CBSE-i

V
CLASS
UNIT-6
Shelter and
Community
Mathematics
Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India
V
CLASS
UNIT-6
Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India
CBSE-i
Shelter and
Community
Mathematics
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 may be taken are duly mentioned. In
case any thing 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.
Education plays the most important role in acquiring professional and social skills, and a positive attitude towards face the
challenges of life. Curriculum is a comprehensive plan of any educational programme. It is also one of the means for bringing
about qualitative improvement in an educational system. The Curriculum initiated by the Central Board of Secondary
Education-International (CBSE-i) is a progressive step in making the educational content responsive to 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 CBSE has introduced the CBSE-i curriculum as a pilot project in a few schools outside India in 2010, in classes I and IX and
extended the programme to classes II, VI and X in the session 2011-12. It was further extended to classes III, VII and for Senior
Secondary classes with class XI in the session 2012-13. It is going to be introduced in classes IV, V, VIII and XII in the session
2013-14 in the schools outside India and in classes I, II and III in the schools within the country.
The Senior Secondary stage of education determines the course of life of a student. At this stage, it becomes extremely important
for students to develop the right attitude, a willingness to learn and an understanding of the world around them and to be able to
take the right decisions for their future. The senior secondary curriculum is expected to provide the necessary base for the
growth of knowledge and skills, and thereby enhance a student's potential to face the challenges of global competitiveness. The
CBSE-i Senior Secondary Curriculum aims at developing the desired professional, managerial and communication skills as
required in of the world of work. CBSE-i is for the current session offering curricula in ten subjects i.e. Physics Chemistry,
Biology, Accountancy, Business-Studies, Economics, Engineering Graphics, Home Science, Computer Science, Information
Practices, ICT, English, Mathematics I and Mathematics II. Mathematics at two levels caters to the differing needs of students of
pure sciences and commerce. The curriculum has been designed to nurture multiple intelligences like linguistic or verbal
intelligence, logical mathematical intelligence, spatial intelligence, sports intelligence, musical intelligence, inter-personal
intelligence and intra-personalintelligence.
The Core skills are the most significant aspects of a learner's holistic growth and learning curve. The objective of this part of the
core of curriculum is to scaffold the learning experiences and to relate tacit knowledge with formal knowledge. This involves
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 CBSE-i Curriculum evolves by 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
practising teachers become skil ful and lifelong learners and also transfer their learning experiences to their peers through the
interactive platforms provided by the Board. The success of this curriculum depends upon its effective implementation and it is
expected that the teachers will apply themselves to creating better facilities, developing linkages with the world of work and
fostering conducive environment, as per the recommendations of the curriculum document.
I appreciate the effort of Dr. Sadhana Parashar, Director (Academics, Research, Training and Innovation), CBSE, and her team
involved in the development of this document. I specially appreciate the efforts of (Late) Dr. Srijata Das for working tirelessly
towards meeting deadlines.
The CBSE-i website enables all stakeholders to participate in this initiative through the discussion forums. Any further
suggestions on improving the portal are always welcome.
Vineet Joshi
Chairman, CBSE
Preface
Acknowledgement
Chief Co-ordinator: Ms. Kshipra Verma, EO
Co-ordinators :
Material Production Groups: Class V
Advisory
Shri Vineet Joshi, Chairman, CBSE
Dr. Sadhana Parashar, Director
(Academics, Research, Training and Innovation), CBSE
Conceptual Framework
Shri G. Balasubramanian, Former Director (Acad), CBSE
Ms. Abha Adams, Consultant, Step-by-Step School, Noida
Dr. Sadhana Parashar, Director
(Academics, Research, Training and Innovation), CBSE
Ideators: Classes I-V
Dr. Indu Khetarpal
Sh. Akshay Kumar Dixit
Ms. Soumya Gulati
Ms. Anita Makkar
Dr. Om Vikas
Ms. Rupa Chakravorty
Dr. Rajesh Hassija
English:
Hindi:
Ms. Anjali Nagpal
Ms. Deb Rani Chakravorty
Ms. Payal Uppal
Ms. Sunita Yadav
Ms. Shivali Joshi
Ms. Usha Bhajan
Ms. Poonam Bharij
Gen Science:
Dr. Alka Saxena
Ms. Meenakshi Malhotra
Ms. Sapna Sinha
Mr. Parmanand Chaudhary
Ms. Anshuka Aneja
Ms. Pooja Nasa
Ms. Shilpi Rana
Performing and
Visual Arts:
Mathematics:
ICT:
Social Studies:
Ms. Purvi Srivastava
Ms. RituArora
Ms. Swati Panhani
Ms. Chanchal Chandna
Ms. Shally Arora

Ms. Dipti Chandak
Ms. Rachna Sharma
Ms. Rita Bhandari
Core-SEWA:
Ms. Kshipra Verma
Ms. Kalpana Kapoor
(Late) Dr. Srijata Das, EO
Mr. Sanjay Sachdeva,
Desk Officer
Mr. Navin Maini, RO (Tech) Ms. Neha Sharma,
Deputy Director
Shri Al Hilal Ahmed,
Assistant Professor / Deputy
Director
Preface
Acknowledgment
Essential Components of Unit 6 1
Syllabus Matrix 4
Introduction 5
Teachers Notes 6
Lesson Plan A 17
Lesson Plan B 26
Lesson Plan C 39
Assessment Rubrics 54
Teachers Resource Material 56
Students Manual 149
Time Frame 162
Contents
1
ESSENTIAL COMPONENTS OF UNIT 6
SHELTER AND COMMUNITY
CLASS V
This Unit has been designed around the theme Shelter and Community.
The spirit of NCF 2005 is clearly visible in the Unit.
Some unique features have been carefully incorporated and crafted into the Unit.
1. Format :
Adhered to as per the guidelines of CBSE-i.
Sufficient scope for taking the unit through different levels of mental
complexity (Blooms Taxonomy).
Learning Objectives: activities to meet the objectives and subsequently the
Learning Objectives have been carefully mapped.
Assessments for teacher and taught have been integrated into the lesson
An effort has been made to bring about a clarity of instructions for the
teacher and the taught.
A special Students Manual has been created for the students to help them
understand the content of each unit.
Time Frame for each sub topic kept in mind.
Fun at Home concept for each subject to reinforce the concepts.
Attempt made not to dilute the conceptual learning.
Visual appeal kept in mind.
2. Curriculum Transaction:
Student centric activities.
Clarity of instructions.
2
Activities focusing on Skill Building and emphasizing on Blooms
Taxonomy.
Integration of components of Multiple Intelligences and Dimensions of
Learning.
Elements of components of Multiple Intelligences and Dimensions of
Learning.
Elements of Life Skills, Health, Values, ICT also incorporated into the lesson
plan.
Focus on experimental, exploration, investigation and learning by doing
approach.
Correlation of activities with real life.
An assured outcome to every activity.
Interesting elements - My Portfolio has been incorporated in this unit
wherein students will compile their entire work in their Portfolio and the
progression of a childs learning can be viewed. Since students learn best
through hands on learning, a number of concepts have been taken up
through various activities which would be showcased in their Portfolio.
Comic Strips, dialogue writing, poems using similes and metaphors, letter
writing, Radio Show, Passages for Comprehension, Manipulative strategies
in Math, Case Studies, Power Point Presentations, Research, Community
Tree, Adoption of Monuments and Appreciation of Heritage, Map Work,
Working Models, Investigations, Integration of Values etc bring alive the
concept of learning is fun.
Checking for understanding at the end of each sub topic.
Reflection Time for students to understand where they are on their
developmental continuum
Flexibility to the teacher/facilitator as to when to take up Formative
Assessment.
3
3. Worksheets:
Mapped with the activity.
Elements of Blooms Taxonomy incorporated.
Statements related to real life or concept statements have been incorporated
in the worksheets from time to time.
Reinforcement sheets available.
Emoticons at the end of worksheets for the learners self assessment.
Element of Reflection Time by the learner to assess his/her own learning.
The Reflection Time worksheet to assist the teacher/facilitator in making
accommodations in her teaching styles to suit the learning styles of the
students.

4
Syllabus Matrix










English





Science


Mathematics

Social Science



Visual Arts/Performing Arts



Physical Education




- Direct and Indirect speech
- Similes and Metaphors
- Interview
- Recount (biography)
-Letter Writing
-
-
- Ant or bee colony and their
life cycle
-Rearing of important insects-
apiculture and sericulture
- Communicable diseases,
Understand the ways to care
for environment
-Reports on weather data,
Natural Disasters
Fractional Numbers:
- Multiplication and Division
- Word Problems
Decimals
- Basic operations
addition/subtraction/multipli
cation/division and word
problems
-Variation of shelter
-Need of society
-Important heritage Monuments
and their historical background
-Seven Wonders of the World
-Mapping and sketching
-Displacement, demolition and
reconstruction
-Perspective distance and over
lapping
- Poster making-depicting the
qualities of famous
monuments
-snow in the desert from ants
view point


5
CLASS : V
UNIT : 6
Subjects : Maths
Introduction:
At class IV level the students are already familiar with fractional numbers and the
process of addition and subtraction of fractional numbers. In this unit students will
understand the process of multiplication and division of fractions. Students are already
familiar with term decimal and are aware of the equivalence between the decimal and
fraction forms of tenths and hundredths. The present unit moves ahead and reinforces
the understanding of decimals. Students will be able to understand the importance of
decimal point and will be able to perform mathematical operations of addition,
subtraction, multiplication and division using decimals. This lesson will help students
understand the role of the decimal and the relationship of decimals with money.
Teacher will reinforce how important mathematics can be to the real world and
decimals are a part of this system.
The content is student centered and activity based laying the utmost emphasis on
developing problem solving skills, encouraging the child to think creatively and
independently. This is a hands-on, minds-on mathematics topic that engages students
to develop manipulative and strategic learning and co-relate the concept with real life
situation.

6
Teachers Note:
The unit satisfies the inquisitiveness of the students in knowing more about fractions.
Students learn more through activities. The format of the lesson has been designed
keeping this characteristic in mind. Each lesson includes certain activities which will
help the students in self-learning and understanding of the concepts.
Students build their own mathematical understanding by interacting with the world
around them through a range of learning experiences using real life contexts to explore
mathematical concepts. To develop a rich conceptual understanding of mathematical
ideas, students need to learn the concept with great thoroughness and clarity and this
can be achieved using different teaching strategies and tools in the form of activities to
reflect their learning. To assist the teacher, the unit is equipped with resource material
and activities to cater to the different needs of the students. The unit is supported with
worksheets to reinforce the learning.
A portfolio is a purposeful collection of student work that exhibits the student's efforts,
progress and achievements in one or more areas of the curriculum.
In this Unit, students will develop their Mathematics Portfolio. The entire learning of
the Expected Outcomes will be reflected in the Portfolio. The instructions for compiling
the portfolio have been given at the end of the last lesson plan.
Critical thinking, Life Skills, Fun at home and SEWA have been incorporated while
constructing the unit .The assessment rubrics have been designed to help the facilitator
in assessing the understanding of the students and ensure that learning takes place in a
desired way.
General Objectives:
The students will be able to
make and investigate mathematical conjectures
analyze and evaluate the mathematical thinking and strategies
develop manipulative and strategic learning
co-relate the concept with real life situation
apply their knowledge to solve the given problems
7
Specific Objectives:
The students will be able to:
multiply a whole number with a fractional number
multiply a fractional number with a fractional number
understand the reciprocal of a fractional number
divide the fractional numbers
explore decimal place value
read and write decimals
compute addition of decimals
compute subtraction of decimals
use decimals in money
multiply a decimal number with a decimal number
divide the decimal numbers
apply the operations of multiplication and division in solving real life situations
correlate and apply decimals in real life situations.
Topic: A) Multiplication and Division of
Fractional Numbers
Duration: 2 hrs. 55 min.
Skill Activity Multiple Intelligences
Incorporated
Observation
and Identification
Lets Revise
Students will be able to
observe and identify
fractions around them in
a house
Repeated Additions
Students will be able to
identify numerator and
Interpersonal and
Intrapersonal
8
denominator for a
fraction and multiply
accordingly
Paper Pizza
Students will be able to
identify numerator and
denominator for a
fraction and multiply
accordingly
Matching and Dividing
Students will be able to
identify numerator and
denominator for the
given fraction and
divide fractions
Conceptual Learning Lets Revise
Students will be able to
add and subtract
fractions
Repeated Additions
Students will be able to
understand
multiplication of a
whole number with a
fractional number
Paper Pizza
Students will
understand
multiplication of a
fractional number with a
fractional number
Matching and Dividing
Kinesthetic and Logical
9
Students will
understand the
reciprocal of the fraction
and be able to divide
fractions
Logical Thinking Repeated Additions
Through hands-on
activity students will be
able to multiply a whole
number with a fractional
number
Paper Pizza
Students will be able to
multiply a fractional
number with a fractional
number
Matching and Dividing
Students will
understand the
reciprocal of the fraction
and be able to divide
fractions
Logical, Interpersonal,
Intrapersonal and Spatial
Application Repeated Additions
Students will be able to
compute and apply the
process in solving real
life problems
Paper Pizza
Students will be able to
compute and apply the
process in solving real
life problems
Interpersonal, Kinesthetic,
Intrapersonal and Spatial
10
Matching and Dividing
Students will be able to
compute and apply the
process in solving real
life problems

Learning Outcomes
The students will now be able to:
operate the whole number with a fractional number using the process of
multiplication
demonstrate the ability to multiply one fractional number with another fractional
number
understand the reciprocal of a fractional number
demonstrate the ability to divide one fractional number with another fractional
number

11
Topic: B) Decimals: Addition and Subtraction Duration: 2 hrs. 55 min.
Skill Activity Multiple Intelligences
Incorporated
Observation and
Identification
Lets Rewind
Students will be able to observe
fraction and convert it into decimal
number
Human Decimal Machine and
Decimal War
Students will be able to identify the
decimal according to place value
chart and hence arrange them in
increasing or decreasing order

Fun with Colours
Students will be able to observe the
process of addition of decimals

Colouring Effect
Students will observe the decimals
and arrange them accordingly for
subtraction

Lets Join Hands
Students will be able to observe and
identify decimals in cost of objects
around them and in usage money
Interpersonal and
Intrapersonal
12
Conceptual
Learning
Lets Rewind
Students will be able to correlate
fractions and decimals
Human Decimal Machine and
Decimal War
Students will be able to understand
the decimal according to place value
chart and also arrange it in increasing
or decreasing order

Fun with Colours
Students will understand and
compute the answer by addition of
decimals

Colouring Effect
Students will understand subtraction
of decimal numbers
Kinesthetic and Logical
Logical
Thinking
Lets Rewind
Students will be able to correlate
fractions and decimals
Human Decimal Machine and
Decimal War
Students will be able to form the
decimal according to place value
chart and also arrange it in
increasing or decreasing order
Fun with Colours
Students will understand and
Logical, Interpersonal
and Intrapersonal
13
compute the answer by addition of
decimals

Colouring Effect
Students will understand and
compute the value by subtraction of
decimal numbers
Application Lets Join Hands
Students will be able to apply the
concept of decimals in solving real
life problems
Interpersonal,
Kinesthetic and Spatial

Learning Outcomes:
The students will now be able to:
explore decimal place value
read and write decimals
compute addition of decimals
compute subtraction of decimals
use decimals in money
develop empathy and compassion for disaster victims








14

Topic: C) Topic: Multiplication and Division of
Decimal Numbers
Duration: 2 hrs. 55 min.

