Imagine_Maths_TM_Grade2 by Uolo

Imagine Mathematics seamlessly bridges the gap between abstract mathematics and real-world relevance, offering engaging narratives, examples and illustrations that inspire young minds to explore the beauty and power of mathematical thinking. Aligned with the NEP 2020, this book is tailored to make mathematics anxiety-free, encouraging learners to envision mathematical concepts rather than memorize them. The ultimate objective is to cultivate in learners a lifelong appreciation for this vital discipline.

Imagine Mathematics

About the Book

MATHEMATICS Teacher Manual

Key Features • Let’s Recall: Helps to revisit students’ prior knowledge to facilitate learning the new chapter • Real Life Connect: Introduces a new concept by relating it to day-to-day life • Examples: Provides the complete solution in a step-by-step manner

• Do It Together: Guides learners to solve a problem by giving clues and hints • Think and Tell: Probing questions to stimulate Higher Order Thinking Skills (HOTS) • Error Alert: A simple tip off to help avoid misconceptions and common mistakes • Remember: Key points for easy recollection • Did You Know? Interesting facts related to the application of concept • Math Lab: Fun cross-curricular activities • QR Codes: Digital integration through the app to promote self-learning and practice

About Uolo Uolo partners with K-12 schools to provide technology-based learning programs. We believe pedagogy and technology must come together to deliver scalable learning experiences that generate measurable outcomes. Uolo is trusted by over 10,000 schools across India, South East Asia, and the Middle East.

Singapore

IM_G02_MA_MB_Cover_TM.indd All Pages

Gurugram

Bengaluru

hello@uolo.com

NEP 2020 based

NCF compliant

CBSE aligned

07/02/24 4:02 PM

Teacher Manual

MATHEMATICS Master Mathematical Thinking

Grade 2

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Fo re wo rd

Mathematics is not just another subject. It is an integral part of our lives. It shapes the very foundation of our understanding, personality and interaction with the world around us. However, due to the subject’s abstract nature, the stress of achieving high academic scores and complex teaching methods, most children develop a fear of mathematics from an early age. This fear not only hinders their mathematical thinking, logical reasoning and general problem solving abilities, but also negatively impacts their performance in other academic subjects. This creates a learning gap which widens over the years. The NEP 2020 has distinctly recognised the value of mathematical thinking among young learners and the significance of fostering love for this subject by making its learning engaging and entertaining. Approaching maths with patience and relatable real-world examples can help nurture an inspiring relationship with the subject. It is in this spirit that Uolo has introduced the Imagine Mathematics product for elementary grades (1 to 8). This product’s key objective is to eliminate the fear of mathematics by making learning exciting, relatable and meaningful for children. This is achieved by making a clear connection between mathematical concepts and examples from daily life. This opens avenues for children to connect with and explore maths in pleasant, relatable, creative and fun ways. This product, as recommended by the NEP 2020 and the recent NCF draft, gives paramount importance to the development of computational and mathematical thinking, logical reasoning, problem solving and mathematical communication, with the help of carefully curated content and learning activities. Imagine Mathematics strongly positions itself on the curricular and pedagogical approach of the Gradual Release of Responsibility (GRR), which has been highly recommended by the NEP 2020, the latest NCF Draft and other international educational policies. In this approach, while learning any new mathematical concept, learners first receive sufficient modelling, and then are supported to solve problems in a guided manner before eventually taking complete control of the learning and application of the concept on their own. In addition, the book is technologically empowered and works in sync with a parallel digital world which contains immersive gamified experiences, video solutions and practice exercises among other things. Interactive exercises on the digital platform make learning experiential and help in concrete visualisation of abstract mathematical concepts. In Imagine Mathematics, we are striving to make high quality maths learning available for all children across the country. The product maximises the opportunities for self-learning while minimising the need for paid external interventions, like after-school or private tutorial classes. The book adapts some of the most-acclaimed, learner-friendly pedagogical strategies. Each concept in every chapter is introduced with the help of real-life situations and integrated with children’s experiences, making learning flow seamlessly from abstract to concrete. Clear explanations and simple steps are provided to solve problems in each concept. Interesting facts, error alerts and enjoyable activities are smartly sprinkled throughout the content to break the monotony and make learning holistic. Most importantly, concepts are not presented in a disconnected fashion, but are interlinked and interwoven in a sophisticated manner across strands and grades to make learning scaffolded, comprehensive and meaningful. As we know, no single content book can resolve all learning challenges, and human intervention and support tools are required to ensure its success. Thus, Imagine Mathematics not only offers the content books, but also comes with teacher manuals that guide the pedagogical transactions that happen in the classroom; and a vast parallel digital world with lots of exciting materials for learning, practice and assessment. In a nutshell, Imagine Mathematics is a comprehensive and unique learning experience for children. On this note, we welcome you to the wonderful world of Imagine Mathematics. In the pages that follow, we will embark on a thrilling journey to discover wonderful secrets of mathematics—numbers, operations, geometry and measurements, data and probability, patterns and symmetry, algebra and so on and so forth. Wishing all the learners, teachers and parents lots of fun-filled learning as you embark upon this exciting journey with Uolo. ii

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Key El emen t s o f a L e sso n— A Q u i c k G lanc e 1

Numbers up to 200 Imagine Mathematics Headings

CB Page

Clear and concise lessons that can be implemented through the

Clear, specific and measurable learning outcomes that show Building Numbers up to 200 3

academic year with each perfectly aligned to the topics covered

Place Value and Expanded Form what students should know, understand, or do by the end4 of

1 Numbers up content to 200 in the Imagine Mathematics learners’ book. 1

Numbers up to 200

Odd and Even Numbers

Imagine Mathematics Headings

CB Page

Numbers up to 200

Building Numbers up to 200

Place Value and Expanded Form

Comparing and Ordering Numbers

Ordinal Numbers

10 CB12Page

Imagine Mathematics Headings Odd and Even Numbers Building Numbers up to 200

Place Value and Expanded Form Learning Outcomes

Comparing and Ordering Numbers

Ordinal Numbers the lesson.

Numbers up to 200

Odd andthe Even Numbers identify place value for numbers up to 200 and write them in expanded form.

compare and order numbers up to 200.

Learning Outcomes

Imagine Mathematics Headings Students will be able to: Building Numbers up to 200 write numbers up to 200 using numerals and number names. Place Value and Expanded identify the place valueForm for numbers up to 200 and write them in expanded form.

CB Page 3 4

Comparing Numbers compareand andOrdering order numbers up to 200.

Numbers up to 200

readNumbers and write ordinal numbers from 1st to 10th. Ordinal odd and even numbers. Oddidentify and Even Numbers

10 12

Alignment to NCF Learning Outcomes

Comparing and Ordering Numbers Students will be able to: Ordinal Numbers write numbers up to 200 using numerals and number names.

C-8.3: Reads and writes Indian numerals for numbers up to ninety-nine using place value in groups of tens Students will be able to: and ones Imagine Mathematics Headings CB Page write to 200 using number names. C-8.4:numbers Arrangesup numbers from numerals a given setand of numbers in ascending and descending order Building Numbers up to 200 3 identify the place and value for numbers up toand 200smallest and write them innumbers expanded form. C-8.5: Compares forms the greatest two-digit (with and without repetition of Place Value and Form 4 compare andExpanded order numbers up to 200.number names and numerals up to 99 using place value concept given digits). Recognises, reads, writes

Learning Outcomes asfrom recommended by the NEP 2020 and the read and write ordinal numbers 1st to 10th. Learning Outcomes

Comparing Ordering Numbers 6 read andand write ordinal numbers from the 1st to 10th. Recap exercises to check understanding of prerequisite

Students will be able to: Imagine Mathematics Headings latest National Curricular Framework (NCF). write numbers up to 200 using numerals and number names.

concepts before starting OddRecap and Even Numbers to check if students know howa to topic. count numbers from 1 to 9.

identify odd and even numbers.

CB Page

Alignment to NCFup to 200 Building Numbers

identify the place value for numbers up to 200 and write them in expanded form. C-8.3: Readsand andExpanded writesnumbers Indian Place Value Formnumerals compare and order up to 200.for numbers up to ninety-nine using place value in groups4 of tens and ones and Ordering Numbers Comparing 6 read and write ordinal numbers from 1st to 10th. C-8.4: Arranges numbers from a given set of numbers in ascending and descending order identify odd and even numbers. Ordinal Numbers 10 C-8.5: Compares and forms the greatest and smallest two-digit numbers (with and without repetition of Odd and Even Numbers 12 given digits). Recognises, reads, writes number names and numerals up to 99 using place value concept

Alignment to NCF

C-8.3: Reads and writes Indian numerals for numbers up to ninety-nine using place value in groups of tens

Let’s Recall Outcomes Learning and ones

Let’s Recall identify odd and even numbers. Ordinal Numbers

numbers upand to 200 using and number names. Askwrite students to solve the questions given in thesmallest Let’s Warm-up section. C-8.5: Compares forms the numerals greatest and two-digit numbers (with and without repetition of given digits). Recognises, writes names and numerals up to 99 using place value concept identify the place value forreads, numbers upnumber to 200 and write them in expanded form.

compare and order numbers up to 200. Vocabulary Let’s Recall read and write ordinal numbers from 1st to 10th.

Recap toAids check if students know how to count numbers from 1 to 9. Teaching

Ask students to solve the questions given in the Let’s Warm-up section.

Alignment toblocks NCFof 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s; Number cards for Place value

8 numbers 50 Indian to 200:numerals 58, 189, 79, 118, 146, 152, 176; Number with 8of tens C-8.3: Readsbetween and writes for197, numbers up to ninety-nine usingchart place1–200; value Strip in groups Vocabulary squares; and ones Coloured square cut-outs with L in the orange square, E in blue, A in yellow, R in red, N in green, counting forward: counting by adding one I in purple, N in pink, G in grey; 2 groups of every small time straws—6 small straws and 9 small straws; 6 Bangles C-8.4: Arranges numbers from a given set of numbers in ascending and descending order counting backward: counting by subtracting one every time C-8.5: Compares and forms the greatest and smallest 1 two-digit numbers (with and without repetition of place value: value of a digit based on its position in the number given digits). Recognises, reads, writes number names and numerals up to 99 using place value concept expanded form: the way to write a number by adding the value of its digits

counting forward: counting by adding one every time identify odd andif even numbers. how to count numbers from 1 to 9. Recap to check students counting backward: countingknow by subtracting one every time Askvalue: students to of solve the questions given in thein Let’s place value a digit based on its position theWarm-up numbersection.

Alignment to NCF

expanded form: the way to write a number by adding the value of its digits

C-8.3: Reads and writes Indian numerals for numbers up to ninety-nine using place value in groups of tens Vocabulary and ones

counting Teaching Aidsforward: counting by adding one every time

C-8.4: Arranges from a giventhe set of numbers in ascending and descending Vocabulary tonumbers help know important terms thatorder are counting backward: counting by subtracting one every time

Let’s Recall Teaching Aids

introduced, defined or emphasized in the chapter. Teaching Aids

1 Recap to check if students know how to count numbers from 1 to 9. Place value blocks of 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s; Number cards for Ask students to solve the questions given in the Let’s Warm-up section. 8 numbers between 50 to 200: 58, 189, 79, 197, 118, 146, 152, 176; Number chart 1–200; Strip with 8 squares; Coloured square cut-outs with L in the orange square, E in blue, A in yellow, R in red, N in green, Vocabulary I in purple, N in pink, G in grey; 2 groups of small straws—6 small straws and 9 small straws; 6 Bangles counting forward: counting by adding one every time 2/3/2024 11:58:41 AM

Recap to check if students know how to count numbers from 1 to 9.

Place value blocks of 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s; Number cards for Aids and resources that the Ask students to solve the questions given inteachers the Let’s Warm-upmay section.use to significantly

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Place value blocks ofand 100s, 10sthe andgreatest 1s; Place value charttwo-digit showingnumbers 100s, 10s(with and and 1s; Number cards for of C-8.5: Compares forms and smallest without repetition place value: value of a digit based on its position in the number 8 numbers between 50 to 200: 58, 189, 79, 197, 118, 146,and 152,numerals 176; Number 1–200; Strip with 8 given digits). Recognises, reads, writes number names up to chart 99 using place value concept expanded form:square the way to writewith a number byorange addingsquare, the value ofblue, its digits squares; Coloured cut-outs L in the E in A in yellow, R in red, N in green, I in purple, N in pink, G in grey; 2 groups of small straws—6 small straws and 9 small straws; 6 Bangles Let’s Recall

improve the teaching and learning process for the students. 1

counting backward: counting by subtracting one every time

place value: value of a digit based on its position in the number

expanded form: the way to write a number by adding the value of its digits

Teaching Aids

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expanded form: the way to write a number by adding the value of its digits

Teaching Aids

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2 groups of small straws—6 small straws and 9 small straws; 6 Bangles

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Place value blocks of 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s; Number cards for 8 numbers between 50 to 200: 58, 189, 79, 197, 118, 146, 152, 176; Number chart 1–200; Strip with 8 squares; Coloured square cut-outs with L in the orange square, E in blue, A in yellow, R in red, N in green, I in purple, N in pink, G in grey; 2 groups of small straws—6 small straws and 9 small straws; 6 Bangles

Activity

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Learning Outcomes Students will be able to identify odd and even numbers.

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activities and extension

Discuss some real-life things that come in pairs like socks, gloves, etc. Instruct students to form groups of 4. Distribute a set of 6 straws, 9 straws and 6 bangles to each group. Ask them to first use 6 straws and 3 bangles and put pairs of straws inside the bangles. They will then use 9 straws and 5 bangles to make pairs. Discuss that any number that forms pairs with no leftover is an even number and that a number that has a leftover is an odd number. Instruct students to draw 6 lines and 9 lines to show the straws in their notebooks, circle pairs of lines and then write the number and whether it is odd or even. Ask questions like: What type of number will you get if you add one more straw to 9 straws?

learning.

Answers, provided at

Imagine Maths Page 12

Odd and Even Numbers

plan that outlines the

used to facilitate

Activity

Extension Idea Ask: If we add two even numbers, do we get an odd number or an even number? Say: If we add two even numbers, we will get an even number because the two numbers already form pairs without any leftovers.

1. Building Numbers up to 200

4. Ordinal Numbers

Think and Tell

Do It Together

20 boxes with 10 sweets in each = 20 tens = 200. It has 20 tens or 2 hundreds.

1. B

We write this as 2 hundreds 0 tens. Do It Together 1. 1 hundred, 1 ten and 4 ones – one hundred fourteen

2. Place Value and Expanded Form Do It Together In 196, the place value of 1 is 100, 9 is 90 and 6 is 6. The expanded form of 196 is 100 + 90 + 6.

3. Increasing and Decreasing Order Do It Together Increasing order: 109, 111, 123, 132, 143

Decreasing order: 143, 132, 123, 111, 109 4

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3. T

given in Do It Together

11:58:41 AM

Ask: If we add two even numbers, do we get an odd number or an even number? Say: If we add two even numbers, we will get an even number because the two numbers already form pairs without any leftovers.

Answers 1. Building Numbers up to 200

4. Ordinal Numbers

Think and Tell

Do It Together

20 boxes with 10 sweets in each = 20 tens = 200. It has 20 tens or 2 hundreds.

1. B

We write this as 2 hundreds 0 tens. Do It Together 1. 1 hundred, 1 ten and 4 ones – one hundred fourteen 2. 1 hundred, 1 ten and 2 ones – one hundred twelve

and Think and Tell

2. Place Value and Expanded Form

sections of the Imagine

3. Increasing and Decreasing Order

Mathematics book.

Answers 2. A

the end of each chapter, for the questions

2 groups of small straws—6 small straws and 9 small straws; 6 Bangles

2. 1 hundred, 1 ten and 2 ones – one hundred twelve

Discuss some real-life things that come in pairs like socks, gloves, etc. Instruct students to form groups of 4. Distribute a set of 6 straws, 9 straws and 6 bangles to each group. Ask them to first use 6 straws and 3 bangles and put pairs of straws inside the bangles. They will then use 9 straws and 5 bangles to make pairs. Discuss that any number that forms pairs with no leftover is an even number and that a number that has a leftover is an odd number. Instruct students to draw 6 lines and 9 lines to show the straws in their notebooks, circle pairs of lines and then 2/3/2024 write the number and whether it is odd or even. Ask questions like: What type of number will you get if you add one more straw to 9 straws?

Extension Idea

Teaching Aids

ideas that are to be

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Place value blocks of 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s; Number cards for 8 numbers between 50 to 200: 58, 189, 79, 197, 118, 146, 152, 176; Number chart 1–200; Strip with 8 Odd and Even Numbers Imagine Maths Page 12 squares; Coloured square cut-outs with L in the orange square, E in blue, A in yellow, R in red, N in green, Learning Outcomes will be able to small identify odd straws and even numbers. I in purple, N in pink, G in grey; 2 groups of smallStudents straws—6 and 9 small straws; 6 Bangles

place value: value of a digit based on its position in the number

organized lesson

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8 numbers between 50 to 200: 58, 189, 79, 197, 118, 146, 152, 176; Number chart 1–200; Strip with 8 squares; Coloured square cut-outs with L in the orange square, E in blue, A in yellow, R in red, N in green, Vocabulary I in purple, N in pink, G in grey; 2 groups of small straws—6 small straws and 9 small straws; 6 Bangles counting forward: counting by adding one every time

counting backward: counting by subtracting one every time

A concise and

Ask students to solve the questions given in the Let’s Warm-up section. C-8.3: Reads and writes Indian numerals for numbers up to ninety-nine using place value in groups of tens Learning Outcomes and ones Vocabulary Students be able to: C-8.4: will Arranges numbers from a given set of numbers in ascending and descending order counting forward: counting by adding one every time write upand to 200 using andsmallest number two-digit names. numbers (with and without repetition of C-8.5:numbers Compares forms the numerals greatest and counting backward: counting by subtracting one every time given digits). Recognises, writes names and numerals up to 99 using place value concept identify the place value forreads, numbers upnumber to 200 and write them in expanded form. place value: value of a digit based on its position in the number compare and order numbers up to 200. expanded form: the way to write a number by adding the value of its digits Let’s Recall read and write ordinal numbers from 1st to 10th. identify odd and even numbers.

Students beifable to: know Recap to will check students to count 1 to 9. and descending order C-8.4: Arranges numbers fromhow a given set ofnumbers numbers from in ascending

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Alignment to NCF

Do It Together In 196, the place value of 1 is 100, 9 is 90 and 6 is 6. The expanded form of 196 is 100 + 90 + 6.

2. A

3. T

4. No

5. Odd and Even Numbers Think and Tell If we add two odd numbers, we will get an even number because the two leftovers without a pair will be paired together. Do It Together 2

Even

Odd

Even

Odd

Do It Together Increasing order: 109, 111, 123, 132, 143

Decreasing order: 143, 132, 123, 111, 109 4

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4. No

5. Odd and Even Numbers Think and Tell If we add two odd numbers, we will get an even number because the two leftovers without a pair will be paired together. Do It Together 2

Even

QR Code: Access to Even

Odd

Even

Odd

digital solutions and other interactive 2/3/2024 11:58:42 AM

resources.

iii

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Pe ri od Plan

The teacher manuals corresponding to Imagine Mathematics books for Grades 1 to 8 align with the recently updated syllabus outlined by the National Curriculum Framework for School Education, 2023. These manuals have been carefully designed to support teachers in various ways. They provide recommendations for hands-on and interactive activities, games, and quizzes that aim to effectively teach diverse concepts, fostering an enriched learning experience for students. Additionally, these resources aim to reinforce critical thinking and problem-solving skills while ensuring that the learning process remains enjoyable. In a typical school setting, there are approximately 180 school days encompassing teaching sessions, exams, tests, events, and more. Consequently, there is an average of around 120 teaching periods throughout the academic year. The breakdown of topics and the suggested period plan for each chapter is detailed below.

Chapters

No. of Periods

Break-up of Topics

Building Numbers up to 200

Place Value and Expanded Form 1. Numbers up to 200

Comparing and Ordering Numbers Ordinal Numbers Odd and Even Numbers Revision Addition Without Regrouping

2. Addition of 2-Digit Numbers

Addition With Regrouping; Adding More Than 2 Numbers Story Sums Revision Subtraction Without Regrouping

3. Subtraction of 2-Digit Numbers

Subtraction With Regrouping; Finding the Missing Number Story Sums Revision Grouping

4. Multiplication

Repeated Addition What Is Multiplication? Revision Multiplication by 2

5. Multiplication Tables: 2, 5, and 10

Multiplication by 5 6

Multiplication by 10 Story Sums Revision

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Forming Numbers up to 999 6. Numbers up to 999

Place Value and Expanded Form Comparing and Ordering Numbers Revision Addition of 3-digit Numbers

7. Addition and Subtraction of 3-Digit Numbers

Subtraction of 3-digit Numbers Word Problems on Addition and Subtraction Revision Multiplying by 3 Multiplying by 4

8. Multiplication Tables 3, 4, and 6

Multiplying by 6 9

Multiplication Without Regrouping Multiplication With Regrouping Story Problems on Multiplication Revision Division as Equal Sharing Division as Repeated Subtraction

9. Introduction to Division

Division and Multiplication Are Related Long Division Word Problems on Division Revision Parts of Whole

10. Understanding Fractions

Halves, Thirds and Fourths Writing Fractions Revision Length Using Things Around Us Centimetre Metre

11. Measurement

Weight Using Things Around Us Weight by Standard Units Capacity Using Things Around Us Capacity by Standard Units Revision

Period Plan

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All About Lines Features of Flat Shapes Drawing Flat Shapes Features of Solid Shapes 12. Shapes and Patterns

Flat Shapes in Solid Shapes Repeating Patterns Growing Patterns Number Patterns Revision Time on a Clock Days of the Week

13. Time

Months of the Year Seasons and Festivals Story Problems on Time Revision Indian Coins and Notes

14. Money

Exchange of Money Adding and Subtracting Money Revision Counting Data Organising Data

15. Data Handling

Finding Information Pictograph Revision

Total Number of Periods

122

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C o nt e nt s

Numbers up to 200 ��1

Addition of 2-digit Numbers ��5

Subtraction of 2-digit Numbers ��9

Multiplication ��13

Multiplication Tables: 2, 5, and 10 ��16

Numbers up to 999 ��20

Addition and Subtraction of 3-digit Numbers ��24

Multiplication Tables 3, 4 and 6 ��28

Introduction to Division ��33

10 Understanding Fractions ��37 11 Measurement ��40 12 Shapes and Patterns ��46 13 Time ��52 14 Money ��56 15 Data Handling ��60 Solutions ��64

Contents

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Numbers up to 200 Imagine Mathematics Headings

CB Page

Building Numbers up to 200

Place Value and Expanded Form

Comparing and Ordering Numbers

Ordinal Numbers

Odd and Even Numbers

Learning Outcomes Students will be able to:

write numbers up to 200 using numerals and number names. identify the place value for numbers up to 200 and write them in expanded form. compare and order numbers up to 200. read and write ordinal numbers from 1st to 10th. identify odd and even numbers.

Alignment to NCF C-8.3: Reads and writes Indian numerals for numbers up to ninety-nine using place value in groups of tens and ones C-8.4: Arranges numbers from a given set of numbers in ascending and descending order C-8.5: Compares and forms the greatest and smallest two-digit numbers (with and without repetition of given digits). Recognises, reads, writes number names and numerals up to 99 using place value concept

Let’s Recall Recap to check if students know how to count numbers from 1 to 9. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary counting forward: counting by adding one every time counting backward: counting by subtracting one every time place value: value of a digit based on its position in the number expanded form: the way to write a number by adding the value of its digits

Teaching Aids Place value blocks of 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s; Number cards for 8 numbers between 50 to 200: 58, 189, 79, 197, 118, 146, 152, 176; Number chart 1–200; Strip with 8 squares; Coloured square cut-outs with L in the orange square, E in blue, A in yellow, R in red, N in green, I in purple, N in pink, G in grey; 2 groups of small straws—6 small straws and 9 small straws; 6 Bangles 1

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Chapter: Numbers up to 200 Building Numbers up to 200

Imagine Maths Page 3

Learning Outcomes Students will be able to write numbers up to 200 using numerals and number names.

Teaching Aids Place value blocks of 100s, 10s and 1s

Activity Instruct the students to work in groups. Distribute the place value blocks to each group. Instruct the students to show the numbers 115 and 148 using the blocks. Ask them to count the number of hundreds, tens and ones shown by the blocks. Then, in their notebooks, they will write that number, and the number of hundreds, tens and ones in words to get the number name. Ask questions like: If I have place value blocks for the number 234, which place value blocks will we add to get the next 3 numbers?

