages.
Extension activities:
1.
Students will explore the history of numbers down the civilizations, and put up
an exhibition of the same.
2.
Prepare a math dictionary of all the words learnt.
3.
Students will research and investigate about palindromes.
www.numeracysoftware.com/palindromes.pps http://www.mariamilani.com/ancient_rome/roman_numerals.htm
Resource links:
http://www.armoredpenguin.com/crossword/Data/best/math/vocabulary.11.h
tml
http://www.funtrivia.com/crossword/play.cfm?gid=1515
http://www.learn-with-math-games.com/Place.html
http://homeschooling.about.com/od/gamesmath/Games_Online_Math_Games.
htm
http://homeschooling.about.com/gi/o.htm?zi=1/XJ&zTi=1&sdn=homeschooling
2
MATHEMATICS UNIT - 1
&cdn=education&tm=4&f=00&tt=14&bt=0&bts=0&zu=http://www.arcademicski
llbuilders.com/games/meteor/meteor.html
http://sagebe.freewebspace.com/estimation15.html
http://www.softschools.com/manage/themes/testreview?id=3&themeId=837
http://www.softschools.com/math/worksheets/print_sheets2.jsp
(More worksheets to be generated for practice)
Cross curricular links:
Art
Different numerological scripts used and mastered by different civilizations would
be explored.
Language Arts/Writing:
1.
Research and write, about how the people of different civilizations were using the
knowledge of numbers.
2.
Research and write an article for the school magazine about palindromes.
3.
Research and write a paragraph on the importance of 0.
Social Studies:
How did the knowledge of numbers help in the development of different
civilizations down the ages? Explore any one civilization in a reasonable detail.
MATHEMATICS UNIT - 1
3
Activity - skill Matrix
Activities
Learning objectives
Content worksheet C1
Exploring the importance Place value and Communiof place value
cation skills (communicating
in terms of numbers)
Task 1 to Task 3
Content worksheet C2.1
Task 1 to Task 4
Content worksheet C3.1
Task 1 to Task 4
Content worksheet C3.2
Task 1 to Task 4
Content worksheet C4.1
Task 1 to Task 2
Content worksheet C4.3
Task 1 to Task 3
Content Worksheet C5
Skills learnt
Read and write numbers Comparing and ordering the
(more than 5 digits) in the numbers
Indian and the international system
Compare numbers and Representing numbers in
order them in ascending Indian and International
and descending order system
applying knowledge of
place value.
Perform the four basic Four basic operations of
operations of arithmetic M a t h e m a t i c s f o r l a r g e
extending their knowledge numbers
of the four basic operations,
and compute fluently with
and without using
manipulative
Simplification
DMAS - Order of Operations
Make reasonable estimates
Approximation and
Estimation
Task 1
Content Worksheet C6
Task 1 to Task 3
Content worksheet C7
Task 1
4
Research about Roman Representing numbers in the
form Roman Numerals
numerals and use them
MATHEMATICS UNIT - 1
TEACHERS’
SUPPORT
MATERIALS
MATHEMATICS UNIT - 1
5
WARM UP ACTIVITY W1
Activity 1 - Importance of mathematics
Description -
Teacher will show the video clip 1 to the students. This video highlights
the importance of mathematics through images.
Pre preparation -
Teacher will give a handout to the students where they write there own
views on importance of Mathematics in real life.
Students write their views and the teacher will show them video clip 1. to
get more ideas.
Students describe on the same hand out, what they like in the video.
Follow up -
WARM UP ACTIVITY W1
Activity 2 - Word Puzzle
Description -
This is a recapitulation activity to make students recall different
mathematical words. It is a mathematical puzzle. Ask students to look for
words which communicate mathematical concepts and processes.
Pre Preparation -
Prepare a word search puzzle containing mathematical terms learnt by
students in the previous classes.
Execution -
Each student will search for mathematical words with the help of a math
dictionary (available online)
Word Puzzle (Answer Sheet)
Answers
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MATHEMATICS UNIT - 1
WARM UP ACTIVITY W1
Activity 3 -
Cross word
Description -
Teacher will handout photocopies of the crossword to the students. This
activity can be a group work. Teacher will decide the number of members in
the group.
Execution -
Students work in groups and complete the cross word
Follow up -
Different groups together will discuss their answers.
Solution
MATHEMATICS UNIT - 1
7
WARM UP ACTIVITY W2
8
Activity 1 -
SUDOKU
Objective -
Students are encouraged to solve sudoku. This will help them to be more
observant and analytical in nature.
Description -
Teacher will ask students to first complete each 3x3 grid by using the digit
1 to 9 and no digit should be repeated in the same row or column of 9 x 9
grid.
Pre Preparation -
Prepare a sudoku sheet according to the level of students. Teacher can
prepare different levels of Sudoku for the students of different levels in
the same class at the same time.
MATHEMATICS UNIT - 1
PRE CONTENT WORKSHEET P1
Activity 1 - Hands on Activity
Specific Objectives To recall 3, 4 or 5 digit numbers
To recall correct formation of number for a given number name and place values
To practice making of greatest and smallest numbers out of the given digits
To understand distinction between smallest possible number and smallest
possible four digit number (The two are different).
Material Required - Giant digits printed on paper.
Pre preparation - Teacher will prepare Handout of giant sized digits printed on paper.
Description - Teacher will hand out digit cards to the students randomly.
Each student should have only one card.
Teacher will ask them to form a specific number and check if they have made the
correct number.
Then, ask place value questions about the number.
Example: You hand the digits 0, 6, 7 and 8 to four different students.
Then you say, "Make the number eight thousand sixty-seven."
The student line up in front of the other students and hold the digits in front of
their chest for the rest of the class to see.
Billy has the digit 8. He lines up first and holds up his digit.
