IM_TM_G03_MA_MB_Text_AY25-26_eBook by Uolo

Master Mathematical Thinking MATHEMATICS

Teacher Manual

MATHEMATICS

Master Mathematical Thinking

Acknowledgements

Academic Authors: Muskan Panjwani, Anjana AR, Anuj Gupta, Simran Singh

Creative Directors: Bhavna Tripathi, Mangal Singh Rana, Satish

Book Production: Sanjay Kumar Goel, Vishesh Agarwal

Project Lead: Neena Aul

VP, Learning: Abhishek Bhatnagar

All products and brand names used in this book are trademarks, registered trademarks or trade names of their respective owners.

First impression 2024

Second impression 2025

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Book Title: Imagine Mathematics Teacher Manual 3

ISBN: 978-81-984519-7-2

Published by Uolo EdTech Private Limited

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CIN: U74999DL2017PTC322986

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Preface

Mathematics is an essential tool for understanding the world around us. It is not just another subject, but an integral part of our lives. It shapes the very foundation of our understanding, personality and interaction with the world around us. Studies from across the globe have shown that proficiency in mathematics significantly influences career prospects and lifelong learning.

According to the NEP 2020, mathematics and mathematical thinking are crucial for empowering individuals in their everyday interactions and affairs. It focuses on competencies-based education, which essentially means actively and effectively applying mathematical concepts in real life. It also encourages innovative approaches for teaching maths, including regular use of puzzles, games and relatable real-world examples to make the subject engaging and enjoyable.

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 math exciting, relatable and meaningful for children.

Imagine Mathematics 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 NCF 2023 and other literature in learning and educational pedagogies. Subsequent pages elaborate further on this approach and its actualisation in this book.

This book incorporates highly acclaimed, learner-friendly teaching strategies. Each chapter introduces concepts through real-life situations and storytelling, connecting to children’s experiences and transitioning smoothly from concrete to abstract. These teacher manuals are designed to be indispensable companions for educators, providing well-structured guidance to make teaching mathematics both effective and enjoyable. With a focus on interactive and hands-on learning, the manuals include a variety of activities, games, and quizzes tailored to enhance conceptual understanding. By integrating these engaging strategies into the classroom, teachers can foster critical thinking and problem-solving skills among students. Moreover, the resources emphasise creating an enriched and enjoyable learning environment, ensuring that students not only grasp mathematical concepts but also develop a genuine interest in the subject.

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 worksheets, among other things. Interactive exercises on the digital platform make learning experiential and help in concrete visualisation of abstract mathematical concepts. We invite educators, parents and students to embrace Imagine Mathematics and join us in nurturing the next generation of thinkers, innovators and problem-solvers. Embark on this exciting journey with us and let Imagine Mathematics be a valuable resource in your educational adventure.

Numbers up to 8 Digits 1

Imagine Mathematics Headings: Clear and concise lessons, aligned with the topics in the Imagine Mathematics book, designed for a seamless implementation.

Alignment

C-1.1:

C-4.3:

Numbers up to 8 Digits 1

Imagine Mathematics Headings

Place Value, Face Value and Expanded Form

Indian and International Number Systems

Comparing and Ordering Numbers

Numbers up to 8 Digits 1

Learning Outcomes: Clear, specific and measurable learning outcomes that show what students should know, understand, or do by the end of the lesson.

Learning Outcomes

Students will be able to:

Rounding–off Numbers

Learning Outcomes

Students will be able to: write the place value, face value, expanded form and number names for numbers up to write numbers up to 8 digits in the Indian and International number system. compare numbers up to 8 digits and arrange them in ascending and descending order. round off numbers up to 8 digits to the nearest 10, 100 and 1000.

Alignment to NCF

Numbers up to 8 Digits 1

C-1.1: Represents numbers using the place value structure of the Indian number system, numbers, and knows and can read the names of very large numbers

C-4.3: Selects appropriate methods and tools for computing with whole numbers, such as computation, estimation, or paper pencil calculation, in accordance with the context

C-5.1: Understands the development of zero in India and the Indian place value system for the history of its transmission to the world, and its modern impact on our lives and in all technology

Let’s Recall

write the place value, face value, expanded form and number names for numbers up to 8 digits. write numbers up to 8 digits in the Indian and International number system. compare numbers up to 8 digits and arrange them in ascending and descending order. round off numbers up to 8 digits to the nearest 10, 100 and 1000.

Alignment to NCF

Place Value, Face Value and Expanded Form

Recap to check if students know how to write the place value, expanded form and number 6-digit numbers.

Indian and International Number Systems

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

Comparing and Ordering Numbers

C-1.1: Represents numbers using the place value structure of the Indian number system, compares whole numbers, and knows and can read the names of very large numbers

Alignment to NCF: Learning Outcomes as recommended by NCF 2023.

Vocabulary

Rounding–off Numbers

C-4.3: Selects appropriate methods and tools for computing with whole numbers, such as mental computation, estimation, or paper pencil calculation, in accordance with the context

Learning Outcomes

C-5.1: Understands the development of zero in India and the Indian place value system for writing numerals, the history of its transmission to the world, and its modern impact on our lives and in all technology

Let’s Recall

expanded form: writing a number as the sum of the values of all its digits order: the way numbers are arranged estimating: guessing an answer that is close to the actual answer rounding off: approximating a number to a certain place value for easier calculation

Teaching Aids

Recap to check if students know how to write the place value, expanded form and number names for 6-digit numbers.

Students will be able to: write the place value, face value, expanded form and number names for numbers up to 8 digits. write numbers up to 8 digits in the Indian and International number system. compare numbers up to 8 digits and arrange them in ascending and descending order. round off numbers up to 8 digits to the nearest 10, 100 and 1000.