Extension Idea Ask: How many 1s blocks will you use to show the number one hundred fifty? Say: The number one hundred fifty can be written as 150. Number of 1s blocks used = 0.

Place Value and Expanded Form

Imagine Maths Page 4

Learning Outcomes Students will be able to identify the place value for numbers up to 200 and write them in expanded form.

Teaching Aids Place value blocks of 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s

Activity Distribute the place value blocks and place value charts among the students. Ask them to show the number 182 using place value blocks. Instruct the students to identify and write the same number in the place value chart by writing each digit in its correct place. Then, in their notebooks, they will write the number of hundreds, tens and ones as 100 + 80 + 2 to write the expanded form of the number and the place value of each digit. Ask questions like: What is the place value of 5 in the number 159?

Extension Idea Ask: What would be the expanded form of the number 157 if the digits in the ones and the tens places are interchanged? Say: The digit in the ones place in 157 is 7, and the digit in the tens place is 5. On interchanging the places, the number that we get is 175. So, the expanded form of 175 = 100 + 70 + 5. 2

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Imagine Maths Page 6

Comparing and Ordering Numbers Learning Outcomes Students will be able to compare and order numbers up to 200.

Teaching Aids Place value blocks of 100s, 10s and 1s; Number cards for 8 numbers between 50 to 200: 58, 189, 79, 197, 118, 146, 152, 176; Number chart 1–200

Activity Ask the students to work in groups. Distribute the number cards for 8 numbers to each group. Instruct them to pick any two number cards, show the numbers using the place value blocks, and then compare them. They will first compare the hundreds blocks in both numbers, then the tens and finally the ones. They will then shade the two numbers on the number chart. Ask them to write the comparison using the symbol <, >, or =, in their notebooks. Discuss how the bigger number will come after the smaller number on the number chart. Then, ask them to use the remaining number cards, locate the numbers on the number chart and then shade them. Ask them to arrange the number cards in increasing and decreasing order and write the answers in their notebooks. Ask questions like: Can a 2-digit number be greater than a 3-digit number?

Extension Idea Ask: Find a number that lies between 95 and 107. There should be 4 numbers between 95 and this number. Say: The number is 100 since it lies between 95 and 107, and has 4 numbers between 95 and itself.

Imagine Maths Page 10

Ordinal Numbers Learning Outcomes Students will be able to read and write ordinal numbers from 1st to 10th.

Teaching Aids Strip with 8 squares; Coloured square cut-outs of letters L, E, A, R, N, I, N, G

Activity Call 10 students to the front of the class and ask them to stand in a line. Ask questions like: Who is second in the line? Who is tenth?

Ask the students to work in groups. Distribute the strips and cut-outs to each group. Ask them to place the cut-outs on the square strip as per the instructions to get the word LEARNING. Use ordinal words for the positions of the letters. For example, ask them to place the orange cut-out in the first square and the green cut-out in the fifth square.

Ask them to write the letters in their notebooks with the correct position of each letter.

Chapter 1 • Numbers up to 200

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Imagine Maths Page 12

Odd and Even Numbers Learning Outcomes Students will be able to identify odd and even numbers.

Teaching Aids 2 groups of small straws—6 small straws and 9 small straws; 6 Bangles

Activity Discuss some real-life things that come in pairs like socks, gloves, etc. Instruct students to form groups of 4. Distribute a set of 6 straws, 9 straws and 6 bangles to each group. Ask them to first use 6 straws and 3 bangles and put pairs of straws inside the bangles. They will then use 9 straws and 5 bangles to make pairs. Discuss that any number that forms pairs with no leftover is an even number and that a number that has a leftover is an odd number. Instruct students to draw 6 lines and 9 lines to show the straws in their notebooks, circle pairs of lines and then write the number and whether it is odd or even. Ask questions like: What type of number will you get if you add one more straw to 9 straws?

Answers 1. Building Numbers up to 200

4. Ordinal Numbers

Think and Tell

Do It Together

20 boxes with 10 sweets in each = 20 tens = 200. It has 20 tens or 2 hundreds.

1. B

We write this as 2 hundreds 0 tens. Do It Together 1. 1 hundred, 1 ten and 4 ones – one hundred fourteen 2. 1 hundred, 1 ten and 2 ones – one hundred twelve

2. Place Value and Expanded Form Do It Together In 196, the place value of 1 is 100, 9 is 90 and 6 is 6. The expanded form of 196 is 100 + 90 + 6.

3. Increasing and Decreasing Order

2. A

3. T

4. No

5. Odd and Even Numbers Think and Tell If we add two odd numbers, we will get an even number because the two leftovers without a pair will be paired together. Do It Together 2

Even

Odd

Even

Odd

Do It Together Increasing order: 109, 111, 123, 132, 143

Decreasing order: 143, 132, 123, 111, 109 4

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Addition of 2-digit Numbers Imagine Mathematics Headings

CB Page

Addition Without Regrouping

Addition With Regrouping; Adding More Than 2 Numbers

Story Sums

Learning Outcomes Students will be able to:

add 2-digit numbers without regrouping.

add 2-digit numbers with regrouping (sums up to 200).

solve story problems on adding numbers (sums up to 200).

Alignment to NCF C-8.6: Adds two numbers using place value concept (sum not exceeding 99) and applies them to solve simple daily life problems

C-8.6: Identifies appropriate operation (addition or subtraction) to solve problems in a familiar situation/ context C-8.6: Comprehends and solves simple word problems

C-8.12: Comprehends texts and extracts simple mathematical problems embedded in the text

Let’s Recall Recap to check if students know how to add two 1-digit numbers.

Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary regrouping: rearranging numbers into groups according to their place values number line: a line showing numbers at equal distances

Teaching Aids Place value blocks of 100s, 10s and 1s; Word problem written on a sheet of paper with space given for each element of the CUBES strategy

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Chapter: Adding 2-digit Numbers Addition Without Regrouping

Imagine Maths Page 18

Learning Outcomes Students will be able to add 2-digit numbers without regrouping.

Teaching Aids Place value blocks of 10s and 1s

Activity

Ask the students to work in groups. Distribute the place value blocks to each group. Instruct them to show 42 and 36 using the place value blocks by placing them side by side.

Ask them to put together or add the 1s blocks, count the total number of 1s blocks and write the number of 1s in their notebooks. Ask them to repeat this with the 10s blocks. Then, in their notebooks, they will add the numbers using the vertical method by first adding the digits in the 1s place, then the digits in the 10s place. Ask them to compare the answers that they got using the place value blocks and the vertical method.

Give them 2 more numbers and ask them to find the total using the place value blocks and the vertical method.

Extension Idea Ask: What is the total number of 10s blocks that you will use to show the sum of five 10s blocks and six 1s blocks with 31? Say: Five 10s blocks and six 1s blocks make the number 56. 56 + 31 = 87; hence, we need eight 10s blocks to show the sum.

Addition With Regrouping; Adding More Than 2 Numbers Imagine Maths Page 21 Learning Outcomes Students will be able to add 2-digit numbers with regrouping (sums up to 200).

Teaching Aids Place value blocks of 100s, 10s and 1s

Activity Ask the students to work in groups. Distribute the place value blocks to each group. Instruct them to show 87 and 25 using the blocks by placing them side by side. Ask them to put together or add the 1s blocks. Ask how many blocks have they got on adding the 1s blocks. Discuss how ten 1s become one 10s block, so we need to replace ten 1s blocks with one 10s block. Ask them to repeat the process with the 10s blocks and discuss how ten 10s become one 100s block. Then, in their notebooks, they will add the numbers using the vertical method by first adding the digits in the 1s place, then the digits in the 10s place and finally the digits in the 100s place. Ask them to check if the sums that they got using the place value blocks and the vertical method match. Ask questions like: What is 30 tens? How will you show this using the 100s blocks? 6

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Imagine Maths Page 28

Story Sums Learning Outcomes Students will be able to solve story problems on adding numbers (sums up to 200).

Teaching Aids Word problem written on a sheet of paper with space given for each element of the CUBES strategy

Activity Distribute the sheet with the word problem to the students.

Circle the Numbers

Rhea sold 15 red roses, 12 white roses and 28 pink roses. How many roses did she sell altogether?

Underline the Question

Box the Keywords

Evaluate/Draw

Solve and Check!

Instruct them to circle the numbers, underline the question, and box the keywords. Discuss what they need to find. Ask them to evaluate the problem, solve it and write the answer using the vertical method. Ask questions like: How will you find out if your answer is correct?

Extension Idea Ask: Create your own word problem where you need to add the numbers 118 and 56. Say: Multiple story problems can be created based on adding 2 numbers. One such word problem could be: Kamal sold 118 oranges and 56 apples in a day. What is the total number of fruits that Kamal sold?

Chapter 2 • Addition of 2-digit Numbers

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Answers 1. Vertical Method Do It Together

Tens Ones +

Think and Tell No, we cannot regroup the ones as 2 tens. The biggest 1-digit number is 9. While adding the ones, we can get up to 19 ones, which has only 1 ten.

5. Adding More Than 2 Numbers Think and Tell Tens Ones

The answer is 65.

2. Horizontal Method Do It Together

Tens Ones +

34 + 42 = 76

Do It Together

Tens Ones

The sum of 48 and 22 is 70.

4. Regrouping to More Than 10 Do It Together

Tens Ones 1

1 2 4

We get 0 in the ones place if we add 34 and 16. Do It Together +8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

3. Addition With Regrouping 10

6 6 2

2 + 8 + 5 = 15

Tens Ones 2

8 + 5 + 2 = 15 5 + 8 + 2 = 15 Are all the answers the same? Yes/ No

8 1

5 5

6. Story Sums Do It Together Rohan solved 15 sums on Monday, 23 sums on Tuesday, and 17 sums on Wednesday. How many sums did he solve in total? Evaluate: Total sums solved = 15 + 23 + 17 = 55 Solve: Total sums solved = Sums solved on Monday + Sums solved on Tuesday + Sums solved on Wednesday = 15 + 23 + 17 = 55 Rohan solved 55 sums in total.

Tens Ones 1

+ +

2 5

3 5

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Subtraction of 2-digit Numbers Imagine Mathematics Headings

CB Page

Subtraction Without Regrouping

Subtraction With Regrouping; Finding the Missing Number

Story Sums

Learning Outcomes Students will be able to:

subtract 2-digit numbers without regrouping. subtract 2-digit numbers with regrouping.

solve story problems on subtracting 2-digit numbers.

Alignment to NCF C-8.6: Subtracts two numbers up to 99 using place value and applies them to solve simple daily life problems/situations C-8.6: Appreciates and applies relationship between addition and subtraction of numbers

C-8.6: Identifies appropriate operation (addition or subtraction) to solve problems in a familiar situation/ context C-8.6: Comprehends and solves simple word problems

C-8.12: Comprehends texts and extracts simple mathematical problems embedded in the text

Let’s Recall Recap to check if students know how to subtract 1-digit numbers.

Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary regrouping: rearranging numbers into groups according to their place values

addition fact: showing two numbers with a (+) sign in between them followed by the (=) sign and the sum of the two numbers subtraction fact: showing two numbers with a (−) sign between them followed by the (=) sign and the difference of the two numbers

Teaching Aids Places value blocks of 10s and 1s; Ice-cream sticks; Word problem sheets with a word problem written on a sheet of paper and space given for What is given? What do we need to find? and How do we find?

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Chapter: Subtraction of 2-digit Numbers Subtraction Without Regrouping

Imagine Maths Page 33

Learning Outcomes Students will be able to subtract 2-digit numbers without regrouping.

Teaching Aids Places value blocks of 10s and 1s

Activity Ask the students to work in groups. Distribute the place value blocks to each group. Instruct the students to subtract 17 from 39 by first showing the bigger number using place value blocks and then taking away or removing as many blocks as the smaller number. For example, to solve 39 − 17, they will take three 10s blocks and nine 1s blocks to show 39. They will then remove one 10s block and seven 1s blocks to subtract 17. Ask them to count the number of the 10s and the 1s blocks left to get the answer. Then, in their notebooks, they will subtract using the vertical method by first subtracting the digit in the 1s place and then the digit in the 10s place. Ask them to compare the answers that they got using both the methods. Instruct them to subtract 33 from 45 using the place value blocks and the vertical method.

Subtraction With Regrouping; Finding the Missing Number Imagine Maths Page 35 Learning Outcomes Students will be able to subtract 2-digit numbers with regrouping.

Teaching Aids Place value blocks of 10s and 1s

Activity Ask the students to work in groups. Distribute the place value blocks to each group. Instruct them to solve 58 − 29. Ask them to first show the bigger number using the place value blocks and then take away as many blocks as the smaller number. As 9 ones is less than 8 ones, they will need to replace a 10s block with ten 1s blocks, and then subtract the ones and the tens. Then, in their notebooks, they will subtract using the vertical method by first subtracting the digit in the 1s place, then the digit in the 10s place and regrouping wherever needed. Ask questions like: What will you get if you add the ice-cream sticks and the smaller number?

Extension Idea Ask: Can you think of two 2-digit numbers that give 15 after subtracting one from the other? What could the possible numbers be? Say: Think of any two-digit number, say 52, and subtract 15 from it. 52 – 15 = 37. So, 52 and 37 are two such numbers that give 15 after subtraction. 10

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Story Sums

Imagine Maths Page 40

Learning Outcomes Students will be able to solve story problems on subtracting 2-digit numbers.

Teaching Aids Ice-cream sticks; Word problem sheets with a word problem written on a sheet of paper and space given for What is given? What do we need to find out? and How do we find out?

Activity Invite 2 students to the front of the class. Give 12 ice-cream sticks to one student and 15 ice-cream sticks to the other. Ask questions to help students understand the keywords: Who has more ice-cream sticks? Who has fewer icecream sticks? How many more ice-cream sticks does the second student have? How many fewer ice-cream sticks does the first student have? Distribute the word problem sheet to the students with the problem written as: Priya has 25 toys and Satish has 18 toys. How many fewer toys does Satish have than Priya? Priya has 25 toys and Satish has 18 toys. How many fewer toys does Satish have than Priya? What is given? What do we need to find? How do we find? Solve to find the answer.

Instruct them to read the problem. Ask them to write what is given, what they need to find out and how to find the answer. Ask them to solve and write the final answer. Discuss the answers.

Extension Idea Ask: Create your own word problem where you need to subtract 39 from 58. Say: There can be multiple word problems on subtracting 39 from 58. One such problem could be: Richa read 58 pages of a book and Shalini read 39 pages of the book. How many more pages did Richa read than Shalini?

Chapter 3 • Subtraction of 2-digit Numbers

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Answers 1. Subtraction Without Regrouping

4. Using Subtraction to Compare

Do It Together

–

Tens

Ones

Number of sunflowers = 37 Number of roses = 25

How many more sunflowers? = 37 – 25

–

Number of toy cars = 33

2 12

Number of toy cars sold = 13

Do It Together

Ones

5. Checking Subtraction Using Addition

Do It Together

There are 12 more sunflowers than roses.

2. Subtraction With Regrouping Tens

–

Number of toy cars left = 33 – 13 = 20

3. Finding the Missing Number

–

Tens

Ones

3 2

3 0

Checking the answer:

Do It Together – 6

–6

–7

Tens

Ones

3 2

3 0

Tens

Ones

2 3

0 3

The addition and subtraction facts of 6, 7 and 13 are: 6 + 7 = 13

7 + 6 = 13

13 – 6 = 7

13 – 7 = 6

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Multiplication Imagine Mathematics Headings

CB Page

Grouping

Repeated Addition

What Is Multiplication?

Learning Outcomes Students will be able to:

make equal groups and find the total.

find the total using repeated addition.

write a multiplication sentence using the symbols (×) and (=) for a given group of things.

Alignment to NCF C-8.7: Uses repeated adding to solve simple multiplication problems up to 99

Let’s Recall Recap to check if students know how to add two numbers using pictures. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary equal groups: same number of things in each group

unequal groups: different number of things in each group

repeated addition: adding equal groups of numbers together

Teaching Aids Circular paper plates; Counters; Repeated addition sentence cards; Multiplication sentence cards

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Chapter: Multiplication Imagine Maths Page 49

Grouping Learning Outcomes Students will be able to make equal groups and find the total.

Teaching Aids Circular paper plates; Counters

Activity Draw stars to show an example of equal groups. Ask students questions around the number of groups, the number of stars in each group and the total number of stars. Instruct the students to work in groups. Distribute the circular plates and counters. Instruct them to show 3 groups of 9 using the plates and counters. Then, in their notebooks, they will first write the number of plates, then the number of counters on each plate, and finally the total number of counters. Instruct them to show 4 groups of 8 using the plates and counters. Ask questions like: What if we remove one counter from 4 groups of 8? Will it still be equal grouping?

Imagine Maths Page 51

Repeated Addition Learning Outcomes Students will be able to find the total using repeated addition.

Teaching Aids Circular paper plates; Counters; Repeated addition sentence cards

Activity Discuss how to write the things given in equal groups as repeated addition sentences. Instruct the students to work in groups. Distribute the counters, plates and repeated addition sentence cards to each group. 3 + 3 + 3 + 3 = ______________

4 + 4 = ______________

Instruct the students to show 4 groups of 3 and 2 groups of 4 using the plates and counters. They will choose the correct repeated addition sentence, place the card below each group of plates and counters, and fill in the blank to write the answer. Then, in their notebooks, they can write the repeated addition sentences. Ask questions like: How did you match the repeated addition sentence with the group of counters?

Extension Idea Ask: Which of these is the correct way of writing 8 groups of 4: 8 + 8 + 8 + 8 or 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4? Say: We write the number of things in each group as many times as the number of groups. 8 groups of 4 show 8 groups with 4 things in each group. So, 8 groups of 4 will be written as 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4.

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Imagine Maths Page 54

What Is Multiplication? Learning Outcomes

Students will be able to write a multiplication sentence using the symbols (×) and (=) for a given group of things.

Teaching Aids Circular paper plates; Counters; Multiplication sentence cards

Activity Discuss how to write the things given in equal groups as a multiplication sentence. Instruct the students to work in groups. Distribute the counters, plates and multiplication sentence cards to each group. 4 � 2 = ______________

2 � 5 = ______________

Instruct the students to show 4 groups of 2 and 2 groups of 5 using the plates and counters. They will choose the correct multiplication sentence, place the card below each group of plates and counters, and fill in the blank to write the answer. Then, in their notebooks, they can write the multiplication sentences. Ask questions like: How did you match the multiplication sentence with the group of counters?

Extension Idea Ask: How is 9 × 4 different from 4 × 9? How are they similar? Say: 9 × 4 shows 9 groups with 4 things in each group. 4 × 9 shows 4 groups with 9 things in each group. Both multiplications give the same answer, which is 36.

Answers 1. Grouping

3. What Is Multiplication?

Think and Tell

No, it will not be easy to find the total. We will have to count the number of things to get to the answer.

3 groups of 5 stars = 3 × 5 = 15 stars

Do It Together

There are 3 boxes of crayons. Each box has 5 crayons. How many crayons are there in total?

There are 3 plates. Each plate has 4 guavas.

3 groups of 4 guavas = 12 guavas.

2. Repeated Addition Do It Together There are 3 bunches of flowers with 5 flowers in each. How many flowers are there in all the bunches together?

Do It Together

3 groups of 5 5 + 5 + 5 = 15 3 × 5 = 15 There are 15 crayons in all.

3 groups of 5 flowers

There are 15 flowers altogether.

Chapter 4 • Multiplication

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Multiplication Tables: 2, 5, and 10 Imagine Mathematics Headings

CB Page

Multiplication by 2

Multiplication by 5

Multiplication by 10

Story Sums

Learning Outcomes Students will be able to:

skip count to write the multiplication table of 2. skip count to write the multiplication table of 5.

skip count to write the multiplication table of 10.

solve story problems on multiplication using the multiplication tables of 2, 5 or 10.

Alignment to NCF C-8.3: Demonstrates skip counting in 2s or 3s on a number line (graduated) or blocks/pictures C-8.7: Uses repeated adding to solve simple multiplication problems up to 99

C-8.12: Comprehends texts and extracts simple mathematical problems embedded in the text

Let’s Recall Recap to check if students know the concept of repeated addition.

Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary repeated addition: adding equal groups of numbers together skip count: jumps of the same number again and again

multiplication table: a list that shows the results of multiplying a number by different numbers

Teaching Aids Number charts; Ice-cream sticks; Paper cups; Coloured pencils; Question cards; Table charts with 2 times, 5 times and 10 times tables

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Chapter: Multiplication Tables 2, 5, and 10 Multiplication by 2

Imagine Maths Page 63

Learning Outcomes Students will learn to skip count to write the multiplication table of 2.

Teaching Aids Number charts; Ice-cream sticks; Paper cups; Coloured pencils

Activity Ask the students to work in groups of 5. Draw a number line on the floor and ask one student from each group to come up to the line and skip count first by 1 and then by 2 and jump. Distribute the number charts, ice-cream sticks and paper cups to each group. Instruct the groups to place 2 paper cups in front of them. Ask them to put one ice-cream stick in each cup. Discuss how the cups show 2 groups and the ice-cream sticks in them show 2 groups of 1.

Ask the students to count the total number of ice-cream sticks (2) in both cups and shade the same number on the number chart. Instruct them to then show 2 groups of 2 using the ice-cream sticks and cups (by putting one more ice-cream stick in each cup), count the total and circle the result on the number chart. Repeat the same steps 10 times. Discuss how the numbers shaded on the chart give the multiplication table of 2. Show them how to write the table using the multiplication sign. Ask questions like: How will you show 2 groups of 12?

Multiplication by 5

Imagine Maths Page 67

Learning Outcomes Students will learn to skip count to write the multiplication table of 5.

Teaching Aids Number charts; Ice-cream sticks; Paper cups; Coloured pencils

Activity Discuss the concept of skip counting by 5. Ask the students to work in groups. Distribute the number charts, ice-cream sticks and paper cups to each group. Instruct the groups to place 5 paper cups in front of them. Ask them to put one ice-cream stick in each cup. Discuss how the cups show 5 groups and the ice-cream sticks in them show 5 groups of 1.

Ask the students to count the total number of ice-cream sticks in all the cups and shade the same number on the number chart. Instruct them to then show 5 groups of 2 using the ice-cream sticks and cups (by putting one more ice-cream stick in each cup), count the total and circle the result on the number chart. Repeat the same steps 10 times. Discuss how the numbers shaded on the chart give the multiplication table of 5. Show them how to write the table using the multiplication sign.

Extension Idea Ask: Is putting 2 ice-cream sticks in each of the 5 cups the same as putting 5 ice-cream sticks in each of the 2 cups? Say: 2 ice-cream sticks each in 5 cups = 2 + 2 + 2 + 2 + 2 = 10 and 5 ice-cream sticks each in 2 cups = 5 + 5 = 10. The result is the same. Chapter 5 • Multiplication Tables: 2, 5, and 10

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Multiplication by 10

Imagine Maths Page 70

Learning Outcomes Students will learn to skip count to write the multiplication table of 10.

Teaching Aids Number charts; Ice-cream sticks; Paper cups; Coloured pencils

Activity Discuss the concept of skip counting by 10. Ask the students to work in groups. Distribute the number charts, ice-cream sticks and paper cups to each group. Instruct the groups to place 10 paper cups in front of them. Ask them to put one ice-cream stick in each cup. Discuss how the cups show 10 groups and the ice-cream sticks in them show 10 groups of 1. Ask the students to count the total number of ice-cream sticks in all the cups and shade the same number on the number chart. Instruct them to then show 10 groups of 2 using the ice-cream sticks and cups (by putting one more ice-cream stick in each cup), count the total, and circle the result on the number chart. Repeat the same steps 10 times. Discuss how the numbers shaded on the chart give the multiplication table of 10. Show them how to write the table using the multiplication sign.

Story Sums

Imagine Maths Page 73

Learning Outcomes Students will learn to solve story problems on multiplication using the multiplication tables of 2, 5 or 10.

Teaching Aids Question cards; Table charts with 2 times, 5 times and 10 times tables

Activity Distribute the word problem cards and multiplication table charts to the students. Emily plants 5 rows of flowers, and each row has 7 flowers. How many flowers did Emily plant? What is given? What do we need to find? How do we find?