Mary has the digit 0. She lines up second and holds up her digit.
Jane has the digit 6. She lines up third and holds up her digit.
Joey has the digit 7, so he lines up last and holds up his digit.
Together, they made the number 8,067
Than ask questions like:
1.
Which student has the digit in the hundreds place?
2.
Which student's digit has the greatest value?
3.
What would we get if a thousand is added to this number?
And so on……, so as to involve all the students of the class.
MATHEMATICS UNIT - 1
9
Follow up - Suggestive Activity:
Teacher can also ask students to make the greatest possible number using the
digits (8,760) or the smallest possible number (0,678).
Teacher needs to clearly make the distinction between smallest possible number
and smallest possible four digit number.
(Note: This game can be played with numbers as large or as small as they like.
Students often face difficulty with zeros in large numbers.)
Example: - 1,070 is more difficult than 1,345.
For an added challenge, hand out commas and have the students place them in
the correct-places.
PRE CONTENT WORKSHEET P2
Activity 1 - Practice Worksheet
Objective - Recapitulation of the work done in class V on numbers.
Description - Teacher monitors the level of knowledge and then plans the lessons
accordingly.
(Note: Ideally students would have already worked on all the objectives but
with four digit numbers.)
Pre-Preparation 1.
Use cards with digits 0 - 9 as a manipulative.
2.
Prepare worksheet based on the work done in class V on numbers.
Execution - Each student of the class solves the worksheet.
Follow up - Teacher checks the worksheet for concepts and accuracy.
CONTENT WORKSHEET C1
Understanding Numbers
Activity 1 - Remedial
Description - Teacher has identified the weakness of his/her students in pre content
worksheet P2. Teacher is advised to make the worksheets similar to pre content
worksheet 2 to ensure that all students are at same level and then start with the
following tasks.
10
MATHEMATICS UNIT - 1
CONTENT WORKSHEET C1
Understanding Numbers
Activity 2 - Explore and Create
Objective - Explore and know about the history of mathematics
Description - Teacher will show Video clip 2 to the students. This video talks about the
need for developing numbers and how they were represented by different
civilizations around the world.
Pre-Preparation - Show video clip 2 to the students. Prepare a questionnaire for the
students to answer and prepare for the exhibition.
Follow up - Based on the video clip 2 and the hand out, students will prepare for an
exhibition on history of mathematics.
CONTENT WORKSHEET C 2.1
Compare and Order
Activity 1 - Explore
Specific Objective 1. Recall formation of 4-digit numbers.
2. To practice comparing two numbers and find greatest or smallest out of
them.
3. To order numbers by arranging the numbers in increasing or decreasing
order.
Material used - Giant sized digits cards (0 - 9)
Description - A set of four digits is given in random order to a group of four students. The
students are asked to arrange the numbers as they want. Allow them to make as
many numbers as possible.
The students place their cards to represent a number each and then together
identify which number is greater and then arrange them accordingly.
Similarly they identify the smallest number.
They tabulate their numbers in the given table.
One member comes and explains how they have arranged their numbers.
(Note: Stress should be on communication using words like face value and place
value.)
MATHEMATICS UNIT - 1
11
Execution -
Ask the students to tabulate the given numbers.
Let one student from each group stand in front and explain how they have
arranged their numbers using the words face value and place value.
CONTENT WORKSHEET C 2.1
Compare and Order
Activity 2 -
Find Word Meaning
Objective -
To Make students know the meaning of the words Ascending and
Descending.
Material Required - Dictionary/Picture, math dictionary available online.
Description -
Student would refer to the dictionary and find the meaning of the word
Ascending.
The meaning is put up on the board to be referred to by the other students.
Students then find the antonym (opposite) of the word ascending i.e.
descending.
This is also written on a flash card and displayed on the board.
Execution -
Ask the students to refer to the dictionary to find the meaning of the words
ascending and descending.
Follow up -
Recapitulate whatever was done on the previous day.
Ask students to volunteer to write the meaning of ascending and
descending on A-4 sheets, with sketch pens and big print and put it on
board. This will helps those student who have difficulty retaining the
meanings and concepts.
CONTENT WORKSHEET C 2.1
Compare and Order
Activity 3 -
Number Game
Objective -
Reinforce the concept of ascending and descending order.
Material Required - Flash cards with 5 and more digit numbers written. (One for each
child)
Description -
12
Give each child a number card that they can hold or that can be attached to
them in front.
MATHEMATICS UNIT - 1
Make the numbers large enough to be seen from a distance.
Starting with a given number let them put themselves in order as their turn
comes up.
(Note: Don't forget to try ordering the numbers backward.)
A number line can also be drawn and numbers depicted for better clarity.
Execution -
Ask the numbers to arrange themselves first in ascending order and then in
descending order. Ask them to draw a number line.
Follow up -
Students display their work in the class for recap and retention (I see, I
remember)
CONTENT WORKSHEET C 2.1
Activity 4 - Independent practice
Objective - Recapitulation of the work done in content C2.1
Description - This is a recapitulation worksheet to make students recall all the concepts
learnt in content C2.1 Ask students to do the work as directed.
Execution - Students will solve the worksheet given to them and note down their answers.
Teacher will discuss answers to check for accuracy and understanding.
CONTENT WORKSHEET C 2.2
Activity 1- Remedial
Description - Teacher needs to identify the area of weakness of his/her students on the
basis of Content Worksheet C2.1, Activity 4.
Teacher is advised to make the worksheet according to the need of the students
to ensure that all the students are at same level and then start with following
tasks.
If the students do not feel encouraged, the teacher may advise them to practice
more on weblinks for more help on concept clarity.
(Alternatively teacher can make more worksheets based on student's
requirements).