Skill Activity Multiple Intelligences
Incorporated
Observation and
Identification
Merging Multiples
Students will observe the decimal
number and identify the number of
places after the decimal
Interpersonal and
Intrapersonal
Conceptual
Learning
Merging Multiples
Students will understand the process
of multiplication of decimals

Dividing Equally
Students will understand the process
of division of decimals
Kinesthetic and Logical
Logical
Thinking
Merging Multiples
Students will be able to compute the
value by the process of multiplication

Dividing Equally
Students will be able to compute the
value by the process of division

No Time
Students will be able to logically
apply the concept and solve the
problems in given time
Logical, Interpersonal
and Intrapersonal
15
Application Merging Multiples
Students will be able to apply the
process of multiplication in solving
real life problems

Dividing Equally
Students will be able to apply the
process of division in solving real life
problems

No Time
Students will be able to apply the
concept and solve the problems in
given time

Interpersonal,
Kinesthetic and Spatial

Learning Outcomes:
The students will now be able to:
operate a decimal number with a decimal number by the process of multiplication
demonstrate the ability to divide the decimal numbers
apply the operations of multiplication and division in solving real life situations

Material Required: Colour Pencils Or Oil Pastels Or Water Colours, A4 Size Coloured
Pastel Sheet, Scissors, Glue, A4 sheets, equation slips, Base 10 models, 3 strips, Flash
cards (digits 0 9 and decimal point), square ruled sheet of dimension 10 cm x10cm (10-
by- 10 grid), bowl, String/ribbon and Handout 1, 2, 3, 4, 5 and 6 (Teachers Resource
Material).

16
Trans Disciplinary Activities
Subject Activity
Social Science Lets Join Hands, Lets Revise
Visual Arts Mathemingle, Lets Revise

Critical Thinking:
Refer to activities : Repeated Addition, Paper Pizza, Human Decimal Machine and
Decimal War, No Time
Life Skills / SEWA:
Self Awareness Lets Revise, Lets Join Hands
Creative Thinking/ Goal Setting Mathemingle, Lets Revise
Interpersonal Lets Join Hands
Critical Thinking - Repeated Addition, Paper Pizza, Human Decimal Machine and
Decimal War, No Time
Decision Making- Lets Join Hands, No Time
Problem Solving Repeated Addition, Paper Pizza, Human Decimal Machine and
Decimal War, No Time
SEWA-
Suggested Activities:
Plan a lunch for children in your neighborhood who do not have enough to eat.
Prepare a mini budget for 10 children together with your parents and execute the
same.
Divide the class into groups and each group may be given the task of either
adopting a tree, or an animal or giving time to seniors in old age homes etc.
Students may be asked to prepare a proposal for the same and execute it after
prior approvals from school and family.
17
Lesson Plan A

Topic: Multiplication and Division of Fractional Numbers
Duration: 2 hrs. 55 min.
Brief Description: The students are already familiar with fractional numbers and the
process of addition and subtraction of fractional numbers. In this lesson students will
understand the process of multiplication and division of fractions. They will also be
able to define the reciprocal of a fractional number.
The outcome of all the activities in all the Lesson Plans will culminate in My
Portfolio prepared by each student.
Learning Objectives: The students will be able to
operate the whole number with a fractional number using the process of
multiplication
demonstrate the ability to multiply one fractional number with another fractional
number
understand the reciprocal of a fractional number
demonstrate the ability to divide one fractional number with another fractional
number
Material Required:
Activity 1 : Mathemingle
Colour Pencils or Oil Pastels or Water Colours, A4 Size Coloured Pastel Sheet, Scissors,
Glue
Activity 2 : Let Revise
Colour Pencils or Oil Pastels or Water Colours, A4 Size Coloured Pastel Sheet, Scissors,
Glue, Worksheet 2
Activity 3 : Repeated Additions
A4 sheet, A4 coloured sheets, equation slips and colours
18
Activity 4 : Paper Pizza
A4 sheet, A4 colored sheets, equation slips and colours
Activity 5 : Matching and Dividing
Handout 1 (Teachers Resource Material), rectangular strips ( 1 x 10 cm), A4 sheet
Activity 1 : Mathemingle

The teacher will ask the students to design the cover page of the Mathematics
Portfolio - Mathemingle.
The teacher will distribute Worksheet 1 to the students for designing the cover
page.
The students will draw pictures related to Mathematics (Puzzles, mathematical
signs, famous mathematicians etc) in the given space and also colour it using
colour pencils or oil pastels or water colours.
The teacher will ask the students to cut Worksheet 1 along the coloured border
and paste this sheet on an A4 size coloured pastel sheet.
(Refer to Worksheet 1)
Activity 2 : Lets Revise
Students will sit in groups.
Each student will be given Worksheet 2.
Students within the group will discuss the given layout in Part A Worksheet 2 and
answer the related questions.
The students will then sketch and represent the layout of their house on Part B of
Worksheet 2
The students will put Worksheet 2 and 3 after the cover page in My Portfolio.
(Refer to Worksheets 2, 3)

19
Activity 3 : Repeated Addition
Students will work in pairs.
Each pair will be provided with an A4 sheet and an A4 size colored paper.
Students will be given the following question to solve.



Lets take the example of: - 5/8 x 4
Students will be told that this equation means - five eighths, four times.
Teacher will then give the following instructions:
Look at the question and read it carefully.
Take the colored A4 sheet. Cut 4 circles of radius 7cm each.
Divide each circle into 8 equal parts.
Cut 5/8 parts from each circle.
Colour 5/8 part of each circle in different colours.
Step 1







I II III IV
Step 2







5/12 x 6 5/8 x 4



7
cm
cmc
m



7
cm
cmc
m



7
cm
cmc
m



7
cm
cmc
m
20
Step 3



Arrange the four sets in such a way that they form a circle and paste them on the
space provided on Worksheet 4 (Part A).

Step 4


=

Teacher will then conclude that multiplication is a repeated addition.
Hence (5/8) x 4 = 5/8 + 5/8 + 5/8 + 5/8 =
Teachers Note: Teacher will then state the steps of multiplication to the students and
can further demonstrate over the interactive board:
Step 1: Write the whole number as a fraction.
Step 2: Multiply the numerators and the denominators.
Step 3: Reduce to the lowest terms


OR
20 10 = 10 = 5
8 4 2 2
21
Note : Students will demonstrate both the methods on Worksheet 4.
Checking for understanding : Each pair can then be given another question to solve
through activity and mathematical method.
Question: (5/12) x 6
The students will attempt Worksheets 4, 5 and 6 and place them after Worksheet 3 in
My Portfolio.
(Refer to Worksheets 4, 5, 6)

Activity 4 : Paper Pizza
Students will work in pairs.
Each student will be provided with Worksheet 7 and A4 size colored paper.
Students will be asked to make a circle of 6 cm radius.
Students will decorate the circle as a paper pizza.
Students will further divide the circle into 10 equal parts.




Pairs will be given a question to solve: 1/3 x 9/10
Teachers Note: Teacher will inform the students that they have to find 1/3 rd of
9/10.
Students will then take 9 parts out of the 10 equal parts.



22
Students will further be asked to divide 9 equal parts into 3 shares of equal size.



Each share can be reflected as 3/10.
Students will then write the question on the Worksheet 7 and paste the equal
shares in the provided space.

Teachers Note: Teacher will further explain the process over the interactive board:

Students will understand and copy the mathematical representation on Worksheet 7.
Students will be given another example to solve on an A4 sheet.
Question to solve: x 8/10
(For Teachers Reference)





The students will put Worksheet 7 and 8 after Worksheet 6 in My Portfolio.
(Refer Worksheets 7, 8)

23
Activity 5 : Matching and Dividing
Students will form pairs.
Each pair will be given two colored stips of equal length ( 1 x 10 cm).
They will also be given Worksheet 9.
Students will be given the following question to solve - 2/3 1/6
Teacher will then give the following instructions:
Divide a strip into 3 equal parts.

Shade 2 parts of the strip to get 2/3.
1/3 1/3
Refold the strip and divide it into 6 equal parts.
Open the strip.
How many parts are shaded? ( Expected Answer : 4)

Teacher will then conclude that: 2/3 rd part when divided into 1/6

parts give 4 equal
parts.
2/3 1/6 = 4
Students will then paste their strip on Worksheet 9 in the space provided.
Students will also give mathematical solution to the question on Worksheet 9.
Teachers Note: Teacher will further inform the steps of division on the
Interactive board. Handout 1 (Teachers Resource Material) will then be
distributed to explain the methods of division of fractional numbers. Students
will go through the Handout 1 and observe the process of division.Teacher will
further take up few examples on the interactive board to reinforce the methods.
The students will put Worksheet 9, 10 and 11 after Worksheet 8 in My Portfolio.
(Refer Worksheets 9, 10 and 11)
24
Activity 6 : Reflection Time
In this activity the student will reflect upon his/her comprehension of the various
concepts. The teacher will use it as a formative assessment tool to identify the areas
easily comprehended by the learner and the concepts which proved to be difficult and
need reinforcement. This will also help the teacher to make necessary accommodation
in her teaching style to suit the learning styles of the learner.
My Learnings Areas
Have understood and ready to go
ahead

Oops! A few speed breakers ahead
Help ! Help! Help!!!!
(Refer Worksheet 12)
Review
The teacher will recapitulate the concepts:















Fractions Multiplication and
Division of Fractional Numbers

Multiplication of a whole number
with a fractional number.
Step 1: Write the whole number as a
fraction.
Step 2: Multiply the numerators and
the denominators.
Step 3: Reduce to the lowest terms
(3/7) x 21 = = = = 9


Multiplication of a fractional
number with a fractional number.
1/6 x 2/3 = =
25

























(Refer Worksheet 13)

Assessment
i) Assessment will be based on learning objectives :
operating the whole number with a fractional number using the process of
multiplication
demonstrating the ability to multiply one fractional number with another
fractional number
understanding the reciprocal of a fractional number
demonstrating the ability to divide one fractional number with another
fractional number
ii) Worksheets / students response / group work/ activities (Lets Revise, Repeated
Additions, Paper Pizza) may be used for formative and summative assessment.

Division of fractions
Reciprocal of A Number: Two numbers are said to be
reciprocal of each other if their product is 1. For Example:
The reciprocal of is
Divide: 1/8
x 8 = = 4
Step 1: Turn the second fraction (the one you want to
divide by) upside down.
Step 2: Multiply the first fraction by that reciprocal.
Step 3: Simplify the fraction if needed.

26
Lesson Plan B
Topic: Decimals- Addition and Subtraction
Duration: 2 hrs. 55 min.
Brief Description: Students are already familiar with the term decimal. In this lesson
the activities will reinforce and enrich the understanding of decimals .Students will be
able to understand the importance of a decimal point. Students will be able to add and
subtract decimals .This lesson will help students understand the role of the decimal and
the relationship of decimals with money.
Learning Objectives: The students will be able to
explore decimal place value
read and write decimals
compute addition of decimals
compute subtraction of decimals
use decimals in money
develop empathy and compassion for disaster victims
Material Required:
Activity 1 : Lets Rewind
A4 sheet, Base 10 models, 3 strips, colours, Handout 2 (Teacher Resource Material)
Activity 2 : Human Decimal Machine and Decimal War
Flash cards (digits 0 9 and decimal point), pencil colours
Activity 3 : Fun with Colours
Handout 3 (Teacher Resource Material), square ruled sheet of dimension 10 cm x10 cm
(10 -by- 10 grid), A4 sheet, pencil colours


27
Activity 4 : Colouring Effect
Handout 4 (Teacher Resource Material), question slip, bowl, 10 cm x10 cm (10 -by- 10
grid).
A4 sheet, pencil colours.
Activity 5 : Lets Join Hands
Activity 1
Lets Rewind
Teacher puts the following question to the students for the introduction of the
concept.
Question: Where can we find decimal numbers outside the class?
Expected Answer: Bills, money, weights, measurements, medicine and any other
relevant answer.
Teacher will distribute one A4 sheet to each child and the Base 10 models and 5
strips each to the students
Teacher will ask the students to label each section of the strip as 1/10.
1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10
Teacher will ask the students to colour 3 parts of the strips or 3/10 of the strip as
shown.
1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10
Teacher will ask the students what fraction of the rectangle has been coloured?
Expected Answer : 1/10 + 1/10 + 1/10
Or
3/10
28
Teacher will make the students understand that since fractions and decimals
represent a part of the whole, they can represent the same amount and further
explain that 3/10 can be written in another way... i.e. 0.3
Teachers Note: The teacher will write 7/10 on the Interactive board and ask the
following questions :
Is 7 /10 a fraction or a whole number?
Expected Answer : Fraction
How will you represent 7/10 as decimal?
Expected Answer : 0.7
What is the position of the whole number when you write a number with a
decimal?
Expected Answer : Left of the decimal point
When we write 0 before the decimal point what does this represent?
Expected Answer : The whole number is less than 1
How will you write 0.7 in words?
Expected Answer : seven tenths
Students would be given Handout 2 available in Teacher Resource Material.
They will be asked to go through the Handout 2 and then attempt Worksheet 2
and 3.
Worksheet 1 may be placed as a separator for the next topic in the Portfolio.