Solve to find the answer. Instruct the students to read the question, note down what they know and what they want to know. Discuss how they will find the answer. Ask them to identify the correct multiplication sentence in the table chart and write the answer. Ask questions like: How many flowers would Emily have planted if she had used only 2 rows with the same number of flowers?

Extension Idea Ask: Create your own word problem where you need to multiply the numbers 8 and 10. Say: There can be many word problems on multiplying the numbers 8 and 10. One such problem could be: There are 10 rows of students. If each row has 8 students, what is the total number of students?

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Answers 1. Multiplication by 2

4. Multiplication by 10

Do It Together

1×2=2

2+2

2×2=4

2+2+2

3×2=6

2+2+2+2

4×2=8

2+2+2+2+2

5 × 2 = 10

2. Multiplication by zero Do It Together 0+0+0=0 3×0=0

3. Multiplication by 5 Do It Together

90 100

5 jumps of 10 steps each. 5 × 10 = 50 5 × 10 = 50

5. Story Sums Do It Together What do we know? The number of vases in the garden = 5 The number of flowers in each vase = 5 What do we want to know? The total number of flowers in all the vases How do we find the answer? The total number of flowers = the total number of vases × the flowers in each vase

5 groups of 4 flowers equals 20 5 × 4 = 20

Chapter 5 • Multiplication Tables: 2, 5, and 10

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Solve to find the answer. = 5 × 5 = 25 flowers So, there are 25 flowers in total.

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Numbers up to 999 Imagine Mathematics Headings

CB Page

Forming Numbers up to 999

Place Value and Expanded Form

Comparing and Ordering Numbers

Learning Outcomes Students will be able to:

form numbers up to 999 using place value blocks and write their number names. identify the place value of numbers up to 999 and write them in expanded form.

compare numbers up to 999 and arrange them in ascending or descending order.

C-8.5: Compares and forms the greatest and smallest two-digit numbers (with and without repetition of given digits). Recognises, reads, writes number names and numerals up to 99 using place value concept

Let’s Recall Recap to check if students know the place value and expanded form for numbers up to 200.

Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary place value: value of a digit based on its position in the number

expanded form: the sum of the values of all the digits in a number

Teaching Aids Place value blocks of 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s; 20 number cards with numbers between 80 to 999

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Chapter: Numbers up to 999 Forming Numbers up to 999

Imagine Maths Page 79

Learning Outcomes Students will be able to form numbers up to 999 using place value blocks and write their number names.

Teaching Aids Place value blocks of 100s, 10s and 1s

Activity Show the students some 100s blocks and ask them to identify the number shown. Repeat this with 10s and 1s blocks and then all the blocks together. Instruct the students to work in groups. Distribute the place value blocks to each group. Instruct the students to show the numbers 358 and 884 using the blocks. Ask them to count the number of hundreds, tens and ones shown by the blocks. Then, in their notebooks, they will write the number and the number of hundreds, tens and ones in words to get the number name. Ask questions like: How many 10s blocks will you need to show the numbers 802 and 820?

Extension Idea Ask: If four 10s blocks are added to the blocks showing 304, what would be the new number?

Say: The number of 10s blocks in 304 is 0. So, zero 10s blocks + four 10s blocks = four 10s blocks. So, the new number would be 344.

Place Value and Expanded Form

Imagine Maths Page 83

Learning Outcomes Students will be able to identify the place value of numbers up to 999 and write them in expanded form.

Teaching Aids Place value blocks of 100s, 10s and 1s; Place value chart showing 100s, 10s and 1s

Activity Instruct the students to work in groups. Distribute the place value blocks and place value charts to each group. Ask them to show the numbers 253 and 352 using place value blocks. They should then identify and write the same numbers in the place value chart by writing each digit in its correct place. Then, in their notebooks, they will write the number of hundreds, tens and ones, the expanded form of the number and the place value of each digit in both numbers. Ask questions like: Which digit has the same place value in both numbers?

Extension Idea Ask: What is the expanded form of a number which is 5 more than three hundred twenty-five?

Say: Three hundred twenty-five = 325. Five more than 325 is the 5th number when counting forward from 325, which gives us 326, 327, 328, 329, 330. So, in expanded form, 330 = 300 + 30 + 0.

Chapter 6 • Numbers up to 999

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Comparing and Ordering Numbers

Imagine Maths Page 86

Learning Outcomes Students will be able to compare numbers up to 999 and arrange them in ascending or descending order.

Teaching Aids 20 number cards with numbers between 80 to 999; Place value chart showing 100s, 10s and 1s

Activity Ask the students to work in groups. Display the place value chart on the board. Invite one student from each group to come up to the board. Ask them to write numbers in the place value chart and compare the hundreds, then the tens and finally the ones. Next, invite the students to write 3 numbers in the place value chart and order these in ascending order. Once the students understand comparison and ordering, turn the activity into a game. Create number lines for each group in an open area. Scatter the number cards with numbers around the open area. Instruct the students that they need to place cards on the number line in the correct order by comparing the numbers. One student from each group goes and picks any one card and runs back to their number line and places the card in the correct place. Then, the next student from the group goes to pick another card and places it on the number line. Repeat this process until every student gets a chance to put a card on the number line.

Extension Idea Ask: How will you arrange numbers given in different forms in ascending order? Arrange the numbers four hundred fifty-two, 300 + 40 + 8, 300 + 80 + 4, and five hundred six in ascending order. Say: Four hundred fifty-two = 452; 300 + 40 + 8 = 348; 300 + 80 + 4 = 384; five hundred six = 506. So, the numbers are 452, 348, 384 and 506. The increasing order is 348 < 384 < 452 < 506.

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Answers 1. Forming Numbers up to 999

4. Comparing Numbers

Think and Tell

Do It Together

1. 1000 is the smallest 4-digit number.

Both 491 and 466 are 3-digit numbers.

2. We know 10 tens = 1 hundred. 11 tens is 10 tens + 1 ten. So, we can write it as 1 hundred, 1 ten, 0 ones = 110.

Do It Together

6 hundreds

3 tens

2 tens

2 ones

Six hundred thirty-three _____________

5 hundreds

3 ones

Different digit at the tens place. ___________ 9>6 __________________________ > 466. So, 491 _______

5. Ordering Numbers

Do It Together

2. Place Value

Same digits in the hundreds place. 4 = _______ 4 _______

Five hundred twenty-two _______________

81 is a 2-digit number while 421 and 612 are 3-digit numbers. So, 81 is smaller than both 421 and 612. We can also see that 421 < 612 because the digit in the hundreds place is smaller in 421. So, the increasing order (smallest to largest) is 81, 421, 612. And the decreasing order (largest to smallest) is 612, 421, 81.

Do It Together 234

953

806

662

4 ones

9 hundreds

0 tens

6 tens

3. Expanded Form Do It Together 453

400

102

100

340

300

980

900

Chapter 6 • Numbers up to 999

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Addition and Subtraction of 3-digit Numbers Imagine Mathematics Headings

CB Page

Addition of 3-digit Numbers

Subtraction of 3-digit Numbers

100

Word Problems on Addition and Subtraction

107

Learning Outcomes Students will be able to:

add 3-digit numbers with regrouping using vertical addition.

subtract 3-digit numbers without regrouping using vertical subtraction. solve word problems on adding and subtracting 3-digit numbers.

Alignment to NCF C-8.6: Adds two numbers using place value concept (sum not exceeding 99) and applies them to solve simple daily life problems/situations C-8.6: Subtracts two numbers up to 99 using place value and applies them to solve simple daily life problems/situations

C-8.6: Identifies appropriate operation (addition or subtraction) to solve problems in a familiar situation/ context C-8.6: Comprehends and solves simple word problems

Let’s Recall Recap to check if students know how to add and subtract 2-digit numbers. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary regrouping: rearranging numbers into groups according to their place values place value: value of a digit based on its position in the number

vertical addition: adding numbers by writing them one below the other

vertical subtraction: subtracting numbers by writing them one below the other

Teaching Aids Place value blocks of 1000s, 100s, 10s, and 1s; Question cards; Addition (+) and subtraction (–) cards

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Chapter: Addition and Subtraction of 3-digit Numbers Addition of 3-digit Numbers

Imagine Maths Page 95

Learning Outcomes Students will be able to add 3-digit numbers with regrouping using vertical addition.

Teaching Aids Place value blocks of 1000s, 100s, 10s, and 1s

Activity Ask the students to work in groups. Distribute the place value blocks to each group. Instruct them to use the place value blocks to show two numbers, 341 and 259, and add them. Ask them to begin by adding the 1s blocks. Tell them if the total of the 1s blocks is more than 9, they should replace ten 1s blocks with one 10s block. Next, guide them on how to add the 10s blocks, reminding them to regroup if necessary. Finally, ask them to add the 100s blocks. Now, instruct the students to write the numbers in columns in their notebooks by placing the digits one below the other and then add. Ask them to compare the answers that they got using the place value blocks and the vertical method. Ask questions like: What did you do if the total of the digits in the tens place was more than 9?

Extension Idea Ask: What do you do when the number of hundreds is more than 9? Say: When the number of hundreds is more than 9, we remove ten 100s blocks and add one 1000s block.

Subtraction of 3-digit Numbers

Imagine Maths Page 100

Learning Outcomes Students will be able to subtract 3-digit numbers without regrouping using vertical subtraction.

Teaching Aids Place value blocks of 1000s, 100s, 10s, and 1s

Activity Ask the students to form groups. Distribute the place value blocks to each group. Instruct the students to use the place value blocks to show two numbers, 567 and 123. To subtract, they should pick as many place value blocks as the bigger number and then take away the same number of blocks as in the smaller number. Explain that the leftover blocks give the answer. Then, in their notebooks, the students should write the numbers in columns and subtract. Ask them to compare the answers that they got using the place value blocks and the vertical method. Ask questions like: Does the number of thousands, hundreds, tens and ones decrease when we subtract two numbers? Can you subtract the bigger number from the smaller number using place value blocks?

Extension Idea Ask: How would you subtract if the number of ones in the bigger number is less than the number of ones in the smaller number?

Say: We would take 1 ten from the tens place in the bigger number and exchange it for 10 ones so that we have enough ones to subtract from. Chapter 7 • Addition and Subtraction of 3-digit Numbers

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Word Problems on Addition and Subtraction

Imagine Maths Page 107

Learning Outcomes Students will be able to identify the right operation and learn to solve word problems on adding and subtracting 3-digit numbers.

Teaching Aids Question cards; Addition (+) and subtraction (–) cards

Activity Ask the students to form groups. Distribute the question cards (as given in the picture) and addition (+) and subtraction (–) cards to each group. Anna has 451 stamps. Susan has 167 stamps. How many stamps do they have in all? What is given? What do we need to find? How do we find? Solve to find the answer.

Ask the students to share some situations from real life where they need to add or subtract. Instruct them to understand the situation, analyse it and show the correct operation for it using the addition/subtraction cards for some situations. Then, ask them to use the strategy to solve the problem on the question card. Ask questions like: How will you know whether you need to add or subtract in a problem?

Extension Idea Ask: Write a word problem that involves both addition and subtraction, and ask your classmates to solve it. Say: There can be multiple word problems on both adding and subtracting numbers. One problem could be: I have 10 apples. I eat 3 apples and then my friend gives me 5 more. How many apples do I have now?

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Answers 1. Addition of 3-digit Numbers

4. Word Problems on Addition and Subtraction

Do It Together H

Do It Together

There were 124 candies.

What do we find?

What do we know? 120 candies were given away.

Number of candies left.

2. Subtraction of 3-digit Numbers

How do we find (keyword)?

Do It Together

The keyword ‘left’ tells us that we need to subtract. Number of candies left = Number of candies – Number of candies given away Solve the problem to find the answer.

H –

_____ 4

–

0 4

_____ 4

So, 4 candies are left.

3. Identifying the Right Operation Do It Together Situation There were 234 students in the hall. 150 more students joined them. How many students are there in the hall now? Rahul had 262 crayons, he lost 130 crayons. How many crayons are left?

Addition Subtraction

Solve

+ 

H 2 1 3

H 

–

O 4 0 4

Chapter 7 • Addition and Subtraction of 3-digit Numbers

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2 2

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Multiplication Tables 3, 4 and 6 Imagine Mathematics Headings

CB Page

Multiplying by 3

113

Multiplying by 4

115

Multiplying by 6

118

Multiplication Without Regrouping

121

Multiplication With Regrouping

123

Story Problems on Multiplication

126

Learning Outcomes Students will be able to:

skip count to write the multiplication table of 3. skip count to write the multiplication table of 4. skip count to write the multiplication table of 6.

multiply a 2-digit number by a 1-digit number using the multiplication tables of 3, 4 or 6 (without regrouping).

multiply a 2-digit number by a 1-digit number using the multiplication tables of 3, 4 or 6 (with regrouping).

solve story problems on multiplying a 2-digit number by a 1-digit number using the multiplication tables of 3, 4 or 6.

Alignment to NCF C-8.3: Demonstrates skip counting in 2s or 3s on a number line (graduated) or blocks/pictures C-8.7: Uses repeated adding to solve simple multiplication problems up to 99

C-8.12: Comprehends texts and extracts simple mathematical problems embedded in the text

Let’s Recall Recap to check if students know how to find the total using repeated addition. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary multiplication fact: showing 2 numbers with a (×) sign in between them followed by the (=) sign and the product of the two numbers multiplication statement: a sentence that shows two numbers being multiplied order: the way numbers are arranged

regrouping: rearranging numbers into groups according to their place values

Teaching Aids Paper plates; Counters; Number chart that goes from 1 to 40 (or higher); Crayons; Pair of dice; Multiplication tables; Multiplication sheets with the column table drawn; Word problem cards 28

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Chapter: Multiplication Tables 3, 4 and 6 Multiplying by 3

Imagine Maths Page 113

Learning Outcomes Students will be able to skip count to write the multiplication table of 3.

Teaching Aids Paper plates; Counters

Activity Instruct the students to work in groups. Distribute paper plates and counters to each group. Instruct the students to take 3 plates and place 1 counter on each plate. Discuss that the plates show the number of groups and the counters show the number of items in each group. Guide them to write 3 groups of 1 as 3 × 1 = 3 and say it as “3 ones are 3”. They will then write the multiplication statement in their notebooks.

Next, have them add one more counter to each plate, and guide them to skip count to find the product as 3 × 2 = 6.

Encourage them to continue adding counters to each plate and writing the multiplication statements until they reach 3 × 10 = 30. Then, in their notebooks, they will write the multiplication table for 3.

Extension Idea Ask: Is 3 groups of 8 equal to 8 groups of 3? Say: Yes, 3 groups of 8 = 8 + 8 + 8 = 24 and 8 groups of 3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24.

Multiplying by 4

Imagine Maths Page 115

Learning Outcomes Students will be able to skip count to write the multiplication table of 4.

Teaching Aids Number chart that goes from 1 to 40 (or higher); Crayons

Activity Instruct the students to work in groups. Distribute number charts to each group.

Ask the students to begin at 4 and colour the box with the number 4. Then, direct them to count and continue colouring every 4th cell, such as 8, 12, 16, and so on, until they reach 40. Next, instruct them to skip count by 4, verbally stating each number as they land on the shaded cells. Encourage them to say “4 ones are 4, 4 twos are 8, 4 threes are 12, 4 fours are 16…” and so on, highlighting the multiplication pattern of 4 on the chart.

Extension Idea Ask: Think of some real-life situations where skip counting might be useful. What could these situations be?

Say: There can be many such situations, such as counting bundles of 4 notebooks in a stationery shop or setting a dining table for 4 people by arranging items like plates, glasses, napkins, and spoons in groups of four. Chapter 8 • Multiplication Tables 3, 4 and 6

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Multiplying by 6

Imagine Maths Page 118

Learning Outcomes Students will be able to skip count to write the multiplication table of 6.

Teaching Aids Paper plates; Counters

Activity Instruct the students to work in groups. Distribute paper plates and counters to each group. Instruct the students to take 6 plates and place 1 counter on each plate. Discuss that the plates show the number of groups and the counters show the number of items in each group. Guide them to write 6 groups of 1 as 6 × 1 = 6 and say it as “6 ones are 6”. Next, have them add one more counter to each plate, and guide them to skip count to find the product as 6 × 2 = 12. Encourage them to continue adding counters to each plate and writing the multiplication statements until they reach 6 × 10 = 60. Then, in their notebooks, they will write the multiplication table for 6. Teacher Tip: If resources are unavailable, students can be asked to draw circles to show the plates and dots to show the counters.

Multiplication Without Regrouping

Imagine Maths Page 121

Learning Outcomes Students will be able to multiply a 2-digit number by a 1-digit number using the multiplication tables of 3, 4 or 6 (without regrouping).

Teaching Aids Multiplication tables; Multiplication sheets with the column table drawn

Activity Begin by reviewing the concept of multiplication as repeated addition. Ask questions like: How many items will there be in 22 groups of 4? Introduce the need for using the column method to multiply. Then, show the students the steps to multiply a 2-digit number by a 1-digit number without regrouping using multiplication tables. Instruct the students to work in groups. Distribute the multiplication tables and multiplication sheets to each group.

Ask them to multiply and write the answer using the multiplication tables.

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Imagine Maths Page 123

Multiplication With Regrouping Learning Outcomes

Students will be able to multiply a 2-digit number by a 1-digit number using the multiplication tables of 3, 4 or 6 (with regrouping).

Teaching Aids Pair of dice; Multiplication tables; Multiplication sheets

Activity Begin by reviewing the concept of regrouping in addition.

Show the students the steps to multiply a 2-digit number by a 1-digit number with × 4 × 6 regrouping using multiplication tables. Instruct the students to work in groups. Distribute pairs of dice, multiplication sheets and multiplication tables to each group. Ask the students to take turns and roll the pair of dice. Ask them to write the number formed on the dice as the first number of the multiplication. Instruct them to multiply the number on the dice by the given 1-digit number using multiplication tables and find the answer. Repeat the activity as many times as the number of students in the group.

Imagine Maths Page 126

Story Problems on Multiplication Learning Outcomes

Students will be able to solve story problems on multiplying a 2-digit number by a 1-digit number using the multiplication tables of 3, 4 or 6.

Teaching Aids Word problem cards

Activity Start by asking questions on situations in real life where students need multiplication. Instruct the students to work in groups. Distribute the word problem cards to each group.

Neha has 40 friends in her class and she wants to give 3 chocolates to each of them. How many chocolates does Neha need in total? What is given?

Instruct them to read the problem: Neha has 40 friends in her What do we need to find? class and she wants to give 3 chocolates to each of them. How many chocolates does Neha need in total? Ask them to write what is How do we find? given, what they need to find and how to find the answer. Ask them to evaluate and find the answer using the multiplication tables. Discuss the answers with the students.

Extension Idea Ask: Create your own word problem where you need to multiply 54 by 6. Say: There can be many word problems where we need to multiply 54 by 6. One such problem can be: Ravi purchased 54 boxes of toys for his toy shop. If one box contains 6 toys, what is the total number of toys that he purchased?

Chapter 8 • Multiplication Tables 3, 4 and 6

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Answers 1. Multiplying by 3

4. Multiplication Without Regrouping

Do It Together

Do It Together 1.

3×8

3×2 3×9

3×5

3×6

4 × 11 = 44

Do It Together 3

19 29

Do It Together

Think and Tell

5. Multiplication With Regrouping

2. Multiplying by 4

3. Multiplying by 6

H +2

6. Story Problems on Multiplication Do It Together H

Think and Tell 7 + 7 + 7 + 7 + 7 + 7 = 6 × 7 = 42 Do It Together 2

So, 324 people can sit in the hall.

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Introduction to Division Imagine Mathematics Headings

CB Page

Division as Equal Sharing

131

Division as Repeated Subtraction

135

Division and Multiplication Are Related

139

Long Division

142

Word Problems on Division

143

Learning Outcomes Students will be able to:

divide using equal sharing to find the number or groups or number of things in each group. divide using repeated subtraction and write the division sentence.

write division facts for the given multiplication fact and understand the relationship between multiplication and division. divide a 2-digit number by a 1-digit number using long division.

solve story problems on dividing a 2-digit number by a 1-digit number using the multiplication tables.

Alignment to NCF C-8.7: Uses repeated subtraction to find out how many groups for solving division problems C-8.13: Talks about different ways in which to solve a simple mathematical problem

Let’s Recall Recap to check if students know how to write a multiplication statement for given pictures. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary repeated subtraction: taking away the same number over and over again

multiplication fact: showing 2 numbers with a (×) sign between them followed by the (=) sign and the product of the two numbers

division fact: showing 2 numbers with a (÷) sign between them followed by the (=) sign and the quotient of the two numbers

Teaching Aids Ice-cream sticks; Paper cups; Sheet of paper with a table and ice-cream sticks drawn; A sheet of paper with a word problem written on it and a table showing each element of the CUBES strategy

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Chapter: Introduction to Division Division as Equal Sharing

Imagine Maths Page 131

Learning Outcomes Students will be able to divide using equal sharing to find the number or groups or number of things in each group.

Teaching Aids Ice-cream sticks; Paper cups

Activity Instruct the students to work in groups of 4. Distribute 20 ice-cream sticks and 4 paper cups to each group.

Instruct them to take turns to pick one ice-cream stick at a time from their shared collection and put them in the paper cups one by one until all the ice-cream sticks are distributed. Ask them to record the total number of ice-cream sticks, number of paper cups and the number of ice-cream sticks in each cup, in their notebooks. Discuss whether each paper cup has the same number of ice-cream sticks and how many ice-cream sticks does each paper cup have. Repeat the activity with 5 paper cups and 20 ice-cream sticks to reinforce the concept.

Ask questions like: How is 20 ice-cream sticks shared equally in 4 cups different from 20 ice-cream sticks shared equally in 5 cups?

Extension Idea Ask: Can you distribute 19 ice-cream sticks equally among 4 paper cups? Explain. Say: No, 19 ice-cream sticks cannot be shared equally among 4 paper cups. There will be 3 cups with 5 ice-cream sticks in each, but the fourth cup will have only 4 ice-cream sticks.

Division as Repeated Subtraction

Imagine Maths Page 135

Learning Outcomes Students will be able to divide using repeated subtraction and write the division sentence.

Teaching Aids Sheet of paper with a table and ice-cream sticks drawn; 12 ice-cream sticks

Activity Instruct the students to work in groups of 4. Distribute 12 ice-cream sticks and the sheets to each group.

Instruct them to take turns to pick 3 ice-cream sticks at a time from their shared collection until no ice-cream sticks are left. Each time a student takes 3 ice-cream sticks, the group should cross out 3 ice-cream sticks from the sheet and write the subtraction sentence. Help them write the first subtraction sentence as 12 – 3 = 9. Ask them to repeat the steps until all the ice-cream sticks have been crossed out.

Ask the students to count the number of times 3 was subtracted and the number of students who got the ice-cream sticks. Show them how to write the division fact. Ask questions like: How will you write the division fact if you have 20 ice-cream sticks and you take away 4 ice-cream sticks at a time? 34

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Division and Multiplication Are Related

Imagine Maths Page 139

Learning Outcomes Students will be able to write division facts for the given multiplication fact and understand the relationship between multiplication and division.

Teaching Aids Ice-cream sticks

Activity Instruct the students to work in groups. Distribute 20 ice-cream sticks to each group. Ask them to make 5 groups with 4 ice-cream sticks in each group. Then, in their notebooks, they will write the multiplication fact for the groups formed as 5 × 4 = 20. Next, ask them to put all the ice-cream sticks together and remove 5 ice-cream sticks at a time until they are left with 0 ice-cream sticks. Then, in their notebooks, they will write the division fact for the ice cream sticks removed as 20 ÷ 5 = 4. Discuss how multiplication and division work together. Repeat the activity with more sets of things to practice. Ask questions like: What are the division facts for 7 × 8 = 56?

Long Division

Imagine Maths Page 142

Learning Outcomes Students will be able to divide a 2-digit number by a 1-digit number using long division.

Teaching Aids Ice-cream sticks

Activity Discuss the need for long division and the use of multiplication tables in long division. Show the students the use of the division house and the placement of the numbers in it. Instruct the students to work in groups. Give 20 ice-cream sticks to each group. Instruct them to arrange the ice-cream sticks first in groups of 2, then in groups of 4, and then in groups of 5. Ask them to note down the result in terms of a division sentence. Then, in their notebooks, they will divide 20 by 2, 20 by 4 and 20 by 5 using the long division method to compare the answers they get with the results of the activity.