MATHEMATICS UNIT - 1
13
CONTENT WORKSHEET C 2.2
Activity 2 - Further Practice
Objective - To enable students to understand the distinction between smallest possible
number and smallest possible 4-digit number
To make students to arrange the given numbers in proper order
To enable students to compare and arrange large numbers in order
To enable them to apply the knowledge of ordering numbers in real life
To enable students to apply the knowledge of ordering number
To understand the concept of greatest and smallest number.
Description Q1. Teacher will give 4 different digits and ask students to distinguish between
smallest possible number and smallest possible 4-digit number.
Q2. Teacher will give some numbers to arrange them in ascending order.
Q3. Chart of 10 countries will be given with their areas and population. Ask students
to compare countries on the basis of the numbers given.
Q4. The odometer of four cars showed the given distances traveled. Students are
asked to arrange the cars and the distance traveled by the four in the descending
order.
Q5. On the basis of the given table showing death toll of year 2004 due to tsunami,
students will arrange the countries in the descending order of the causalities.
Q6. The sale of tickets in the opening ceremony of the common wealth games 2010 is
given. On the basis of the given table students will find the ticket which fetched
the most money and which fetched the least amount?
Execution - Students will read the question carefully and give justification on the basis of it.
CONTENT WORKSHEET C 2.2
Activity 3 - Extension (Independent practice)
Description - Teacher will give set of 5 (non zero) digits to each student.
Execution - Students will form as many 5 digits numbers (without repetition) as they can
from the given 5 digits.
Then arrange them in order. (Increasing or decreasing)
Follow up - Teacher will randomly call students to explain their work to the class.
14
MATHEMATICS UNIT - 1
CONTENT WORKSHEET C 3.1
Indian and International place value system
Activity 1 - Explore
Understand place value system
Understand the meaning of million and billion.
Description - The teacher will ask the students to enquire about million and billion from
their family members This activity will be done by students as homework.
Pre-preparation - For this, teacher will prepare a response sheet and ask the students to fill
it.
Family
Members
Responses
1 Million
1 Billion
Grand Father
Grand Mother
Father
Mother
Sister/Brother
Execution - Each student will bring back responses from their homes and discuss the same
in next class.
Follow up - Students watch video clip 3 as a follow up activity and then write their own
views on what a million is?
MATHEMATICS UNIT - 1
15
CONTENT WORKSHEET C 3.1
Activity 2 - Who wants to be a Millionaire?
Objective - Understand the concept of place value.
Form the largest and smallest numbers with the given digits.
Description - The teacher will divide the students into groups of two or three, and provide
them deck of cards with jokers, kings, jacks and tens removed.
All queens represent 0 and aces represent 1 and remaining cards represent their
own value.
Students will be asked to form the greatest six digits number, by drawing cards
from the stack and use the acquired number to fill any space in their mystery
number (student can draw the cards turn by turn).
For this purpose teacher can provide cardboards to fill student's responses.
Pre preparation - To fill the responses of student, teacher will prepare a response sheet on a
cardboard and ask the students to place their card once on any place value.
Hundred
Thousand
Ten Thousand
Thousand
Hundred
Tens
Ones
Execution - When all the students in the group fill their six spaces, they line up their
number to see who is closest to one million.
CONTENT WORKSHEET C 3.1
Activity 3 - Do it yourself
Objective - Place values in a number of 5 or more digits
Specific Place values
Place value in expanded form
Representation of number in standard form
Description - Teacher will show Video clip 4 for the introduction to face value and base ten
blocks.
Teacher will explain the concepts of base ten blocks to the students.
Pre-Preparation - For this teacher will provide the worksheet to students which they will
do as a follow up activity to the video clip 4
16
MATHEMATICS UNIT - 1
Execution - Teacher will distribute the worksheet in the class and ask students to complete
it.
(Note: Teacher can prepare more worksheets according to level of the students)
CONTENT WORKSHEET C 3.1
Activity 4 - Remedial
Description - Students must be advised to watch all the video clips and games to revise the
concepts to become comfortable and feel encouraged.
Execution - Teacher will distribute the worksheet in the class and ask the students to
complete it.
(Note: Teacher can provide more worksheets according to the level of students.)
CONTENT WORKSHEET C 3.2
Activity 1- I see with my little eyes
Objective - This activity will enhance the students’ listening and interpreting skills.
Description - This is a warm up activity. The teacher will prepare the cards with numbers
written on it and distribute among the students .
Pre preparation - Teacher will prepare the cards and say:
I see with little eyes the number
6 in the thousand place,
4 in the ten thousand place,
2 in the hundred place
4 in the tens place
1 in the ones place
What number am I seeing?
1.
6 4, 2 4 1
2.
4 6, 4 2 1
3.
1 4, 2, 4, 6
4.
1 4, 2, 6 4
6.
4 6, 2 4 1
MATHEMATICS UNIT - 1
17
Execution - Once the students are able to answer the first one, they can be engaged more by
giving clues like - the number in the ones place is two less than the number in the
tens place, and I see 4 in ones place.
Student answer once again
What number did I see?
CONTENT WORKSHEET C 3.2
Activity 2 - Find the Mystery numbers.
Objective - This will enhance the student's thinking skills and they will learn to write the
numbers according to their place value.
Description - Teachers are supposed to prepare the worksheet and distribute it in the class.
Pre-preparation - The teacher will prepare the worksheet.
Execution - Teacher can vary the level of difficulty according to the level of students.
CONTENT WORKSHEET C 3.2
Activity 3 - Place Value - Mystery Number
Objective - Students will be able to form the number according to the place value of the
digits.
Description - Teacher will form groups of 8 to 10 students. Teacher will prepare the clues
of numbers and their hints and distribute in it the groups. Half of the group will
get the cards of numbers and rest will get the cards of hints written on it.
Pre-preparation - The Teacher will prepare the following clue cards.