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

Vocabulary

Chart papers with empty place value chart drawn; Buttons; Beads; Bowls; Digit

Alignment to NCF

5 number cards with a 7-digit or 8-digit number written on them; Two bowls with number 8-digit numbers in one bowl and rounded-off places in another bowl

Teaching Aids

Let’s Recall: Recap exercises to check the understanding of prerequisite concepts before starting a topic.

C-1.1: Represents numbers using the place value structure of the Indian number system, compares whole numbers, and knows and can read the names of very large numbers

C-4.3: Selects appropriate methods and tools for computing with whole numbers, such as mental computation, estimation, or paper pencil calculation, in accordance with the context

Let’s Recall

Chart papers with empty place value chart drawn; Buttons; Beads; Bowls; Digit cards; Bowls with 5 number cards with a 7-digit or 8-digit number written on them; Two bowls with number cards having 8-digit numbers in one bowl and rounded-off places in another bowl

Recap to check if students know how to write the place value, expanded form and number names for 6-digit numbers. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary

Teaching Aids

Chart papers with empty place value chart drawn; Buttons; Beads; Bowls;

cards; Bowls

Learning Outcomes

Numbers up to 8 Digits 1

Numbers up to

Alignment to NCF

C-1.1: Represents numbers using the place value structure of the Indian number system, compares whole numbers, and knows and can read the names of very large numbers

C-4.3: Selects appropriate methods and tools for computing with whole numbers, such as mental computation, estimation, or paper pencil calculation, in accordance with the context

QR Code: Provides access to digital solutions and other interactive resources.

Learning Outcomes

Let’s Recall

Recap to check if students know how to write the place value, expanded form and number names for 6-digit numbers.

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

Vocabulary

Alignment to NCF

Teaching Aids

Vocabulary: Helps to know the important terms that are introduced, defined or emphasised in the chapter.

C-1.1: Represents numbers using the place value structure of the Indian number system, compares whole numbers, and knows and can read the names of very large numbers

C-4.3: Selects appropriate methods and tools for computing with whole numbers, such as mental computation, estimation, or paper pencil calculation, in accordance with the context

Let’s Recall

expanded form and number names for numbers up to 8 digits. Indian and International number system. arrange them in ascending and descending order. nearest 10, 100 and 1000.

place value structure of the Indian number system, compares whole names of very large numbers and tools for computing with whole numbers, such as mental pencil calculation, in accordance with the context zero in India and the Indian place value system for writing numerals, world, and its modern impact on our lives and in all technology

Teaching Aids: Aids and resources that the teachers can use to significantly improve the teaching and learning process for the students.

Chapter: Numbers up to 8 Digits

Recap to check if students know how to write the place value, expanded form and number names for 6-digit numbers.

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

Vocabulary

Teaching Aids

Place Value, Face Value and Expanded Form Imagine Maths Page 2 Learning Outcomes

write the place value, expanded form and number names for given in the Let’s Warm-up section.

the sum of the values of all its digits close to the actual answer to a certain place value for easier calculation

Place Value, Face Value and Expanded Form

Learning Outcomes

Teaching Aids

Imagine Maths Page 2

Students will be able to write the place value, face value, expanded form and number names for numbers up to 8 digits.

Chart papers with empty place value chart drawn; Buttons; Bowls; Digit cards

Activity

Teaching Aids

Chart papers with empty place value chart drawn; Buttons; Bowls; Digit cards

Activity

Instruct the students to work in small groups. Distribute the teaching aids among the groups. Keep number cards (0–9) in a bowl. Pick a card from the bowl and say the digit aloud along with a place, for example “3 in the thousands place.” Instruct the groups to place as many buttons as the digit in that place on the place value chart. Repeat this to form a 7-digit or 8-digit number. You can repeat digits in more than 1 place. Once the 7-digit or 8-digit number is formed, have each group record the expanded form and number names in their notebooks. Discuss the face value and place value of a few digits in the class. Ask the students to say the number names aloud.

Extension Idea

Activity: A concise and organised lesson plan that outlines the activities and extension ideas that are to be used to facilitate learning.

Ask: In a number 1,67,48,950, if we interchange the digit in the ten thousands place with the digit in the crores place, then what is the difference in the place values of the digits in the ten thousands place?

Extension Idea

Say: On interchanging the digits, the new number is 4,67,18,950. Difference in the place values = 40,000 – 10,000 = 30,000.

Extension Idea: A quick mathematical-thinking question to enhance the critical thinking skill.

Indian and International Number Systems Imagine Maths Page 5

Say: On interchanging the digits, the new number is 4,67,18,950. Difference in the place values = 40,000 – 10,000 = 30,000.

chart drawn; Buttons; Beads; Bowls; Digit cards; Bowls with number written on them; Two bowls with number cards having rounded-off places in another bowl

Learning Outcomes

Students will be able to write numbers up to 8 digits in the Indian and International number system.

Indian and International Number Systems Imagine Maths Page 5

Teaching Aids

Learning Outcomes

Chart papers with empty place value chart drawn; Buttons; Beads

Students will be able to write numbers up to 8 digits in the Indian and International number system.

Activity

Teaching Aids

Chart papers with empty place value chart drawn; Buttons; Beads

Activity

Arrange the class in groups of 4, with each group split into teams of 2 students. Distribute the teaching aids among the groups. Guide the students to form 7-digit or 8-digit numbers on the chart using buttons and beads as in the previous lesson. Ask them to place buttons for the Indian number system on one chart and beads for the International number system on the other. The two teams should record the expanded form of the numbers using commas in their notebooks and number names. Ask the groups to find the similarities and differences between the two systems. Discuss the answers with the class.

Extension Idea

Ask: How many lakhs are there in 10 million?