29
Handout 2
(Teacher Resource Material)
Let's examine these decimals in our place-value chart
PLACE VALUE AND DECIMALS







D
e
c
i
m
a
l

1/10

1/100

1/1000








In Words (while
Reading)







In Words (while Writing)

3 . 2 4 Three point two four Three and twenty four hundredths

3 . 0 7 2 Three point zero seven
two
Three and seventy two thousandths

3 7 . 0 2 Thirty seven point zero
two
Thirty seven and two hundredths

3 2 7 . 4 Three hundred twenty
seven point four
Three hundred twenty seven and four
tenths
As we move left, each position is 10 times bigger and as we move right, each
position is 10 times smaller
3.24 = (3 x 1) + (2 x ) + (4 x 1/ 100)
3.072 = (3 x 1) + (0 x 1/10) + (7 x 1/100) + (2 x 1/1000)
37.02 = (3 x10) + (7 x 1) + (0 x 1/10) + (2 x 1/100)
327.4 = (3 x 100) + (2 x 10) + (7 x 1) + (4 x 1/10)

30
Checking For Understanding :
Write in decimal form and expanded form:
Decimal form Nine point zero eight nine = 9.089
Expanded form : 9 + 0 x + 8 x + 9 x
Teachers Note: The teacher may use Worksheet 1 as a separator page for Lesson Plan
B.
The students will put Worksheet 2 and 3 after the Worksheet 1.
(Refer to Worksheets 1, 2 and 3)
Activity 2 : Human Decimal Machine and Decimal War
Teacher asks for 11 volunteers from the class.
The teacher will then hand over one blank flash card randomly to each student.
The teacher will ask 10 students to write any one digit between 0 and 9 on their
flash card and one student will make a decimal point/dot on his/her flash card.
Then the teacher will call out a decimal number and tell the students to arrange
themselves in the correct order. For example, form a number with 4 at tens place,1
at ones place, 5 at tenths place and 8 at hundredths place (41.58) and the five
students holding those symbols would have to arrange themselves in that order.
If the students do so correctly, the teacher can have the rest of the class applaud
and then have those students hand their cards to next group in the classroom that
has not yet been part of the human decimal machine.
After the game is over teacher can ask the students to sit in pairs.
Each pair will then prepare their own 12 flash cards ( from numbers 0 to 9 and two
decimal cards).
Teacher will instruct the players to hold the cards face down in a stack on the table
and place the decimal point flash cards on the top.
31
Both the players count to three and form a decimal number using those cards.
The player that lays the greatest decimal number wins the game.
Checking For Understanding:
Teacher will write the following decimal number on the interactive board.
Students are asked to arrange them in ascending order.
Question: 0.324, 0.342, 0.243, 0.234, 0.432, 0.423
Expected Answer:
The students will put Worksheet 4 after Worksheet 3.
(Refer to Worksheet 4)
Activity 3 : Fun with Colours
Teacher will distribute Worksheet 5 to each student.
Students will observe Worksheet 5 part A provided with 10 by 10 grids.
Teacher will remind the students that one grid represents 1 whole that has been
divided into 100 equal parts.
Teacher will ask the students to colour 70 squares out of 100 with red colour to
represent 0.7 as shown








Teacher will now ask students to colour 20 squares out of 30 remaining squares
with yellow colour to represent 0.20 as shown










0.234 < 0.243 < 0.324 < 0.342 < 0.423 < 0.432
32


0.70




0.20


Teachers Note: Now teacher will ask the following questions:
What is the total coloured portion of the grid?
Expected Answer : 0.70 + 0.20
OR
0.90
Students will complete Part B of Worksheet 5.
Students would be given Handout 3 available in Teacher Resource Material.
They will be asked to go through the Handout and then attempt Worksheet 6.











33
Handout 3 (Teachers Resource Material)
Adding decimals is very much like adding whole numbers.
To add two Decimals, first these should be converted into like Decimals
(Decimal numbers having same number of decimal places in the fractional part
for example 2.45, 415.78, 9.02)
Then the Decimal point of the two numbers should be aligned and all the digits
should be put in that order, i.e units place of second number should be aligned to
unit place, tens to tens, tenth to tenth and so on.
All these should be added like simple addition and a decimal point should be put
in total alignment with Decimal point of the two numbers
As usual in addition, start on the right, and add each column in turn.
22.3 22.3 22.3
+ 34.1 + 34.1 + 34.1
.4 6.4 56. 4
Checking For Understanding :
Add the following : 11.22 + 3.14 = 14.36





Teachers Note: The students will put Worksheet 5 and 6 after Worksheet 4.
(Refer to Worksheets 5, 6)
Activity 4 : Colouring Effect
Teacher distributes Worksheet 7 to each student.
Students will observe the 10 by 10 grid in the Worksheet.
Students will solve the question as per instructions given by the teacher.
T O . Th HTh
1 1 . 2 2
+ 3 . 1 4
1 4 . 3 6
34
For example:

Teacher will ask the students to colour 90 squares out of 100 in the grid with any
light colour to represent 0.9 as shown below:







Teacher will now ask students to colour 25 squares out of those 90 squares with a
darker colour to represent 0.25 as shown.












Teachers Note: Teacher explains that each light square gets cancelled with a darker
square and the remaining squares out of the coloured portion will represent the
difference between the two numbers.
0.90 - 0.25 = 0.65
Handout 4 (Teachers Resource Material) will then be distributed to explain the
method of subtraction of decimals. Students will go through the Handout and observe
the process of subtraction.Teacher will further take up few examples on the interactive
board to reinforce the method.




















0.90 0.25
35
Handout 4
(Teachers Resource Material)
To subtract decimals, follow these steps:
The most important thing to remember when subtracting decimals is to line up all the
decimal points in a column!
Write down the two numbers, one under the other, with the decimal points
aligned to each other.
Add zeros so the numbers have the same length ( like decimals)
Then subtract normally, remembering to put the decimal point in the same
position.
Example: Calculate 7.005-0.55
6 9 10
7 . 0 0 5
__ 0 . 5 5 0
6 . 4 5 5
Subtracting decimals is very much like subtracting whole numbers.
Subtract 7005 550
7 0 0 5
__ 5 5 0
6 4 5 5



36
Checking For Understanding :
Subtract the following : 760.374 510.041 = 250.333










The above solution may be done on the Interactive board together with the
students.
The students will put Worksheet 7 and 8 after Worksheet 6.
(Refer to Worksheets 7, 8)
Activity 5 : Lets Join Hands
Students will sit in pairs.
Teacher will distribute Worksheet 9 to each student.
Student will go through Worksheet 9 and within the pair discuss.
Students will then answer related questions given in Worksheet 9.
The students will put Worksheet 9, 10, 11 and 12 after Worksheet 8.
(Refer to Worksheets 9, 10, 11, 12)
Activity : Reflection Time
In this activity the student will reflect upon his/her comprehension of the various
concepts. The teacher will use it as a formative assessment tool to identify the areas
easily comprehended by the learner and the concepts which proved to be difficult and
need reinforcement. This will also help the teacher to make necessary accommodation
in her teaching style to suit the learning styles of the learner.

H T O Th HTh TTh
7 6 0 . 3 7 4
- 5 1 0 . 0 4 1
2 5 0 . 3 3 3
37
My Learnings Areas
Have understood and ready to go
ahead

Oops! A few speed breakers ahead
Help ! Help! Help!!!!

(Refer Worksheet 13)
Review
The teacher will recapitulate the concepts:




























Write in words and in
expanded form 3.24 = Three
and twenty four hundredths
3.24 = 3 x 1 + 2x 1/10 + 4 x
1/100
Relationship of decimals with
money: e.g Rahul purchased a
pen worth Rs 3.40 and pencil
worth Rs. 2.10.How much did
he spends in all?
Rs 3. 40
+ Rs. 2. 10
Rs. 5. 50



Addition of decimals: For
addition of decimals, change
the addends to like decimals
(Decimal having same number
of decimal places e.g 2.34,
13.67, 0.78)
Add: 2.345 + 4.46
2. 345
+ 4. 460
6. 805
Decimals: Addition and Subtraction
Subtraction of decimals: For
subtracting decimals change the
addends to like decimals
Subtract: 6.801 - 2.34
6. 801
- 2. 340
4. 461


38
(Refer Worksheet 14)
Assessment
Assessment will be based on learning objectives :
exploring decimal place value
reading and writing decimals
computing addition of decimals
computing subtraction of decimals
using decimals in money
developing empathy and compassion for disaster victims
ii) Worksheets/students response/group work/activities (Lets Rewind, Human
Decimal Machine and Decimal War, Fun with colours, Colouring Effect, Lets
Join Hands) may be used for formative and summative assessment.


39
Lesson Plan C

Topic: Multiplication and Division of Decimal Numbers
Duration: 2 hrs. 55 min.
Brief Description: The students are already familiar with the process of addition and
subtraction of decimal numbers. In this lesson students will understand the process of
multiplication and division of decimals. They will also be able to apply the above
operations to real life situations.
Learning Objectives: The students will be able to
operate a decimal number with a decimal number by the process of multiplication
demonstrate the ability to divide the decimal numbers
apply the operations of multiplication and division in solving real life situations
Material Required:
Activity 1 : Merging Multiples
A4 sheet, scale, Handout 5 (Teachers Resource Material), square grid paper (10 x 10)
and colours
Activity 2 : Dividing Equally
String/ribbon, pair of scissors, glue, A4 sheets, equation slips, Handout 6 ( Teachers
Resource Material) and colours
Activity 3 : No Time
Worksheet 5
Activity 1 : Merging Multiples
Use Worksheet 1 as a separator.
Students will work in pairs.
Each pair will be given a scale and an A4 sheet.
40
Students will be asked to look around in the class. The teacher can then ask the
following questions.
Question: Identify the different shapes in the class.
Expected Answer: Rectangle, Circle, Square, Quadrilateral, etc
Question: What is the shape of your desk?
Expected Answer: Rectangle/ any other
Question: Pick up any rectangular book/ notebook/A4 sheet and measure its
length and breadth.
Question: How will you find its area?
Expected Answer: By multiplying its length and breadth.
Question: Find the area of rectangular book/ notebook/A4 sheet.
Students will now be given Handout 5 (Teachers Resource Material).
Students will go through the Handout 5 and understand the methods of
multiplication of Decimal numbers.
Sample of Handout 5
Merging Multiples
Steps to multiply Decimals:
Let us multiply 45.234 x 6.2
Step 1: Multiply the given numbers as you normally multiply whole numbers ignoring
the decimal points.




+



Step 2: Count the total number of decimal places of both numbers together.
4 5 2 3 4
x 6 2
9 0 4 6 8
2 7 1 4 0 4 x
2 8 0 4 5 0 8
41

45.234 - 3 decimal places
6.2 - 1 decimal place
Total - 4 decimal places
Step 3 : To insert the decimal point in the product (calculated in Step 1), move from the
right towards the left and place the decimal point at the position which is equal to the
decimal places as calculated in Step 2.
2 8 0 .4 5 0 8
Answer: 45.234 x 6.2 = 280.4508


7.9438 x 10 = 79.438
The decimal point moves to the right by one place if the number is
multiplied by 10.
7.9438 x 100 = 794.38
The decimal point moves to the right by two places if the number is
multiplied by 100.
7.9438 x 1000 = 7943.8
The decimal point moves to the right by three places if the number is
multiplied by 1000.

Remember:
Number of decimal places in the product is the sum of decimal
places in the decimals.
Place the decimal point, counting from the extreme right in the
product.

42





Each pair will then be given Worksheet 2 containing square grids (10 x 10).
The teacher will then randomly give any 2 questions each from the given set to
each student.
Remember : To convert a decimal number into a whole number, always
multiply with the multiple of 10 having the same number of zeroes as the
number of decimal places.
For Example: Convert 7.943 into a whole number.
To convert 7.943 into a whole number, count the number of decimal places
in 7.943.
7 .9 4 3 (3 decimal places)
To cover 3 decimal places we need to multiply by 1000.
Hence 7.943 x 1000 = 7943
We want to multiply 7943.8 by 100
An extra zero is placed, as the decimal point is to be shifted
2 places to its right.
7943.8 x 100 = 794380
43


Students will then mark each block from 0.1 to 1.0 both horizontally and vertically
on the grid.
Students will then colour the appropriate number of boxes according to the
question.
For Example: For 0.3 x 0.4
The pair can represent the number on the grid either vertically or horizontally.

Sample given below:














Result : Number of shaded boxes = = 0.12

Students will also represent the solution mathematically on the A4 sheet.

Hence 0. 3 x 0. 4
1 decimal place 1 decimal place

= 0. 12 2 (1 + 1) decimal places

Teachers Note: On completion of the activity, the teacher can reinforce the process of
multiplication by giving number of questions to the students on multiplication of
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.1 x 0.5 0.3 x 0.4 0.2 x 0.7 0.4 x 0.6 0.9 x 0.8
3 x 4 = 12


44
numbers having 2 decimal or 3 decimal places. Students can also be called to the
Interactive board to solve such problems to gain confidence.
Worksheet 1 may be used as a separator for Lesson Plan C. The students will put
Worksheet 2, 3 and 4 after Worksheet 1.
(Refer Worksheets 1, 2, 3, 4)
Activity 2 : Dividing Equally
Class will be divided into groups A and B
Each group will be given an A4 sheet and the following activity to perform:
Group A: Make square flash cards of size 20.5 cm each. How many flash cards are
needed to cover your desk?
Group B:
Measure the length and breadth of your soft board.
Take a chart paper and measure its length and breadth. How many chart papers
are required to cover the board?
Students of the group can perform the calculations on the A4 sheet which can then be
validated by the teacher.
Now the students will be given a string/ ribbon and a pair of scissors.
2 different lengths from a string are cut by the teacher and any one of the lengths
distributed to each student.
For example: 49.7cm and 63.9 cm








Students will then be told to cut the string into equal parts of length 7.1 cm.

49.7cm
63.9cm
45



Each student will be given Worksheet 6.
Students will cut the string of equal length of 7.1cm each and paste each part on
Worksheet 6.




Students to count the number of parts and write the answer mathematically under
the string.