Extension Idea Ask: Which of the following numbers would not appear in the table of 4 – 13, 17, 24, 16 or 26? Say: 6 × 4 = 24 and 4 × 4 = 16. So, 24 and 16 appear in the table of 4 while 13, 17 and 26 do not appear in the table of 4.

Chapter 9 • Introduction to Division

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Imagine Maths Page 143

Word Problems on Division Learning Outcomes

Students will be able to solve story problems on dividing a 2-digit number by a 1-digit number using the multiplication tables.

Teaching Aids A sheet of paper with a word problem written on it and a table showing each element of the CUBES strategy

Activity Instruct the students to work in groups. Distribute the word problem cards to each group. Instruct them to use the CUBES strategy to solve the word problem: Jyoti purchased 35 apples and she distributed them equally among 7 people. How many apples did each person get?

Ask the students to circle the numbers in the word problem, underline the question and box the keywords.

C Circle the Numbers Jyoti purchased 35 apples and she distributed them equally among 7 people. How many apples will each person get? U Underline the Question

B Box the Keywords

E Evaluate/Draw

S Solve and Check 

Discuss what the students need to find out and then solve the problem using the long division method, on the sheet.

Extension Idea Ask: Create your own word problem where you need to divide 54 by 6.

Say: There can be multiple word problems on dividing 54 by 6. One such problem could be: Rohan takes 6 days to read 54 pages of a book. How many pages does he read in a day?

Answers 1. Division as Equal Sharing

Each friend will get 3 apples and 1 apple will be left.

Do It Together

The children will get 4 strawberries each. We get 4 groups of 4 strawberries.

3 × 5 = 15

2. Division as Repeated Subtraction

15 ÷ 3 = 5 _____

Do It Together

4. Long Division

10 15 – 5 = ____ 5 =5 10 – ____ 5 – ____ 5 =0 ____ 0

3 times until we get 0. 5 is subtracted ____ 3 Division fact is 15 ÷ 5 = ____.

3. Division and Multiplication Are Related Think and Tell 13 mangoes cannot be equally divided among 4 friends.

5 =3 15 ÷ _____ 4

Do It Together We say the table of 4 until we get 16. 4 × 4 = 16. So, 4 is the answer.

5. Word Problems on Division Do It Together Total number of sweets = 30

Number of family members = 6 Number of sweets each family member will get = 30 ÷ 6

Each family member will get 5 sweets.

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Understanding 10 Fractions Imagine Mathematics Headings

CB Page

Parts of Whole

149

Halves, Thirds and Fourths

150

Writing Fractions

152

Learning Outcomes Students will be able to:

identify wholes divided into equal parts.

identify halves, thirds and fourths of a whole and show them using pictures. write the fractions for given pictures showing halves, thirds and fourths.

Let’s Recall Recap to check if students know how to classify things or shapes that are divided into equal or unequal parts. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary unequal parts: parts that are not the same size one-half: one out of two equal parts

one-third: one out of three equal parts quarter: one out of four equal parts

three-fourths: three out of four equal parts two-thirds: two out of three equal parts

Teaching Aids Paper cutouts of shapes divided into equal or unequal parts with dotted lines; Crayons; Rectangular cutouts; Sheet of paper; Circular cutouts with one-half, one-fourth, two-thirds, and three-fourths shaded

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Chapter: Understanding Fractions Parts of Whole

Imagine Maths Page 149

Learning Outcomes Students will be able to identify wholes divided into equal parts.

Teaching Aids Paper cutouts of shapes divided into equal or unequal parts with dotted lines; Crayons

Activity Fold square and circular cutouts to make equal and unequal parts and show them to the students. Discuss the concepts of equal and unequal parts.

Instruct the students to work in groups. Distribute paper cutouts of shapes that have been divided into equal or unequal parts to each group.

Ask the students to identify the shapes that are divided into equal and unequal parts and to colour those divided into equal parts in green and those divided into unequal parts in red. Ask questions like: How did you find out if the shape was divided into equal parts?

Halves, Thirds and Fourths

Imagine Maths Page 150

Learning Outcomes Students will be able to identify halves, thirds and fourths of a whole and show them using pictures.

Teaching Aids Rectangular cutouts; Crayons

Activity Instruct the students to work in groups. Distribute 3 rectangular cutouts and crayons to each group.

Instruct them to take the first cutout and fold it along the centre. Tell them to open the cutout and look at the fold line. Discuss how the line has divided the cutout into halves.

Ask them to take the second cutout and fold it in a way that it is divided into 3 equal parts. Ask them to take the third cutout and fold it in a way that it is divided into 4 equal parts. Instruct the students to draw lines on the folds of all the rectangles and then shade to show the fractions one-half in the first rectangle, two-thirds in the second rectangle and three-fourths in the third rectangle. Ask questions like: What is the fraction of the unshaded parts in the three rectangles?

Extension Idea Ask: Can we divide a circle into 3 equal parts and show one-fourth by shading 1 part? Say: No. To show one-fourth, the circle must be divided into 4 equal parts with 1 part shaded. 38

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Imagine Maths Page 152

Writing Fractions Learning Outcomes

Students will be able to write the fractions for given pictures showing halves, thirds and fourths.

Teaching Aids Sheet of paper; Circular cutouts with one-half, one-fourth, two-thirds, and three-fourths shaded

Activity Demonstrate how to write the fraction for the shaded part of a figure with a numerator and denominator. Instruct the students to work in groups. Distribute the circular cutouts to each group. Ask the students to stick the cutouts on a sheet of paper and write the correct fraction for the shaded part of each cutout. Ask questions like: Can the number of shaded parts be greater than the total number of parts?

Extension Idea Ask: Alice sliced an apple into 3 parts. She ate one of the slices. What fraction of the apple is remaining now? Write the fraction in numbers. Say: As two of the three slices are remaining, the fraction of the apple remaining is two-thirds. Two-thirds in numbers is represented as 2 . 3

Answers 1. Parts of Whole

3. Writing Fractions

Think and Tell

Yes, we can divide all things into equal parts.

1 5

Do It Together



 ________ 2

________ 2

 ________ 4

2 3

3 4

1 2

1 4

2. Halves, Thirds and Fourths Do It Together 1. Three-fourths

2. Two-thirds

Chapter 10 • Understanding Fractions

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11 Measurement Imagine Mathematics Headings

CB Page

Length Using Things Around Us

160

Centimetre

163

Metre

165

Weight Using Things Around Us

168

Weight by Standard Units

170

Capacity Using Things Around Us

173

Capacity by Standard Units

175

Learning Outcomes Students will be able to:

measure the length of things using other smaller things or body parts. measure the length of things using a ruler.

estimate the correct standard unit that can be used to measure the length of different things. measure the weight of things using non-standard units.

estimate and find the weight of things in grams or kilograms.

measure the capacity of containers using non-standard units.

estimate the correct standard unit that can be used to measure the capacity of different containers.

Alignment to NCF C-8.9: Measures lengths and distances along short and long paths using uniform (non-standard) units, extends to longer lengths; Estimates and measures length/distances and capacities of containers using uniform non-standard units like a rod/pencil, cup/spoon/bucket; Appreciates the need for a simple balance; Compares weights of given objects using simple balance; Arranges in order containers as per their volumes based on perception & verifies by pouring out

Let’s Recall Recap to check if students know how to compare the lengths, weights, or capacities of daily life objects. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary length: horizontal distance from one end to the other end weight: measurement of the heaviness of an object

capacity: the amount that can be held in a particular space

Teaching Aids Imagine Mathematics book; Pencils; Ruler; Metre tape; Simple weighing balance; Unit cubes; Pencil box; Standard weights of 500 g, 1 kg and 2 kg; Bags of rice of weight 500 g, 1 kg and 2 kg; Jug; Paper glass; Paper cup; 10 mL medicine bottle; 500 mL and 1 L water bottles; Picture cards 40

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Chapter: Measurement Length Using Things Around Us

Imagine Maths Page 160

Learning Outcomes Students will be able to measure the length of things using other smaller things or body parts.

Teaching Aids Imagine Mathematics book; Pencils

Activity Show the students how to measure things starting from one end to the other. Instruct them to use their handspans to measure the length of their desks and to use their pencils to measure the length of their Imagine Mathematics books. Ask them to write the answers in their notebooks and compare answers with their partners. Ask questions like: Are the measures the same or different?

Discuss the reason for this. Bring out the fact that the measures can be different since the sizes of the handspans and pencils might differ.

Extension Idea Ask: Can we compare the lengths of the desk and the Imagine Mathematics book, if the length of the desk is 5 handspans and the length of the book is 2 pencils? Why?

Say: We cannot compare the lengths of the desk and the textbook because both are measured using different non-standard units.

Centimetre

Imagine Maths Page 163

Learning Outcomes Students will be able to measure the length of things using a ruler.

Teaching Aids Ruler; Pencil; Imagine Mathematics book

Activity Demonstrate how to use a ruler. Explain that the number written below each long line shows the measure in cm and that two cm lines have 9 shorter mm lines between them. Distribute the rulers among the students. Ask them to measure the length of their pencil and their Imagine Mathematics book using the ruler and note down the result in their notebook.

Ask questions like: Is the length of the pencil and the Imagine Mathematics book the same or different for all students?

Discuss the reason for this. Bring out the fact that measuring objects using a standard way makes it easy to get accurate measures and compare them.

Extension Idea Ask: What is the length of a crayon if it is placed along the ruler starting from the number 3 to 13?

Say: The distance between every two consecutive numbers on the ruler is 1 unit or 1 cm. So, the length of the crayon is 10 cm. Chapter 11 • Measurement

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Metre

Imagine Maths Page 165

Learning Outcomes Students will be able to estimate the correct standard unit that can be used to measure the length of different things.

Teaching Aids Metre tape

Activity Demonstrate how to use a metre tape. Explain the rules to be kept in mind while measuring using the metre tape and how to measure objects using it. Discuss when to measure lengths in metres. Instruct the students to work in pairs. Distribute metre tapes to each pair. Ask them to measure the length of their desks and the height of their chairs using the metre tape. Discuss why a metre tape was used to measure the length of the desk and not a ruler and how it would be difficult to measure the length of the desk using a ruler. Encourage the students to write their answers in their notebooks and compare with their partners.

Weight Using Things Around Us

Imagine Maths Page 168

Learning Outcomes Students will be able to measure the weight of things using non-standard units.

Teaching Aids Imagine Mathematics book; Pencil; Simple weight balance; Unit cubes; Pencil box; Water bottle

Activity Instruct the students to take out their pencils and Imagine Mathematics books. Ask them to hold the pencil in one hand and the book in the other. Ask questions like: Which is heavy? Which is light? Instruct the students to work in groups and take the simple balance and unit cubes. Ask them to measure the weight of the book and the pencil using the unit cubes. Let them measure the weight of more objects from their bags like a pencil box or water bottle. Discuss the weights and bring out the fact that if the two sides of the balance are at equal levels, the weight is the same; otherwise, the heavier side goes down. Teacher Tip: We may refer to https://www.youtube.com/watch?v=rkM8wlheqZ8 to make the balance. We can encourage students to make the balance and bring it to class the next day. Ask questions like: How is putting 2 things on either side of the balance different from measuring weight using unit cubes?

Extension Idea Ask: The weight of a suitcase which is 18 kg is equal to the total weight of a pumpkin and a handbag. If the weight of the pumpkin is 6 kg, what is the weight of the handbag? Say: The pumpkin and the handbag together weigh as much as the suitcase. So, the weight of the handbag is 18 – 6 = 12 kg.

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Weight by Standard Units

Imagine Maths Page 170

Learning Outcomes Students will be able to estimate and find the weight of things in grams or kilograms.

Teaching Aids Simple balance; Standard weights of 500 g, 1 kg and 2 kg; Bags of rice of weight 500 g, 1 kg and 2 kg

Activity Set up a weighing station in the class with weighing balance, standard weights of 500 g, 1 kg and 2 kg, and bags of rice of weight 500 g, 1 kg and 2 kg. Demonstrate how to use the balance with standard weights using one of the rice bags. Instruct the students to work in groups. Distribute one simple balance, standard weights and bags of rice weighing 500 g, 1 kg and 2 kg to each group. Instruct the students to guess the weight of each bag and then measure the weight of each rice bag by placing the bag on the left side and a standard weight on the right side. Repeat the activity by asking them to place more than one rice bag on the left and measure the total weight. Let students compare their estimate with the actual weight.

Extension Idea Ask: The weight of 1 block is 1 kg. The weight of 5 blocks and a ball is 7 kg. What is the weight of the ball? Say: The weight of 1 block is 1 kg. The weight of 5 blocks is 5 kg. So, the weight of the ball is 7 – 5 = 2 kg.

Capacity Using Things Around Us

Imagine Maths Page 173

Learning Outcomes Students will be able to measure the capacity of containers using non-standard units.

Teaching Aids Jug; Glass; Paper cup; Water bottle

Activity Instruct the students to work in groups. Distribute the jug, glass, paper cup and a bottle of water to them. Ask them to fill the paper cup with water and pour it into the jug; and should continue to do so until the jug is full to the brim. Ask them to count each time they pour water from the cup into the jug. Ask them to perform the same task with the glass in place of the jug. Let them write the capacity of the jug and the glass in their notebooks in terms of cups and compare their capacities. Ask questions like: Does the jug hold more water than the glass? Can we use some other vessel to measure the capacity? Will the capacity of the jug and the glass change?

Extension Idea Ask: My bottle can be filled with 5 cups of water. My friend’s bottle can be filled with 3 more cups of water. How many cups of water does it take to fill my friend’s bottle? Say: The capacity of your bottle is 5 cups of water. So, the capacity of your friend’s bottle will be 5 + 3 = 8 cups of water.

Chapter 11 • Measurement

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Capacity by Standard Units

Imagine Maths Page 175

Learning Outcomes Students will be able to estimate the correct standard unit that can be used to measure the capacity of different containers.

Teaching Aids 10 mL medicine bottle; 500 mL and 1 L water bottles; Picture cards

Activity Show the students a 10 mL medicine bottle, a 500 mL water bottle and a 1 L water bottle and discuss the different units of measuring capacity. Show the picture cards with containers of different sizes. Ask the students what measuring unit they will use to measure the capacity of each container. Discuss the answers with the class. Instruct the students to work in groups. Ask them to prepare a chart and draw 2 vessels that will hold water in litres and 2 vessels that will hold water in millilitres. Ask them to write the estimated capacity of each vessel below its picture. Show the charts drawn by different groups to the rest of the class.

Extension Idea Ask: The capacity of the bucket is 8 L. How many bottles of water are needed to fill a bucket completely if the capacity of a bottle is 2 L? Say: The capacity of the bucket is 8 L. The capacity of 1 bottle is 2 L. As 4 × 2 = 8, 4 bottles of water will be needed to fill the bucket completely.

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Answers 1. Length Using Things Around Us

5. Gram

Think and Tell

Do It Together

We cannot measure a tall door with a small crayon because a crayon is a very small object. It would become a very time-consuming task to measure bigger objects using it.

Bag of rice

A candle

600 g

100 g

We can measure a tall door with a roll of newspaper. Do It Together 1. The teddy is 4 blocks tall.

6. Kilogram

2. The toy giraffe is about 7 blocks tall.

Think and Tell

3. The paper fan is 6 blocks tall. 4. The drum and car are each about 2 blocks tall. 5. The teddy is 2 blocks taller than the toy car. The toy giraffe is 1 block taller than the fan. (2 blocks/1 block).

2. Centimetre

Another way to measure 5 kg of potatoes with 1 kg and 2 kg weights is: 1 kg + 1 kg + 1 kg + 2 kg Do It Together 1. 2 kg + 2 kg = 4 kg

Do It Together

So, the seller needs to put 2 weights of 2 kg to weigh 4 kg of potatoes.

1. Toothbrush – 12 cm

2. 2 kg + 2 kg + 1 kg = 5 kg

2. Pencil – 10 cm

7. Capacity Using Things Around Us

3. Key – 7 cm

Think and Tell

4. Iron screw – 6 cm

A river holds more water than a tank.

5. Bottle cap – 2 cm

Do It Together

3. Metre

The blue colour pot has less (less/more) capacity. It can be filled with 3 glasses while the red pot takes 5 glasses to fill.

Do It Together 1. A door

is measured in ___________. (m, cm) m

8. Millilitre Do It Together

2. A lamp post

m is measured in ___________. (m, cm)

3. A mirror

cm is measured in ___________. (m, cm)

4. A phone

cm is measured in ___________. (m, cm)

4. Weight Using Things Around Us Do It Together

30 mL

250 mL _________

10 mL _________

700 mL _________

9. Litre Do It Together 1.

1. 2 _____

8 = _____

300 L _________

1L _________

20 L _________

2. 1 _____ Chapter 11 • Measurement

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12 Shapes and Patterns Imagine Mathematics Headings

CB Page

All About Lines

183

Features of Flat Shapes

186

Drawing Flat Shapes

186

Features of Solid Shapes

189

Flat Shapes in Solid Shapes

191

Repeating Patterns

193

Growing Patterns

195

Number Patterns

198

Learning Outcomes Students will be able to:

identify the different types of lines and curves in a figure and trace them. name flat shapes and list their features. draw flat shapes on dot paper.

name solid shapes and list their features.

trace solid shapes to identify the flat shapes in them.

identify and extend repeating patterns with shapes or figures. identify and extend growing patterns with shapes or figures. identify and extend number patterns.

Alignment to NCF C-8.2: Describes the rule of patterns and applies this on abstract patterns such as number, symbol, and analogic thinking patterns

C-8.8: Identifies 3D shapes by their names and describes their observable characteristics; Identifies 2D shapes by their names and describes their observable characteristics; Distinguishes between straight and curved lines and draws/represents straight lines in various orientations; Traces 2D outlines of 3D objects

Let’s Recall Recap to check if students know how to distinguish sizes of the objects. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary flat shape: shape that can be drawn on plane paper

solid shape: shape that have 3 dimensions (length, breadth and height)

Teaching Aids Ice-cream sticks; Pencils; Sheets of paper; Thread; Glue stick; Flat shape cutouts; Pair of scissors; Crayons; Wooden solid shapes; 2 objects for each solid shape; Building blocks of the same shape and size; Number cards 46

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Chapter: Shapes and Patterns Imagine Maths Page 183

All About Lines Learning Outcomes

Students will be able to identify the different types of lines and curves in a figure and trace them.

Teaching Aids Ice-cream sticks; Pencils; Sheets of paper; Thread; Glue stick

Activity Show the students an ice-cream stick. Hold it vertically, horizontally and then in a slanting position, and discuss standing, sleeping and slanting lines. Use a piece of thread to show them curves. Ask the students to work in groups. Distribute ice-cream sticks, a glue stick and a sheet of paper to each group. Instruct them to make 2 letters and 2 numbers using the ice-cream sticks on the sheet of paper. They can use the glue to paste the ice-cream sticks on the paper. Below each letter or number, they should write the types of lines in it.

Standing line and sleeping lines

Sleeping line and slanting lines

Extension Idea Ask: Name a letter and a number that have both lines and curves. Say: The letter B and the number 5 have both lines and curves.

Features of Flat Shapes

Imagine Maths Page 186

Learning Outcomes Students will be able to name flat shapes and list their features.

Teaching Aids Flat shape cutouts (square, rectangle, triangle, circle, oval)

Activity Demonstrate how to find the sides and corners in a square. Invite a student to come up and put a finger at one corner of the shape. Ask the student to move his/her finger along the side of the shape as all the students say ‘SIDE’. When the finger reaches a corner, then all the students should say ‘CORNER’. Continue this until the finger reaches the point where it started from. Ask the students to call out the number of sides and corners in the shape. Ask the students to work in groups. Distribute the shape cutouts to each group. Ask them to find the number of sides and corners in each shape cutout and write the features in their notebooks. Ask questions like: How many corners are there in a circle?

Extension Idea Ask: What are the differences and similarities between a square and a rectangle? Say: Both a square and a rectangle have 4 sides and 4 corners but all four sides of a square are equal while all four sides are not equal in a rectangle. Chapter 12 • Shapes and Patterns

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Drawing Flat Shapes

Imagine Maths Page 186

Learning Outcomes Students will be able to draw flat shapes on dot paper.

Teaching Aids Sheets of paper; Pair of scissors; Crayons; Glue stick

Activity Distribute sheets of paper showing traces of different shapes. Ask the students to trace the shapes and cut them out. Ask them to colour the shapes and stick them together on a sheet of paper to form a robot-like structure.

Extension Idea Ask: What shape will be formed when two squares are joined side by side? Say: When two squares are joined side by side, a rectangle is formed.

Features of Solid Shapes

Imagine Maths Page 189

Learning Outcomes Students will be able to name solid shapes and list their features.

Teaching Aids Wooden solid shapes (cube, cuboid, cylinder, cone, sphere); 2 objects for each solid shape like a dice, book, sugar cube, rectangular pencil box, cylindrical bottle, juice can, birthday cap, ice-cream cone, ball, globe

Activity Show the students the different wooden solid shapes and discuss what faces, edges and vertices are. Place the solid shapes on the table. Ask the students to work in groups. Distribute the objects. Instruct the students to look at each object, identify its shape and sort it as per its shape. Ask them to identify the faces, edges and vertices in each shape and write the number of each in their notebooks. Ask questions like: Which of these shapes have the same features? Discuss how a cube and cuboid have the same number of faces, edges and vertices but are still different.

Extension Idea Ask: What shape is formed when multiple circles are put one on top of another? Say: When multiple circles are put one on top of another, a cylinder is formed.

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Flat Shapes in Solid Shapes

Imagine Maths Page 191

Learning Outcomes Students will be able to trace solid shapes to identify the flat shapes in them.

Teaching Aids Wooden solid shapes (cube, cuboid, cylinder, cone, sphere)

Activity Discuss the faces of a cube and ask students to guess the shapes that they will get on tracing the sides of the cube on a piece of paper. Instruct the students to work in groups. Distribute the wooden solid shapes among them by giving 1 shape to each group. Instruct the students to look at the shape, place it on the sheet of paper, and use a pencil to trace 2 sides of the solid shape. Instruct the students to look at the shapes formed after tracing. Ask questions like: What flat shapes did you get on tracing the faces of a cylinder? Discuss how flat shapes are formed on tracing the faces of solid shapes.

Extension Idea Ask: Two cubes are joined together and then one face of the resulting solid shape is traced. What shape does it form? Say: Two cubes put together form a cuboid. On tracing a cuboid, we get a rectangle.

Repeating Patterns

Imagine Maths Page 193

Learning Outcomes Students will be able to identify and extend repeating patterns with shapes or figures.

Teaching Aids Flat shape cutouts; Sheets of paper

Activity Instruct the students to work in pairs. Distribute cutouts of different shapes and blank sheets of paper to each pair. Instruct the students to paste the shape cutouts on the sheet of paper in a line. For example, the students can paste a circle, a square, a circle, and a square or 2 circles, 1 square, 2 circles, and 1 square. Ask them to then exchange sheets with their partner and extend the pattern made by their partners by pasting the same shapes. Allow the students to repeat the activity with other shapes. Discuss the patterns that the students formed.

Chapter 12 • Shapes and Patterns

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Growing Patterns

Imagine Maths Page 195

Learning Outcomes Students will be able to identify and extend growing patterns with shapes or figures.

Teaching Aids Building blocks of the same shape and size

Activity Ask the students to work in groups. Distribute building blocks to each group. Instruct them to make towers using the blocks (for example: 1 block, 2 blocks, 3 blocks, 4 blocks and so on) where each student in a group makes one tower and the next student makes a tower that has 1 more block. Let them continue making the towers until 6 towers are formed. Further, instruct the students to make one more set of towers with different numbers of blocks making sure that the pattern made is different from the previous one and that the same number of blocks is added each time. Discuss growing patterns and how to identify the rule in a growing pattern.

Extension Idea Ask: How many blocks will be in the fifth tower if the first tower has 3 blocks, the second has 6 blocks and the third has 9 blocks? Say: There are 3 blocks in the first tower, 6 blocks in the second tower, 9 blocks in the third tower, 12 blocks in the fourth tower and 15 blocks in the fifth tower.

Number Patterns

Imagine Maths Page 198

Learning Outcomes Students will be able to identify and extend number patterns.