Answers: Answers, provided at the end of each chapter, for the questions given in Do It Together and Think and Tell sections of the Imagine Mathematics book.

Answers

Say: To find out, we divide 10,000,000 by 100,000. So, there are 100 lakhs in ten million.

Extension Idea

Ask: How many lakhs are there in 10 million?

Say: To find out, we divide 10,000,000 by 100,000. So, there are 100 lakhs in ten million.

Period 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

1. Place Value 7

2. Addition of 3-digit Numbers 10

3. Subtraction of 3-digit Numbers 10

4. Multiplication Tables 10

Break-up of Topics

Place Value and Expanded Form of 4-digit Numbers

Number Names; 4-digit Numbers on the Abacus Comparing Numbers; Ordering Numbers

Forming 4-digit Numbers

Rounding off 3-digit Numbers

Revision

Properties of Addition

Addition by Expanding Numbers; Adding by Counting Forward

Addition without Regrouping

Addition with Regrouping

Adding 4-digit Numbers

Estimating the Sum

Word Problems

Revision

Properties of Subtraction By Counting Forward on a Number Line; By Expanding the Smaller Number

Subtraction without Regrouping

Subtraction with Regrouping; Adding and Subtracting Together

Subtracting 4-digit Numbers

Estimating the Difference

Word Problems

Revision

Properties of Multiplication

Table of 6

Table of 7

Table of 8

Table of 9

Tables of 10, 20, ..., 90

Tables of 100, 200, ..., 900 Revision

5. Multiplication by 2-digit Numbers 9

6. Division 7

7. Division by 1-digit Numbers 5

Multiplying by Expanding the Bigger Number

Multiplying by 1-digit Number

Multiplying by 2-digit Numbers without Regrouping

Multiplying by 2-digit Number with Regrouping

Estimating the Product Word Problems

Revision

Equal Sharing

Division as Repeated Subtraction

Writing Division Sentences; Division and Multiplication Facts Using Multiplication Tables

Properties of Division

Revision

Long Division without Remainder Division with Remainder Word Problems

Revision

Features of 2-D Shapes

Symmetry

Mirror Image

Simple Maps

8. Shapes and Patterns 16

9. Length, Weight and Capacity 14

Features of 3-D Shapes 3-D Shapes as 2-D Shapes

Repeating Patterns

Rotating Patterns

Growing Patterns

Number Patterns

Tiling Patterns

Revision

Units of Length

Measuring Length Using a Ruler

Converting Units of Length Word Problems on Length Units of Weight

Converting Units of Weight

Word Problems on Weight Units of Capacity

Converting Units of Capacity

Word Problems on Capacity

Revision

10. Time

Reading Time on a Clock Time as a.m. and p.m.

Converting Time

Estimating Time

Reading a Calendar

Making a Timeline

Reading a Birth Certificate

Revision 11. Money

Rupee and Paise Amounts

Counting Money

Converting Rupees into Paise

Converting Paise into Rupees

Word Problems on Money

Making Bills

Revision

Parts of a Whole Fractions of a Collection

12. Fractions

13. Data Handling 7

Writing a Fraction

Word Problems

Revision

Data Tables

Drawing a Pictograph

Reading a Pictograph

Drawing a Bar graph

Interpreting a Bar graph

Revision

Place Value 1

Learning Outcomes

Students will be able to: write the place value and expanded form for 4-digit numbers. show a 4-digit number using the abacus and place value blocks and write its number name. compare 2 or more 4-digit numbers and arrange them in ascending and descending order. form 4-digit numbers using the given 4 digits. round off numbers up to 3 digits to the nearest 10 using a number line.

Alignment to NCF

C-1.1: Represents numbers using the place value structure of the Indian number system, compares whole numbers, and knows and can read the names of very large numbers

Let’s Recall

Recap to check if students know how to read, write and show 2-digit and 3-digit numbers. 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 abacus: a set of rods, showing the place of digits in a number, with beads that slide along the rods expanded form: the sum of the values of all the digits in a number round off: to write the closest 10 or 100 number instead of the actual number

Teaching Aids

Place value chart showing 1000s, 100s, 10s and 1s; Place value blocks of 1000s, 100s, 10s and 1s; 4-rod abacus; Number line showing numbers from 300 to 400

Chapter: Place Value

Place Value and Expanded Form of 4-digit Numbers

Learning Outcomes

Students will be able to write the place value and expanded form for 4-digit numbers.

Teaching Aids

Place value chart showing 1000s, 100s, 10s and 1s; Place value blocks of 1000s, 100s, 10s and 1s

Activity

Distribute the place value charts and blocks to the students.

Instruct the students to show the 4-digit numbers 4319 and 6725 using place value blocks and on the place value chart by writing each digit in its correct place. This will help them identify the place value of each digit in a number. Then, in their notebooks, they will write the number of thousands, hundreds, tens and ones, and the numbers in their expanded form.

Ask questions like: How many thousands, hundreds, tens and ones are there in the number? How did you write the number using the place value and the expanded form?

Extension Idea

Ask: How will you write the expanded form for a number which has 2 hundreds more than 8623?

Say: 8623 has 6 hundreds. 2 hundreds more than 8623 will give us 8823. So, the expanded form of 8823 = 8 thousands + 8 hundreds + 2 tens + 3 ones = 8000 + 800 + 20 + 3.

Number Names; 4-digit Numbers on the Abacus

Learning Outcomes

Students will be able to show a 4-digit number using the abacus and place value blocks and write its number name.

Teaching Aids

Place value blocks of 1000s, 100s, 10s and 1s; 4-rod abacus

Activity

Discuss with the students how to show a number on an abacus and tell them that the number of beads on the rod of an abacus tells us the value of the digit.