Card : 1
This mystery number has 4 digits. Every digit is an odd number. None of the
digits is a 9. Every digit in the number is different. The smallest digit is in the
thousands place. The greatest digit is in the ones place. On the basis of the above
instructions we can have two possible numbers. The mystery number is the
greater of those two numbers. What is the mystery number?
Card : 2
This mystery number has 5 digits. There is a 4 in the ten thousand place. None of
the other digits is a 4. What is the smallest number that this mystery number can
be?
18
MATHEMATICS UNIT - 1
Card : 3
This mystery number has 6 digits. If you add one to this number it will be a 7 digit
number. What is the mystery number?
Card : 4
This mystery number is one half of a billion. How many zeros are in this
number?
Card : 5
5, 1, 3, 7
Card : 6
40,000
Card : 7
999,999
Card : 8
500,000,000
Execution - Once the numbers are distributed teacher will ask the students to speak the
hints one by one and find their partner.
CONTENT WORKSHEET C 4.1
Four basic operations with large numbers
Activity 1- Hands on activity (Base ten blocks)
Objective - Students will be able to learn addition and subtraction of large numbers.
Description - Teacher will show Video clip 5 as a starter to the students and then start the
activity.
Teacher will provide the students with base ten blocks and a base ten counting
mat with a space for ones, tens and hundreds. First teacher will give some simple
problems and demonstrate the operations in front of students and then let the
students practice the skill independently.
MATHEMATICS UNIT - 1
19
Eg. : 1.
Add 123 + 184
1+1 = 2 hundred mats
2+8 = 10 ten mats = 1 hundred mat
(So we have 2+1 = 3 hundred mats)
And 3 + 4 = 7 ones.
Special instruction : 10 ten mats can be replaced by 1 hundred mat.
So we have 3 hundreds, 0 tens and 7 ones blocks.
So, answer is 307.
2.
184 -123.
1 -1 = 0 hundred
8 - 2 = 6 tens mats
4 - 3 = 1 ones
So the answer is 61.
After the instruction teacher can distribute the worksheets and ask the students
to complete it.
Pre-preparation - The teacher will prepare the worksheet.
Execution - After the distribution of worksheet teacher will work as a facilitator.
CONTENT WORKSHEET C 4.1
Activity 2 - Addition and subtraction of large numbers.
Objective - Students will be able to learn the addition and subtraction of large numbers.
Description - Teacher will make a worksheet and distribute it in the class and ask the
students to add the adjacent numbers together and write their sum in the blocks
above them and complete the pyramid.
Execution - Teacher will distribute the worksheet in the class and ask the students to
complete it.
20
MATHEMATICS UNIT - 1
CONTENT WORKSHEET C 4.1
Activity 3 - Remedial
Objective - To solve the problems of students and revise the concept and make the
students comfortable with the concept and feel encouraged.
Description - If the students are comfortable in doing the worksheet C4.1 Then teacher can
go ahead.
If some of students are not comfortable, they must be given some more
worksheets on the same pattern and thereafter the teacher can go ahead.
CONTENT WORKSHEET C 4.2
Activity 1: Fill up the grid
Objective: Enhancing the skills of four basic operations of arithmetic.
Pre preparation: Teacher will prepare photocopies of grid shown below to distribute
among the students.
Description:
•
Teacher will ask students divide the grid in 3 x 3 squares.
•
Teacher will ask the students to fill up one 3 x 3 square with the digits from 1 - 9.
•
Then following the numbers already filled in other squares, teacher will ask
students to complete the grid.
Execution: Ask the students to fill up the 3 x 3 square at a time and add simultaneously to
check if the sum comes out to be same as given in the shaded area.
This is to avoid any confusion at any stage of solving the grid.
MATHEMATICS UNIT - 1
21
CONTENT WORKSHEET C 4.2
Activity 2: Common Coins
Objective: Students are encouraged to decode the puzzle and know more about the coins
mentioned.
Pre Preparation: Get the photocopy of the information about the coins and distribute to the
students. This will encourage students to know more about these coins.
Description:
22
•
Teacher will hand over the photocopy of the following content to every student.
•
She/he will then encourage the students to solve the problems to know the
answers of the two secret codes given in the worksheet.
MATHEMATICS UNIT - 1
CONTENT WORKSHEET C 4.2
Activity 3
: Independent practice
Objective
: Recapitulation of the work done in Content worksheet C 4.1.
Description
: Teacher will prepare a worksheet to check the concept and the speed of
the students.
Execution
: Students will read the questions carefully and do as directed.
Follow up
: Teacher will check the questions for the concept, understanding and
accuracy.
CONTENT WORKSHEET C 4.3
Activity 1: HANDS ON ACTIVITY (BASE TEN BLOCKS)
Objective
:
To perform basic numerical operations using unit blocks to
demonstrate the concept of grouping between place values.
Material required: Provide students with base ten blocks and a base ten counting mat
with a space for ones, tens and hundreds.
Description
:
Teacher will help student understand the following example using
base ten blocks.
Teacher will reinforce that to do multiplication, one essentially does
repeated addition.
For example, to multiply 7 x 12, you group together 7 set of 12 units.
Teacher will demonstrate Multiplications using the backdrop shown
in the picture below.
7 x 12 = 12 + 12 + 12 + 12 + 12 + 12 + 12
7 x 12 = (7 x 10) + (7 x 2) = 70 + 14 = 84
(Note: Teacher will make her/his students understand that the
blocks that represent the 12 as well as the ones in the rectangle are
not touching. This is done to make it easier to count the blocks.)
MATHEMATICS UNIT - 1
23
CONTENT WORKSHEET C 4.3
Activity 2:
Recapitulation by doing Independent practice
Objective:
To enhance the skills of multiplication of small and big numbers.
Pre preparation: Teacher will prepare the worksheet and give it to the students to solve
Execution:
Teacher will encourage the students to read the questions carefully and
solve them.