Teaching Aids Number cards; Pencils

Activity Write a number pattern, say 2, 4, 6, 8, 10, on the board. Ask the students what they notice and how to identify the rule in a number pattern. Ask the students to work in groups. Distribute number cards to each group. Instruct one student in each group to place 4 number cards next to each other making sure that there is a pattern in the numbers. The next student in the group will then identify the rule in the pattern and place a number card that helps extend the pattern. Let the students take turns at extending the pattern. Repeat the activity by asking them to put all the number cards together with another student forming a number pattern and the other students in the group extending it. Ask questions like: What helped you identify the rule in a number pattern?

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Answers 1. All About Lines

5. Flat Shapes in Solid Shapes

Do It Together

Sleeping Line

Curved Line

2. 3.

Standing Line

Slanting Line

2. Features of Flat Shapes Think and Tell Yes, there are more flat shapes. A star and a heart drawn on paper are also flat shapes. Do It Together

6. Repeating Patterns Do It Together 1. 2. 3.

7. Growing Patterns Do It Together 1.

3. Drawing Flat Shapes Think and Tell No, we cannot make a circle or an oval with ice-cream sticks. Do It Together

8. Number Patterns Do It Together 1.

3 9 3 9 3 9

1 3 5 7 9 11

4. Features of Solid Shapes Think and Tell When two cylinders are put one on top of another, then the shape formed is also a cylinder. Do It Together 1. 2. 3. 4.

Chapter 12 • Shapes and Patterns

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13 Time Imagine Mathematics Headings

CB Page

Time on a Clock

203

Days of the Week

206

Months of the Year

207

Seasons and Festivals

211

Story Problems on Time

214

Learning Outcomes Students will be able to:

read the time to the half hour on a clock.

recall the days of the week and use today, tomorrow and yesterday. name the months of the year and arrange them in order.

read a calendar and identify the different seasons and festivals in a year. solve problems on reading a timetable.

Alignment to NCF C-8.10: Gets a feel for sequence of seasons (varying locally)

C-8.10: Measures duration of time using standard units – days, hours (e.g. 7 days a week and 24 hours in a day)

Let’s Recall Recap to check if students know the different parts of a day as morning, afternoon, evening and night; and the activities that they do in each part of the day. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary clock: helps us to read and show time

timetable: a list or table that tells us the times when different events take place

seasons: one of the 5 parts of the year—summer, winter, spring, monsoon and autumn

Teaching Aids Clock with movable hour and minute hands; Monthly calendar; Circular chart paper divided into 7 sectors; Year calendar; Circular chart paper divided into 12 sectors; Crayons; Chart paper; Class timetable; Template for creating a timetable 52

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Chapter: Time Time on a Clock

Imagine Maths Page 203

Learning Outcomes Students will be able to read the time to the half hour on a clock.

Teaching Aids Clock with movable hour and minute hands

Activity Discuss how the time to the hour and half hour is read by looking at the minute and hour hands of a clock. Discuss a few examples. Move the hands of the clock to show the times 1:30, 6:30 and 10:30. Instruct the students to look at the clock and read the time on the clock each time. In their notebooks, they will write the time in 2 different ways. Ask questions like: What times do you see in the clock? What is the same and different in the clock each time?

Extension Idea Ask: A train takes 2 hours to reach Station B from Station A. If the train starts from Station A at 9:30, what will be the time on the clock when the train reaches Station B? Say: The train will reach Station B at 11:30.

Days of the Week

Imagine Maths Page 206

Learning Outcomes Students will be able to recall the days of the week and use today, tomorrow and yesterday.

Teaching Aids Monthly calendar; Circular chart paper divided into 7 sectors; Crayons

Activity Show the monthly calendar to the students and let them recite the days of the week. Discuss the concepts of today, yesterday and tomorrow in terms of the day. Ask the students to work in groups. Distribute the circular chart paper to each group. Write the days of the week on the board in random order. Instruct the students to write the days of the week from Monday to Sunday on the chart paper in the order in which they come. They can decorate the calendar of the week the way they like. Then, in their notebooks, they will write the names of all the days of the week. Ask questions like: What day is it today? If it is Monday today, what day will it be tomorrow? What day was it yesterday?

Extension Idea Ask: Surbhi attends night school every Tuesday, Thursday and Saturday. What days does Surbhi not have school? Say: Surbhi does not have school on Monday, Wednesday, Friday and Sunday.

Chapter 13 • Time

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Month of the Year

Imagine Maths Page 207

Learning Outcomes Students will be able to name the months of the year and arrange them in order.

Teaching Aids Year calendar; Circular chart paper divided into 12 sectors; Crayons

Activity Show the year calendar to the students and let them recite the months of the year. Discuss the number of months in a year. Ask the students to work in groups. Distribute the circular chart paper to each group.

Instruct students to write the months of the year from January to December on the chart paper in the order in which they come. Ask them to shade the months that have 30 days in yellow, 31 days in blue, and others in green. They can decorate the calendar of the month the way they like. Then, in their notebooks, they will write the names of all the months of the year. Ask questions like: Which months have 30 days? Which months have 31 days? What month is it now? What is the next month?

Extension Idea Ask: Rahul’s birthday is in a month that has 31 days. The name of the month starts with the letter ‘J’ and it is not the first month of the year. In which month is Rahul’s birthday? Say: The months that have 31 days are January, March, May, July, August, October and December. January and July start with the letter ‘J’. As Rahul’s birthday is not in the first month of the year, his birthday is in July.

Seasons and Festivals

Imagine Maths Page 211

Learning Outcomes

Students will be able to read a calendar and identify the different seasons and festivals in a year.

Teaching Aids Chart paper; Crayons

Activity

Discuss the 5 seasons—winter, spring, summer, monsoon and autumn—and the different festivals that are celebrated in different seasons. Instruct the students to work in groups of 5 such that each group chooses one season. Distribute the chart paper to each group. Ask each group to draw a picture of that season and write the festivals of that season. Ask questions like: What season is it now? Are you wearing your winter clothes or summer clothes? What festival is in this season?

Extension Idea

Ask: Richa visited her grandparents after April and came back before the monsoon. In which season did she visit her grandparents? For how many months did she stay there? Say: Richa visited her grandparents in the month of May and came back before July. So, she visited her grandparents in the summer season. She visited them for 2 months. 54

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Imagine Maths Page 214

Story Problems on Time Learning Outcomes Students will be able to solve problems on reading a timetable.

Teaching Aids Class timetable; Template for creating a timetable

Activity

Event

Show the class timetable to the students and discuss it.

Time

Instruct the students to use the template as shown to make a new timetable for their daily routine including tasks like Waking up, School start time, Lunch break, School end time, Homework, Play, Dinner, Bedtime. Ask questions like: How is your timetable different from the timetable made by your partner? How is it the same?

Extension Idea Ask: A timetable shows that Train A leaves at 3:30 and Train B leaves 3 hours later. What is the time written on the timetable for Train B? Say: The time of departure written on the timetable for Train B is 6:30.

Answers 1. Time on a Clock

4. Seasons and Festivals

Do It Together

Think and Tell

2:30, Half past 2

Different people celebrate different festivals. For example, the Sikhs celebrate Guru Nanak Jayanthi that falls in the autumn. Christians celebrate Easter that falls in the spring.

2. Days of the Week

Do It Together

12:30, Half past 12 12:00, 12 o’clock

Do It Together 1. Pudding 3. Monday

2. Wednesday 4. Thursday

1. July and August 2. 3

3. Spring

3. Months of the Year

4. Spring

Do It Together

5. Story Problems on Time

Students will colour April and June in yellow and January, March, May, July and August in green.

1. April, June 2. January, March, May, July, August 3. January – 31 days and February – 28 days 4. Answers may vary. Sample answers: Hours – going to school, watching television; Days – exams, camping; Months – summer vacations, seasons Chapter 13 • Time

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5. Monsoon

Do It Together 1. 8:00

2. Swimming 3. Friday 4. Art

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14 Money Imagine Mathematics Headings

CB Page

Indian Coins and Notes

221

Exchange of Money

224

Adding and Subtracting Money

225

Learning Outcomes Students will be able to:

identify different coins and notes (up to ₹500).

count the money amounts (up to ₹100) to find the notes and coins needed for pay of something that is bought. solve problems on adding and subtracting money amounts.

Alignment to NCF C-8.11: Adds up notes and coins to form amounts up to ₹100

Let’s Recall Recap to check if students know where to use money and its value.

Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary rupee: the money in India is called the Indian Rupee, shown by the symbol ₹ total amount: the sum of the prices of items bought coin: a piece of metal money

Teaching Aids Sheets of paper; Play money (1 note each of ₹500, ₹100, ₹50, ₹20, ₹10 and 1 coin each of ₹20, ₹10, ₹5, ₹2, ₹1); Cards showing toys and prices written (any number of cards can be made)

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Chapter: Money Imagine Maths Page 221

Indian Coins and Notes Learning Outcomes Students will be able to identify different coins and notes (up to ₹500).

Teaching Aids Play money (1 note each of ₹500, ₹100, ₹50, ₹20, ₹10 and 1 coin each of ₹20, ₹10, ₹5, ₹2, ₹1)

Activity Discuss with the students the money that they’ve seen in their daily lives and how to read the values of notes and coins. Show them one note and point to the value and symbol. Instruct the students to look at the play money and sort them into notes and coins. Then, in their notebooks, they will write the notes and coins and their value using the rupee symbol. Ask questions like: What money amount did you see that has the same value both in notes and coins? Which note or coin has the highest value? Discuss and show the notes and coins that are no longer available and if the students have seen them.

Extension Idea Ask: Which is costlier: a chocolate costing ₹50 or a toy costing ₹200? How do you know? Say: Since 200 > 50, the toy is costlier.

Imagine Maths Page 224

Exchange of Money Learning Outcomes

Students will be able to count the money amounts (up to ₹100) to find the notes and coins needed for pay of something that is bought.

Teaching Aids Sheets of paper; Play money (1 note each of ₹500, ₹100, ₹50, ₹20, ₹10 and 1 coin each of ₹20, ₹10, ₹5, ₹2, ₹1); Cards showing toys and prices written: any number of cards can be made

Activity Discuss how to make ₹60 in different ways: ₹60 = ₹20 + ₹20 + ₹20 or ₹60 = ₹10 + ₹10 + ₹10 + ₹10 + ₹10 + ₹10. Ask the students to work in groups of 4. Distribute the play money to each group. Place the toy cards on the table. Invite 1 student from each group to come up and pick any 3 items that they want to buy and take it back to their group. Instruct the students to use the notes and coins to make up the amount for each of the items that they want to buy. They will then write the notes and coins used to make up the amounts for the three items on their sheets. Open the class for discussion.

Duck

Teddy Bear

₹40

₹100

Robot

₹75

Toy Car ₹80

Ask questions like: Which notes or coins did you use to make ₹75? Chapter 14 • Money

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Imagine Maths Page 225

Adding and Subtracting Money Learning Outcomes Students will be able to solve problems on adding and subtracting money.

Teaching Aids Play money (1 note each of ₹500, ₹100, ₹50, ₹20, ₹10 and 1 coin each of ₹20, ₹10, ₹5, ₹2, ₹1); Cards showing toys and prices written – any number of cards can be made

Activity Discuss with the students how much they need to pay when they buy 2 items costing ₹40 and ₹80. Ask the students to form groups of 4. Distribute play money worth ₹200 to each group. Place the toy cards on the table. Ask the groups to decide on any 2 toys that they want to buy. Ask them to add the money amounts to find the total amount to be paid for the two items and how much money will they get back on paying ₹200 for those two items. In the notebooks, they will then add or subtract using the column method.

Duck

Teddy Bear

₹40

₹100

Robot

Toy Car

₹75

₹80

Ask questions like: What is the total amount? Do we add or subtract if we buy 2 items together? 3 items together?

Extension Idea Ask: Anna buys a book for ₹85. She pays for it with a ₹100 note. Which coins can be used by the shopkeeper to give her the change amount due? Say: To find the amount of money that the shopkeeper will return, we subtract. ₹100 – ₹85 = ₹15. The shopkeeper can pay in different ways. He can pay with one ₹10 and one ₹5 coin. He can also pay with three ₹5 coins.

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Answers 1. Indian Coins and Notes

3. Adding and Subtracting Money

Do It Together

Think and Tell Riya can use ₹50 + ₹50 + ₹20 + ₹20 to make ₹140. Do It Together

`200

2. Exchange of Money Do It Together

`25

`40

`65

Chapter 14 • Money

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`50

Add and tell the total cost. 1 bag

`55

1 toy train

47 + `____

Total cost

102 = `_____

How much will I get back? I give

`80

I will buy 1 bag

55 – `____

I will get back

25 = `____

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15 Data Handling Imagine Mathematics Headings

CB Page

Counting Data

233

Organising Data

236

Finding Information

238

Pictograph (Drawing)

241

Pictograph (Reading)

241

Learning Outcomes Students will be able to:

count the number of things in each group and make a table. organise data in a table in the form of lists.

read the data given in a table and answer questions on the data. draw a pictograph to show the given data.

read a pictograph and answer questions based on the given data.

Alignment to NCF C-8.1: Sorts objects into groups and subgroups (e.g., in a group of blocks, first sorts based on colour, then within the colour, sorts based on shape, then sorts based on size. Sorts between trees and creepers, within that sort fruit bearing and non-fruit bearing, within that edible or non-edible) C-8.12: Comprehends texts and extracts simple mathematical problems embedded in the text C-8.13: Talks about different ways in which to solve a simple mathematical problem

Let’s Recall Recap to check if students know how to sort objects of the same kind and count them. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary data: facts, figures, or other pieces of information that can be used to learn about something pictograph: a table that shows the given data using pictures or symbols

Teaching Aids Coloured circular paper cutouts (orange, blue, green, yellow); Items from the school bag like notebooks, textbooks, pencils etc.; Chart paper; Straws in red, green and blue; Smiley cutouts; Glue sticks; Pictograph chart representing the number of fruits collected by a boy/girl 60

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Chapter: Data Handling Imagine Maths Page 233

Counting Data Learning Outcomes Students will be able to count the number of things in each group and make a table.

Teaching Aids Coloured circular paper cutouts (orange, blue, green, yellow)

Activity Instruct the students to work in groups. Distribute the circular cutouts to the students and draw a table as shown on the board. Ask the students to copy the table into their notebooks. You can also provide printed sheets of paper with these tables. Colour

Orange

Blue

Green

Yellow

Number of Cutouts Instruct the students to count the number of circular cutouts they have of each colour. Then, in their notebooks, they will record their counts in the respective columns of the table. Ask questions like: How many orange, blue, green and yellow cutouts are there? What is the total number of cutouts?

Extension Idea Ask: If I give you some black circular cutouts, where will you record their count?

Say: You can record the count of the black circular cutouts by adding one more column to the table.

Organising Data

Imagine Maths Page 236

Learning Outcomes Students will be able to organise data in a table in the form of lists.

Teaching Aids Items from the school bag like notebooks, textbooks, pencils, etc.

Activity Ask students to create a list of 5 items such as notebooks, textbooks, pens, pencils, erasers, etc. that they currently have in their school bags. Instruct them to make the list in their notebooks, organising it into two columns: ‘Item Name’ and ‘Number of Each Item’. Encourage students to diligently record all the five items they find in their school bags in the left column and the quantity of each item they typically carry in the right column. Emphasise the importance of accuracy and completeness in their lists.

Extension Idea Ask: If there is a drawing and painting class tomorrow, which two items would you add to your list? How much of each item would you need? Say: Answers may vary. Sample answer: You may need various types of paints (watercolours, acrylics) and paintbrushes. Chapter 15 • Data Handling

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Finding Information

Imagine Maths Page 238

Learning Outcomes Students will be able to read the data given in a table and answer questions on the data.

Teaching Aids Items from the school bag like notebooks, textbooks, pencils, etc.

Activity Instruct students to refer to the list of all the items they have in their school bag. Ask them to find specific information from the table. For example: How many notebooks are there? How many textbooks are there? How many items are there in all? What is the largest number of any item on the list? Instruct the students to locate the information in the table and write down their answers in their notebooks.

Extension Idea Ask: Which do you have more of: notebooks or textbooks? By how much? Say: Answers may vary. Sample answer: I have 2 more notebooks in my bag than textbooks.

Pictograph (Drawing)

Imagine Maths Page 241

Learning Outcomes Students will be able to draw a pictograph to show the given data.

Teaching Aids Chart paper; Straws in red, green and blue; Smiley cutouts; Glue sticks

Activity Explain what a pictograph is and how it represents data using pictures or symbols. Instruct the students to work in groups. Distribute the chart paper, coloured straws, smiley cutouts and glue sticks among the groups. Show them how to make a table with the colour names on the left and the number of straws written on the right. Ask them to count the number of red straws and paste that many smiley cutouts in front of the colour red in the table. Ask them to repeat the activity for the other two colours of straws. Explain that the data so formed is a pictograph.

Extension Idea Ask: If you want to use 1 picture to show 2 items, how many pictures will you use to show 10 items? Say: We will use 5 pictures to show 10 items.

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Imagine Maths Page 241

Pictograph (Reading) Learning Outcomes

Students will be able to read a pictograph and answer questions based on the given data.

Teaching Aids Pictograph chart representing the number of fruits collected by a boy/girl.

Activity Instruct the students to work in groups. Distribute the pictograph charts to each group. Ask the students to examine the pictograph carefully. Explain that each fruit picture represents one fruit. Ask questions like: How many apples did he/she collect? How many bananas did he/she collect? How many fruits did he/she collect in all? Which fruit did he/she collect the most of? Which fruit did he/she collect the least number of? Encourage students to answer orally first and then write down the answers in their notebooks.

Answers 1. Counting Data

3. Finding Information

Do It Together

Do It Together 1. Which month had the most flowers? March

Colour Number of Cutouts

2. April has the least flowers – True or False? True 3. How many flowers grew in January? 13

4. March has one less flower than January – True or False? False

2. Organising Data Think and Tell There would be: 3 kg + 3 kg = 6 kg of mangoes Do It Together Cap

2 __

Umbrella

Coat

Pants

2 pair __

Bag

Bottles

2 __

Chips

3 __

Shoes

1 pair

4. Pictograph Do It Together Sport

Number of Students

Badminton Hockey Cricket Football Tennis 1. How many students participated in Football? 3 2. Which activity had the most students? Cricket

3. Was there any activity with only one student? Yes 4. Which activity had the least students? Tennis

Chapter 15 • Data Handling

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S o lu t i o ns 1D 1.

Chapter 1 Let's Warm-up 1.

Odd

Even

Odd

Do It Yourself 1A 1. a. 112, 114, 115, 117, 120 b. 152, 154, 156, 157, 159, 160

c. 192, 194, 196, 197, 199 d. 188, 186, 184, 182, 181 2. a. 111 b. 133 c. 150 3. a. 143 b. 161 c. 111 d. 197 4. a. 30 b. 4 c. 100 d. 6 e. 50 f. 100 5. a. 138 b. 104 c. 192 d. 152 e. 146 f. 149 6. 2 tens + = 7. 2 tens and 5 ones

3. a. True b. False c. True d. True 4. Drawings may vary. Even

1B 1. a. 122

5. a. Rupa can make 3 pairs. b. She needs 2 more pairs to make 10 mangoes

100 b. 66 166 c. 43 102 d. 110 101 e. 198 189 2. a. 123 < 143 b. 133 < 193 c. 129 = 129 d. 132 < 136 e. 123 < 143 3. a. 122 123 b. 133 134 c. 198 199 4. a. 112 113 b. 100 101 c. 179 180 5.

Increasing

Decreasing

a. 109, 114, 123, 134, 154

154, 134, 123, 114, 109

b. 110, 112, 117, 118, 119

119, 118, 117, 112, 110

c. 73, 99, 100, 101, 111

111, 101, 100, 99, 73

d. 99, 100, 111, 119, 187

187, 119, 111, 100, 99

6. a. True b. False c. True d. False

1C 1.

Odd

Chapter Checkup

1. a. 101 102 103 104 105 106 107 108 b. 162 163 164 165 166 167 168 169 c. 180 181 182 183 184 185 186 187 2. a. 1 hundred + 5 tens + 6 ones = 156 b. 1 hundred + 7 tens + 5 ones = 175. c. 1 hundred + 9 tens + 0 ones = 190. 3. a. 136 b. 161 4.

a. b. c. d.

Before 123 197 112 134

5. a. 133

142

Between 124 198 113 135

After 125 199 114 136

134 b. 195

154

143 c. 184

132

198

d. 123 176 154 6. a. 1 hundred + 7 tens + 9 ones = 179 b. 159 remains if 2 tens is taken away from 179 First

7. a.

H 1

6. Meena’s position = 5th Soham’s position = last Tina is between Meena and Soham. So, Tina is 6th in the line.

2 90 100

1st 3rd 4. a. The grapes are in the third position. b. The mango is in the 5th position. c. The apple is in the second position. d. The sunflower is in the fourth position. 5.

H 1

O 0

0 40 100

8. a. 134 = 100 + 30 + 4 b. 187 = 100 + 80 + 7 c. 122 = 100 + 20 + 2 d. 199 = 100 + 90 + 9 e. 120 = 100 + 20 + 0 f. 167 = 100 + 60 + 7 g. 176 = 100 + 70 + 6 h. 103 = 100 + 3 9. a. False b. True c. True d. False 10.

1st

START

5th

3rd

4th

1st

2nd

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11.

2B 1. a.

Even

+ 2. a.

Odd

12. Riya lives on the 2nd floor Juhi lives on the floor above Riya, The floor above 2nd will be 3rd floor. So, Juhi lives on the 3rd floor.

Let's Warm-up 1. 2 + 3 2. 4 + 0 3. 8 + 1 4. 5 + 2 5. 4 + 4

7 5 8 9 4

Tens

Ones

+ 31 + 20 =

Tens Ones 2 0 + 1 3 3 3

Tens Ones 3 2 4 2 7 4

d. +

Tens Ones 2 2 + 2 3 4 5

Tens Ones 7 2 2 1 9 3

5. a. 34 + 12 = 46 b. 33 + 14 = 87 c. 72 + 22 = 50 d. 34 + 21 = 55 e. 14 + 13 = 21 f. 56 + 21 = 77

Tens Ones 2 8 1 1 3 9 Tens Ones 2 4 5 3 7 7

+ b.

Tens Ones

+ c.

Tens Ones

a. 25 + 45 =

b. 23 + 19 =

c. 35 + 15 =

d. 34 + 27 =

3 +

Tens Ones 2

1 +

Tens Ones 1

0 e.

Tens Ones

3 d.

Ones

+ 32 + 22 =

Tens Ones

4. a.

Do It Yourself 2A 1. a. 7 tens 6 ones = 76 b. 10 tens 1 ones = 101 2. a.

Tens Ones

Tens Ones 1

3 3.

Chapter 2

3. a.

Tens Ones

Tens Ones 1

Tens Ones

+ f.

Tens Ones 1 +

5. N umber of flowers in pot A = 13 Number of flowers in pot B = 17 We need to add 3 tens to get the answer.

2C 1. a. 3 + 2 + 4 = 9 3+2=5

5+4=9

Tens Ones 1 +

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

b. 1 + 3 + 8 = 12 1+3=4

4 + 8 = 12

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

c. 2 + 2 + 4= 8 2+2=4

4+4=8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Solutions

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d. 1 + 2 + 5 = 8 1+2=3

3+5=8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4. Number of stickers with Arun = 42 Number of stickers given by Arjun = 26 Total number of stickers with Arun = 42 + 26 = 68 Thus, Arun has 68 stickers. Let’s check 26 + 42= 68, so, the answer is right. Tens Ones

e. 5 + 5 + 1 = 11 5 + 5 = 10

10 + 1 = 11

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2. a. 3 + 2 + 1 = 6 b. 4 + 4 + 1 = 9 c. 2 + 3 + 5 = 10 d. 6 + 6 + 1 = 13 e. 2 + 2 + 2 = 6 3. a.

Tens Ones + +

4. a.

Tens Ones + +

Hundreds Tens Ones

+ 1 c.

Tens Ones 3

5. W e have 2 and 5, let’s add it 2 + 5 = 7 To get 10, how much do we need to add to 7 Thus, we need to add 3 to get 10.

6. There are a total of 20 books. 2 tens = 20 5 tens = 50 So, from 2 tens to 5 tens, we need more 3 tens to get 5 tens. 3 tens is 30 Thus, we need 30 more books.

2D 1. Number of candies bought by Riya = 24 Number of candies given by Aryan = 37 Total candies with Riya = 24 + 37 = 61 Thus, Riya has 61 candies now.