Ask the students to take the place value blocks and the abacus and show the number 5691 using each. They will then write the number of thousands, hundreds, tens and ones; the number in its expanded form; and as a number name. Finally, they will compare to see if they got the same number of 1000s, 100s, 10s and 1s using both the place value blocks and the abacus.

Ask questions like: How is showing 1000s, 100s, 10s and 1s on the abacus different from showing them using place value blocks?

Learning Outcomes

Students will be able to compare 2 or more 4-digit numbers and arrange them in ascending and descending order.

Teaching Aids

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

Activity

Instruct the students to work in groups and use the place value blocks to show 2 numbers, 1234 and 1252, using the place value blocks. They will first compare the number of thousands blocks in both numbers. The number with the greater 1000s blocks is bigger. If the 1000s blocks are the same, tell them to compare the 100s blocks, then the 10s and finally the 1s blocks. Ask them to write the answer in their notebooks. Ask them to repeat with 2 more numbers and then write all the numbers in ascending order, in their notebooks.

Extension Idea

Ask: Which is a smaller number: 5000 + 300 + 20 or five thousand three hundred two?

Say: 5000 + 300 + 20 is 5320 and five thousand three hundred two is 5302. 5320 has two 10s and 5302 has zero 10s. So, 5302 is smaller or 5302 < 5320.

Forming 4-digit Numbers

Learning Outcomes

Students will be able to form 4-digit numbers using the given 4 digits.

Teaching Aids

4-rod abacus

Activity

Discuss with the students how, in an abacus, when the number of beads are arranged in descending order, starting from the highest value to the lowest value, the digits are also arranged from the highest to the lowest, thus forming the largest number. Show them an abacus where the beads are arranged in descending order to form the number 7643.

Ask the students to form groups and take 1 abacus. Instruct them to show the smallest and then the largest 4-digit numbers using each of the digits, 5, 1, 8, 6, only once. Then, in their notebooks, they will then draw the abacus for each number and write the numbers formed.

Ask questions like: Which rod will have no beads when we want to form the smallest number using the digits 3, 1, 0 and 6?

Extension Idea

Ask: How many 3-digit numbers can be formed using the digits 1, 2 and 3 only once, such that the number can be divided by 2, leaving no remainder?

Say: The possible 3-digit numbers using each of the digits 1, 2 and 3 only once are: 123, 132, 231, 213, 312, and 321. Out of these, the numbers that can be divided by 2 with no remainder are 132 and 312.

Learning Outcomes

Students will be able to round off numbers up to 3 digits to the nearest 10 using a number line.

Teaching Aids

Number line showing numbers from 300 to 400

Activity

Discuss the terms ‘about’ and ‘estimate’ that show rounded off numbers.

Distribute number lines from 300 to 400 with 10 divisions shown between 350 and 360.

Ask the students to show the numbers 353 and 358 on the number line, find the nearest 10 and 100 for each number and write the rounded off numbers in their notebooks.

Extension Idea

Ask: A number, when rounded off to the nearest 10, reaches 80. The number was an even number less than 80 and more than 77. What is the number?

Say: The numbers that can be rounded off to 80 are: 75, 76, 77, 78, 79, 80, 81, 82, 83, 84. But the number is an even number so the number can be 76, 78, 80, 82 or 84. Since the number is less than 80 and more than 77, the number is 78.

1. Place Value and Expanded Form of 4-digit Numbers

Do It Together

Th H T O

4 3 1 9

Answers

4319 = 4000 + 300 + 10 + 9

Standard Form Expanded Form

9 ones or 9 × 1 = 9

1 tens or 1 × 10 = 10

3 hundreds or 3 × 100 = 300

4 thousands or 4 × 1000 = 4000

2. Number Names

Do It Together

3000 + 400 + 50 + 7

three thousand fifty seven four hundred

The number 3457 can be read as three thousand four hundred fifty-seven

3. 4-digit Numbers on the Abacus

Do It Together

Th H T O 5 2 4 1

The number 5241 is read as five thousand two hundred forty-one.

4. Comparing Numbers; Ordering Numbers

Do It Together

Start comparing from the thousands place.

1765 4372 6145 4538 6 > 4 > 1

Compare the hundreds place for 4372 and 4538.

4372 4538 5 > 3

The ascending order is: 1765 < 4372 < 4538 < 6145.

5. Forming 4-digit Numbers

Do It Together

Smallest number place the digits in ascending order: 3059

Th H T O 3 0 5 9

Greatest number place the digits in descending order: 9530

Th H T O 9 5 3 0

Therefore, 3059 is the smallest and 9530 is the greatest 4-digit number formed using the digits 3, 5, 9, 0.

6. Rounding off 3-digit Numbers

Do It Together

Closer to 290

Look for the nearest 10 of the number on the number line. 286 is between 280 and 290 but is closer to 290 Therefore, it is rounded off to 290.

Addition of 3-digit Numbers 2

Learning Outcomes

Students will be able to:

add using the order property and addition by 1 and 0 properties. mentally add 2-digit numbers by expanding numbers. add two 3-digit numbers without regrouping. add two 3-digit numbers with regrouping. add two 4-digit numbers without regrouping. round off two 2-digit numbers and estimate their sum. solve word problems on adding numbers with 3 or 4 digits.

Alignment to NCF

C-1.3: Understands and visualises arithmetic operations and the relationships among them, knows addition and multiplication tables at least up to 10 × 10 (pahade) and applies the four basic operations on whole numbers to solve daily life problems

C-4.3: Selects appropriate methods and tools for computing with whole numbers, such as mental computation, estimation, or paper-pencil calculation, in accordance with the context

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

successor: the number that comes after a number regrouping: rearranging numbers into groups according to their place values estimating: finding the approximate value of a number or a

Teaching Aids

Small boxes; Green and blue marbles; Chits with numbers, along with the method (add mentally or add by expanding numbers); Place value blocks of 100s, 10s and 1s; Straws in red, blue, yellow and white; Sheets with blank number lines drawn on them; Word problem written on a sheet of paper with spaces given for each element of the CUBES strategy

Chapter: Addition of 3-digit Numbers

Properties of Addition

Learning Outcomes

Students will be able to add using the order property and addition by 1 and 0 properties.