Each student will further be given Handout 6 (Teachers Resource Material) for
understanding the different methods of division of decimals.
Student will go through the Handout 6 and then solve the above problem on an
A4 sheet using mathematical solution and then compare both results.

49.7 7.1 = 7 63.9 7.1 = 9
7.1 cm each
46
Sample of Handout 6
Dividing Equally
Division of Decimal Number by a Whole Number
Let us divide 435.6 by 12
(Dividend) (Divisor)
Step 1: First divide the whole number of the dividend.
3 6
12 4 3 5 .6
- 3 6
7 5
- 7 2
3 6


Step 2: Then place the decimal point (.) at exactly the same position in the quotient as
in the dividend.

3 6.
12 4 3 5 . 6
- 3 6
7 5
- 7 2
3 6



47
Step 3: Divide the decimal part of the dividend.
3 6 . 3
12 4 3 5 . 6
- 3 6
7 5
- 7 2
3 6
- 3 6
0 0





Let us divide 7.4 by 4
1 . 8 5
4 7 . 4
4
3 4
3 2
2 0
2 0
0 0

Dividing a decimal by Another Decimal
Let us divide 270.3 by 0. 17
(Dividend) (Divisor)
number.
Remember: The decimal point is only placed in the quotient and the dividend.
Elsewhere in the calculation, the decimal point is not required to be shown.
Remember: Place extra zeroes to complete the
division wherever there is a remainder which is
less than the divisor.
48
0.1 7
2 decimal places To cover 2 decimal places we need to multiply by 100
Step 2: Also multiply the dividend by the same number (10, 100, 1000) to keep the value
of divisor and dividend same.
Hence = = = 1590

1590
17 27030
-17
100
- 85
153
- 153
0000
0
0
_______
Dividing a decimal by 10, 100, 1000








For Example:
3276.4 10 = 327.64
3276.4 100 = 32.764
3276.4 1000 = 3.2764
Remember: The decimal point moves 1 place, 2 places and 3 places to the right
when multiplied by 10, 100 and 1000 respectively. In case of division, the decimal
point moves to the left as many places as number of zeroes in the divisor.
49
Solution:
A) 49.7 7.1 = = = =
B) 63.9 7.1 = = = =
Teachers Note: Teacher can further ask questions to each pair and ask them to give
mathematical solution to the questions. Teacher can also call the students on the
interactive board to represent the solutions.
For Example:
51.84 6
28. 60 4
2.268 3.6
Students will put Worksheets 5, 6, 7 and 8 after Worksheet 4.
(Refer Worksheets 5, 6, 7 and 8)
Activity 3 : No Time
Students will work in pairs.
Each pair will be given Worksheet 9.
There are 2 sides to Workseet 9 Part A and Part B.
Each part contains 15 questions.
Within the pair Student 1 will solve Part A of the Woksheet and Student 2 will
solve Part B of Worksheet 9.
Students have to solve the questions in 15 min.
After the stipulated time, both the students in each pair will interchange their
sheets for peer evaluation.
Teachers Note: During the activity, the teacher can move around in the class and can
discuss the solutions during validation of the worksheets.
Students will put Worksheets 9 and 10 after Worksheet 8
50
(Refer Worksheets 9, 10)
Teachers Note: The teacher will distribute the following Templates available in the
Teachers Resource Material to the students:
Editorial
Acknowledgement
Contents
The teacher will instruct the students to compile the Portfolio as per the following
Format:
Cover page
Editorial (Experiences of the students while working on the Portfolio)
Acknowledgements (Acknowledgements to teachers/parents/friends/books/
websites/any other source of input)
Contents (can include illustrations as per the topics)
Worksheets
The Portfolio may be spiral bound or presented in any other creative manner.
Activity 4 : Reflection Time
In this activity the student will reflect upon his/her comprehension of the various
concepts. The teacher will use it as a formative assessment tool to identify the areas
easily comprehended by the learner and the concepts which proved to be difficult and
need reinforcement. This will also help the teacher to make necessary accommodation
in her teaching style to suit the learning styles of the learner.
My Learnings Areas
Have understood and ready to go
ahead

Oops! A few speed breakers ahead
Help ! Help! Help!!!!
51
(Refer Worksheet 11)
Review
The teacher will recapitulate the concepts:





































Steps to multiply Decimals:
Step 1: Multiply the given
numbers as you normally
multiply whole numbers
ignoring the decimal points.
Step 2: Count the total number
of decimal places of both
numbers together.
Step 3: Insert the decimal point
in the product as calculated in
Step 1, from the right, equal to
the number of decimal places
counted in Step 2.
45.234 x 6.2 = 280.4508

Multiplication of a Decimal
Number By 10, 100, 1000
7.9438 x 10 = 79.438
The decimal point moves to the
right by one place if the number is
multiplied by 10.
7.9438 x 100 = 794.38
The decimal point moves to the
right by two places if the number
is multiplied by 100
7.9438 x 1000 = 7943.8
The decimal point moves to the
right by three places if the number
is multiplied by 1000.
Multiplication and Division of
Decimal Numbers

52











































(Refer Worksheet 12)
Division of Decimal Number by a
Whole Number
Step 1: First divide the whole
number part of the dividend.
Step 2: Then place the decimal point
(.) at exactly the same position in the
quotient as in the dividend.
Step 3: Divide the decimal part of the
dividend.
3 6 . 3
12 4 3 5 . 6
3 6
7 5
7 2
3 6
3 6
0 0

Dividing a Decimal by another
Decimal
We follow the given steps:
Step 1: First multiply the divisor
by 10, 100 or 1000 to convert the
divisor into a whole number.
Step 2: Also multiply the
dividend by the same number (10,
100, 1000) to keep the value of
divisor and dividend same.
For Example: 270.3 0.17
= = = 1590


Dividing a decimal by 10, 100, 1000
The decimal point moves 1 place, 2 places and 3 places to the right when
multiplied by 10, 100 and 1000 respectively. In case of division, the decimal
point moves to the left as many places as number of zeroes in the divisor.
For example: 390.4 100

53
Assessment
Assessment will be based on learning objectives :
i. operating a decimal number with a decimal number by the process of
multiplication
ii. demonstrating the ability to divide the decimal numbers
iii. applying the operations of multiplication and division in solving real life situations
iv. Worksheets/students response/group work/activities (Merging Multiples,
Dividing Equally and No Time) may be used for formative and summative
assessment.







54
Assessment Rubric
Mathematics (Community and Shelter)
Expected
Learning
Outcome

Indicators of students performance
Beginning Developing Achieved Exemplary
Topic The student will
be able to :
The student
will be able to :
The student will
be able to :
The student
will be able to :
Multiplication
and Division
of Fractional
Numbers
comprehend
the meaning
of fractions
identify the
numerator
and
denominator
demonstrate
the ability to
multiply the
whole
number/
fractional
number with
a fractional
number
understand
the
reciprocal of
a fractional
number and
solve simple
division
related
question

demonstrate
the ability to
solve
complex
multiplication
and division
related
question
apply the
process of
multiplication
and division
to real life
situations
demonstrate
exceptional
thinking and
use multiple
strategies in
solving
fractions
related to
real life
situations
create new
questions
based on
similar
concepts
55
Decimals:
Addition and
Subtraction
read place
value chart
for decimals
read and
write
decimals

read and
write
decimals
state and
demonstrate
the addition
and
subtraction
of decimals
analyze the
correlation of
decimals to
quantities in
real life
situations


understand
and identify
important
elements of
a problem
demonstrate
exceptional
thinking and
show
multiple
strategies in
solving
decimal
related
problem
Multiplication
and Division
of Decimal
Numbers
identify the
place value of
the decimal
demonstrate
the ability to
multiply and
divide one
decimal
number with
another
decimal
number

apply the
process of
multiplication
and division
to real life
situations
demonstrate
exceptional
thinking and
use multiple
strategies in
solving
decimals
related to
real life
situations
create new
questions
based on
similar
concepts



56
Teachers Resource Material
Material Required: Colour Pencils Or Oil Pastels Or Water Colours, A4 Size Coloured
Pastel Sheet, Scissors, Glue, A4 sheets, A4 colored sheets, equation slips, Base 10
models, 3 strips, Flash cards (digits 0 9 and decimal point), square ruled sheet of
dimension 10 cm x 10cm (10-by- 10 grid), bowl, String/ribbon and Handout 1, 2, 3, 4, 5
and 6 (Teachers Resource Material).
Vocabulary to be taught: Numerator and Denominator of a fraction, Reciprocal of a
number, place value chart of a decimal
Books :
Maths 4 u by Kriti Prakashan Limited.
Mathsight ( Britannica )
Composite Mathematics
Mathematics: Oxford Publication
Excellence In Mathematics: Prachi [India ] PVT. LTD
NCERT Mathematics
Links:
http://www.google.com/search?q=puzzles+for+class+5&safe=active&source=ln
ms&tbm=isch&sa=X&ei=xIBrUeToAcrHrQfhmoHwCQ&ved=0CAcQ_AUoAQ&b
iw=1440&bih=775#safe=active&as_qdr=all&tbm=isch&sa=1&q=puzzles+on+deci
mals++for+class+5&oq=puzzles+on+decimals++for+class+5&gs_l=img.3...48572.5
8987.0.59549.20.20.0.0.0.0.0.0..0.0...0.0...1c.1.9.img.jFOvVOj9-
p4&bav=on.2,or.r_qf.&fp=d579872777c0afd7&biw=1440&bih=775&imgrc=rdIjsOc
0vN_UiM%3A%3BjinbbUHHiAWdhM%3Bhttp%253A%252F%252F01.edu-
cdn.com%252Ffiles%252F84801_84900%252F84887%252Ffile_84887_350x440.png%
3Bhttp%253A%252F%252Fwww.education.com%252Fslideshow%252Fdecimal-
dash-practice-ordering-decimals%252F%3B349%3B440
http://www.google.co.in/url?sa=i&rct=j&q=maze+games+puzzles+for+class+5&
source=images&cd=&cad=rja&docid=71kX_pQvV4A6CM&tbnid=PNX96TRMFcz
57
hvM:&ved=0CAUQjRw&url=http://www.business2community.com/social-
media/how-delhi-safari-maximised-facebook-engagement-with-images-and-
games-
0357653&ei=2PxPUcuvAcGFkAW2goGIAw&psig=AFQjCNGzoxCQ4KTXacqaBe
UIKVPD8QnxvA&ust=1364282866164284
http://en.wikipedia.org/wiki/File:Maya.svg
http://scienceblogs.com/startswithabang/files/2012/07/triangle.001.jpg
http://www.google.co.in/url?sa=i&rct=j&q=colourful+maze+games+on+decimal
s&source=images&cd=&cad=rja&docid=pD7ZJnqE-
Y7_EM&tbnid=adxcCL4NsSo78M:&ved=0CAUQjRw&url=http://www.picstopin
.com/500/maze-
1/http:||blackdog4kids*com|holiday|mom|maze|1*gif/&ei=yANQUfW1Es6lk
QXKn4HAAQ&bvm=bv.44158598,d.bmk&psig=AFQjCNH1eCm7asfAyGuW1WX
yNJYQ-uk-EA&ust=1364284520756970
Websites for reference:
Http://en.wikipedia.org/wiki
Http://www.innovationsleraning.co.uk/
Http://ozschool.com
Http://fun4maths.com
Http://coolmaths.com
Http://www.superteachers.com


58
Handout 1
Matching and Dividing
When you divide you are cutting into equal shares:
There are 3 Simple Steps to Divide Fractions:
Step 1: Turn the second fraction (the one you want to divide by) Upside Down. This is
now a reciprocal.












Step 2: Multiply the first fraction by the reciprocal of other.
For Example: Divide
The reciprocal of is
Hence x = =
Step 3: Simplify the fraction (if needed).
Therefore = =

Reciprocal of a Number: Two numbers are said to be reciprocal of each other
if their product is 1.
For Example: The reciprocal of is
i.e. x = 1
The Reciprocal of a fractional number is obtained by interchanging its
numerator and denominator.
59
Handout 2
Lets Rewind
Let's examine these decimals in our place-value chart
PLACE VALUE AND DECIMALS







D
e
c
i
m
a
l

1/10

1/100

1/1000








In Words (while
Reading)







In Words (while Writing)

3 . 2 4 Three point two four Three and twenty four hundredths

3 . 0 7 2 Three point zero seven
two
Three and seventy two thousandths

3 7 . 0 2 Thirty seven point zero
two
Thirty seven and two hundredths

3 2 7 . 4 Three hundred twenty
seven point four
Three hundred twenty seven and four
tenths

As we move left, each position is 10 times bigger and as we move right, each
position is 10 times smaller
3.24 = 3 x 1 + 2 x + 4 x 1/ 100
3.072 = 3 x 1 + 0 x 1/10 +7 x 1/100 + 2 x 1/1000
37.02 = 3 x 10 + 7 x 1 + 0 x 1/10 + 2 x 1/100
327.4 = 3 x 100 + 2 x 10 + 7 x 1 + 4 x 1/10




60
Handout 3
Fun With Colours
Adding decimals is very much like adding whole numbers.
To add two Decimals, first these should be converted into Like Decimals
(Decimal numbers having same number of decimal places in the fractional part
for example 2.45, 415.78, 9.02)
Then the Decimal point of the two numbers should be aligned and all the digits
should be put in that order, i.e units place of second number should be aligned to
unit place, tens to tens, tenth to tenth and so on.
All these should be added using simple addition method and a decimal point
should be put in the answer aligned to the Decimal point of the two numbers that
have been added.
As usual in addition, start from the right, and add each column as you move left.

22.3 22.3 22.3
+ 34.1 + 34.1 + 34.1
.4 6.4 56. 4
Add 1.22 + 13.14 = 14.36













T O . Th HTh
1 . 2 2

+
1 3 . 1 4
1 4 . 3 6
61
Handout 4
Matching Colours
To subtract decimals, follow these steps:
The most important thing to remember when subtracting decimals is to line up all the
decimal points in a column!
Write down the two numbers, one under the other, with the decimal points
aligned to each other.
Add zeros so the numbers have the same length ( like decimals)
Then subtract normally, remembering to put the decimal point in the same
position.
Example: Calculate 7.005-0.55
6 9 10
7 . 0 0 5
__ 0 . 5 5 0
6 . 4 5 5

Subtracting decimals is very much like subtracting whole numbers.
Example: Subtract 7005 550

7 0 0 5
__ 5 5 0
6 4 5 5



62
Handout 5
Merging Multiples
Steps to multiply Decimals:
Let us multiply 45.234 x 6.2
Step 1: Multiply the given numbers as you normally multiply whole numbers ignoring
the decimal points.