2. Number of red balloons = 56 Number of blue balloons =21 Number of green balloons = 12 Total balloons = 56 + 21 + 12 = 89 Thus, there are 89 balloons in all. 3. Number of red roses = 48 Number of yellow roses = 32 Number of white roses = 17 Total roses in the garden = 48 + 32 + 17 = 97 Thus, there are 97 roses in the garden.

Tens Ones

6. Number of cars with Esha = 7 Number of cars with Alim = 5 more than Esha Total cars with Alim = 7 + 5 = 12 Total cars with both of them = 7 + 12 = 19 Thus, they have 19 cars in total. So let’s check 12 + 7 = 19, Thus, the answer is right

Tens Ones 4

5. Number of mangoes on one shelf = 42 Number of mangoes on other shelf = 39 Total mangoes in the shop = 42 + 39 = 81 Thus, there are 81 mangoes in total. Let’s check 39 + 42 = 81, so the answer is correct.

Tens Ones

1 3

Tens Ones

Tens Ones 1 2 4 + 3 7 6 1

Tens Ones 5 6 2 1 + 1 2 8 9 Tens Ones 1 4 8 3 2 + 1 7 9 7

Tens Ones

7 +

1 +

2 7

Chapter Checkup 1. a. 8 + 2 = 10 8 + 2 = 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

b. 7 + 5 + 2 = 14 7 + 5 = 12

12 + 2 = 14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

c. 7 + 3 + 2 = 12 7 + 3 = 10

10 + 2 = 12

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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d. 12 + 5 = 17

4. a. 26 + 13 = 39 First add the ones 6 + 3 = 9 So, write 9 in ones place. Now add the tens 2 + 1 = 3 tens

12 + 5 = 17

b. 48 + 22 = 70 First add the ones 8 + 2 = 10 So, write 0 in ones place and add 1 ten to the tens place Now add the tens 4 + 2 + 1 = 7 tens

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

e. 16 + 3 + 5 = 24 16 + 3 = 19

19 + 5 = 24

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 21 22 23 24 25 26 27 28 29 30

2. a. 13 + 21 = 34 Tens

b. 18 + 2 = 20 Ones

Tens

Solutions

UM24TMG2.indb 67

Ones

Tens Ones +

Tens

Tens Ones +

12 + 11

32 + 25

62 + 14

6. Number of marbles with Rohan = 23 Number of marbles given by Soham = 46 Total marbles with Rohan = 23 + 46 = 69 Thus, Rohan has 69 marbles in total.

Tens Ones 2 3 + 4 6 6 9

7. Number of apples = 28 Number of oranges = 41 Number of bananas = 29 Total fruits = 28 + 41 + 29 = 98 Thus, the fruit vendor has 98 fruits.

Tens Ones 1 2 8 + 4 1 + 2 9 9 8

8. Bangles sold on Monday = 15. Bangles sold on Tuesday = 12 Bangles sold on Wednesday = 10 Total bangles sold = 15 + 12 + 10 = 37 Thus, 37 bangles were sold in total.

Tens Ones 1 5 + 1 2 + 1 0 3 7

10. Smallest 2-digit number = 10 1 dozen=12 Let’s add, 10 and 12 10 + 12 = 22 Word Problems 1. Number of books Mohan bought for himself = 5 Number of books bought for his sister = 6 Number of books bought for his brother = 7 Total books bought = 5 + 6 + 7 = 18 Thus, Mohan bought 18 books in total.

23 + 42

9. 3 tens and 2 ones = 32 4 tens and 5 ones = 45 Let’s add, 32 and 45 Thus, Seema gets 77 in all.

f. 18 + 0 + 27 = 45 Ones

Ones

e. 32 +19 = 51

3. a.

d. 26 + 14 = 40 Ones

Tens

Ones

c. 24 + 35 = 59 Tens

Tens

c. 57 + 38 = 95 First add the ones 7 + 8 = 15 So, write 5 in ones place and add 1 ten to the tens place Now add the tens 5 + 3 + 1 = 9 tens

Tens Ones

Tens Ones +

Tens Ones 1 5 + 6 + 7 1 8

2. Number of mangoes in the tree on Tens Ones Monday = 13 1 Number of extra mangoes in the tree on 1 3 Tuesday = 16 + 1 6 Number of extra mangoes in the tree on + 1 8 4 7 Wednesday = 18 Total number of mangoes = 13 + 16 + 18 = 47 Thus, there were a total of 47 mangoes on the tree.

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4. a.

Chapter 3 Let's Warm-up

–

1. a.

– =

1 pot broken

5 pots pots left

–

– 6 apples =

2 apples 0 2 6

b. 5 – 5 c. 2 – 0

Do It Yourself 3A 1. a.

Tens

Ones

Tens

Ones

–

b. – 2. a.

3. a.

–

–6

–9

6 16

Tens

Ones

5 15

– c.

–

Ones

9 3

Tens

Ones

3 13

–

7–4=3

4+4=8

9–7=2

–

Number of flowers Raju had = 31 Number of flowers that Jiya has more than Raju = 51 – 31 = 20 Thus, Jaya has 20 more flowers than Raju.

Tens

7+1=8 5–3=2

3+0=3 7–2=5

Tens Ones –

15 – 9 = 6 11 – 8 = 3

2. Number of items of fruit with Mohan = 45 Number of items of fruit with Minal = 21 Number of less items of fruit that Minal has = 45 – 21 = 24 Thus, Minal has 24 less items of fruit than Mohan.

Tens Ones –

3B 1. Number of flowers Jiya had = 51

The addition and subtraction facts of 9, 6, and 15 are: 9 + 6 = 15 6 + 9 = 15 15 – 6 = 9 b. The addition and subtraction facts of 3, 8, 11 are 3 + 8 = 11 8 + 3 = 11 11 – 3 = 8

4+2=6

Word Problem 1. Number of children in Bus A = 45 Number of children in Bus B = 78 Number of children that are more in Bus B = 78 – 45 = 33 Thus, there are 33 children more in Bus B than in Bus A.

2 3

5. Number of bags in the shop = 56 Number of bags Meena bought = 4 Number of bags left = 56 – 4 = 52 Number of bags left after Neha bought some bags = 42 Number of bags bought by Neha = 52 – 42 = 10

apples left

2. a. 7 – 1

Tens Ones –

3. Number of pens Gini had = 27 Number of pens she gave to Jimmy = 15 Number of pens left with Gini = 27 – 15 = 12 Thus, Gini is left with only 12 pens. Checking answer: Tens Ones 2 7 – 1 5 1 2

Tens Ones 1 5 – 1 2 2 7

4. Number of birds in a tree = 28 Number of birds that flew away = 11 Number of birds left = 28 – 11 = 17 Thus, 17 birds are left in the tree. Checking answer: Tens Ones 2 8 – 1 1 1 7

Tens Ones 1 7 – 1 1 2 8

5. Number of cupcakes Sheetal has = 23 Number of cupcakes Monal has = 34 Monal has greater number of cupcakes. Number of cupcakes that Monal has more than Sheetal = 34 – 23 = 11 Thus, Monal has 11 more cupcakes than Sheetal.

Tens Ones –

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7. a.

Chapter Checkup 1. a.

–

45 – 23

87 – 68

–

22 78 – 48

d. 28 – 12

16 79 – 56

2. 8 3 – 73 = 10 (S) 91 – 56 = 35 (L)

83 – 73 = 10

72 – 51 = 21 91 – 56 = 36 – 19 = 17 35 92 – 38 = 78 – 65 = 54 13 74 – 42 = 87 – 55 = 32 32

78 – 65 = 13 (N) 36 – 19 = 17 (I)

72 – 51 = 21 (H) 92 – 38 = 54 (T)

74 – 42 = 32 (G)

87 – 55 = 32 (U) S

3. 9 9 – 6 7 3 2

3 9 – 2 2 1 7

4 6 – 3 6 1 0

4. a.

Tens Ones 4 5 – 1 2 3 3

Tens Ones 3 3 + 1 2 4 5

Tens Ones 7 0 – 3 0 4 0

Tens Ones 4 0 + 3 0 7 0

5. a. 9, 8 and 17 9 + 8 = 17 8 + 9 = 17 17 – 8 = 9 17 – 9 = 8 6.

3+2=5

b. –

8–5=3

5+3=8

0–0=0

–

9. Number of ice creams in the store = 67 Number of ice creams sold = 12 Number of ice creams left = 67 – 12 = 55 Thus, 55 ice creams are left in the store. 10. Number of balls Leena has = 45 Number of balls Misty has = 35 Number of more balls that Leena has than Misty = 45 – 35 = 10 Thus, Leena has 10 more balls than Misty. Word Problems 1. Number of crayons Twisha has in her box = 56 Number of crayons Aarav has in his box = 42 Number of less crayons that Aarav has = 56 – 42 = 14 Thus, Aarav has 14 less crayons than Twisha.

4+5=9 9–4=5

6+1=7 5–3=2

Tens Ones –

Tens Ones 2. Number of balloons Nisha had in her shop = 78 7 8 Number of balloons sold = 67 – 6 7 Number of balloons left = 78 – 67 1 1 = 11 Thus, 11 balloons are left with Nisha.

c. 5, 9 and 14 5 + 9 = 14 9 + 5 = 14 14 – 5 = 9 14 – 9 = 5

45 – 34

35 – 12

67 – 18

13 – 12

78 – 67

39 – 27

66 – 33

82 – 62

26 – 17

77 – 18

42 – 18

44 – 42

98 – 82

78 – 49

88 – 33

45 – 35

Solutions

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b. 4, 3 and 7 4+3=7 3+4=7 7–4=3 7–3=4

8. Number of mangoes Sunita had = 46 Number of mangoes sold = 35 Number of mangoes left = 46 – 35 = 11 Thus, 11 mangoes are left with Sunita.

3. Number of fruits Lily had = 54 Number of fruits Robin took = 13 Number of fruits left = 54 – 13 = 41

Tens Ones 5 4 – 1 3 4 1

Number of fruits John took = 10 Number of fruits left = 41 – 10 = 31 Thus, 31 fruits are left with Lily.

Tens Ones 4 1 – 1 0 3 1

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5 × 2 = 10 There are 10 keys in all.

Chapter 4 Let's Warm-up Vegetables bought 1. 2.

3 Tomatoes and 4 Brinjals 1 Tomato and 4 Cauliflowers

3. 4.

4 Brinjals and 2 Cabbages 4 Tomatoes and 5 Cabbages

4 Brinjals and 4 Cauliflowers

Total vegetables

4. a. 2 times 4 b. 5 times 2

8 vegetables

c. 4 times 2

7 vegetables 5 vegetables

d. 3 times 3 e. 4 times 5 5. a. 2×3

6 vegetables

9 vegetables

4×2 c.

Do It Yourself 4A 1. 3 groups of 3 stars = 9 stars 2. 2 groups of 4 balls = 8 balls 3. a. There are 3 bicycles. Each bicycle has 2 wheels. b. There are 4 baskets. Each basket has 3 items of fruit. 4. There are 3 groups here. Each group has 8 grapes. 5. There are 5 groups of crayons. There are 25 crayons in all. Word Problem 1. Number of boxes of colour pencils = 2 Number of colour pencils in each box = 6 Total number of colour pencils = 2 groups of 6 = 12 Thus, Gyan has 12 colour pencils in all.

4B 1. 2 + 2 + 2 + 2 = 8

There are 8 leaves altogether.

2. 1 + 1 + 1 + 1 + 1 = 5 There are 5 cookies in all.

3. 3 + 3 + 3 = 9 There are 9 flowers altogether.

3×6

Word Problem 1. Number of rooms = 4 Number of pillows in each room = 2 Total number of pillows = 4 groups of 2 = 2 + 2 + 2 + 2 = 8 So, Hira kept 8 pillows in all.

Chapter Checkup

1. a. 4 groups of 5 chalks in each group. b. 3 groups of 10 marbles in each group. 2. a. 8 + 8 + 8 + 8 = 32 There are 32 mangoes in all. b. 5 + 5 = 10 There are 10 books in all.

3. A. a. 6 groups of 3 b. 2 groups of 3 c. 3 groups of 6 d. 3 groups of 8 B. a. 2 groups of 4 b. 3 groups of 2 c. 5 groups of 3 d. 4 groups of 2 4. a. 3 × 6 b. 2 × 2 c. 3 × 7 5. 2 groups of 9. There are 18 sweets. 6.

4. 5 + 5 + 5 + 5 + 5 + 5 = 30 There are 30 eclairs in total.

5. 3 + 3 + 3 = 9 There are 9 cherries altogether.

Word Problem 1. Number of vases = 3 Number of flowers in each vase = 4 Total number of flowers = 3 groups of 4 = 4 + 4 + 4 = 12 Thus, Sara put 12 flowers in all.

4C 1. 7 groups of 3 = 7 times 3 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21 7 × 3 = 21 There are 21 roses in total.

2. 4 groups of 4 = 4 times 4 4 + 4 + 4 + 4 = 16 4 × 4 = 16 There are 16 candles in total. 3. 5 groups of 2 = 5 times 2 2 + 2 + 2 + 2 + 2 = 10

9. Number of boxes: 3 Number of sweets in each box: 4 Total number of sweet: 3 groups of 4 = 12 Pooja bought 12 sweets in total.

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10. Number of bags: 5 Number of boxes in each bag = 3 Total number of boxes: 3 + 3 + 3 + 3 + 3 = 15 5 × 3 = 15 There are 15 boxes in total. Word Problems 1. Number of groups: 6 Number of children in each group: 4 Total number of children = 6 × 4 There are 24 children in all. 2. Number of boxes: 2 Number of toys in ach box: 10 Total number of toys: 2 × 10 There are 20 toys in all.

5C 1. a. 5 × 6 = 30 b. 5 × 4 = 20 c. 5 × 10 = 50

2. a. 5 jumps of 10 each 5 × 10 = 50 b. 3 jumps of 10 each 3 × 10 = 30 c. 7 jumps of 10 each 7 × 10 = 70

Chapter 5

5D 1. Number of book shelves = 10

Do It Yourself Repeated addition fact

Multiplication fact

2+2+2+2=8

4×2=8

2+2=4

2×2=4

2+2+2=6

3×2=6

2 + 2 + 2 + 2 + 2 = 10

5 × 2 = 10

2 × 5 = 10

5B 1. 4

5×1=5

5 × 2 = 10

+5 0

5 × 5 = 25

+5 3

10 11 12

4. Tom jumps 9 times. 9 jumps of 5 steps each 9 x 5 = 45 5.

100

b. 10 × 7

c. 10 × 4

d. 10 × 8

e. 10 × 6

100

Number of books each shelf can hold = 6 The total number of books the bookstore can hold = 10 × 6 = 60 books Thus, the bookstore can hold 60 books.

4. Number of batches with Tom = 4 Number of cupcakes made in each batch = 10 Total cupcakes = 4 × 10 = 40 cupcakes Thus, Tom made 40 cupcakes altogether. 5. Number of jars collected by Lisa = 2 Number of marbles in each jar = 10 The total number of marbles Lisa collected = 2 × 10 = 20 marbles Thus, the total marbles collected by Lisa are 20. 1. a. True b. False c. False d. True

Number of 1 × 5 2 × 5 3 × 5 4 × 5 5 × 5 6 × 5 7 × 5 8 × 5 9 × 5 10 × 5 fingers = 5 = 10 = 15 = 20 = 25 = 30 = 35 = 40 = 45 = 50 2. 5 × 3 = 15

Chapter Checkup

Total apples = 10

3. Number of baskets = 10 Number of oranges in each basket = 6 The total number of oranges in 10 baskets = 10 × 6 = 60 oranges Thus, the baskets can hold 60 oranges.

5 + 5 = 10

2. Number of boxes = 9 Number of cookies each box can hold = 10 The total number of cookies = 9 × 10 = 90 cookies Thus, the boxes can hold 90 cookies.

2. a. 5 × 2 = 10 b. 3 × 2 = 6 c. 4 × 2 = 8 3. a. 6 jumps of 2 steps each 6 x 2 = 12 b. 5 jumps of 2 steps each 5 x 2 = 10 4. a. 6 + 6 or 6 × 2 = 12 b. 8 + 8 or 8 × 2 = 16 c. 12 + 12 or 12 × 2 = 24 d. 10 + 10 or 10 × 2 = 20 e. 5 + 5 or 5 × 2 = 10 f. 2 + 2 or 2 × 2 = 4

4. a. 10 × 3

5. 10

1. 3 pears + 3 pears = 6 pears 2. These are 2 groups of 3 pears each. 3. We can say, 2 × 3 pears = 6 pears

Number of hands

4 jumps of 10 steps each = 4 × 10 = 40

Let's Warm-up

5A 1.

2. a. 0

b. 0

9 10 11 12 13 14 15 16 17 18 19 20

3. a. 5 + 5 = 10 b. 2 + 2 + 2 + 2 + 2 = 10 4. a. 2 times 8 b. 5 times 8 c. 10 times 1 d. 0 times 8

2×8 5×8 10 × 1 0×8

= 16 = 40 = 10 =0

5. a. 10 × 5 = 50 b. 10 × 9 = 90 c. 10 × 1 = 10 6. Number of packs = 10 Number of crayons in each pack = 6 Total number of crayons = 10 × 6 = 60 Thus, 10 packets can hold 60 crayons.

6 + 6 + 6 + 6 + 6 or 5 × 6 = 30 Thus, there are 30 grapes in total.

Solutions

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7. Number of candy packs =10 Number of candies in each pack = 10 Total number of candies = 10 × 10 =100 Shreya has 100 candies in all.

c. 567

Five hundred sixty-seven

8. Total number of bundles = 5 Number of sticks in each bundle = 8 Total number of sticks in 5 bundles = 5 × 8 = 40 Thus, there are 40 sticks in 8 bundles.

d. 678

Six hundred seventy-eight

9. Number of boxes = 10 Number of balls in each box = 7 Total number of balls = 10 × 7 = 70 Thus, 10 boxes can hold 70 balls. 10.

e. 999

Things Needed Multiplication for Each Child Sentence

Items

Nine hundred ninety-nine

Total

a. Hats

5 × 2 = 10

10 hats

b. T-shirts

5 × 6 = 30

30 t-shirts

c. Shoes

2 pairs

5 × 2 = 10

10 pairs

f. 108 One hundred eight 5.

Word Problem 1. Number of friends invited for the party = 10 Number of balls given to each friend = 1 Total number of tennis balls given = 10 × 1 = 10 Thus, Akshay gave 10 tennis balls.

nine hundred thirty-five → 935

1. 93 2. 121 3. 148 4. 163 5. 199

1 hundred, 2 tens, 1 one 1 hundred, 4 tens, 8 ones 9 tens, 3 ones 1 hundred, 9 tens, 9 ones 1 hundred, 6 tens, 3 ones

Do It Yourself 6A 1. 416

415

414

413 412

407

404

408

403

409

410

402

c. 6 hundreds + 5 tens + 4 ones Expanded form: 600 + 50 + 4

d. 2 hundreds + 3 tens + 7 ones Expanded form = 200 +30 +7

984

b. d.

c. 810 811 812 813 814 815 816 817 818 819 820

a. 345

Three hundred forty-five

Four hundred fifty-nine

900

500

700

7 is 700

701

679

3 is 300

345

639

693 290 900

324

132 199 After

322

323

324

430

431

432

221

222

223

325

326

327

888

889

890

130

Between

896

Before

567

459

702 2

9 is 900

2 is 2

6 is 60

b. 720 721 722 723 724 725 726 727 728 729 730

3. a. 465 b. 777 c. 603 d. 505 e. 960 f. 623

80 401

576

411

2. a. 300 301 302 303 304 305 306 307 308 309 310

b. 459

b. 1 hundred + 7 tens + 0 ones Expanded form: 100 + 70 + 0

four hundred nineteen → 419

one hundred twenty-seven → 127 six hundred fifty-eight → 658 Expanded form: 300 + 90 + 8

Let's Warm-up

405

three hundred six → 306

two hundred twenty-seven → 227 seven hundred ten → 710

6B 1. a. 3 hundreds + 9 tens+ 8 ones

Chapter 6

406

five hundred sixty-one → 561

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6. We can write 6 numbers using the digits 2,4,7 without repeating them. 247, 274, 427, 472, 742, 724

6C 1. a. d. 2.

167

879

480

b. e.

799

901

982

984

459, 234

c. f.

204

178

278

940

9. There are 13, 3-digit numbers between 101 and 115. Count on fingers the 3-digit numbers between 101 and 115. Hint: Do not count 101 and 115. 10. Less than 500: 123, 229, 289, 459 More than 500: 590, 769, 890, 985 11.

340, 348

459

348

234

340

H 4

T 5

O 1

H 8

T 6

O 2

H 1

T 4

O 9

H 8

T 7

O 9

H 5

T 3

O 6

H 2

T 0

O 7

Word Problems 1. Diya’s grandfather has more coins than his friend as 450 > 299. 2. Toni used more bricks than Ramu as 790 > 689.

3. a.

239

709

551

446

783

Chapter 7

269

175

865

159

537

538

Let's Warm-up

4. a. c.

892

834

847

213

913

951

b. d.

596

443

436

293

693

337

5. 100, 345, 789, 1000 1. a. 201 b. 301 c. 601

2. a.

202

203

204

205

206

207

208

209

210

302

303

304

305

306

307

308

309

310

602

603

604

605

606

607

608

609

610

567

202

500

200

900

before 78 179 966 554 339

79 180 967 555 340

4. a. 349: ones = 9 tens = 4 hundreds = 3

900 + 80 + 6

between 245 433 254 219 995

246 434 255 220 996

b. 847: ones = 7 tens = 4 hundreds = 8

456 515 698 357 951

457 516 699 358 952

c. 456: ones = 6 tens = 5 hundreds = 4 349 < 456 < 847

5. a. 345 > 232 b. 1000 > 678 c. 945 = 945 d. 34 < 344 e. 123 < 856 6. a. 376 comes after 375. b. 887 comes before 888. c. 60 is 10 more than 50. d. 700 is 50 less than 750. e. 1000 comes after 999. 7.

a. 234, 567, 986 986 567 234 b. 559, 678, 345 678 559 345 c. 109, 289, 678 678 289 109 d. 345, 696, 873 873 696 345

a. 1000, 170, 590 170 590 1000 b. 540, 330, 257 257 330 540 c. 678, 447, 567 447 567 678

Solutions

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2. a.

d. 600, 120, 499 120 499 600

H +

2 2

3 2

41 7 6

H +

1 H

4 5

6 9

5 O

8 c.

O 7

71 8 8

H +

O 5 5

41 7 8 5 O

71 9 5 4

61 71 8

H +

1 1

51 7

61 6 7

2 3

H +

41 51 7

H +

–

after 247 435 256 221 997

7 8

200 + 2

7 9

Do It Yourself 7A 1. a.

986

500 + 60 +70 3.

Chapter Checkup

3 7

51 61 8 6

3. a. 123 + 543 = 666 +

b. 801 + 111 = 912 +

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c. 453 + 212 = 665

e. 923 – 112 = 811

= 2. a.

d. 720 + 158 = 878

–

4. a.

e. +

H +

5 4 9

2 4

5 9

9 i.

6 5

–

3. a.

1 6

4 9

4 3

4 6

3 7

Dan spent ₹380 in all. 2. Number of students in centre 1 = 125 Number of students in centre 2 = 543 Total number of students = 125 + 543 = 668 There are 668 students in the dance academy.

7B 1. a. 457 – 14 = 443

d. 854 – 301 = 553

b. 458 – 327 = 131

H +

3 T

5 O 5 3 8

– g. –

0 0

9 0

–

2 T

4 2

–

7 0

9 0

7 4

2 O

H –

–

H –

Word Problems 1. Money spent on roses = ₹345 Money spent on wrapping paper= ₹35 Total money spent = ₹345 + ₹35 = ₹380

c. 668 – 118 = 550

4. a.

H –

H +

5. We need 111 to add 245 to get 356. H

5 4

O 4 4 0

5. We have to take 167 from 567 to get 400. H –

7 0

Word Problems 1. Number of apples Sarah picked = 364 Number of apples Sarah sold = 251 Number of apples left = 364 – 251 = 113 113 apples were left with Sarah.

H –

4 3

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2. Number of beads Diya had = 357 Number of beads Diya used = 145 Number of beads left = 357 – 145 = 212

H –

Diya is left with 212 beads.

7C 1. a. Addition H

–

There are 336 toys left.

b. Subtraction

There are 654 books on the table.