Teaching Aids

Small boxes; Green and blue marbles

Activity

Instruct the students to work in groups. Distribute 2 boxes of marbles to each group with 4 green and 5 blue marbles in one box and 5 green and 4 blue marbles in another box.

Ask the students to count the green and blue marbles, and the total number of marbles in the first box. Help them to write the addition sentence for it in their notebooks. Then, ask them to count the green and blue marbles in the second box, along with the total, and write the addition sentence.

Discuss with them how the order of addition doesn’t change the final result.

Next, ask them to put 4 green marbles in one box. Ask them to add 1 more green marble and tell the sum. Explain that when we add 1 to any number, we get its successor. Now, ask the students to put 5 blue marbles in a box and to not add anything to it. Ask them to show this with the help of an addition sentence. Discuss the fact that when 0 is added to any number, the number remains unchanged.

Extension Idea

Ask: Which is bigger: 67 + 1 or 67 + 0?

Say: When we add 1 to any number, the sum is the successor of that number, so 67 + 1 = 68. Similarly, if we add 0 to any number, the sum remains the same, so 67 + 0 = 67. Therefore, 67 + 1 is bigger.

Addition by Expanding Numbers; Adding by Counting Forward

Learning Outcomes

Students will be able to mentally add 2-digit numbers by expanding numbers.

Teaching Aids

Imagine Maths Page 19

Chits with numbers, along with the method (add mentally or add by expanding numbers)

Activity

Instruct the students to work in groups. Distribute the chits with numbers among the groups. Write a 2-digit addition problem on the board, like 23 + 12. Discuss both the the methods of adding numbers –adding mentally by counting forward and adding by expanding smaller numbers. Instruct them to read the addition sums on the chits carefully and find the sum using the given method. The group that solves all the sums first will win a point. Make them practice more such problems.

Addition

without Regrouping

Learning Outcomes

Students will be able to add two 3-digit numbers without regrouping.

Teaching Aids

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

Activity

Instruct the students to work in groups. Distribute the place value blocks among the groups. Display an addition problem, like 435 + 242, on the board. Introduce the column method by creating 3 columns (hundreds, tens and ones) and writing the digits of 435 and 242 in their corresponding columns.

Instruct the students to copy the table and place the same number of 100s, 10s and 1s blocks as given in both numbers. Ask them to count the place value blocks of each type and record the total below their corresponding columns. Give them 1 more problem to solve.

Addition with Regrouping Imagine Maths Page 24

Learning Outcomes

Students will be able to add two 3-digit numbers with regrouping.

Teaching Aids

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

Activity

Instruct the students to work in groups. Distribute the place value blocks among the groups.

Instruct them to show 545 and 456 using the blocks by placing them side by side. Ask them to add the 1s blocks. Discuss how ten 1s blocks become one 10s block. Ask them to now add the 10s blocks. Discuss how ten 10s blocks become one 100s block. Ask them to now add the 100s blocks. Ask how many blocks they have after adding the 100s blocks. Discuss how ten 100s blocks become one 1000s block. Then, in their notebooks, they will add the numbers using the vertical method and verify their answer. Ask questions like: How will you show thirty 100s blocks in 1000s blocks?

Extension Idea

Ask: How many 100s should we add to 625 to regroup the 100s as 1000s?

Say: There are 6 hundreds in 625. Let us count forward to make it 1000 as 700, 800, 900, 1000. We need to add 4 hundreds to 625 to regroup the 100s as 1000s.

Learning Outcomes

Students will be able to add two 4-digit numbers without regrouping.

Teaching Aids

Straws in red, blue, yellow and white

Activity

Instruct the students to work in groups. Distribute the straws among the groups.

Display an addition problem, like 2541 + 7354, on the board. Introduce the column method by creating four columns (thousands, hundreds, tens and ones) and writing the digits of 2541 and 7354 in their corresponding columns. Specify that the red straws represent thousands, the blue straws represent hundreds, the yellow straws represent tens and the white straws represent ones.

Instruct the students to copy the table and organise the straws based on the numbers: 2541 with 2 red, 5 blue, 4 yellow and 1 white straw; and 7354 with 7 red, 3 blue, 5 yellow and 4 white straws. Ask them to count the straws of each colour and record the total below their corresponding columns.

Estimating

the Sum

Learning Outcomes

Students will be able to round off two 2-digit numbers and estimate their sum.

Teaching Aids

Sheets with blank number lines drawn on them

Activity

Instruct the students to work in pairs.

Distribute the sheets with number lines drawn to the students.

Give them two 2-digit numbers, say 48 and 64, and ask the students to first write numbers on the number lines that have these numbers on them, and then find the nearest 10 for each number. Ask them to add the rounded-off numbers in their notebooks. Explain that the sum they got is the estimated sum. Ask them to find the actual sum and compare it with the estimated sum. Give more problems for practice.

Extension Idea

Ask: Find the estimated sum of 10 + 23. Is it >, = or < than the estimated sum of 17 + 12?

Say: 10 + 23 on rounding off will be 10 + 20 = 30. 17 + 12 on rounding off will be 20 + 10 = 30. So, the estimated sums of both the problems are equal.

Learning Outcomes

Students will be able to solve word problems on adding numbers with 3 or 4 digits.