+



Step 2: Count the total number of decimal places of both numbers together.

45.234 - 3 decimal places
6.2 - 1 decimal place
Total - 4 decimal places
Step 3 : To insert the decimal point in the product (calculated in Step 1), move from the
right towards the left and place the decimal point at the position which is equal to the
decimal places as calculated in Step 2.
2 8 0 .4 5 0 8
Answer: 45.234 x 6.2 = 280.4508







Multiplication of a Decimal Number By 10, 100, 1000


4 5 2 3 4
x 6 2
9 0 4 6 8
2 7 1 4 0 4 x
2 8 0 4 5 0 8
Remember:
Number of decimal places in the product is the sum of decimal
places in the decimals.
Place the decimal point, counting from the extreme right in the
product.

63
7.9438 x 10 = 79.438
The decimal point moves to the right by one place if the number is
multiplied by 10.
7.9438 x 100 = 794.38
The decimal point moves to the right by two places if the number is
multiplied by 100.
7.9438 x 1000 = 7943.8
The decimal point moves to the right by three places if the number is
multiplied by 1000.



























We want to multiply 7943.8 by 100
An extra zero is placed, as the decimal point is to be shifted
2 places to its right.
7943.8 x 100 = 794380
Remember : To convert a decimal number into a whole number, always
multiply with the multiple of 10 having the same number of zeroes as the
number of decimal places.
For Example: Convert 7.943 into a whole number.
To convert 7.943 into a whole number, count the number of decimal places
in 7.943.
7 .9 4 3 (3 decimal places)
To cover 3 decimal places we need to multiply by 1000.
Hence 7.943 x 1000 = 7943
64
Handout 6
Dividing Equally
Division of Decimal Number by a Whole Number
Let us divide 435.6 by 12
(Dividend) (Divisor)
Step 1: First divide the whole number of the dividend.
3 6
12 4 3 5 .6
- 3 6
7 5
- 7 2
3 6


Step 2: Then place the decimal point (.) at exactly the same position in the quotient as
in the dividend.

3 6.
12 4 3 5 . 6
- 3 6
7 5
- 7 2
3 6



65
Step 3: Divide the decimal part of the dividend.
3 6 . 3
12 4 3 5 . 6
- 3 6
7 5
- 7 2
3 6
- 3 6
0 0





Let us divide 7.4 by 4
1 . 8 5
4 7 . 4
4
3 4
3 2
2 0
2 0
0 0

Dividing a decimal by Another Decimal
Let us divide 270.3 by 0. 17
(Dividend) (Divisor)
number.
Remember: The decimal point is only placed in the quotient and the dividend.
Elsewhere in the calculation, the decimal point is not required to be shown.
Remember: Place extra zeroes to complete the
division wherever there is a remainder which is
less than the divisor.
66
0.1 7
2 decimal places To cover 2 decimal places we need to multiply by 100
Step 2: Also multiply the dividend by the same number (10, 100, 1000) to keep the value
of divisor and dividend same.
Hence = = = 1590

1590
17 27030
-17
100
- 85
153
- 153
0000
0
0
_______
Dividing a decimal by 10, 100, 1000








For Example:
3276.4 10 = 327.64
3276.4 100 = 32.764
3276.4 1000 = 3.2764
Remember: The decimal point moves 1 place, 2 places and 3 places to the right
when multiplied by 10, 100 and 1000 respectively. In case of division, the decimal
point moves to the left as many places as number of zeroes in the divisor.
67
Template 1 - Editorial











































68
Template 2- Acknowledgement










































69
Template 3- Contents






S. No. Topics





























70
Answer key
Lesson Plan A
Worksheet 1
Mathemingle Cover page
Worksheet 2
Lets Revise
PART A
1. Balcony, Bedroom, Bath, Dining/Living Room, Kitchen ( Any four of the given)
2. of the total area
3. ( of of the total area)
4. All relevant answers will be acceptable
PART B All relevant answers will be acceptable
Worksheet 3
Lets Revise
2) Parking and Play Area 1/6
3) Community hall, Adult Education
Centre and Animal Shelter
10/16 = 5/8
4) Both Gardens and Play Area 5/24









71
Worksheet 4
Repeated Additions Activity
All relevant answers will be acceptable
B.










Worksheet 5
Repeated Additions

1. i) 25 ii) 4 iii) 8 iv) 14 v) 6
2. Red Coloured 6, Brown Colour 8, Green Colour- 6
3. i) 200 ml ii) 18 km iii) 700 cents iv) 8 g v) 20 m
4. 18 cups of cocoa
Worksheet 6
Repeated Additions
A. (i) 5/2 (ii) 8/3 (iii) (iv) 4 (v) 8/5 (vi) 18/13
(vii) 4/3 (viii) 8/5 (ix) 7 (x) 12
B. 4 m
C. 5 m
D. miles
E. 8 parts
72
Worksheet 7
Paper Pizza
Worksheet 8
Paper Pizza
A. i) 7/12 ii) 2/5 iii) 7/50 iv) 4/3 v) 1/14
vi) 13/4 vii) 7/18 viii)
B. 15 feet
C. 6 ounces
D. laps
Worksheet 9
Matching and Dividing
Worksheet 10
Matching and Dividing
A. i) 9/5 ii) 4/13 iii) 6/13 iv) 7 v) 1/26 vi) 2/25
B. 21/51 or 7/17
C. 18 baskets
D. 4/3 m
E. 34 residents
Worksheet 11
Matching and Dividing
1) a. 1/20 b. 1/10 c. 1/21 d. 1/12 e. 1/9
2) 1/3 kg
3) i) 1 ii) 5/3 iii) 6/5 iv) 5/7 v) 2/5
4) 6 scoops
5) a. b. 4/9 c. 1/18
73
Lesson Plan B
Worksheet 1
Lets Rewind
Worksheet 2
Lets Rewind
A. 1. Twelve and thirty five hundredths
2. Ninety nine and seven thousandths
3. Twenty three and four hundred fifty six thousandths
4. Forty five thousandths
5. Seven hundred eighty nine and five hundred sixty eight thousandths
6. One thousand forty nine and sixty three hundredths
B.1. 1. 02 2. 408.005 3. 6005.010 4. 342.105 5. 400.31 6. 3.004 7. 69.34
C. i) 6.623 ii) 803.402 iii) 824.008 iv) 250.095 v) 64.508 vi) 500.055
D. i) 2 ii) 1 iii) 4 iv) 5 v) 9
Worksheet 3
Lets Rewind
Q1. 0.1
Q2. Two hundredths
Q3. 5, 10, 0, 1000
Q4. a. 0.7 b. 0.19 c. 0. 637
Q5. 8.371
Q6. a. 20+9 + + b. 1+ + + c. 600+60+6+ +
74
Q7. a. thousandths b. hundred c. hundredths
Q8.
Column 1 Column 2 Column 3
1. 0.63 0.6+0.03 0.6300
2. 0.4050 0.4+0.0050 0.405
3. 0.940 0.9+0.04 0.9400
4. 0.360 0.300+0.060 0.36
5. 0.904 0.9+0.004 0.9040
6. 0.1200 0.1+0.020 0.12
7. 0.212 0.2+0.01+0.002 0.2120
8. 0.5400 0.5000+0.040 0.54
9. 0.603 0.6+0.003 0.6030
10. 0.102 0.1+0.002 0.1020

Q9. a) Green Bee- 3.194, 6.294 b) Yellow Bee 8.14 c) Pink Bee 5.40, 19.42, 1.40
Worksheet 4
Human Decimal Machine and Decimal War
A. 1)> 2)< 3)< 4)< 5)< 6) = 7)>
B. i) 0.234, 0.243, 0.324, 0.342, 0.423, 0.432
ii) 8.07, 8.707, 8.77, 80.7, 787.0, 7078
iii) 0.4444, 4.444, 40.44, 44.44, 444.4, 4444
iv) 0.05434, 0.5434, 5.434, 54.34, 543.4, 5434
C. i) 23.650, 23.560, 23.456, 23.443
ii) 7078, 787.0, 80.7, 8.734, 8.707, 8.307
iii) 543.4, 534.43, 534.34, 533.231, 532.234
75
D a) Descending Order: 1.10, 1.01, 1.0, 0.54, 0.504, 0.44, 0.405, 0.145
b) Scientists do EXPERIMENT
Worksheet 5
Fun with colours
PART A - 0.90
PART B - 0.68
PART C - $33.58
Worksheet 6
Fun with colours
A. I. 8.70,7.81
II. 3.001, 3.010, 3.100
III. 12.03, 120.30
IV. 2.2000, 0.2200, 0.2020, 0.2020
B. 1. 14.36 2. 69.06 3. 67.05 4. 74.11 5. 732.064 6. 63.284
C. 1. 143.287 2. 776.982 3. 1841.417 4. 953.347
Worksheet 7
Colouring Effect
Activity (0.65)
Worksheet 8
Colouring Effect
A. 1. 85.008 2. 438.839 3. 581.636 4. 462.171 5. 10.957 6. 250.333
B. 1. 324.65 2. 314.52 3. 270.246 4. 152.109
Worksheet 9
Lets Join Hands
76
B. All mathematically correct answers will be acceptable
C. All relevant answers will be acceptable.
Worksheet 10
Lets Join Hands
A. Solved B. 138.80 C. 502.60
D. Total amount spent = 554.60, Amount left = 445.40
Worksheet 11
Lets Join Hands
Q1. Solved Q2. 119.25
Q3.

Q4. 6217.60 Q5. 4887.75
Worksheet 12
Lets Join Hands
1x8+1=9
12 x 8 + 2 = 98
123 X 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8__ + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + _8_ = 98765432
123456789 x 8 + 9 = 987654321
Amount spent by Radha 755.70
Amount returned by shopkeeper 744.30
77
Lesson Plan C
Worksheet 2
Merging Multiples
I. A) 280.4508 B) 2804508
II.
ANSWER A B
Number name Two hundred eighty point four
five zero eight
Two million eight hundred four
thousand five hundred eight
Expanded form 200 + 80 + 4/10 + 5/100 + 8/10000 2000000 + 800000 + 4000 + 500 + 8
Face value of 4 4 4
Place value of 4 4/10 4000
Difference 2804227.5492
Sum 2804788.4508

Worksheet 3
Merging Multiples
A. 1) 0.12 2) 0.30 3) 0.20 4) 0.0204 5) 0.0006 6) 3
B. i) 22.96km ii) 307.125 iii) 315.6 iv) 57.75 km.
C. 1) 78.752 2) 84.6 3) 3447.36 4) 7.788 5) 52.953 6) 6.5983129
Worksheet 4
Merging Multiples

78
A. 499.50 B. 153.75 C. 446.25 D. 184.30 E. All Mathematically
correct answers will be acceptable.
Worksheet 6
Dividing Equally
All mathematically correct answer will be acceptable
Worksheet 7
Dividing Equally
A. 1) 5 2) 0.5 3) 132 4) 2 5) 4 6) 11.025
B. (i) 18.3 cm (ii) 7.1875 m
2
(iii) 3.60 m
2

Worksheet 8
Dividing Equally
A. 1) 22.15 2) 12.9 3) 40.5 4) 312.2 5) 85.4
B. 45.20
C. 52.95
D. 22.65
E. 2.98
Worksheet 9
No Time
PART A
1. 0+ 7/10 + 2/100 + 8/1000 2. 39.31 3. smaller 4. 9.028, 9.029, 9.030
5. 6.1 6. 441m 7. 20 8. 0.5
9. 0.2 10. 10 11. 0.3 12. 2
13. 8.2, 8.22, 8.56 14. 15. 4
79
PART B
1. 2 + 6/10 + 3/100 +8/1000 2. 6.704 3. smaller 4.8.09, 8.10, 8.11 5.9.1
6. 1635

7. 3 8. 481.6 9.5 feet 10.10
11. 10000 12.0.33 or 1/3
13. 0.60, 6.04, 60.04, 60.4 14. 15. 8 hours
Worksheet 10
No Time

3
6 . 5
8


1
2 . 5 4 .
4
. 7 .
9
. 8
. . 1 .
2 8
2
7 . 1
8
. 2
2 9
. 0
1
. .

1 3
. 6
. 8
7


80
After completing the worksheet
I felt
(Tick your response)
Lesson Plan A
Worksheet 1
Mathemingle
Name: ____________ Class: _____________

Date: ______________ Subject: _____________


NAME: ________________
CLASS: ________________
81
Lesson Plan A
Worksheet 2
Lets Revise
Name: ____________ Class: _____________

Date: ______________ Subject: _____________
Part A


1. Name any 4 main areas in the house visible in the layout shown above.
_________________________________________________________________________
2. Approximately how much area of the total is covered by both living and kitchen
together (in fraction)?
_________________________________________________________________________
3. Approximately how much area of the total is covered by both balcony and
bedroom together (in fraction)?
_________________________________________________________________________
4. If you are given a chance to increase the area of any of the part, which one would
you prefer and why?
_________________________________________________________________________
82
After completing the worksheet
I felt
(Tick your response)
Part B
Draw a rough sketch representing the layout of your Dream House.



