Follow up:
Teacher will correct the worksheet to check the student's concept,
understanding and accuracy.
CONTENT WORKSHEET C 4.3
Activity 3:
Modelling division using base ten blocks
Objective:
To model basic numerical operations using unit blocks to visually
demonstrate the concept of grouping between place values.
Material required: Provide students with base ten blocks and a base ten counting mat with
a space for ones, tens and hundreds.
Description:
Teacher will explain Division with Remainders with the help of base ten blocks.
Teacher gives an example (say) 231 ÷ 15.
Then gives instructions :
Lay out 231, then group them into piles of 15 each.
Teacher then asks the following questions to facilitate thinking.
a)
How many piles can be made? That is the quotient.
b)
How many are left over? That is the remainder.
(Note: Teacher must give at least 6 - 7 examples before passing on the game to the students)
Follow up: Teacher will give few questions for practice of this concept.
24
MATHEMATICS UNIT - 1
CONTENT WORKSHEET C 4.3
Activity 4:
Try the following questions
Objective:
To enhance the skills of division.
Pre Preparation:
Teacher will prepare a worksheet and give it to the students for
practice.
Execution:
Teacher will encourage the students to read the questions carefully
and solve them.
Follow up:
Teacher corrects the worksheet for checking the students’ concept,
understanding and accuracy.
CONTENT WORKSHEET C 4.3
Activity 5:
Remedial
Objective:
To get all the students of the class to the same level
Description:
Teacher needs to identify the area of weaknesses of his/her
students on the basis of content worksheet C 4.3 activity 2 and
activity 4.
Teacher will do the following to overcome the weaknesses:
1.
Revision of the concepts done on previous day.
2.
More similar worksheets depending on the need of the students can be prepared
by the teacher.
3.
Advising the students to go through the resource links provided and
revise/practice.
Follow up:
Teacher will make a worksheet of 1 or 2 questions to give it to the
students as a formative assessment
CONTENT WORKSHEET C 5
ORDER OF OPERATIONS
Activity 1:
Show PPT 2
Objective:
To understand DMAS
MATHEMATICS UNIT - 1
25
Description:
With the help of PPT 2 teacher would explain the concept of DMAS
rules. After showing the PPT the teacher can show the students
how to apply DMAS on few questions.
For example:
1.3 + 88 8 - 2
= 3 + 11 - 2 (divide first - D)
= 14 -2 (add next - A)
= 12 (subtract next - S)
2.6 + 2 x 90 6 (divide first - D)
= 6 + 2 x 15 (Multiply next - M)
= 6 + 30 (Add next - A)
= 36
Follow up:
Students are given few questions to work on DMAS.
CONTENT WORKSHEET C 5
Activity 2:
More on DMAS
Objective:
To understand the importance of DMAS and problem solving.
Pre Preparation:
Teacher will prepare a hand out of few problem stories.
Description:
Teacher will distribute hand out to the students.
Teacher will then encourage the students to solve each problem
using DMAS.
Follow up:
Teacher will check the students' work for concept, understanding
and accuracy.
CONTENT WORKSHEET C 5
26
Activity 3:
Remedial
Objective:
To get all the students of the class to the same level
Description:
Teacher needs to identify the area of weaknesses of his/her
students on the basis of content worksheet C 4.3 activity 2 .
MATHEMATICS UNIT - 1
Teacher will do the following to overcome the weaknesses:
1.Revision of the concepts done on previous day.
2.More similar worksheets depending on the need of the students can
be prepared by the teacher.
3.Advising the students to go through the resource links provided
and revise/practice.
Follow up:
Teacher will prepare worksheet to give it to the students as a
formative assessment
CONTENT WORKSHEET C 6
ESTIMATION AND ROUNDING OFF
Activity 1:
Video watch
Objective:
Understanding rounding off.
Description:
Teacher will make students Watch video clip 6 and video clip 7 to
understand the concept and importance of Estimation
Follow up:
Teacher will then give a class activity (guess the number) to the
students to reinforce the idea of estimation.
Teacher brings the jar filled with Macaroni/candies and asks students
to guess the number.
To make it more interesting teacher will extend the activity,
CONTENT WORKSHEET C 6
Activity 2:
Explore
Objective:
To appreciate estimation.
Pre Preparation:
Teacher will ask students to get cuttings from newspaper or some
magazines where some examples of estimations are given.
Description:
Teacher will discuss the examples brought by the students,
Teacher will also quote some examples where estimations are used
MATHEMATICS UNIT - 1
27
Examples
1. A hockey match between India and Pakistan ended in a draw. It
was watched by 51,000 spectators in the stadium and 40 million
television viewers world wide.
2. Approximately, 2000 people were killed and more than 50,000
injured in a cyclonic storm in coastal areas of India and
Bangladesh.
3. Over 13 million passengers are carried over 63,000 kilometer route
of railway track every day.
Can we say that the numbers quoted in these news items are exact?
Teacher then poses some questions to the students to understand
that the aboe quotes are just the estimations and can not be the
accurate figure.
For example, in (1), were there exactly 51,000 spectators in the
stadium? Or did exactly 40 million viewers watch the match on
television?
Follow up:
Rules of rounding off are recapitulated and a worksheet is given as a
recapitulation of the concept of estimation.
CONTENT WORKSHEET C 7
Roman numerals
Activity 1:
Follow weblink 2 and weblink 3
Objective:
To know the origin and need of Roman numbers.
Description:
Teacher will ask the student to explore the Roman numerals and
answer the questions that are given in the worksheet
Follow up:
Teacher will ask the students to make a scrap file.
Teacher will mark this as a project.
28
MATHEMATICS UNIT - 1
CONTENT WORKSHEET C 7
Activity 2:
Independent practice
Objective:
To test the understanding of Roman Numerals.