Teaching Aids

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

Activity

Instruct the students to work in groups. Distribute the word problem sheets among the groups. Instruct them to circle the numbers, underline the question and box the key words. Discuss with the students what needs to be found. Then, ask them to solve and write the answer using the vertical method.

Ask questions like: How many 1000s, 100s, 10s and 1s blocks will you need to show the total number of t-shirts?

Extension Idea

Instruct: Create your own word problem where you need to add 1542 and 3435.

Say: There can be many such word problems. One can be: A toy factory produced 1542 toys in the month of January and 3435 toys in the month of February. What is the total number of toys produced in these 2 months?

A cloth store sold 526 shirts and 745 t-shirts in a month. How many shirts and t-shirts were sold altogether?

C Circle the numbers.

U Underline the question. B Box the key words.

E Evaluate/draw S Solve and check. 3

1. Properties of Addition

Do It Together

1 6 + 9 = 9 + 6 2 13 + 1 = 14

3 8 + 0 = 8 4 18 + 1 = 19

2. Addition by Expanding Numbers

Do It Together

1 15 + 53 15 → 10 + 5 53 → 50 + 3 1 5 → 10 + 5 5 3 → 50 + 3 6 8 ← 60 + 8

Thus, 15 + 53 = 68.

3. Adding by Counting Forward

Think and Tell

The smallest 2-digit number is 10.

The largest 2-digit number = 99

So, the sum is 109.

Do It Together

Keep the number 32 in mind.

Skip count by 5 tens.

Count forward by 3 ones.

32 + 53 = 85

4. Addition without Regrouping

Do It Together H T O 6 5 4 + 3 2 1 9 7 5 654 + 321 = 975

Answers

5. Addition with Regrouping Do It Together Do It Together Th

5 876 + 129 = 1005

6. Adding 4-digit Numbers Do It Together Th H T O 1 4 5 4 + 2 3 2 3 3 7 7 7 1454 + 2323 = 3777

7. Estimating the Sum Do It Together

24 rounded off to the nearest 10 is 20 78 rounded off to the nearest 10 is 80.

So, the estimated sum of 24 and 78 is 20 + 80 = 100.

100 is close to 102. So, the estimated sum is close to the actual sum.

8. Word Problems Do It Together

Number of girls = 480

Number of boys = 435

Total number of students = 480 + 435

Thus, the total number of students in the school is 915

Subtraction of 3-digit Numbers 3

Learning Outcomes

Students will be able to:

subtract using the property of subtraction by 1, 0 or the same number. mentally subtract a 2-digit number from a 2-digit number. subtract a 3-digit number from a 3-digit number without regrouping. subtract a 3-digit number from a 3-digit number with regrouping. subtract a 4-digit number from a 4-digit number without regrouping. round off two 2-digit numbers and estimate their difference. solve word problems on subtracting numbers with 3 or 4 digits.

Alignment to NCF

C-1.3: Understands and visualises arithmetic operations and the relationships among them

C-4.3: Selects appropriate methods and tools for computing with whole numbers, such as mental computation, estimation, or paper pencil calculation, in accordance with the context

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 subtraction: finding the difference of two numbers

Teaching Aids

Counters; Paper cups; Number grid (1 to 100); Place value blocks; Place value chart; Paper slips with numbers up to 50; Bowls; Word problem sheets with spaces for each element of the CUBES strategy

Chapter: Subtraction of 3-digit Numbers

Learning Outcomes

Students will be able to subtract using the property of subtraction by 1, 0 or the same number.

Teaching Aids

Counters; Paper cups

Activity

Distribute a few counters of different colours and a paper cup to each pair. Instruct them to put a few counters in the cup, and then take away 1 counter and give it to their partner. Then, ask them the number of counters they are left with. Ask them to write the subtraction sentence in their notebooks. Repeat the process for taking away 0 counters and for taking away all the counters that they have.

Discuss the properties of subtraction: subtracting 0, subtracting 1 and subtracting the same number. Bring out the fact that, on subtracting 1, the number we get is nothing but the predecessor of the given number.

Extension Idea

Ask: What is the predecessor of one hundred forty?

Say: One hundred forty is 140. So, 140 – 1 is 139. Thus, 139 is the predecessor of 140.

By Counting Forward on a Number Line; By Expanding the Smaller Number

Learning Outcomes

Students will be able to mentally subtract a 2-digit number from a 2-digit number.

Teaching Aids

Number grid (1 to 100); Counters

Activity

Distribute a number grid with numbers up to 100 and some counters to each group. Instruct them to use the counters to subtract 2-digit numbers on the number grid. Write a subtraction sentence on the board, say 45 – 24 = ?

Ask: What number would you start from to find the difference? In which direction would you move your counter to subtract?

Instruct them to start from the bigger number and move the counters up by jumping to the previous ten to subtract the tens first. Then, tell them to move to the left to subtract the ones. Explain that the number that they land on is the difference of the 2 numbers.

Ask the students to find the difference of 84 and 31.

Subtraction without Regrouping

Learning Outcomes

Students will be able to subtract a 3-digit number from a 3-digit number without regrouping.

Teaching Aids

Place value blocks

Activity

Instruct the students to form groups. Distribute the place value blocks to each group. Write a subtraction sentence on the board, say 245 – 124 = .

Ask them to use the place value blocks to subtract the 2 numbers.

Instruct the students to show the subtraction using the place value blocks by first showing the bigger number using the place value blocks and then removing the place value blocks equivalent to the smaller number. Now, ask them the value of the remaining place value blocks. Then, instruct them to solve the subtraction problem by writing the numbers one below the other in their notebooks. Finally, ask them to compare the answers they got using the 2 methods.

Extension Idea

Ask: From what number should 730 be subtracted from, to get 250?