Answer the following:
1. Give a name to your Dream House.
_________________________________________________________________________
2. How many rooms are there in your house?
_________________________________________________________________________
3. Which room of your house do you like the most? Give reason.
_________________________________________________________________________

83
After completing the worksheet
I felt
(Tick your response)
Lesson Plan A
Worksheet 3
Lets Revise
Name: ______________ Class: _____________
Date: ______________ Subject: _____________
Marie has bought a plot for a Community Centre. She is working on its layout in the
following manner:









Find a
fraction for
each one:

1) Animal Shelter and
Adult Education Centre
1/16 + 1/16 = 2/16 1/8
2) Parking and Play Area
3) Community Hall, Adult
Education Centre and
Animal Shelter

4) Both Gardens and Play
Area


Gymnasium
Parking Vegetable Herbal
(1/24) Garden (1/24) Garden
(1/24)

Play Area (1/8)
Animal Shelter (1/16)
Adult Education
Centre (1/16)
COMMUNITY HALL ()
Store
Room
OFFICE
84
Lesson Plan A
Worksheet 4
Repeated Additions
Name: ____________ Class: _____________
Date: ______________ Subject: _____________



A.
REPEATED ADDITIONS Multiplication of Fractions
85
You are wrong if you think
Mathematics is not fun!

After completing the worksheet
I felt
(Tick your response)





B. Solve the fractions and trace the path to come out of the maze.






86
Lesson Plan A
Worksheet 5
Repeated Additions
Name: ______________ Class: _____________
Date: ______________ Subject: _____________
1) Multiply the given fraction by the whole number.

i) x 55

ii) x 14

iii) x 10

iv) x 22

v) x 10


2) In a neighborhood of 20 houses, 3/10 of the roofs are made of red asbestos sheet,
2/5 of the roofs are of brown bamboo. Rest of them are sloping roofs painted
green. How many red, brown and green sloping roofs are there? Represent the
answer by coloring them accordingly.





87
After completing the worksheet
I felt
(Tick your response)
3) Solve the following:
i) x 550 ml

ii) x 48 km

iii) x 300 cents

iv) x 38 g

v) x 28 m


4) 3/5 cups of cocoa is needed to make a chocolate bar for a Christmas celebration.
The entire community gets together and decides to give 1 bar of chocolate to all
the 30 children of the community. How many cups of cocoa are required?















88
Lesson Plan A
Worksheet 6
Repeated Additions
Name: ______________ Class: _____________
Date: ______________ Subject: _____________
A. Multiplying the given:
(i) 5

(ii) 8


(iii) 3 5

(iv) 5

(v) 2

(vi) 2

(vii) 4

(viii) 8

(ix) 14

(x) 15


B. From a string 20 m long, Rhea cut off 3 pieces of 2 m each and Nadia cut off 2
pieces of 4 m each. What is the length of rope left?





89
After completing the worksheet
I felt
(Tick your response)
C. Ten people have been hired to take care of a Community Centre. It has been
decided that they wear a proper uniform. If m of cloth is required to stitch one
shirt, how much cloth is required to stitch 10 such shirts?







D. Peter is carrying cement bags in his truck for the construction of the Community
Centre. His truck gets him 10 miles per gallon. Suppose Peter's tank is empty
and he puts 5 gallons, how far can Peter go with the truck?





E. On Monday a team of cleaners cleaned 2/3 part of the Community Centre. On
Tuesday, the team cleaned 12 times as much as they had cleaned on Monday.
How many parts did the cleaners clean on Tuesday?











90
Lesson Plan A
Worksheet 7
Paper Pizza
Name: ____________ Class: _____________
Date: ______________ Subject: _____________



PAPER PIZZA
3 Shares of Equal Size
9/10
Multiplication of Fractions
1/3 x 9/10 =
91
After completing the worksheet
I felt
(Tick your response)
BIRTHDAY MAGIC
Step1: Add 18 to your birth month.
Step2: Multiply by 25.
Step3: Subtract 333.
Step4: Multiply by 8.
Step5: Subtract 554.
Step6: Divide by 2.
Step7: Add your birth date.
Step8: Multiply by 5.
Step9: Add 692.
Step10: Multiply by 20.
Step11: Add only the last two digits of your birth year.
Step12: Subtract 32940 to get your birthday!
Example: If the answer is 123199 means that you were born on December 31,
1999. If the answer is not right, you followed the directions incorrectly or lied about
your birthday.










MATHEMAGIC
In a group of 23 people, at least two have the same birthday with
the Probability greater than 1/2


92
Lesson Plan A
Worksheet 8
Paper Pizza
Name: _____________ Class: _____________
Date: ______________ Subject: _____________
A. Multiplying two fractional Numbers
i) by

ii)

iii)

iv)

v)

vi) by 2

vii)

viii)

B. Maria planted a lemon tree and a cherry tree in the vegetable garden of the
Community Centre. The lemon tree is feet tall. The cherry tree is times
as tall as the lemon tree. How tall is Maria's cherry tree?





93
After completing the worksheet
I felt
(Tick your response)

C. As a part of the Vocational Education Programme, the adults of the Adult
Education centre prepared chocolates. They sold ounces of white chocolate.
They further sold times as much milk chocolate as white chocolate. How
many ounces of milk chocolate did they sell?









D. Last week, Christine ran laps around the lake. Everett ran 2/3 as many laps
around the lake as Christine did. How many laps around the lake did Everett
run?

94
After completing the worksheet
I felt
(Tick your response)
Lesson Plan A
Worksheet 9
Matching and Dividing
Name: _____________ Class: _____________
Date: ______________ Subject: _____________










Mathematical Solution
2/3 1/6
95
Lesson Plan A
Worksheet 10
Matching and Dividing
Name: _____________ Class: _____________
Date: ______________ Subject: _____________
A. Find the reciprocal of the following:













B. Find the reciprocal of the product of and 5 .






NUMBER RECIPROCAL NUMBER RECIPROCAL
i)

iv)

ii) 3
v) 26
iii)

vi) 12

Reciprocal of A Number: Two numbers are said to be reciprocal of
each other if their product is 1.
For Example: The reciprocal of is
i.e. = 1
The Reciprocal of a fractional number is obtained by interchanging its
numerator and denominator.

96
After completing the worksheet
I felt
(Tick your response)










C. The people of the community decided to distribute apples to the nearby Old
Age Home and the Orphanage. They bought 31 kg of apples and prepared
apple baskets of 1 kg each. Find the number of baskets prepared by them.






D. A blue colour ribbon roll of 25 m length was bought for decorating the
baskets. It was divided into 19 equal pieces. Find the length of each piece.







E. The members of the community organized World Health Day. The total
expenditure on the event was Rs 4156 . The residents of the society decided to
pool in. If each resident had to pay Rs122 how many total residents are there
in the community?
REMEMBER
The reciprocal of 1 is 1.
The reciprocal of 0 is not
defined.





97
Lesson Plan A
Worksheet 11
Matching and Dividing
Name: _____________ Class: _____________
Date: ______________ Subject: _____________
1) Divide the given fraction by the whole number

a) 55

b) 18

c) 15

d) 26

e) 6


2) Peter divides kg of dog food amongst 5 dogs in the Animal Shelter. How much
will each dog get?









98
After completing the worksheet
I felt
(Tick your response)
3) Solve and write the answer in the lowest term
i)

ii)

iii)

iv)

v)


4) Jennys bird feeder holds 3/4 of a cup of birdseed. Pat fills the bird feeder with a
scoop that holds 1/8 of a cup. How many scoops of birdseed will Pat put into the
feeder?








5) Divide the given fraction by a mixed fraction:
a) 2

b) 5

c) 7





99
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I felt
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Lesson Plan A
Worksheet 12
Reflection Time
Name: _______________ Class:____________
Date: ________________ Subject:____________
Its time to reflect.
My Learning Areas
Have understood and ready to go
ahead

Oops! A few speed breakers ahead
Help ! Help! Help!!!

Where can I use this topic in day to day life?









100
After completing the worksheet
I felt
(Tick your response)
Lesson Plan A
Worksheet 13
Review
Name: _______________ Class: _____________

Date: ________________ Subject: _____________




































Multiplication of a whole number
with a fractional number.
Solve: x 91
Multiplication of a fractional
number with a fractional
number.
Solve: 3 x 6
Division of fractions
Find the Reciprocal of 12


Divide: by
Fractions Multiplication and
Division of Fractional Numbers

101
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I felt
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Lesson Plan B
Worksheet 1
Lets Rewind
Name: ____________________ Class: _________________
Date: ____________________ Subject: ________________
DECIMALS








The weight of the cat is 3.7 kg.
List 5 examples of decimals in your day to day life.
1.
2.
3.
4.
5.
102
Lesson Plan B
Worksheet 2
Lets Rewind
Name: ____________________ Class: _________________
Date: ______________________ Subject: ________________
A. Write the following numerals in words:-

B. Write the following in decimal number:-
Sr.No. Decimal number in words Decimal number
1. One and two hundredths
2. Four hundred eight and five-thousandths
3. Six thousand five and ten thousandths
4. Three hundred forty-two and one hundred five
thousandths

5. Four hundred and thirty one hundredths
6. Three and four thousandths
7. Sixty nine and thirty four hundredths

Sr. No. Decimal number Decimal number in words
1. 12.35
2. 99.007
3. 23.456
4. 0.045
5. 789.568
6. 1049.63
103
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C. Write decimals for each of the following:
i) 6 ones+ 6 tenths+ 2 hundredths+ 3 thousandths

ii) 8 hundreds + 3 ones+ 4 tenths + 2 thousandths

iii) 8 hundreds + 2 tens+ 4 ones+8 thousandths

iv) 2 hundreds + 5 tens + 9 hundredths+ 5 thousandths

v) 6 tens+4 ones+ 5 tenths +8 thousandths

vi) 5 hundreds + 5 hundredths+ 5 thousandths


D. Convert following as fraction in the lowest term or as mixed numbers:
i) 2.25
ii) 1.325
iii) 4.25
iv) 5.25
v) 9.7


104
Lesson Plan B
Worksheet 3
Lets Rewind
Name: ___________________ Class: _______________
Date: ____________________ Subject: ______________
Q1. One in ten people are left handed .Write this in a decimal form.


Q2. 0.02 in words


Q3. Simplify: 55.605 = 50 + + 6 + ___ + 5
100
Q4. Write the following fractions as decimals:
a) 7/10
b) 19/100
c) 637/1000

Q 5. Write as decimal: 8 + 3 + 7 + 1 =
10 100 1000
Q6. Write the given decimal in expanded form:
a) 29.67 b) 1.125 c) 666.66

105
Q7. Write the place value of 5 in the following:
a) 72.105

b) 520.187

c) 23.05
Q.8 Match the decimal in the first column to its expanded form in the second
column and to its equivalent decimal in the third column.
Column 1 Column 2 Column 3
1. 0.63 0.9+ 0.04 0.36
2. 0.4050 0.300+ 0.06 0.9040
3. 0.940 0.9 + 0.004 0.12
4. 0.360 0.4+0.0050 0.2120
5. 0.904 0.6+0.03 0. 405
6. 0.1200 0.5000+0.040 0.9400
7. 0.212 0.6+0.003 0.1020
8. 0.5400 0.1+0.020 0.6300
9. 0.603 0.1 +0.002 0.6030
10. 0.102 0.2 + 0.01+ 0.002 0.54






106
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I felt
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Q9.
a) If the number has a 4 in the thousandths place, colour the bee green.
b) If the number has a 4 in the hundredths place colour the bee yellow.
c) If the number has a 4 in the tenths place, colour the bee pink.
































107
Lesson Plan B
Worksheet 4
Human Decimal Machine and Decimal War
Name: ____________________ Class: ________________
Date: ____________________ Subject: ______________
A. Fill in the boxes using >, < or = to make the statement true:

1) 97.6 6.3
2) 6.85 8.95
3) 8.01 30.1
4) 6.99 6.999
5) 25.29 39.41
6) 11.27 11.270
7) 6.962 0.9628
B. Rewrite the following groups of decimals in ascending order:
i) 0.324, 0.342, 0.243, 0.234, 0.432, 0.423


108
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ii) 8.77, 8.07,8.707,80.7, 787.0, 7078

iii) 444.4,4.444,44.44,4444, 0.4444, 40.44

iv) 5434, 0.05434, 0.5434, 5.434,54.34,543.4

C. Rewrite the following groups of decimals in descending order:
i) 23.560, 23.650 , 23.456, 23.443

ii) 8.734, 8.307,8.707,80.7, 787.0, 7078

iii) 543.4 , 534.34 , 533.231 , 532 .234 , 534.43

D. Arrange the decimal numbers on the beaker from largest to smallest, then use
the letters to answer the questions below:





a) Descending Order: ___________________________________________
b) What do the scientists do? _________________
109
Lesson Plan B
Worksheet 5
Fun with Colours
Name: ____________________ Class: _________________
Date: ____________________ Subject: ________________
PART - A




0.70 + 0.20











0.70 + 0.20 =

110
After completing the worksheet
I felt
(Tick your response)
PART B


























PART C
















0.43 + 0.25











0.43 + 0.25 =

How much do I need to spend to buy one soccer ball each for my brother and
me?



My favorite sportsperson is ___________________.
111
Lesson Plan B
Worksheet 6
Fun With Colours
Name: ____________________ Class: _________________
Date: ____________________ Subject: ________________
A. Convert each of the following groups of unlike decimals into like decimals:
I. 8.7 , 7.81

II. 3.001, 3.01, 3.1

III. 12.03, 120.3

IV. 2.2, 0.22, 0.202, 0.2020

B. ADD THE FOLLOWING:-
1. 2.









T O . Th HTh
1 1 . 2 2
+ 3 . 1 4

T O . Th HTh
6 1 . 2 2
+ 7 . 8 4

112
3. 4.







5. 6.







C. Write each of the following in column and then add :-
1. 72.318 + 27.250 + 43.719
H T O . Th HTh TTh
.
+ .
+ .



T O . Th HTh
5 9 . 2 3
+ 1 4 . 8 8

T O . Th HTh
2 3 . 2 9
+ 4 3 . 7 6

H T O . Th HTh TTh
3 3 9 . 8 1 8
+ 2 8 5 . 3 0 0
+ 1 0 6 . 9 4 6

T O . Th HTh TTh
3 7 . 2 3 8
+ 2 6 . 0 4 6

113
2. 410.38 + 45.392 + 321.21
H T O . Th HTh TTh
.
+ .
+ .


3. 522.482 + 371.750 + 947.185
H T O . Th HTh TTh
.
+ .
+ .


4. 23.546 + 32.678 + 897.123

H T O . Th HTh TTh
.
+ .
+ .



114
After completing the worksheet
I felt
(Tick your response)


























There are 64 triangles hidden in the figure.
Let us see how many you can find?
115
Lesson Plan B
Worksheet 7
Colouring Effect
Name: ____________________ Class: _________________
Date: ____________________ Subject: ________________


































0.90 - 0.25
0.90 0.25 =
116
After completing the worksheet
I felt
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LETS TAKE A BREAK!














































Help the mother to find her cub.
117
Lesson Plan B
Worksheet 8
Colouring Effect
Name: ____________________ Class: _________________
Date: ____________________ Subject: ________________
A. Subtract the following:-
1. 2.