Pre Preparation:
Teacher will prepare the worksheet on Roman Numerals.
Description:
The teacher will give out the worksheet to all the students.
Teacher will then encourage the students to explore more about Roman
Numerals and complete the worksheet
Follow up:
Teacher will mark the worksheet to check the accuracy.
POST CONTENT WORKSHEET PS1
Objective:
To Practice the concepts learnt in the chapter in totality.
Pre Preparation:
Teacher will prepare comprehensive worksheets of the chapter.
Description:
Teacher will hand out the worksheets to the students.
Follow up:
Teacher will assess level of her students on the basis of the post content
worksheets PS1 and give remedial wherever required.
Note for the teacher:
1.
Students weak at the concepts must be given enough practice through the basic
worksheets and then post content worksheets may be given to them.
2.
Students who have grasped the concepts very well and are able to solve regular
problems quite easily may be advised to move to extension activities.
POST CONTENT WORKSHEET PS2
Objective:
To test the concepts learnt in the chapter in totality.
Pre Preparation:
Teacher will prepare the comprehensive worksheets of the chapter.
Description:
Teacher will hand out the worksheets to the students.
This will be a timed test given to the students.
Follow up:
Teacher will assess her students on the basis of the post content
worksheetPS2 as per the rubrics given.
MATHEMATICS UNIT - 1
29
SAMPLE RUBRIC (ASSESSMENT)
Working with numbers
Parameter
1
2
4
0 (LOWEST)
1
2
3
4 (HIGHEST)
No clarity in
Is able to put
Is able to put
Is able to put
Can write
more than
the periods
digits in the
digits in the
digits in the
numbers with
5digit numbers
and places
correct places
correct
correct
5 digits with
in the Indian
of the Indian
70% of times
places
system
place value
accurately,
of times
accurately,
accuracy,
system.
but is unable
accurately,
and is able to
independently
to write the
and is able
recall
and
from recall.
number
to write the
write
the
name,
number
number
independently
name,
name.
or using
referring to
Ability to
write
80%
places
90%
100%
manipulative.
the chart.
No clarity in
Is able to put
Is able to put
Is able to put
Can write
more than
the periods
digits in th
digits in the
digits in the
numbers with
5digit numbers
and places
correct places
correct
correct
5 digits with
in the
of the Indian
70% of times
places
International
place value
accurately,
of times
90% of times
accuracy,
system
system.
but is unable
accurately,
accurately,
independently
to write the
and is able
and is able to
from recall.
number
to write the
recall
and
name,
number
write
the
independently
name,
number
or using
referring to
name.
manipulative.
the chart.
Ability to
Ability to
write
order
e
80%
places
with
100%
Cannot
Can compare
Can
Can
Can
numbers
compare and
and order
compare
compare
with 100%
referring to
order
with 50%
order,
their place
accuracy but
with 80%
90%
with
values.
can not apply
accuracy,
accuracy,
reference to
the
concept
but
order,
with
order,
accuracy,
with
with
place value,
of place
reference to
reference to
and express it
value.
place value.
place
effectively.
value
and
communicate
the same
30
MATHEMATICS UNIT - 1
5
Ability to
Cannot
Can perform
Can perform
Can perform
Can perform
perform basic
perform
operations
operations
operations
operations
operations on
operations
with 5
with 7
with 90%
with 100%
large numbers
Not e
accuracy no
accuracy,
accuracy ,
accuracy ,
extending their
using a
idea about
can explain
and express
and express
knowledge of 4
manipulative.
how the
the concept
and explain
and explain
manipulative
using
with
with
is used.
manipulative.
manipulative
manipulative
ven
digit numbers.
6
Ability to
make
0%
0%
50%
70%
80%
90%
100%
reasonable
accuracy
accuracy with
accuracy
accuracy,
accuracy with
estimates and
with a hit and
a little
knows the
knows the
appropriate
compute
trial
guidance
rules but
rules and
use of
fluently and
approach.
regarding the
gets mixed
method,
method and
accurately.
No clarity on
rules.
up.
uses them
rule.
the rules
MATHEMATICS UNIT - 1
often.
31
WORKING WITH NUMBERS
CONTENT
Section 1 - Recall of Content Learnt Up to Class V
Counting Numbers
Numbers 1, 2, 3….., are called counting numbers. These numbers are also called
natural numbers.
Cardinal numbers
Numbers help us counting the objects. For example, 18 apples, 300 chains etc.
Numbers which show quantities are known as cardinal numbers.
Ordinal numbers
Numbers which tell the order of things in a group such as first, second, third etc., are
called ordinal numbers.
For example: l
Seema stood first in the race.
l
We will start the third chapter tomorrow.
l
India is the seventh largest country in the world.
Comparison of numbers
l
Given two numbers, one with more digits is the greater number.
Example 18930 > 7456
(5-digits)(4-digits)
l
If the number of digits in two given number is the same, the number which has a
greater leftmost digit is larger.
Example:
l
9051 > 8974
4-digits4-digits
If the leftmost digit happens to be the same, look at the next digit and so on.
Example:
l
8610 >8297
4-digits4-digits
First leftmost digit in both the numbers is the same i.e. 8. Second leftmost digit in 8610
is 6 which is larger than second leftmost digit in 8297 which is 2.
32
MATHEMATICS UNIT - 1
Formation of numbers from given digits
In forming number from given digits say 7, 8, 3, 5, the 4 digit greatest number using
the digits without repeating is 8753. We need to use all the four digits, keeping 8 as
the leftmost digit.
Without repetition of digits, the smallest number is 3578
Writing numbers in ascending/descending order
Let the numbers be 82, 4635, 930, 8000, 799, 8901
In ascending order: 82, 799, 930, 4635, 8000, 8901
In descending order: 8901, 8000, 4635, 930, 799, 82.