5 2 3

6 3

3. Number of dogs = 189 Number of sheep = 134 Number of more dogs than sheep = 189 – 134 = 55 There are 55 more dogs than sheep. 4. Number of dogs = 189 Number of sheep = 134 Number of goats = 227 Total number of animals = 189 + 134 + 227 = 550 There are 550 animals in all. 5. Number of cats brought = 100 Total number of animals earlier = 550 Total animals, along with the cat = 100 + 550 = 650

7 2

2 H

–

Shanti has collected 690 seashells.

7D 1. Number of packets shopkeeper had = 583 Number of packets he sold = 272 Number of packets left = 583 – 272 = 311

–

Shopkeeper is left with 311 packets. 2. Number of mangoes in one basket = 764 Number of mangoes in the other basket = 220 Total number of mangoes = 764 + 220 = 984

9 5

1 5 5 1 H

Word Problems 1. Number of toy cars with Anna = 235 Number of toy cars donated = 100 Number of toy cars left = 235 – 100 = 135 135 toy cars are left with Anna. 2. Number of seashells collected on Monday = 567 Number of seashells collected on Tuesday = 123 Total seashells collected = 567 + 123 = 690

H 2 1 1

T 3 2 1

O 4 0 4

H 3 1 2

T 9 7 2

O 8 1 7

4 1 5

5 3 9

6 4 0

H 5 3 2

T O 8 10 9 0 7 8 1 2

1 1 2

2 3 6

9 4 3

2 4 6

3 4 8

4 8 2

H 6 1 5

T 8 4 4

O 2 0 2

–

114 books left with the bookshop. 4. Number of balls with Animesh = 398 Number of balls given to friend = 171 Number of balls left with Animesh = 398 – 171 = 227 Animesh is left with 227 balls.

–

Suresh is left with 212 balloons.

2. Number of beads David had = 234 Number of beads Simran had = 448 Total no of beads = 234 + 448 = 682

542 beads are left with them.

Chapter Checkup

H +

5 5

5 1 6

6 2 9

7 3 0

H 5 2 3

T 8 7 1

O 3 2 1

H 7 2 9

T 6 2 8

O 4 0 4

1. a.

Dravid and Simran had 682 beads in all.

263 trees were planted by grandfather.

–

Word Problems 1. Number of apple trees planted = 129 Number of guava trees planted = 134 Total number of trees planted = 129 + 134 = 263

No. of beads used in bracelet = 140 No. of beads left = 682 – 140 = 542

2 1

Number of balloons he used in function = 378 Number of balloons left = 590 – 378 = 212

–

H +

3. Number of books in the shop = 234 Number of books sold = 120 Number of books left = 234 – 120 = 114

5. Number of red balloons Suresh bought = 456 Number of blue balloons Suresh bought = 134 Total number of balloons Suresh bought = 456 + 134 = 590

There will be 650 animals in the farm.

UM24TMG2.indb 75

There are total 361 sheep and goats.

Solutions

2. Number of sheep = 134 Number of goats = 227 Total number of sheep and goats = 134 + 227 = 361

Total number of mangoes is 984.

2. a. – d.

–

6 3

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3. a.

– d.

+ b.

– e.

–

+ e.

–

+ f.

– 4. a.

8. Number of English books = 568 Number of Hindi books = 345 Hindi books are fewer. Number of Hindi books fewer than English = 568 – 345 = 223 Hindi books are fewer than English books by 223

–

5. a. 9 hundred + 1 tens + 2 ones b. 9 hundreds + 9 tens + 7 ones c. 9 hundred + 8 tens + 1 one d. 8 hundreds + 4 tens + 3 ones e. 8 hundreds + 5 tens + 2 ones 6.

Situation

a. Rahul bought 345 books and arranged 115 books on the shelf. How many books are left to be arranged on the shelf?

b. Mona had 123 marbles. Her friend Tina had 167 marbles. How many marbles are there in all? c. Misty has a book with 167 pages. She read 123 pages. How many pages are left to be read? 7. a. Mr Parikh house no. is 599. b. Mr Ahmad house no. is 300. c. Ms Shah house no. is 916. d. Mrs Paul house no. is 242. e. Mrs Sharma house no. is 601. f. Mr Parikh house no. is 799.

Addition Subtraction

Solve H T O 3 4 5

– 1 1 5 2 3 0

H T O 1 21 3

9. Number of marbles Saanchi had = 456 Number of marbles she lost = 124 Number of marbles left = 456 – 124 = 332

H –

Saanchi is left with 332 marbles. 10. Number of apple trees = 206 Number of mango trees = 145 Total number of trees =206 + 145 = 351

3 O

6 2

There are 351 trees in the garden.

11. a. Number shown with blocks = 2 hundreds + 5 tens + 6 ones = 256 b. The new number if 145 is added = 256 + 145 = 401 New number will be 401 if 145 is added to it

Word Problems 1. Number of people visited on Monday = 345 Number. of people visited on Tuesday = 257 Total no. of people visited = 345 + 257 = 602 Total 602 people visited the book fair.

2. Number of biscuits Rohit baked = 340 Number of more biscuits Rohit baked = 105 Total number of biscuits baked = 340 + 105 = 445 Number of biscuits he sold = 130 No. of biscuits left with Rohit = 445 – 130 = 315 Rohit is left with 315 biscuits.

2 H

0 5

7 O

H –

Chapter 8 Let's Warm-up

H –

5 5

4+4+4

H T O

6+6+6+6

2+2+2+2+2+2

– 1 2 3

6+6+6

8+8+8+8+8

+ 1 6 7 2 9 0 1 6 7 0 4 4

My number is 100 more than 816. My number is the number after 600. My number is the number before 600. My number is 10 less than 310. My number is the number before 800. My number is 25 less than 267.

Do It Yourself 8A 1. a. 3 × 6 = 18 b. 3 × 5 = 15 c. 3 × 3 = 9 d. 3 × 9 = 27

2. a. 3 × 6 = 18 b. 3 × 9 = 27 c. 3 × 5 = 15 d. 3 × 8 = 24 e. 3 × 10 = 30 f. 3 × 4 = 12 3. a. 3 × 6 = 18 b. 3 × 10 = 30 c. 3 × 2 = 6 d. 3 × 9 = 27 e. 3 × 8 = 24 f. 3 × 1 = 3 4. a. 3 × 8 = 24 b. 3 × 4 = 12 c. 3 × 10 = 30 d. 3 × 5 = 15 e. 3 × 3 = 9 f. 3 × 9 = 27 5. a. 3, 6, 9, 12 b. 18, 21, 24, 27 c. 12, 15, 18, 21 d. 21, 24, 27, 30 e. 9, 12, 15, 18 f. 15, 18, 21, 24 Word Problems 1. Number of keychains with Akhil = 3 Number of keys in each key chain = 6 Number of keychains altogether = 3 × 6 = 18 There are 18 keychains altogether.

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2. Number of lines Macy wrote = 3 Number of words in each line = 8 Total number of words = 3 × 8 = 24 There are 24 words in all. 3. Number of children = 3 Number of books with each child = 7 Total number of books = 3 × 7 = 21 There are 21 books in all.

8B 1. a. 4 × 3 = 12 b. 4 × 8 = 32 c. 4 × 2 = 8 d. 4 × 6 = 24

e. 4 × 9 = 36 f. 4 × 1 = 4 2. a. 4 × 5 = 20 b. 4 × 3 = 12 c. 4 × 10 = 40 d. 4 × 1 = 4 e. 4 × 7 = 28 f. 4 × 8 = 32 3. a. 4 fives are 20 b. 4 tens are 40 c. 4 nines are 36 d. 4 fours are 16 e. 4 twos are 8 f. 4 six are 24 4. a. 4 × 7 = 28 b. 4 × 9 = 36 c. 4 × 4 = 16 d. 4 × 10 = 40 e. 4 × 1 = 4 f. 4 × 8 = 32 5. Number of boxes = 4 a. 4 × 6 = 24 books b. 4 × 8 = 32 books c. 4 × 3 = 12 books d. 4 × 7 = 28 books e. 4 × 5 = 20 books f. 4 × 4 = 16 books Word Problems 1. Number of baskets = 4 Number of flowers in 1 basket = 5 Total number of baskets = 4 × 5 = 20 There are 20 flowers in all.

8C 1. a. 6 × 7 = 42 b. 6 × 5 = 30 c. 6 × 4 = 24

2. a. 6 times 7 is 42 b. 6 times 4 is 24 c. 6 times 8 is 48 d. 6 times 10 is 60 e. 6 times 3 is 18 f. 6 times 9 is 54 3. a. 6 × 5 = 30 b. 6 × 7 = 42 c. 6 × 9 = 54 d. 6 × 2 = 12 e. 6 × 8 = 48 f. 6 × 3 = 18 4. a. 6 × 8 = 48 b. 6 ×1 = 6 c. 6 × 7 = 42 d. 6 × 4 = 24 e. 6 ×9 = 54 f. 6 × 6 = 36 5. a. 30, 36, 42 b. 12, 18, 24 c. 24, 30, 36 d. 48, 54, 60 Word Problems 1. Number of baskets with Preetham = 6 Number of apples in each basket = 5 Total number of apples = 6 × 5 = 30 Preetham has 30 apples in all the baskets. 2. Number of packets Sarah wants to buy = 6 Number of stickers in each packet = 9 Total number stickers with Sarah = 6 × 9 = 54 Sarah has total 54 stickers. 3. Number of cookies in a packet = 6 Number of packets for 48 cookies = 8 × 6 = 48 There will be 8 packet for 48 cookies. b. T 1 × 2

1 × 6

2. a. T 2 × 4

O 4 2 8

b. T 3 × 9

O 3 3 9

c. T 4 × 8

O 1 2 2

3. a. T 2 × 8

O 0 4 0

b. T 3 × 6

O 4 2 8

c. T 4 × 8

O 4 2 8

Solutions

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O 4 2 8

c. T 3 × 6

O 1 6 6

O 1 3 3

O 3 3 9

T 1 × 3

e. T 4 × 8

O 0 2 0

f. T 2 × 8

O 2 2 4

O 1 4 4

5. Number of boxes with Sohel = 2 Number of books in each box = 43 Total books in all = 43 × 2 = 86 There are total 86 books.

T 4 × 8

O 3 2 6

Word Problem 1. Number of packets with Sam = 21 Number of cupcakes in each packet = 3 Total cupcakes = 21 × 3 = 63 There are 63 cupcakes with Sam.

T 2 × 6

O 1 3 3

T 1 1 × 7

T 4 × 4

O 1 6 6

T 1 9 × 6

T 4 5 × 9

8E 1. a. T

2. Number of pieces in a puzzle = 4 Number of puzzles which will have 36 pieces = 9 × 4 = 36 9 puzzles will have 36 pieces.

8D 1. a. T

d. T 3 × 9

1 4 × 9

2. a. T 3 1 × 7

e. H

T 4 5 × 9

8 4 2

O 8 2 6

b. T 3 1 × 9

b. T 1 4 × 9 O 9 5 5

O 6 6 6

c. T 1 2 × 9

c. H

5 2 0

f. H

T 4 2 × 6

d. H

3 4 2

T 6 × 6

O 1 6 6

d. H

T 5 × 5

O 2 3 6

T 9 × 7

O 2 3 6

O 8 6 8

3. Number of jars with Martin = 13 Number of marbles in each jar = 6 Total marbles with Martin = 13 × 6 = 78 Martin 78 marbles in all. 4. Number of rows in the farm= 6 Number of corn plants in each row = 41 Total corn plants = 41 × 6 = 246 Farmer has planted 246 corn plants.

5. Number of brothers and sisters in the market = 2 + 3 = 5 Number of sugar canes each person bought = 92 Total sugar canes bought = 92 × 5 = 460 They bought 460 sugar canes in all.

Word Problem 1. Number of boxes of crayons in the store = 59 Number of crayons in each box = 5 Total crayons in the store = 59 × 5 = 295 There are 295 crayons.

8F 1. Number of packets = 98

Number of candies in each packet = 5 Total candies = 98 × 5 = 490 There are 490 candies in all.

T 4 9 × 9

3 6 8

2 5 0

9 5 5

O 8 5 0

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2. Number of seats in bus = 46 Number of buses = 4 Total buses = 46 × 4 = 184 There are 184 seats in all.

3. Number of pencils in box = 85 Cost of each pencil = ₹6 Cost of all pencils = 85 × 6 = ₹510 Cost of all pencils is ₹510

4. Number of pouches = 52 Number of pins in each pouch = 6 Total pins = 52 × 6 = 312 There are total 312 pins.

5. Number of children = 4 Number of stamps each collected = 38 Total stamps collected = 38 × 4 = 114 They collected 114 stamps in all.

Word Problem 1. Number of fishes in pond = 68 Number of fishes in lake = 3 times of fishes in pond = 3 × 68 = 204 There are 204 fishes in the lake.

Chapter Checkup

T 2 4 × 8

T 3 8 × 1

T 1 5 × 1

T 3 3 × 5

T 2 6 × 0

6 4 4

5 6 0

2 6 2

8 4 2

8 3 4

1. 6 × 1 = 6 6 × 2 = 12 6 × 3 = 18 6 × 4 = 24 6 × 5 = 30 6 × 6 = 36 6 × 7 = 42 6 × 8 = 48 6 × 9 = 54 6 × 10 = 60 2. a. 6 × 7 = 42 b. 4 × 9 = 36 c. 6 × 6 = 36 d. 3 × 5 = 15 e. 4 × 8 =32 f. 3 × 9 = 27 3. a. 4 × 8 = 8 × 4 = 32 b. 7 × 6 = 6 × 7 = 42 c. 6 × 10 = 10 × 6 = 60 d. 5 × 3 = 3 × 5 = 15 e. 4 × 5 = 5 × 4 = 20 f. 6 × 5 = 5 × 6 = 30 4. a. T 1 3 × 7

5. a. H

T 2 2 × 0

O 5 4 0

T 1 5 × 6

e. H

6 3 8

T 1 7 × 3

h. H

1 d. H

1 g. H

7 2 4

b. T 4 1 × 9

3 6 8

O 8 5 0

b. H

c. T 2 1 × 8

d. H

4 6 4

T 4 3 × 9

c. H

8 5 0

T 1 8 × 1

f. H

T 6 × 0

O 1 5 5

6. Number of rounds = 6 Runs earned in each round = 7

2 5 0

T 7 × 4

O 4 2 8

Total runs earned = 6 × 7 = 42 Rahul earned 42 runs for his teams. 7. Number of boxes bought by Ramesh = 4 Number of mangoes in each box = 28 Total mangoes he bought = 28 × 4 = 112 Ramesh bought 112 mangoes in all.

8. Number of dosa plates = 6 Cost of each plate = ₹85 Cost of all plates = 85 × 6 = 510 Cost of all the dosas is ₹510.

9. Number of packets of sticker = 5 Number of stickers in each packet = 38 Total stickers = 38 × 5 = 190 Teacher bought 190 stickers in all.

10. Number of days Anaya practice dance = 6 Money spent each day = ₹76 Total money spent = 76 × 6 = 456 Anaya spent ₹ 456 in all.

Word Problem 1. Number of baskets = 5 Number of tomatoes in each basket = 42 Total tomatoes with vegetable seller = 42 × 5 = 210 There are 210 tomatoes with vegetable seller.

T 3 8 × 1

8 4 2

5 6 0

T 4 3 × 9

T 3 7 × 5

T 1 4 × 1

8 5 0

6 6 6

2 5 0

Chapter 9 Let's Warm-up 1. 2. 3.

T 4 4 × 8

T 1 6 × 3

9 2 8

2. a. There are 4 groups of 2 bananas.

7 6 2

T 3 2 × 1

2 groups of 4 3 groups of 2 5 groups of 2 4 groups of 6

9A 1. a. b.

b. There are 4 groups of 3 cupcakes.

c. There are 2 groups of 5 biscuits.

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3. a. Each rabbit will get 3 carrots.

b. Each friend will get 4 apples.

4. a. Each child will get 10 mangoes.

b. Each child will get 4 mangoes.

14 ÷ 2 = 7 So, 7 children will get 2 pens each. d. 8 – 4 = 4 4–4=0 4 is subtracted 2 times. 8÷4=2 So, 2 children will get 4 apples each.

2. a. Total number of books = 12 Number of books in each group = 3 So, 12 ÷ 3 is the correct answer. b. Total number of pencils = 15 Number of pencils in each group = 5 So, 15 ÷ 5 is the correct answer. c. Total number of candies = 20 Number of candies in each group = 5 So, 20 ÷ 5 is the correct answer. 3. a. 15 ÷ 3 = 5 3–3=0 6–3=3 0

9–3=6 6

12 – 3 = 9 15 – 3 = 12

9 10 11 12 13 14 15

b. 10 ÷ 5 = 2 5–5=0 0

10 – 5 = 5 4

9 10 11 12 13 14 15

4. The division fact is 12 ÷ 4 = 3 4 is subtracted 3 times till she gets 0. 4–4=0

5. There are 3 laddoos in each plate.

9B 1. a. 18 – 6 = 12

12 – 6 = 6 6–6=0 6 is subtracted 3 times. 18 ÷ 3 = 6. So, 3 children will get 6 chocolates each. b. 9 – 3 = 6 6–3=3 3−3=0 3 is subtracted 3 times. 9 ÷ 3 = 3. So, 3 children will get 3 books each. c. 14 – 2 = 12 12 – 2 = 10 10 – 2= 8 8–2=6 6–2=4 4–2=2 2–2=0 2 is subtracted 7 times.

Solutions

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8–4=4

12 – 4 = 8

9 10 11 12 13 14 15

5. a. 15 ÷ 3 = 5 So, 5 objects in each group is the correct answer. So, the given statement is true. b. 12 ÷ 4 = 3 So, 3 objects in each group is the correct answer. So, the given statement is false. c. Total number of objects = 12 Number of groups = 4 So, 12 ÷ 4 is the correct division fact. Therefore, the given statement is false. Word Problems 1. Number of flowers Ravi has = 24 Number of vases Ravi has = 8 Number of flowers in each vase = 24 ÷ 8 = 3

Each vase will have 3 flowers in it.

2. Number of candles = 30 Number of boxes = 6 Number of candles in each box = ? 30 – 6 = 24 24 – 6 = 18 18 – 6 = 12 12 – 6 = 6 6–6=0 6 is subtracted 5 times. So, each box will have 5 candles.

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9C 1. 5 × 4 = 20

20 ÷ 4 = 5

6 × 2 = 12 4 × 7 = 28

28 ÷ 4 = 7

5 × 7 = 35

Multiplication Fact Division Fact 3 groups with 5 in each

3 × 5 = 15

15 ÷ 3 = 5

4 groups with 2 in each

4×2=8

8÷4=2

6 groups with 3 in each

6 × 3 = 18

18 ÷ 6 = 3

5 groups with 5 in each

5 × 5 = 25

25 ÷ 5 = 5

b. 3 × 4 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3

c. 5 × 6 = 30 30 ÷ 5 = 6 30 ÷ 6 = 5

7 4

– 30 0

3. a.

– 28 0

– 21 0

12 4

– 20 0

5 4

– 16 0

7 6

Chapter Checkup

18 2

– 42 0

5. Total number of candies = 35 Number of friends = 7 Number of candies each friend will get = 35 ÷ 7 = 5 Sherry can give 5 candies to each of her friends.

3 7

4 2

– 12 0 4

– 20 0 2

– 10 0 3

– 18 0 5

– 35 0

b. There are 6 groups of 2.

– 21 0

1. a. There are 3 groups of 4.

5 9

6 2

– 28 0

4. Total number of books Nidhi has = 18 Number of shelves = 6 Number of books in each shelf = 18 ÷ 6 = 3 There will be 3 books in each shelf.

c. 18 ÷ 2 = 9

3. Total number of apples = 10 Number of friends = 5 Number of Apples each friend will get = 10 ÷ 5 = 2 Each friend will get 2 apples.

b. 20 ÷ 4 = 5

– 18 0

2. Total number of cherries = 20 Number of cakes = 5 Number of cherries in each cake = 20 ÷ 5 = 4 Each cake will have 4 cherries.

– 10 0

a. 12 ÷ 3 = 4

27 5

Number of boxes = 4 Number of pencils in each box = 12 ÷ 4 = 3 Each box will have 3 pencils.

2 5

9E 1. Total number of pencils = 12

Word Problem 1. Number of bottles Anna has = 24 Number of friends = 4 Number of bottles each friend will get = 24 ÷ 4 = 6 Multiplication fact: 4 × 6 = 24 Each friend will get 6 bottles of juice. 6

9 2

5. Number of chocolates = 21 Number of groups = 7 Number of chocolates in each group = 3

5. Number of apples = 20 Number of groups = 4 Multiplication fact: 4 × 5 = 20 Division fact: 20 ÷ 4 = 5

9D 1. a.

4. a.

4. There are 4 groups of 3 pastries. Multiplication fact: 4 × 3 = 12 Division fact: 12 ÷ 4 = 3

50 ÷ 5 = 10

35 ÷ 5 = 7

10 × 5 = 50

3. a. 4 × 2 = 8 8 ÷ 4 =2 8÷2=4

12 ÷ 6 = 2

c. There are 3 groups of 3.

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2. a. 15 ÷ 5 = 3

7. a. 5

b. 12 ÷ 4 = 3

5 25

10 4

– 25 0

– 4 00 –0 0 b. 18 ÷ 3 is 6.

8. a. 25 ÷ 5 is 5.

10 3

10 2

– 3 00 –0 0 c. 28 ÷ 4 is 7.

9. Total number of flowers = 18 Number of vases = 6 Number of flowers in each vase = 18 ÷ 6 = 3 Each vase will have 3 flowers.

3. a. 12 − 4 = 8 8−4=4 4−4=0 4 is subtracted 3 times. So, 12 ÷ 4 = 3. Thus, there will be 3 balls in each box.

b. 18 − 3 = 15 15 − 3 = 12 12 − 3 = 9 9−3=6 6−3=3 3−3=0 3 is subtracted 6 times. So, 18 ÷ 3 = 6. Thus, there will be 6 pencils in each box.

c. 20 – 5 = 15 15 – 5 = 10 10 – 5 = 5 5–5=0 5 is subtracted 4 times. So, 20 ÷ 5 = 4. Thus, there are 4 marbles in each box.

4. a. 9 ÷ 3 = 3

3–3=0

b. 12 ÷ 6 = 6 0

d. 16 – 2 = 14 14 – 2 = 12 12 – 2 = 10 10 – 2 = 8 8–2=6 4–2=4 4–2=2 2−2=0 2 is subtracted 8 times. So, 16 ÷ 2 = 8. Thus, there will be 8 shoes in the racks.

6–3=3 3

6–6=0 2

9 10 11 12 13 14 15

12 – 6 = 9 5

9 10 11 12 13 14 15

c. 14 ÷ 2 = 7 2–2=0

5. a. 2 × 3 = 6

– 21 0

Solutions

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14 – 2 = 12 9 10 11 12 13 14 15

8 6

– 48 0

9÷3=3

9 5

– 20 0 6

2. Total number of chocolates = 16 Number of boxes = 4 Number of chocolates in each box = 16 ÷ 4 = 4 Each box will have 4 chocolates.

– 24 0 4

Chapter 10

– 16 0

Let's Warm-up 1.

Do It Yourself

(Solution may vary)

(Solution may vary) a. One-third

b. One-half

1 3

1 2

24 ÷ 8 = 3

9÷3=3

– 18 0 4

Word Problems 1. Total number of toys = 24 Number of boxes = 4 Number of toys in each box = 24 ÷ 4 = 6 Each box will have 6 toys.

6÷2=3

24 ÷ 3 = 8

c. 3 × 3 = 9 7

6÷3=2

b. 3 × 8 = 24

6. a.

10. Total number of crayons = 20 Number of students = 5 Number of crayons each student will get = 20 ÷ 5 = 4 Each student will get 4 crayons.

4 – 2 = 2 6 – 2 = 4 8 – 2 = 6 10 – 2 = 8 12 – 2 = 10

10A 1.

9–3=6

– 2 00 –0 0

– 45 0

6. a.

c. Three-fourths d. Two-thirds 3 4

2 3 d.

9 2

– 18 0

1 2

Word Problems 1.

1 3

1 4

3 4

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1 means 1 part out of 3 equal parts. 3 3 d. means 3 parts out of 4 equal parts. 4 2 e. means 2 parts out of 3 equal parts. 3 c.

(Solution may vary.)

1 4

Chapter Checkup 1.