3. 4.





5. 6.






H T O Th HTh TTh
2 6 9 . 6 7 5
- 1 8 4 . 6 6 7

H T O Th HTh TTh
4 9 8 . 3 2 6
- 5 9 . 4 8 7

H T O Th HTh TTh
8 7 6 . 0 0 0
- 2 9 4 . 3 6 4

H T O Th HTh TTh
5 3 7 . 4 0 0
- 7 5 . 2 2 9

H T O Th HTh TTh
1 6 4 . 3 2 1
- 1 5 3 . 3 6 4

H T O Th HTh TTh
7 6 0 . 3 7 4
- 5 1 0 . 0 4 1

118
After completing the worksheet
I felt
(Tick your response)
B. Subtract the following:-
1. 567.89-243.24





2. 679.82-365.30





3. 753.214 482.968





4. 806 - 653.891




H T O Th HTh TTh
.
- .

H T O Th HTh TTh
.
- .

H T O Th HTh TTh
.
- .

H T O Th HTh TTh
.
- .

119
Lesson Plan B
Worksheet 9
Lets Join Hands
Name: ____________________ Class: _________________
Date: ____________________ Subject: ________________
A Read the following case studies:



CASE I: Heavy rains have caused destruction, sweeping roads away, destroying
bridges and tearing down houses in Mozambique and Limpopo. The situation
has reached disastrous levels after floods destroyed the southern parts of the
country.
People are living on roadsides, under trees, in halls and in schools. They are
hungry, need medicine and clothes.

CASE II: 20-year-old Marias home, crops and land where the cattle grazed were
destroyed by floods. The town was flooded due to heavy rains into the farmlands.
A temporary bridge was set up to allow the flow of traffic into and out of the
town. The locals were forced to travel on boats to reach their homes on the higher
lying areas.
120
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B. Imagine that your school is sending aid to these people in need.
List any 5 things that you would like to send to these FLOOD VICTIMS. And also
calculate the cost for the same in the Performa of the bill given below:
S.No. Item Cost per Unit* Quantity Total Cost






TOTAL COST

* Note: The number written in the Cost per Unit column should have at least one
decimal place.
C. Write the reason for selecting the above items.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________



121
Lesson Plan B
Worksheet 10
Lets Join Hands
Name: ____________________ Class: _________________
Date: ____________________ Subject: ________________
WORD STORIES
A. Rahul purchased a soap worth 3.40 and a comb worth 2.10.How much did he
spend in all?
Solution



Amount that Rahul spent= 5.50

B. Raja took part in a Relief Camp along with his society members. On the first
day, he spent 48.50, the second day he spent 39.85 and the third day he spent
50.45. How much money he spend in all?






3. 40
2. 10
. 5. 50
122
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C. Shobit wanted to be a part of the rescue team. He rented the following three
items for the rescue operation. How much amount did he spend in all?










D. Riya decided to donate the following items for the flood victims.







Find the total amount she has to pay to buy the above. Further if she gives a 1000
rupee note at the cash counter, how much money does she get back?




Items Price
Boat . 350.75
Search light . 125.55
Life Jacket . 26.30
Items Price
One Blanket 345.75
Medicines 58.60
Rice 95.65
Drinking Water Bottle 54.60
123
Lesson Plan B
Worksheet 11
Lets Join Hands
Name: ____________________ Class: __________________
Date: ____________________ Subject: ________________
Q1. Manu carried 40.40 to a stationery shop. He bought pens and notebooks worth
Rs 35.20.How much money did he take back home?




Amount that Manu took back= .5.20
Q2. Vinita and her friends are raising money for charity. They hope to raise 900 to
reach their goal. So far, they have collected 780.75. How much more do they
need to collect in order to reach their goal?











40. 40
- . 35. 20
. 5. 20
124
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Q3. Radha is participating in a rally organized by an organization. She needs to buy
a pair of shoes for . 195.00, a cap for Rs 27.75 and a health drink for . 9.80 for
herself. Calculate the total amount spent by her. If she gives the shopkeeper a
1000 rupee note, how much money will he give back to her?






Solution:

Q4. An NGO (Non Government Organization) collected 1803.75 for their project.
They already had 4413.85 in their bank .What is their present balance?



Q5. Raj bought clothes for . 5112.25 for the flood victims. He gave the shopkeeper
ten thousand rupees. How much money did the shopkeeper return to Raj?





195 . 00
27 . 75
+ 9 . 80
.
1 0 0 0 . 0 0
_ .
.
Amount spent by Radha
Amount returned by the
shopkeeper

125
Lesson Plan B
Worksheet 12
Lets Join Hands
Name: ____________________ Class: _________________
Date: ____________________ Subject: ________________
COME LETS HAVE FUN
Sequential Inputs of numbers with 8
1x8+1=9
12 x 8 + 2= 98
___ X 8 + 3= 987
1234 x 8 + 4= 9876
12345 x __ + 5 = 98765
123456 x 8 + 6 = _______
1234567 x 8 + _ = 9876543
_________ X __ + __ = _______
123456789 x 8 + 9 = 987654321
Sequential 1's with 9
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10 = 1111111111

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126
After completing the worksheet
I felt
(Tick your response)
Lesson Plan B
Worksheet 13
Reflection Time
Name: ______________ Class: _____________
Date: ________________ Subject:____________
Its time to reflect.
My Learning Areas
Have understood and ready to go
ahead

Oops! A few speed breakers ahead
Help ! Help! Help!!!

Where can I use this topic in day to day life?







127
Lesson Plan B
Worksheet 14
Reflection Time
Name: ______________ Class: _____________
Date: ________________ Subject:____________
The teacher will recapitulate the concepts:
































Write in words and in
expanded form 120.04
120. 04 = ___________
point four
120.04 = ----- x 100 + 2 x _____
+ ___ x 1 + __ x 1/10 +
______ -
Relationship of decimals with money:
e.g Reema purchased a trouser worth
Rs 853.50 and a shirt worth Rs. 910.
How much did she spend in all?
Cost of trouser _______________
Cost of shirt ____________________
Total Money spent = ___________

Addition of decimals: For
addition of decimals change
____________ to like decimals
Add: 2.34 + 4.46 = _______
Decimals
Subtraction of decimals: For
subtracting decimals change the
addends to ________________
Subtract 13.20 2.90
1 3. 2 0
2. 9 0


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128
Lesson Plan C
Worksheet 1
Merging Multiples
Name: ____________ Class: _____________
Date: _____________ Subject: _____________









































MULTIPLICATION
OF
DECIMALS
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129
Lesson Plan C
Worksheet 2
Merging Multiples
Name: _____________ Class: _____________
Date: ______________ Subject: _____________





































0.7 X 0.9












0.7 x 0.9 =
130
Referring to Handout 5 (Teachers Resource Material)
I. Let us multiply
A 45.234 x 6.2 B. 45234 x 62










Answer A: Answer B:
II. Complete the table given below in reference to the above answer:
ANSWER A B
Number name
Expanded form
Face value of 4
Place value of 4
Difference
Sum










MATHE--MAGIC

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131
Lesson Plan C
Worksheet 3
Merging Multiples
Name: ____________ Class: _____________
Date: ______________ Subject: _____________
A. Multiply the given decimals.
1) 0.4 x 0.3
2) 0.5 x 0.6
3) 4/10 x 5/10
4) 17/100 x 12/100
5) 0.02 x 0.03
6) 1.2 x 2.5











B. A community lunch is being organized in the Community Centre
of the society. Mrs. Annies task is to prepare fruit salad. For the
preparation, Mrs. Annie decided to walk down from her house to
the nearby local market to buy things.


Number of decimal places in the product is the sum of decimal places in
the decimals.
Place the decimal point, counting from the extreme right in the product.

Remember
132
i) Mrs. Annie walks at the rate of 6.56 km in one hour. How much distance
will she cover in 3.5 hours?










ii) Mrs. Annie plans to purchase apples for preparing Fruit Salad. If one kg
apples cost 45.50, find the cost of 6.75 kg apples.









iii) Mrs. Annie also buys some other items for the fruit salad: 2 dozen oranges
at the rate of 37.25 per dozen, 2 kg grapes at the rate of 41.75 per kg
and 2 tins of frozen fruits for 78.80 each.
Find the total amount of money spent by Mrs. Annie for the above items.













133
iv) While returning Mrs. Annie decided to hire a cab. If the cab travels 10.5 km
in 1 liter of petrol, how far will it travel in 5.5 liters of petrol?











C. Find the product:
1) 17.12 x 4.6
2) 14.1 x 0.06 x 100
3) 79.8 x 4.32 x10
4) 0.6 x 5.9 x 2.2
5) 9.29 x 5.7
6) 8.123 x 0.8123



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134
Lesson Plan C
Worksheet 4
Merging Multiples
Name: ______________ Class: _____________
Date: ______________ Subject: _____________
It is Divyas Birthday! She has decided not to take any money from her parents for
the celebration as she has been saving 100 from her pocket money each month for
the last 14 months.
A. Divya decides to spend some part of the expenses on giving a treat to all the old
people in the neighborhood. There are 5 grandmothers and 4 grandfathers in
Divyas neighborhood. Divya decided to buy Milkshakes worth 55.50 for each
one of them. What was the amount paid by Divya?



B. Divya invited five of her friends for a small treat to a neighborhood restaurant. She
ordered 5 burgers for 25.75 each. She requested the waiter to add on an extra
topping of salad which would cost her extra 5 each. What was the total amount
paid by her?



C. After the treat Divya takes all her friends to an amusement park. If one entrance
ticket costs 89.25 what is the cost of 5 such tickets?








135
D. Divyas friends decide to pool in and add a few more eatables to the
celebration. They go to a bakery and order the following items. Find the
total amount to be paid to the shopkeeper.
Item Quantity Cost of 1 item Total Cost
Pastry 4 Rs.19.20
Patty 5 Rs. 14.50
Cream roll 4 Rs. 8.75
TOTAL

E. Divyas parents give her Rs. 350 to purchase anything she wants. Divya decides to
buy a dress for herself.
On the way to the market, her younger brother joins her and insists on her buying
a game for him. As she moves further, she notices her gardener walking bare feet.





Help Divya take a decision on what she should purchase. Give your reasons. Find
the amount left with Divya after the purchase.













Rs 250 Rs 175 Rs. 350

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136
Lesson Plan C
Worksheet 5
Dividing Equally
Name: ____________ Class: _____________
Date: ______________ Subject: _____________


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I felt
(Tick your response)
137
Lesson Plan C
Worksheet 6
Dividing Equally
Name: ____________ Class: ____________
Date: ______________ Subject: _____________










138













































The given table shows the way of representing decimals in ancient times using
dots. Complete the given pattern till 50.

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(Tick your response)
139
Lesson Plan C
Worksheet 7
Dividing Equally
Name: ____________ Class: _____________
Date: ______________ Subject: _____________
A. Divide the given Decimals. In the empty space formulate a question of your
own based on the inputs from 1 to 6.
1) 4.5 0.9
2) 2.5 5
3) 26.4 0.2
4) 2.21.1
5) 2.80.7
6) 110.25 10
B. During a design and development class, students decided to create a
toy house from the available waste material.
(i) A wooden board of length 512.40 cm was cut into 28 equal
pieces to fix the walls and the roof. What is the length of each piece so
obtained?








140
(ii) To cover the floor students found an old rug from the store of dimension
5.75m x 2.50 m. But the store keeper instructed the students to use only 1/2
of the rug. Find the area of the rug students could use.









iii) The students decided to make a book shelf of dimensions 1.2m x 1.5m, how
much area will be covered if two such shelves are made by them?














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141
Lesson Plan C
Worksheet 8
Dividing Equally
Name: ______________ Class: _____________
Date: ______________ Subject: _____________
A. Find the value of the following:
1) 79.74 3.6
2) 27.09 2.1
3) 20.25 0.5
4) 62.44 0.2
5) 25.62 0.3

B. The product of two decimals is 525.676. If one decimal is 11.63, find the other?








C. A man spends 370.65 weekly on his food .How much does he spends in one
day if he spends the same amount each day?









142
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(Tick your response)
D. One dozen pineapple pastries cost 271.80.What is the cost of 1 pastry?





E. The cost of a box of 12 pencils is 35.76. What is the cost of one pencil?






Cost of 12 pencils = ___________
Cost of 1 pencil = ___________

143
Lesson Plan C
Worksheet 9
No Time
Name: ____________ Class: _____________
Date: ______________ Subject: _____________
PART A
1. If 7.28 = 7 + 2/10 + 8/100, then 0.728 = ______________________
2. 30 + 9 + 3/10 + 1/100 =
3. 3.657 is . than 4.123 (greater/smaller)
4. Write the next 3 series for : 9.025, 9.026, 9.027,_________, __________, __________
5. 7.2 1.1 = _________
6. A park is 100 m long and 120.5m wide. What is the perimeter of the park?
7. 0.2 __________________
8. 500 x 0.001 __________________
9. ____________
10. 77.9 x = 779
11. 3.0 10 =
12. = _______________
13. Arrange in ascending order: 8.56, 8.2, 8.22, .. , , .
14. Convert 17/6 into a mixed fraction.
15. 1/3 of a dozen = _________



144
Rubrics for assessment and validation
No. of correct answer - /50
14-15 - A
+
12-13 - A
10-11 - B
+
9-8 - B
Below 8 needs to practice
Signature of student Signature of teacher

PART B
1. If 26.38 = 20 + 6 + 3/10 + 8/100, then 2.638 = ______________________
2. 6 + 7/10 + 4/1000 = ( In decimal form)
3. 100.1 is . than 100.24 (greater/smaller)
4. Write the next 3 series for : 8.06, 8.07, 8.08,_________, __________, __________
5. 4.0675 + 5.0325 = _________
6. A park is 100 m long and 16.35 m wide. What is the area of the park?
7. 100 x 0.03__________________
8. 80 x 6.02__________________
9. Rohans height is 2.5 times more than his younger brother. If his younger brother
is 2 feet, find the Rohans height?
10. 0.538 x = 5.38
11. 429 = 0.0429
12. = _______________
13. Arrange in ascending order: 60.04, 6.04, 60.4, 0.60 - ______, ______, ______, ______
14. Convert 43/8 into a mixed fraction.