Place Value and Face Value of a digit in a number
In the number:
TH
H
T
O
5
3
9
3
For 3 at ones place - Place value is 3 face value is also 3
For 3 at hundreds place - Place value is 300 face value is 3
Section 2 - Introducing Large Numbers
When we add greatest one digit number to one, we get smallest two digit number.
The greatest one digit number 9 + 1 = 10, the smallest two digit number
The greatest two digit number 99 + 1 = 100, the smallest three digit number
The greatest three digit number 999 + 1 = 1000, the smallest four digit number
Similarly,
The greatest four digit number 9999 + 1 = 10000, the smallest five digit number
= 10 times one thousand
l
10000 is called ten thousand.
l
20000 is called twenty thousand.
l
30000 is called thirty thousand.
l
90000 is called ninety thousand
MATHEMATICS UNIT - 1
33
The greatest five digit number 99999 +1 = 100000, the smallest six digit number
100000 is called one lakh (in Indian system of numeration)
100000 is called 100 thousand or hundred thousand (International System of Numeration)
Ten hundred thousand = 1000000 = 1 million
10 million = 10000000
100 million = 10 times 10 millions = 10 x 10 millions = 100000000
1000000000 is called one billion
Section 3 - Reading and Writing large Numbers
Use of comas helps in reading and writing large numbers.
In International system of Numeration, commas are placed after every 3 digits starting
from right. The comas after 3 and 6 digits separate thousands and millions respectively.
Section 4 - Operation with large numbers
Use of four basic operations of addition (+), subtraction (-), multiplication (x) and division
(÷) as applicable to numbers up to 4 digits can be extended to large numbers also by
following the same algorithm.
5,892,310 + 603,982
=
5,892, 310
+ 603, 982
6,496,292
34
MATHEMATICS UNIT - 1
5,892,310 - 603,982
=
5,892,310
- 603,982
5,282,328
46932 x 125
=
46932
x 125
234660
938640
+ 4693200
5866500
Section 5 - Order of Operations
When a problem involves more than one operation we follow a rule called DMAS.
This rule states that
1.
To start with, perform all multiplications and divisions, working from left to right.
2.
Next, perform all additions and subtractions, working from left to right.
The result may vary if we follow a different rule than what is mentioned above.
According to DMAS,
1+9x3-6÷2
=1+9x3-3
= 1 + 27 - 3
= 28 - 3
= 25.
MATHEMATICS UNIT - 1
35
Section 6 - Estimation
There are a number of situations in which we do not need the exact quantity but need only a
reasonable guess or an estimate.
For rounding off a number, we have to locate the nearest place to which we need the
approximation. A number 3127 may be approximated to 3130, i.e., to the nearest ten, or
3100 i.e. to the nearest hundred. In this case, 27 is nearest to 30 (to the nearest ten) but not 20.
Similarly, 130 is nearest to 100 (to the nearest hundred) but not 200.
Generally, we see that the numbers 1, 2, 3, 4 are nearer to 0 than to 10. So, we round them off
as 0. Numbers 6, 7, 8, 9 are nearer to 10, so, we round them off as 10. But 5 is equidistant
from 0 and 10, and it is a common practice to round it off as 10. So, we round off 13 to 10, 15
to 20 and 17 to 20, correct to nearest tens.
Similarly, while rounding to the nearest hundred numbers 1 to 49 are closer to 0 than to
100, and so they are rounded off as 0. Numbers 51 to 99 are closer to 100 than to 0, and so
they are rounded off to 100, whereas 50 is equidistant from 0 to 100 both. So, by common
practice, it is rounded off as 100. Thus 437 is rounded off as 400, whereas 481 is rounded of
as 500, correct to nearest hundred.
In a similarly way 1 to 499 are rounded off as 0 and 500 to 1000 are rounded off as 1000,
correct to nearest thousand. Hence, 2482 is rounded off as 2000, where as 2506 is rounded
off as 3000 correct to nearest thousand.
So following the above rules, we can round off the given numbers to their nearest place,
according to our need.
e.g. 54,032 can be rounded off as 50,000 nearest to ten thousand and 8,386,589 can be
rounded off as 8,000,000 nearest to million
Estimating the outcome of number operations is useful in checking answers also.
Section 7 - Roman Numerals
Generally, we used Hindu-Arabic numeral system to represent a number. But Roman
numerals are also used in clocks or naming classes etc. For example we write Class IV for
Class 4 and so on.
Following list shows the numbers denoted by Roman numeral.
36
I
V
X
L
C
D
M
1
5
10
50
100
500
1000
MATHEMATICS UNIT - 1
The rules for the system are:
If a symbol is repeated, its value is added as many times a it occurs:
l
i.e. III is equal 3, XX is 20
A symbol is not repeated more than three times.
l
The symbols V, L and D are never repeated.
l
If a symbol of smaller value is written to the right of a symbol of greater value, its
value gets added to the value of greater symbol.
l
If a symbol of smaller value is written to the left of a symbol of greater value, its value
is subtracted from the value of the greater symbol.
l
IV = 5 - 1 = 4.IX = 10 - 1 = 9
XL = 50 - 10 = 40,XC = 100 - 10 = 90
The symbol V, L and D are never written to the left of a symbol of greater value, i.e., V,
L and D are never subtracted.
l
The symbol I can be subtracted from V and X only.
l
The symbol X can be subtracted from L, M and C only.
l
Following these rules, we get,
1
=
I
10
=
X
100
2
=
II
20
=
XX
and so on….