3 4

1 3

1 4

2 3

10. a. One-half means one part out of two equal parts. So, the sentence is true. b. Two-thirds means two parts out of three equal parts. So, the sentence is true. c. One part out of 4 equal parts is shaded. So, the sentence is true. d. If the numerator is 3, then it shows that 3 parts of the figure are shaded. So, the sentence is false. 11. Figures may vary. Sample figures. a. b.

3. threefourths

Onehalf

Onefourth

(Solution may vary)

1 2

3 4

Word Problem 1. a.

1 3

1 2

1 4

1 3

1 2

1 4

1 3

1 4

5. a.

2 3

1 3

1 2

2 3

one-half

Chapter 11

two-thirds

Let's Warm-up

three-fourths

one-third

one-half

6. a.

onethird

onefourth

Do It Yourself 11A 1. a. A rope b. A sharpener 2. a.

7. a.

One-half d.

One-half 8. a.



A ball A stick



The sofa is about 10 pencils long.

c. b.

1 2

Three-fourths

One-fourth

Two-thirds

1 means 1 part out of 2 equal parts. 2

1 means 1 part out of 4 equal parts. 4

Three-fourths

The mat is about 8 crayons long.

3. a. Book - crayon b. Length of the park – rope c. Length of a curtain - bottles 4. The bottle is about 14 blocks long. The car is about 13 blocks long. The box is about 5 blocks long. The bottle is the longest. 5. The height of Rani’s doll is about 4 crayons.

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Word Problem 1. Height of the bucket = 6 blocks Height of the water can = 1 block taller than the bucket = 6 + 1 = 7 blocks The water can is 7 blocks tall.

2. a. 200 g b. 15 kg 3. a. 100 g + 100 g + 500 g = 700 g b. 2 kg + 5 kg + 1 kg = 8 kg 4. 500 g + 500 g + 500 g + 500 g = 1 kg + 1 kg = 2 kg 2 kg < 3 kg

11B 1. Car is more than a metre long.

So,

500g

9 cm. ____ 3. Length of the car = 2 m Length of the auto = 1 m The car is (2 – 1) m longer than the auto, that is, 1 m. 4. Length of the photo frame = 25 cm The photo frame is 20 cm shorter than the TV. Length of the T.V. = 25 + 20 = 45 cm So, the TV is 45 cm long.

500g

3kg

5. Weight of Onions Rakesh had = 3 kg Weights available to measure = 1 kg and 2 kg Number of weights of 1 kg and 2 kg each to measure 3 kg = 1 (as 1 + 2 = 3) Word Problem 1. Weights Tom has = 5 kg, 3 kg and 2 kg Weight altogether = 5 + 3 + 2 = 8 kg

Tom can weigh a total of 8 kg by combining them together.

Word Problems 1. She should use measuring tape. A measuring tape is used for measuring longer lengths. 2. Length of Sarah’s pencil = 12 cm Length of Heena’s pencil = 18 cm Amount of the length of Heena’s pencil than that of Sarah is = 18 – 12 = 6 cm Heena’s pencil is 6 cm longer than Sarah’s pencil.

11C 1.

500g

11E 1. A bucket can store more water than a pot.

2. a.

= 1 b.

3. a. 10 _______

15 jugs = ______

1 = _______

= 2 _______

1 = _______

6 _______

9 = _______

12 bowls = ______

4. Capacity of 1 jug in glass = 3 glasses Capacity of a glass = 2 cups Capacity of 3 glasses = 3 × 2 = 6 cups The capacity of 1 jug in a cup is = 6 cups

Word Problems 1. Water poured by Jyothi in a tank = 12 buckets

4. Weight of 1 book = Weight of 1 pencil box So, the weight of 5 books = 5 pencil boxes 5. 5 blocks = 15 chillies So, 1 block = 15 ÷ 5 = 3 chillies

Water poured by Ali in the tank = 15 buckets Capacity of the tank = 15 + 12 = 27 buckets.

Word Problems 1. Number of watermelons in Nani’s bag = 2 Number of bananas in Jaya’s bag = 2

A watermelon is heavier than banana.

So, the capacity of the tank is 27 buckets.

2. Capacity of half pot = 6 glasses of water Capacity of full pot is = 6 + 6 = 12 glasses

The capacity of a full pot is 12 glasses of water.

So, Nani’s bag is heavier than Jaya’s bag.

11F 1.

2. Number of blocks equal to one brick = 5

Number of blocks equal to two bricks = 5 + 5 = 10 So, the weight of two bricks is about 10 blocks.

11D 1.

Items a.

A basket of tomatoes

A spoon of salt

A bag of wheat

Candy floss

Solutions

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Units of Weight

kilograms

grams

2/14/2024 11:09:45 AM

3. A mug can hold 150 mL. 4.

b. 5 straight lines

c. 4 straight lines

d. 3 straight lines

3. a. Sleeping lines - 4

b. Standing lines - 5 d. Curved lines - 0 5. She must have used 1 L of milk for making the pudding.

Word Problems 1. Raman must have used 10 L of water to water the plants. 2. Water used by Leela for bathing = 20 L Water used by Riya for washing = 20 L

Total amount of water used by them = 20 L + 20 L = 40 L

curved lines b. 5. LATIN a. Letter with only a standing line - I b. Letters with sleeping and standing lines - L, T c. Letter with slanting and standing line - N

12B 1.

Chapter Checkup 1.

Red strip = 4 blocks. Green strip = 8 blocks. 4. 7 blocks = 2 bottle gourds

5. a.

b. Foxy

c. Montu

Rectangle

Oval

Triangle

Circle

3. a.

The green strip is longer. 3. The straw is 7 cm long.

straight lines

4. a.

Word Problem 1. a. Bruno

Leela and Riya have used 40 L of water in all.

c. Slanting lines - 3

2. a. False b. False c. True

Square Triangle 4. a. Squares – 2, Rectangles – 1, Triangles – 2, Circles – 2, Oval – 0 b. Squares – 5, Rectangles – 1, Triangles – 1, Circles – 4, Oval – 0 c. Squares – 1, Rectangles – 4, Triangles – 3, Circles – 0, Oval – 2 5. (Figures may vary.)

6. (Colours may vary.)

6. a. Weight of object = 2 + 2 + 2 + 2 = 8 kg b. Weight of object = 100 g

7. 100 g + 100 g + 100 g + 100 g + 100 g + 100 g = 600 g

There are 4 triangles in the given rectangle.

100 g + 100 g + 100 g = 300 g

Word Problem 1. We can see a triangle, some rectangles, and a square in Amina’s drawing.

300 g < 600 g

So, 300 g is lighter.

12C 1.

8. Pot A = 4 cups Pot B = 5 cups

2. a.

Pot A has less capacity.

9. The capacity of the jug is around 2 L.

10. 1 kg has 1000 g.

Word Problem 1. Length of the line made by Vani using blocks = 9 cm

Length of the line added by Tina using blocks = 8 cm

Total length of the line made using blocks = 9 + 8 = 17 cm

The total length of the line is 17 cm.

Chapter 12

Crayon box

Let's Warm-up 1.

Do It Yourself 12A 1. a.

4. a.

Pencil b.

Pencil box c.

Glue stick e.

5. 10 such bangles when put one over the other will make a cylinder. b.

2. a. 10 straight lines

Word Problems 1. a. Cubes – 4 b. Cuboids – 2 c. Cylinder – 1 2. If Anya put 3 of such cubes on top of each other, she will get a cuboid.

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12D 1. a. b.

3. a. b.

c. d. e.

2. a.

4. a. In this pattern, we are adding one square each time. b. In this pattern, we are adding 1 circle at the side each time. c. In this pattern, we are adding 1 square and one triangle each time.

b. c.

5. a.

3. a.

b. c.

Word Problem 1. The next 5 shapes in the pattern that Jay drew:

12F 1. a. 2, 3, 4, 2, 3, 4 – This sequence repeats 2, 3, 4 in an order, hence it is a number pattern. b. 2, 4, 6, 8 – This is a number pattern because 2 is added to the next number each time. c. 1, 3, 1, 2, 3, 1, 3 – This is not a number pattern. 2. a. True b. True c. True d. False

4. a.

c. 3

3 5

24 5

5. a.

8 12 16 20

12E 1. a. b. c. d. 2. a. b. c. d.

d. 7

5 ___ 4 354354 c. 3 5 4 3 ___

Word Problem 1. Joy created a pattern using the stickers.

b. 10 9

5. a. 1, 3, 2, 1, 3, 2, 1, 3, 2

3. a. 4

8 7

6 7

5 7

4. a.

0 2 0 ___ 2 02 b. 0 2 0 2 ___

9 ___ 0 ___ 2 ___ 1 9021 d. 9 0 2 1 ___

b. 1, 4, 7, 10, 13, 16,19

Word Problems 1. In 99 68 599 685, since the set of numbers 99685 is repeating itself, hence, it is a pattern. 2. No, this is not a pattern. The cards arranged in a pattern is 5

Chapter Checkup 1. a.

Sleeping line

Standing line

d. Slanting line

2. a. L Standing and sleeping b. V Slanting and slanting d. Z Sleeping and slanting 3. a. b. c.

Curved line c. M Standing d.

Rectangle Oval Triangle Square 4. a. Squares – 2, Rectangles – 1, Triangles – 5, Circles – 1, Ovals – 0 b. Squares – 1, Rectangles – 0, Triangles – 5, Circles – 0, Ovals – 0 c. Squares – 2, Rectangles – 0, Triangles – 5, Circles – 0, Ovals – 0 d. Squares – 1, Rectangles – 0, Triangles – 5, Circles – 0, Ovals - 0 5. a. A cube will give us a square, each time when it is traced. b. A cylinder can give us a circle, when traced.

Solutions

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c. A cuboid can give us a rectangle, when traced. 6. a.

Do It Yourself 13A 1. 2 o’clock or 2:00

3 o’clock or 3:00 Half past 10 or 10:30

Half past 9 or 9:30 2.

b. 3 o’clock

8 o’clock

3. a. False

b. True

c. False

5. Half past 1 is after 1 o’clock. Half past 9 is before 10 o’clock. Half past 3 is after 3 o’clock.

Half past 11

1 o’clock

4. The exam begins at 10:30 and ends at 11:30. Thus, Rina takes 1 hour for the exam.

Word Problem 1. Time Rashi goes to the market = 5 o’clock

7. a.

Time Rashi comes back from the market = 8 o‘clock

5’ o clock

8. a.

GROW

9. a. b.

1 hour

6 ‘o clock

1 hour

8 ‘o clock

Time spent by Rashi = 1 hour + 1 hour + 1 hour = 3 hours Rashi spent 3 hours in the market.

13B 1. a. Thursday comes after Wednesday.

b. Thursday comes before Friday. c. Tuesday lies between Monday and Wednesday. 2. a. Today is Monday. What day is tomorrow? Tuesday What day was yesterday? Sunday b. Today is Thursday. What day is tomorrow? Friday What day was yesterday? Wednesday 3. a. False

b. True

c. False

4. a. December, January, February b. March, April, May

7 ‘o clock

d. True

5. a. Twisha’s birthday is in December. b. Twisha’s birthday is on a Saturday.

10.

Word Problem 1. Saina has dance classes on Saturday. Saina has art classes on Sunday.

a. PATTERN

Monday, Tuesday, Wednesday, Thursday, and Friday are the days Saina does not go to art or dance class.

b. GROWING PATTERN

13C 1. Winter Summer Monsoon Autumn

Spring

(Solution may vary.) Word Problem 1. Rani traced a cube.

Chapter 13

May Cube

October

August

March

December

2. a. Independence Day is celebrated in the monsoon season.

b. Summer season comes after spring.

c. Autumn comes after the monsoon season.

Let's Warm-up 1.

Morning

Noon

Evening

Night

d. Christmas is celebrated in the winter season. 3. a. False.

b. False

c. True

4. a. No, Independence Day is celebrated in the monsoon and Republic Day in the winter. b. There are 3 months of winters. c. Summer starts from May.

5. Lily visits her grandmother every year in March. Word Problem 1. Era spends May and June with her grandmother.

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13D 1. a. Noni has 2 math classes on Tuesday.

6. a. The year begins with winter season. b. Monsoon comes after the summer season. c. Spring falls in March and April. d. July and August are monsoon seasons.

b. Noni has the science class 5 days in a week. c. Noni has 2 sports classes in a week. 2. a. Sports Monday b. Chess Tuesday c. Swimming Wednesday d. Music Thursday e. Art Class Friday

7. a. True

Math

Sports

Tuesday English

Math

Hindi

Wednesday

Art

English

Monday

Math

CompMath uter Friday Hindi Science Saturday OFF OFF Sunday OFF OFF

Thursday

6 Social English Science Science Social Science Library Science ComScience Sports puter Social Hindi English Science English English Music OFF OFF OFF OFF OFF OFF

BREAK

Math Math OFF OFF

5. a. The first period on Monday is math. b. The last period on Thursday is social science. c. The third period on Wednesday is English.

Word Problems 1. a. Raj wakes up at 6:30 in the morning. b. Raj eats breakfast at 7:00. c. His cricket class starts at 5:30. d. Raj has cricket classes on Monday and Wednesday. e. Raj does his homework at 6:30 every day. 2.

7:30

2:00

Let's Warm-up 1. False

2. False

Do It Yourself 14A 1. a. False

3. False

b. False

4. True

c. True

d. True

Chapter Checkup b. 11:30

c. 4:00

d. 2:00

2. In numbers

In words

a. 4:30

Half past four

b. 7:00

Seven o’ clock

c. 8:30

Half past eight

3. a.

10. Time Tanya goes to school = 9 o’clock Time Tanya comes back = 12 o’clock Tanya spends 3 hours in the school.

Chapter 14

Word Problem 1. Time Jia wakes up = 7 o’clock. Jia takes 2 hours to get ready for school. Since, 7 + 2 = 9 Jia goes to school at 9 o’clock. 1. a. 10:30

d. True

9. a. Sunita has her dinner at 8:30. b. Sunita leaves for office at 9:30. c. Sunita goes to bed at 10:00.

4. Class timetable (Solution may vary.)

PERIODS

c. True

8. (Answers may vary) a. Hours – i. Travelling by car. ii. Doing homework. b. Days – i. Growing a plant. ii. Making a project. c. Months – i. Building a house. ii. Making a bridge.

3. a. The train reaches station D at 12:30. b. The train reaches Station E at 2:00. c. The train reaches Station C at 11o’ clock. d. The train reaches station B at half past 10.

DAYS

b. False

3. d.

= So, eight 50-paise coins will be needed to make ₹4.

4. 7:30 4. a.

2:30

10:00

3:30

c. Neha’s father does not go for a walk on Tuesday, Thursday, Saturday, and Sunday. d. He goes to the market every Sunday. e. No, he does not go for a walk on Thursday. 5. a. There are 5 Saturdays in this month. b. There are 31 days in this month. c. There are 5 Mondays in this month.

Solutions

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50 p

₹10

₹20

25 p

5. a. Riya bought a box of crayons for `100. b. Raj bought a packet of balloons for `50. c. Tina bought a red pen for `10.

14B 1.

= ₹18

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b. Amount paid by Tina = ₹15 + ₹15 = ₹30 ₹10

= ₹56

₹10

3. Raj can get a 50-rupee note and five 10-rupee notes in exchange for a 100-rupee note. 4. a. For 20 rupees, we can exchange four 5-rupee coins. b. For 100 rupees, we can exchange two 50-rupee notes. c. Seven 10-rupee notes make 70 rupees.

(The drawing of notes may vary.)

5. Cost of the crayons = ₹200 He can pay for the crayons using 20-rupee notes and 10-rupee notes in the given manner. • Ten 20-rupee notes (10 × 20 = 200) • Twenty 10-rupee notes (20 × 10 = 200)

2. a. Price of the curry leaves = ₹5 b. Price of the semolina = ₹70 Price of the curd = ₹22 Total price = ₹70 + ₹22 = ₹92 Kriti will pay ₹92. c. Amount Kriti gives = ₹80 Price of the vegetables = ₹65 Amount that Kriti will get back = ₹80 − ₹65 = ₹15 Kriti will get back ₹15.

14C 1. Price of 1 ice cream

3. a. Five 10-rupee notes

= ₹45 Price of 1 packet of chips = + ₹10 Total amount to be paid = ₹55 ₹55 will be paid altogether. 2. Amount paid to the shopkeeper = ₹87 Price paid for a cap = − ₹36 Amount received back = ₹51 Nisha will get ₹51 back from the shopkeeper.

₹10

b. Ten 1-rupee coins ₹1

₹1

3. Amount paid to the shopkeeper = ₹90 Price of the toy car = − ₹72 Amount received back = ₹18 Tina will get ₹18 back from the shopkeeper. 4. Price of 1 ice cream = ₹45 Price of 1 toy car = + ₹72 Total amount to be paid = ₹117 Amount paid = ₹200 Money received back = ₹200 − ₹117 ₹083 Mohan will get ₹83 back from the shopkeeper. 5. Price of a flower vase = ₹70 Price of the rose = + ₹10 Total amount to be paid = ₹80 Harish spent ₹80 in all.

4. a.

Word Problems 1. a. Hen’s meal is ₹20.

6. a. Three notes of ₹10 will make ₹30. b. Tina has five coins of ₹1 each. She has 5 rupees in all. c. Raj bought a pencil for ₹10 and an eraser for ₹7. He paid 17 rupees to the shopkeeper. d. My mother gave me ₹35 and I purchased a candy for ₹8. Now, I have 27 rupees left.

b. Two goat’s meals = ₹49 + ₹49 = ₹98 c. Riya paid ₹36 for the sheep’s meal. d. Cost of 3 hens’ meals = ₹20 + ₹20 + ₹20 = ₹60 2. Number of 5-rupee coins Rina had = 3 Money value of 5-rupee coins = ₹5 + ₹5 + ₹5 = ₹15 Number of 2-rupee coins Rina had = 2 Money value of 2-rupee coins = ₹2 + ₹2 = ₹4 Total Money Rina had = ₹15 + ₹4 = ₹19 Price of pencil = ₹7 ₹19 > ₹7. So, the money with Rina is sufficient to buy the pencil. Money that she will get back = ₹19 – ₹7 = ₹12

Chapter Checkup 1. a. Amount paid by Rita and Raj = ₹35 + ₹42 = ₹77 ₹50

₹20

₹5

(The drawing of notes may vary.)

₹2

`15 b.

`70

c. `20 d.

`25

5. ₹1 = 100 p = two 50-paise coins ₹5 = 500 p = ten 50-paise coins Ten 50-paise coins will make ₹5.

7. Money Raj had = ₹30 Price of a toy car = ₹15 Price of a ball = ₹10 Total money Raj spent = ₹15 + ₹10 = ₹25 So, Raj spent ₹25 in total. 8. Money Ravi has = ₹15 Money, he wants to save = + ₹10 Money he will have = ₹25 Ravi will have ₹25 after saving. 9. Money my brother had = ₹67 Money given to me = − ₹35 Money left with him = ₹32 He has ₹32 left now.

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10. Amount of money with Raj = ₹30 Price of the toy = ₹15 Price of the book = ₹10 Total amount = ₹15 + ₹10 = ₹25 Amount of money left with Raj = ₹30 − ₹25 = ₹5 Amount of money Raj got from his friend = ₹5 Amount of money with Raj now = ₹5 + ₹5 = ₹10 So, Raj has ₹10 with him now.

Word Problems 1. Money Priya had = ₹74 More money given by her father = + ₹50 Total money she has = ₹124 Priya has ₹124 now.

5. Rectangle

3 4.

5. 5

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Monday

5 = _________

Tuesday

3 = _________

Wednesday

6 = _________

Thursday

4 = _________

Numbers of Things 2 1 1 3 3

(Answers may vary.) Items

Things Meena Needs to Buy

Numbers of Items 1 2 3 5 Numbers of Things 1 bottle 1 packet 3 1 packet 2 packets

Items

Numbers of Items

Days

Numbers of Things

Bowl Whisk Eggs Flour packet Milk Sugar

Solutions

Things

Shampoo Sugar Plates Chilly powder Biscuits

Do It Yourself 15A 1.

Drawing book Paint bottles Paint brushes White papers 3.

8 = _________

Pencils Eraser Sharpener Notebooks Books

Chapter 15 4. Triangle

Sunday

15B 1.

7 > ₹2. So, Aanya must buy the deal because Aanya will be left with ₹ more money and helping is a good deed.

3. 3

7 = _________

For household chores, money given by her friend = ₹5 Money, Aanya had now = ₹25 + ₹5 = ₹30 Money left with Aanya now = ₹30 − ₹23 = ₹7

2. 2

Saturday

Word Problem 1.

3. Money Aanya had = ₹25 Price of a toy = ₹15 Price of a chocolate box = ₹8 Total money spent = ₹15 + ₹8 = ₹23 Money left with Aanya = ₹25 − ₹23 = ₹2

1. 4

7 = _________

2. Money Anu had = ₹50 Price of a storybook = ₹18 Price of 2 story books = ₹18 + ₹18 = ₹36 Money left with Anu = ₹50 − ₹36 = ₹14 Anu has ₹14 left after buying the books.

Let's Warm-up

Friday

Monday Tuesday Wednesday

1 1 4 1 packet 1 packet 1 packet

2 Bananas 2 + 5 = 7 Bananas 2 + 10 = 12 Bananas

15C 1. a. Mina has 7 comics.

b. Mina has the least books on Science facts. c. Total number of books = 12 + 6 + 5 + 3 + 7 = 33 Mina has 33 books in all. 2. a. 40 students participated in football. b. Football had the greatest number of students. c. Yes, table tennis had only 10 students. 3. a. The most number of pages were read on Day 2. b. The number of pages read on Day 1 is 10 pages.

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c. The number of pages read on Day 3 is less (more/less) than the number of pages read on Day 1. 4. a. True b. False c. True d. True 5. Items Numbers of Items Spoons Plates Towels Rice Notebooks

15D 1.

10 4 2 6 kg 3

Stationery items Pens

No. of students

Pencils

Crayons 2. Solution may vary. Name of the friend Rakhi

No. of family members 5

Sana

Suraj

Mayank

Garvit

Pictograph: 1

2. a. 13 children have crayons. b. Children have the least chalks. c. Children have 19 pencils. d. Yes, pencils are more than pens. e. Most of the children have pencils. 3. a. There are 4 bugs. b. There are 4 bees. c. There are 2 snails. d. Bees and bugs are the most in the picture. e. Bees and bugs are in equal numbers and ants and snails are also in equal numbers. 4. a. Pineapples and Mangoes are the least in number. b. Mangoes and Pineapples are in equal numbers. c. Yes d. Apples are the most in number. 5. a. 5 sandwiches were sold on Thursday. b. More sandwiches were sold on Friday by 9 – 6 = 3 sandwiches. 3 more sandwiches were sold on Friday. c. Total number sandwiches sold in the week = 6 + 3 + 4 + 5 + 9 = 27 sandwiches were sold in the week. 6. a. Joe won 7 medals in the year 2015. b. In 2012 Joe won 3 medals. c. Joe won 4 more medals in 2014 than in 2013. (5 − 1 = 4) Favourite Colour Blue

= 1 member Name of the friend

No. of family members

Red

Rakhi

Green

Sana

Yellow

Suraj

Word Problems 1.

Mayank Garvit 3. a. Sahil bought the most number of potatoes. b. Sahil bought 10 carrots. c. Sahil bought 5 mushrooms. d. Mushrooms are more than tomatoes. Number of more mushrooms than tomatoes = 5 – 4 = 1 4. a. February had the most number of flowers. b. April had the least number of flowers. c. 6 flowers grew in January. d. Total number of flowers = 6 + 8 + 5 + 4 = 23 5. Number of flowers in April = 4 Number of flowers if 4 more flowers grew = 4+ 4 = 8 There will be 8 flowers in April.

Chapter Checkup 1. 4 _________

Number of students

3 _________

4 _________

Toys

Number of toys purchased

Green balls

Red balls

Dolls

Car

Mona purchased 10 toys in all. 2. No. of things Ram bought = 20 No. of toys he bought = 3 No. of books he bought = 5 Total number of toys and books = 3 + 5 = 8 No of crayons he bought = 20 – 8 = 12 Things

Number of things Ram bought

Toys

Books

Crayons

1 _________

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Imagine Mathematics

About the Book

MATHEMATICS Teacher Manual

Singapore

IM_G02_MA_MB_Cover_TM.indd All Pages

Gurugram

Bengaluru

hello@uolo.com

NEP 2020 based

NCF compliant

CBSE aligned

07/02/24 4:02 PM