Say: To find the answer, we will add 730 and 250. So, 730 + 250 is 980.

Subtraction with Regrouping;

Learning Outcomes

Students will be able to subtract a 3-digit number from a 3-digit number with regrouping.

Teaching Aids

Place value blocks

Activity

Instruct the students to form groups. Distribute the place value blocks to each group. Write a subtraction sentence on the board, say 245 – 156 = .

Instruct the students to show the subtraction using the place value blocks. Take as many place value blocks as the bigger number. Start subtracting the ones by taking away as many blocks as the smaller number. If the number of ones are not enough, remove 1 tens blocks with 10 ones blocks, and then take away. Now, repeat the process for tens and hundreds. The remaining blocks show the answer. Then, instruct them to solve the subtraction problem by writing the numbers one below the other. Ask them to write the answers in their notebooks and to compare the answers they got using the two methods. Ask questions like: How will you subtract in the ones place if you have fewer ones to subtract from?

Subtracting 4-digit Numbers

Learning Outcomes

Students will be able to subtract a 4-digit number from a 4-digit number without regrouping.

Teaching Aids

Place value chart; Counters

Activity

Instruct the students to form groups.

Write a subtraction sentence on the board, say 9687 – 7564 =

Instruct the students to show the subtraction using the place value chart.

Instruct the students to show the bigger number on the place value chart using counters and remove as many counters equivalent to the smaller number. Ask them the value of the remaining counters on the place value chart and say that number is the answer.

Then, instruct them to solve the subtraction problem by writing the numbers one below the other, in their notebooks. Finally, ask them to compare the answers they got using the 2 methods.

Extension Idea

Ask: What is two thousand five hundred sixty-seven less than 8977?

Say: Two thousand five hundred sixty-seven is 2567. So, 8977 – 2567 is 6410.

Estimating the Difference

Learning Outcomes

Students will be able to round off two 2-digit numbers and estimate their difference.

Teaching Aids

Paper slips with numbers up to 50; Bowls; Place value blocks

Activity

Divide the class into groups.

Call a student from each group to pick 2 numbers from the paper slips in the bowl kept on the table.

Instruct them to to show the numbers using place value blocks and check if the number of ones blocks is less than 5. They will then remove the ones blocks to get the rounded off number. If the number of ones is 5 or more, they will remove the ones blocks and add a tens block to get the rounded off number. Finally, they will subtract the 2 numbers to get the estimated difference. Encourage them to write the subtraction sentence in their notebooks. Repeat the activity once more if time permits.

Learning Outcomes

Students will be able to solve word problems on subtracting numbers with 3 or 4 digits.

Teaching Aids

Word problem sheets with spaces for each element of the CUBES strategy

Activity

Instruct the students to form groups. Distribute the word problem sheets to each group. Instruct them to circle the numbers, underline the question and box the keywords. Discuss with the students what needs to be found.

Ask them to then solve and write the answer using the vertical method, in their notebooks.

Extension Idea

C Circle the numbers.

Anna has 541 stamps. Susan has 167 stamps. How many stamps do they have in all?

U Underline the question. B Box the key words. E Evaluate/draw S Solve and check. 3

Instruct: Create and solve a word problem using the numbers 118 and 145. Say: There can be multiple word problems. One such problem can be: There are 118 Christmas bells in a box. Jane bought some more bells and added to the box. How many bells did Jane buy if the total number of bells in the box increases to 145?

Answers

1. Properties of Subtraction Do

2. By Counting Forward on a Number Line

3. By Expanding the Smaller Number Do It Together

35 – 12 = 23 The difference between 35 and 12 is 23

– 10 = 35; 35 – 6 = 29 The difference of 45 and 16 is 29.

4. Subtraction without Regrouping Do It

5. Subtraction with Regrouping

Do It Together

640 – 386 = 254

–

6. Adding and Subtracting Together

Do It Together

8. Estimating the

Estimated difference = 30 – 20 = 10

9. Word Problems Do It Together

Manish has 423 seashells. He has 345 more seashells than Babita. How many seashells does Babita have?

Solve:

Evaluate: 423 – 345 = ?

7. Subtracting 4-digit Numbers

Do It

So, 3789 – 1569 = 2220.

Babita has 78 seashells.

Multiplication Tables 4

Learning Outcomes

Students will be able to:

multiply using property of multiplying by 1, 0 or the order property. skip count to write the multiplication table of 6. skip count to write the multiplication table of 7. skip count to write the multiplication table of 8. skip count to write the multiplication table of 9. multiply a 1-digit number by 10, 20, ..., 90. multiply a 1-digit number by 100, 200, ..., 900.

Alignment to NCF

Let’s Recall

Recap to check if students know how to add a set of objects using repeated addition or equal grouping. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary

group: a collection of things or people product: the answer we get when we multiply 2 or more numbers skip count: jumps of the same number again and again

Teaching Aids

Straws; Straws cut into 3 parts; Paper cups; Marbles; 100s grid; Beads of different colours; Pieces of thread; Bundles of 10 ice cream sticks; Place value blocks of 100s

Chapter: Multiplication Tables

Properties of Multiplication

Learning Outcomes

Students will be able to multiply using the property of multiplying by 1, 0 or the order property.

Teaching Aids

Straws

Activity

Instruct the students to form groups of 3, 4 or 5. Distribute 1 straw to each student. Ask them to count the total number of straws in their group and write the multiplication sentence in their notebooks. Discuss how 3 × 1 = 3, 4 × 1 = 4 and 5 × 1 = 5 and any number multiplied by 1 gives the same number. Then, take away the straws from the groups. Ask them to write the multiplication sentence if none of them had any straws. Discuss how 3 × 0 = 0, 4 × 0 = 0 and 5 × 0 = 0 and any number multiplied by 0 gives 0. Discuss examples of the order property of multiplication, using straws.