3
=
III
30
=
XXX
4
=
IV
40
=
XL
5
=
V
50
=
X
6
=
VI
60
=
LX
7
=
VII
70
=
LXX
8
=
VIII
80
=
LXXX
9
=
IX
90
=
XC
MATHEMATICS UNIT - 1
=
C
37
Section 8 - Solved Examples
Example 1 - Encircle the greatest number is each of the following
a)
589, 2053, 15925, 5925
b)
8093, 8903, 9803, 9308
Solution:
Example 2 - Encircle the smallest number is each of the following.
a)
632, 5957, 20991, 88
b)
7892, 2879, 7298, 2987
Solution:
Example 3 - Make the greatest the smallest 4-digit number using 2, 8, 9, 3 such that no
digit is repeated in a number.
Solution:
Greatest number = 9832
Smallest number = 2389
Example 4 - Make greatest and smallest 4-digit number by using 3, 5, 0. (Using any one
digit twice).
Solution:
Greatest number = 5530
Smallest number = 3005
38
MATHEMATICS UNIT - 1
Example 5 - Arrange each of the following in ascending order:
a)
532, 79, 10958, 3693
b)
18273, 12783, 13782, 28731
Solution:
a)
Ascending order:
79, 532, 3693, 10958
b)
Ascending order:
12783,
13782, 18273, 28731
Example 6 - Arrange each of the following in descending order:
a)
3251, 28, 10007, 30251, 351
b)
32890, 30892, 80932, 29803, 89032
Solution:
a)
Descending order:
30251,
b)
10007, 3251, 351, 28.
Descending order:
89032,
80932, 32890, 30892, 29803
Example 7 - Find the difference between place value and face value of 5 in the number
52083.
Solution:
Place value of 5 is 50,000
Face value of 5 is 5
Difference
=50,000 - 5 = 49,995
MATHEMATICS UNIT - 1
39
Example 8 - Find place value of 6 in the following numbers: 76581, 68591, 85961, 18956
Solution:
Place value of 6 in
76581 is 6000
68591 is 60000
85961 is 60
18956 is 5
Example 9 - Complete the following table.
Solution:
Example 10 - In a factory, number of bicycles manufactured in 2009, was 743,000. In 2010,
factory manufactures 800100 bicycles. How many more bicycles were manufactured in
2010?
Solution:
Bicycles manufactured in 2010 = 800100
Bicycles manufactured in 2009 = 743000
So 800100
-
743000
57100
40
more bicycles were manufactured in 2010.
MATHEMATICS UNIT - 1
Example 11 - The town newspaper is published every day. One copy has 12 pages.
Everyday 6,809,501 copies are printed. How many total pages are printed every day?
Solution:
Each copy has 12 pages.
So 6,809,501 copies have 6,809,501 x 12 pages
Now
6809501
x 12
13619002
+ 68095010
81,714,012
So, everyday 81,714,012 pages are printed.
Example 12 - A newspaper company publish a newspaper with 18 pages. If company
prints 633,726 pages in a day than how many copies of newspaper is published
everyday.
Solution:
Number of pages printed every day = 633,726
Number of pages of a newspaper = 18
So the number of copies of the newspaper published everyday is 633,726 ÷ 18
Now
MATHEMATICS UNIT - 1
41
So, everyday 35207 newspapers are published.
Example 13 - Find
a)
3 + 88 ÷ 8 -2
b)
6 + 2 x 90 ÷ 6
Solution :
a)
3 + 88 ÷ 2
= 3 + 11 - 2
= 14 - 2
= 12
b)
6 + 2 x 90 ÷ 6
= 6 + 2 x 15
= 6 + 30 = 36
Example 14 - Round off the given numbers as stated below
Given numberApproximate to Nearest
I)
89359
Tens
ii)
75083
Hundreds
iii)
62594
Thousands
iv)
93980
Ten thousands
i)
89359
to nearest tens is 89360
ii)
75083
to nearest hundreds is 75100
iii)
62594
to nearest thousands is 63000
iv)
93980
to nearest ten thousands is 90000
Solution:
Example 15 - Write the Roman numerals for 73 and 96
Solution:
Roman numeral for 73 = LXXIII
Roman numeral for 46 = XLVI
42
MATHEMATICS UNIT - 1
STUDENTS’
SUPPORT
MATERIALS
MATHEMATICS UNIT - 1
STUDENT'S WORKSHEET - 1
WARM UP ACTIVITY W1
Name of the student ______________________
Date ___________
Activity 1- Importance of Mathematics
Where do you see mathematics in nature? Also paste pictures for evidences.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
How do you think mathematics is important for you? Explain.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
What did you like in video clip 1 and why?
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
44
MATHEMATICS UNIT - 1
STUDENT'S WORKSHEET - 2
WARM UP ACTIVITY W1
Name of the student ______________________Date ______
Activity 2 - Word Puzzle
Search Mathematical words in the grid below.
(you may use a math dictionary available online)
D
M
A
S
Q
M
A
P
C
E
R
T
U
M
E
Q
U
I
V
A
L
E
N
T
P
O
L
U
C
U
N
U
M
B
E
R
S
H
I
L
L
L
I
O
I
C
W
A
R
R
N
I
G
T
O
T
M
T
T
O
E
C
M
P
G
R
O
U
P
I
MATHEMATICS UNIT - 1
A
I
D
N
E
U
K
L
M
D
N
O
P
P
L
E
I
S
R
S
U
C
C
E
S
O
R
L
C
N
V
E
Y
Y
O
A
D
D
P
P
O
Y
A
T
I
C
B
O
R
R
O
W
L
R
U
E
R
H
D
U
A
R
M
R
P
T
A
O
N
N
D
I
E
T
S
D
O
Y
O
R
C
D
D
E
I
I
I
E
I
N
O
R
W
E
U
I
E
N
F
I
V
E
N
E
E
U
T
O
C
N
V
A
A
S
E
T
A
Y
R
T
R
O
T
G
R
L
V
A
I
L
L
D
I
V
I
S
O
R
E
45