145
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I felt
(Tick your response)
15. 1/3 of a day (in hours) = _________
Rubrics for assessment and validation
No. of correct answer - /50
14-15 - A
+
12-13 - A
10-11 - B
+
9-8 - B
Below 8 needs to practice
Signature of student Signature of teacher









146
DECIMAL POINT EVERYWHERE

1

2


3

4

5



6

7

8 9

10


11 12



ACROSS DOWN
1.5.9 X 6.2 1. 6.7 X 5.1
3. 3.3X 3.8 2. 26.4 3
4. 4.7 1 3. 8.1 X 2.2
5. 19.6 2 4. 2.14 X 2
6. 162.6 6 5. 4.8 X 1.9
7. 49.2 6 9. 36.4 4
8. 87.03 3 10. 1.4 X 1.2
11. 27.2 2 12. 22.2 6

After completing the worksheet
I felt
(Tick your response)
Lesson Plan C
Worksheet 10
No Time
Name: ______________ Class: _____________
Date: ______________ Subject: _____________


































147
Lesson Plan C
Worksheet 11
Reflection Time
Name: ______________ Class: _____________
Date: ________________ Subject:____________
Its time to reflect.
My Learning Areas
Have understood and ready to go
ahead

Oops! A few speed breakers ahead
Help ! Help! Help!!!

Where can I use this topic in day to day life?








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I felt
(Tick your response)
148
Lesson Plan C
Worksheet 12
Review
Name: ______________ Class: _____________
Date: ________________ Subject:____________




































Steps to multiply Decimals:
Multiply 42.115 x 6


Multiplication of a Decimal
Number By 10, 100, 1000
6.8945 x 10 =
6.8945 x 100 =
6.8945 x 1000 =
Division of Decimal Number
by a Whole Number
Divide : 244.68 2
Multiplication and Division of
Decimal Numbers

Dividing a decimal by
Another Decimal
Divide: 40.5 0.5


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149
Students Manual
In the previous unit you made yourself familiar with the term fractional
numbers and the process of addition and subtraction of fractional numbers. In
this unit you will understand the process of multiplication and division of
fractions. You will be able to understand the importance of decimal point and
will be able to perform mathematical operations of addition, subtraction, multiplication
and division using decimals.
The activities in the unit are planned in a manner where you can freely express your
ideas, beliefs, values etc and make mathematics an integral part of your system



TOPIC A: Multiplication and Division of Fractional Numbers
In this lesson you will understand the process of multiplication and division of fraction.
A. Multiplication of fractional number with a whole number:
Let us multiply: 5/8 x 4.
Multiplication is a repeated addition

Arranging the four sets in the form of a circle.

=
Hence 5/8 x 4 = 5/8 + 5/8 + 5/8 + 5/8 = 2
OR
150
Steps of Multiplication
Step 1: Write the whole number as a fraction.
Step 2: Multiply the numerators and the denominators.
Step 3: Reduce to the lowest terms
2
OR
20 10 = 10 = 5
8 4 2 2
B. Multiplication of fractional number with a fractional number:
Let us multiply: 5/8 x 2/7
Following the steps of Multiplication, we get:
x = = =
C. Dividing a fractional number with a fractional number:
Let us divide by
When you divide you are cutting into equal shares
There are 3 Simple Steps to Divide Fractions
Step 1: Turn the second fraction (the one you want to divide by) Upside Down. This is
now a reciprocal.
The reciprocal of is
Step 2: Multiply the first fraction by the reciprocal of other

= x =
Step 3: Simplify the fraction (if needed).
151
= =
A Review









































Multiplication of a whole number
with a fractional number.
Step 1: Write the whole number as a
fraction.
Step 2: Multiply the numerators and
the denominators.
Step 3: Reduce to the lowest terms
3/7 x 21 = = = = 9
Multiplication of a fractional
number with a fractional
number.
1/6 x 2/3 =

Division of fractions
Reciprocal of A Number: Two numbers are said to be reciprocal of each
other if their product is 1. For Example: The reciprocal of is
1/8
x 8 = = 4
Step 1: Turn the second fraction (the one you want to divide by)
Upside Down.
Step 2: Multiply the first fraction by that reciprocal.
Step 3: Simplify the fraction if needed.

Fractions Multiplication and
Division of Fractional Numbers

152
Topic B: Decimals : Addition and Subtraction





In this lesson, you will be able to understand the importance of decimal point and will
be able to perform mathematical operations of addition, subtraction, multiplication and
division using decimals. This lesson will help you to understand the role of the decimal
and the relationship of decimals with money.







Let's examine these decimals in our place-value chart
PLACE VALUE AND DECIMALS







D
e
c
i
m
a
l

1/10

1/100

1/1000








In Words (while
Reading)







In Words (while Writing)

3 . 2 4 Three point two four Three and twenty four hundredths

3 . 0 7 2 Three point zero seven
two
Three and seventy two thousandths

3 7 . 0 2 Thirty seven point zero
two
Thirty seven and two hundredths

3 2 7 . 4 Three hundred twenty
seven point four
Three hundred twenty seven and four
tenths
As we move left, each position is 10 times bigger And as we move right, each
position is 10 times smaller
153
3.24 = (3 x 1) + (2 x ) + (4 x 1/100)
3.072 = (3 x 1) + (0 x 1/10) + (7 x 1/100) + (2 x 1/1000)
37.02 = (3 x10) + (7 x 1) + (0 x 1/10) + (2 x 1/100)
327.4 = (3 x 100) + (2 x 10) + (7 x 1) + (4 x 1/10)
Decimal form Nine point zero eight nine = 9.089
Expanded form : 9 x 1+ 0 x + 8 x + 9 x
Like Decimals : Decimal numbers having same number of decimal places in the
fractional part for example 2.45, 415.78, 9.02)
A. Addition of Decimals
Steps:
Adding decimals is very much like adding whole numbers.
To add two Decimals, first these should be converted into like Decimals.
Then the Decimal point of the two numbers should be aligned and all the
digits should be put in that order, i.e units place of second number should be
aligned to unit place, tens to tens, tenth to tenth and so on.
All these should be added like simple addition and a decimal point should be
put in total alignment with Decimal point of the two numbers.
22.3 22.3 22.3
+ 34.1 + 34.1 + 34.1
.4 6.4 56. 4
Add the following : 11.22 + 3.14 = 14.36







T O . Th HTh
1 1 . 2 2
+ 3 . 1 4
1 4 . 3 6
154
B. Subtraction of Decimals
As usual in addition, start on the right, and add each column in turn.
To subtract decimals, follow these steps:
The most important thing to remember when subtracting decimals is to line up all
the decimal points in a column!
Write down the two numbers, one under the other, with the decimal points
lined up.
Add zeros so the numbers have the same length ( like decimals)
Then subtract normally, remembering to put the decimal point in the answer
Example: Calculate 4.059 0.06
3 9 15
4 . 0 5 9
- 0 . 0 6 0
3 . 9 9 9

Subtract: 467.83 from 760.374
760.374 467.83













H T O . Th HTh TTh
7 6 0 . 3 7 4
- 4 6 7 . 8 3 0
= 2 9 2 . 5 4 4
155
A Review



































Multiplication and Division of Decimal Numbers
A. Multiplication of Decimal Numbers:
Steps to multiply Decimals:

Write in words and in expanded
form 3.24
3.24 =Three point two four
3.24 = 3 x 1 + 2 x + 4 x
1/ 100

Relationship of decimals with
money: e.g Rahul purchased a
pen worth Rs 3.40 and pencil
worth Rs. 2.10.How much did
he spends in all?
Rs 3. 40
Rs. 2. 10
Rs. 5. 50



Addition of decimals: For addition
of decimals change the addends to
like decimals (Decimal having
same number of decimal places e.g
2.34, 13.67, 0.78)
Add: 2.34 + 4.46 = 6.80
Decimals: Addition and Subtraction
Subtraction of decimals: For
subtracting decimals change the
addends to like decimals
Subtract: 6.80 - 2.34 = 4.46

156
Let us multiply 45.234 x 6.2
Step 1: Multiply the given numbers as you normally multiply whole numbers
ignoring the decimal points.

4 5 2 3 4
x 6 2
9 0 4 6 8
2 7 1 4 0 4 x
2 8 0 4 5 0 8

Step 2: Count the total number of decimal places of both numbers together.

45.234 - 3 decimal places
6.2 - 1 decimal place
Total - 4 decimal places
Step 3: Insert the decimal point in the product calculated in Step 1, from the right
equal to the number of decimal places counted in Step 2.
2 8 0 . 4 5 0 8
Answer: 45.234 x 6.2 = 280.4508













Remember:
Number of decimal places in the product is the sum of decimal
places in the decimals.
Place the decimal point, counting from the extreme right in the
product.

157
Multiplication of a Decimal Number By 10, 100, 1000
7.9438 x 10 = 79.438
The decimal point moves to the right by one place if the number is
multiplied by 10.
7.9438 x 100 = 794.38
The decimal point moves to the right by two places if the number is
multiplied by 100.
7.9438 x 1000 = 7943.8
The decimal point moves to the right by three places if the number is
multiplied by 1000.
























We want to multiply 7943.8 by 100
An extra zero is placed, as the decimal point is to be
shifted 2 places to its right.
7943.8 x 100 = 794380
Remember: To convert a decimal number into a whole number, always
multiply with the multiple of 10 having the same number of zeroes as the
number of decimal places.
For Example: Convert 7.943 into a whole number.
To convert 7.943 into a whole number, count the number of decimal places
in 7.943.
7 . 9 4 3 (3 decimal places)
To cover 3 decimal places we need to multiply by 1000.
Hence 7.943 x 1000 = 7943
158
Division of Decimal Number by a Whole Number
Let us divide 435.6 by 12
(Dividend) (Divisor)
Step 1: First divide the whole number part of the dividend.
Step 2: Then place the decimal point (.) at exactly the same position in the quotient as
in the dividend.
Step 3: Divide the decimal part of the dividend.
3 6 . 3
12 4 3 5 . 6
3 6
7 5
7 2
3 6
3 6
0 0





Dividing a decimal by Another Decimal
Let us divide 270.3 by 0. 17
(Dividend) (Divisor)
We follow the given steps:
Step 1: First multiply the divisor by 10, 100 or 1000 to convert the divisor into a whole
number.
0.1 7
2 place decimal To cover 2 decimal places we need to multiply by 100

Remember: The decimal point is only placed in the quotient and the dividend.
Elsewhere in the calculation, the decimal point is not required to be shown.
Remember: Place extra zeroes to complete the
division wherever there is a remainder which is
less than the divisor.
159
Step 2: Also multiply the dividend by the same number (10, 100, 1000) to keep the value
of divisor and dividend same.
Hence = = = 1590








Dividing a decimal by 10, 100, 1000










For Example:
3276.4 10 = 327.64
3276.4 100 = 32.764
3276.4 1000 = 3.2764

1590
17 27030
- 17
100
- 85
153
- 153
0000
0
Remember: The decimal point moves 1 place, 2 places and 3 places to the right
when multiplied by 10, 100 and 1000 respectively. In case of division, the
decimal point moves to the left as many places as number of zeroes in the
divisor.
160
A Review


























Steps to multiply Decimals:
Step 1: Multiply the given numbers
as you normally multiply whole
numbers ignoring the decimal
points.
Step 2: Count the total number of
decimal places of both numbers
together.
Step 3: Insert the decimal point in
the product calculated in Step 1,
from the right equal to the number
of decimal places counted in Step 2.
45.234 x 6.2 = 280.4508


Multiplication of a Decimal
Number By 10, 100, 1000
7.9438 x 10 = 79.438
The decimal point moves to the
right by one place if the number
is multiplied by 10.
7.9438 x 100 = 794.38
The decimal point moves to the
right by two places if the
number is multiplied by 100
7.9438 x 1000 = 7943.8
The decimal point moves to the
right by three places if the
number is multiplied by 1000.
Multiplication and Division of
Decimal Numbers

161













































Division of Decimal Number by a
Whole Number
Step 1: First divide the whole
number part of the dividend.
Step 2: Then place the decimal
point (.) at exactly the same
position in the quotient as in the
dividend.
Step 3 : Divide the decimal part of
the dividend.
3 6 . 3
12 4 3 5 . 6
3 6
7 5
7 2
3 6
3 6
0 0

Dividing a decimal by Another
Decimal
We follow the given steps:
Step 1: First multiply the divisor
by 10, 100 or 1000 to convert the
divisor into a whole number.
Step 2: Also multiply the
dividend by the same number (10,
100, 1000) to keep the value of
divisor and dividend same.
For Example: 270.3 0.17

= = = 1590

Dividing a decimal by 10, 100, 1000
The decimal point moves 1 place, 2 places and 3 places to
the right when multiplied by 10, 100 and 1000 respectively.
In case of division, the decimal point moves to the left as
many places as number of zeroes in the divisor.
162
TIME FRAME
Lesson Plans A B C D

Total
No of
periods
Curriculum
Time Min. Min. Min. Min. Min.
Subject
English 70 105 105 140 105 525 15
Direct and Indirect speech
Simlies and Metaphors
Phrasal verbs
Interviewing a famous personality
Letter writing-Formal and
informal
Mathematics 175 175 175

525 15
Multiplication and division of
fractional numbers
Word problems decimals: using all
the basic operations-Addition,
Subtraction, Multiplication
Division
Addition, Subtraction,
Multiplication Division of three
digit and four digit numbers with
same number of decimal places
Science 210 105 175

490 14
Ant or bee colony and their life
cycle
Rearing of important insects-
apiculture and sericulture
Communicable diseases,
Understand the ways to care for
environment
Reports on weather data, Natural
Disasters
Social Science 245 210 105

560 16
Variation in shelter according to
the climate material available
Monuments and their historical
background
Seven wonders of the world
Mapping- sketch the society
neighbourhood using signs and
symbols
163
Displacement and demolition -
Natural and Reconstruction
Visual Arts 70 70

140 4
Perspective distance and
overlapping
Poster making: depicting the
qualities of famous monuments
using symbolic elements and
typography
Snow in the desert from ant's
viewpoint


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CENTRAL BOARD OF SECONDARY EDUCATION