Extension Idea

Ask: Which is greater: 5 × 1 or 1 × 5?

Say: 5 × 1 means 5 groups of 1, so 5 × 1 = 5, and 1 × 5 means 1 group of 5, so 1 × 5 = 5. Since 5 = 5, both are equal.

Learning Outcomes

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

Teaching Aids

Straws cut into 3 parts; Paper cups

Activity

Instruct the students to work in groups of 5.

Distribute the paper cups and straws to each group. Ask the first student from each group to put 1 cup in front and place 6 straws inside it. Explain to the students that this represents 1 group with 6 straws and can be written as: 1 × 6 = 6. Ask them to write the multiplication sentence in their notebooks. Ask the next student to place 2 cups and put 6 straws inside each cup. Ask them to count the total number of straws in the 2 cups and write the multiplication sentence in their notebooks. Repeat the activity by asking the third student to put 6 straws each in 3 cups until the fifth student in the group. Explain that the multiplication sentences written form the table of 6. Ask them to keep on adding cups with 6 straws and writing the multiplication sentences until there are 10 groups of 6.

Table of 7

Learning Outcomes

Students will be able to skip count to write the multiplication table of 7.

Teaching Aids

Marbles; Paper cups

Activity

Instruct the students to work in groups of 5.

Distribute the paper cups and marbles to each group.

Ask the first student from each group to put 1 cup in front and place 7 marbles inside it. Explain to the students that this represents 1 group with 7 marbles and can be written as: 1 × 7 = 7. Ask them to write the multiplication sentence in their notebooks. Ask the next student to place 2 cups and put 7 marbles inside each cup. Ask them to count the total number of marbles in the 2 cups and write the multiplication sentence in their notebooks. Repeat the activity by asking the third student to put 7 marbles each in 3 cups until the fifth student in the group. Explain that the multiplication sentences written form the table of 7. Ask them to keep on adding cups with 7 marbles and writing the multiplication sentences until there are 10 groups of 7.

Extension Idea

Instruct: represents 7 books. Find the total number of books: Say: There are five . One represents 7 books. So, 5 groups of 7 books will represent

= 35 books. So, there are 35 books in total.

Table of 8 Imagine Maths Page 60

Learning Outcomes

Students will be able to skip count to write the multiplication table of 8.

Teaching Aids

100s grid

Activity

Instruct the students to work in pairs.

Distribute the 100s grids to each pair.

Instruct the students to start from 1 and shade every 8th number on the grid. For example, they would count 1, 2, 3 ... and so on until they reach the first number to be shaded, that is, 8.

Ask the students to count the number of jumps it takes to reach each shaded number. Discuss the patterns they observe in the multiplication table of 8. Emphasise that they have just created the multiplication table through skip counting, as shown below:

1 jump of 8 = 1 × 8 = 8

2 jumps of 8 = 2 × 8 = 16

3 jumps of 8 = 3 × 8 = 24

Learning Outcomes

Students will be able to skip count to write the multiplication table of 9.

Teaching Aids

Beads of different colours; Pieces of thread

Activity

Instruct the students to work in groups.

Distribute the beads and thread among the groups.

Ask the students to create their bead strings by stringing a group of 9 beads onto the thread. Explain that this represents 1 group of 9 beads and can be written as 1 × 9 = 9. Ask them to write the multiplication sentence in their notebooks. Ask the students to create 1 more string with another 9 beads. Ask them to count the total number of beads on the 2 strings and write the multiplication sentence in their notebooks. Ask them to create 10 such strings and write the multiplication sentences. Explain that the multiplication sentences written form the table of 9.

Tables of 10, 20, ..., 90

Learning Outcomes

Students will be able to multiply a 1-digit number by 10, 20, ..., 90.

Teaching Aids

Bundles of 10 ice cream sticks

Activity

Instruct the students to work in groups.

Distribute the bundles of 10 ice cream sticks among the groups.

Maths Page 61

Ask them to put 1 bundle in front of them and write the multiplication sentence in their notebooks. Ask them to place 1 more bundle next to the previous one, count the total number of sticks and write the next multiplication sentence. Ask them to keep adding the bundles, one by one, and write the multiplication table of 10. Ask them to create the table of 20 until 5 × 20 using the same bundles of sticks. Ask them to compare the table of 10 with the table of 1, and the table of 20 with the table of 2.

Ask questions like: What is the similarity and difference between the 2 tables?

Show how we can multiply the non-zero digits and place the same number of zeroes as the multiplier or multiplicand in the final product.

Extension Idea

Ask: I have 3 groups of 50 red marbles and 5 groups of 40 blue marbles. How many marbles do I have in total? Say: 3 groups of 50 = 3 × 50 = 150, and 5 groups of 40 = 5 × 40 = 200. 150 + 200 = 350. So, I have 350 marbles.

Learning Outcomes

Students will be able to multiply a 1-digit number by 100, 200, ..., 900.

Teaching Aids

Place value blocks of 100s

Activity

Instruct the students to work in 2 groups.

Distribute the place value blocks of 100s among the groups. Explain that 1 block represents 1 group of 100 and can be written as 1 × 100 = 100.

Ask them to arrange 2 blocks side by side. Explain that this will represent 2 × 100 = 200. Now, ask them to create a multiplication table for 100.

Discuss how multiplying the non-zero digits of a number ending with zeroes with the 1-digit number and then putting the same number of zeroes at the end of the product makes multiplication easier. Discuss some multiplications, such as 500 × 6, 700 × 2 and 900 × 5 in the class.

Extension Idea

Ask: There are 300 marbles in a jar. There are 1500 marbles in total. How many jars are needed for all the marbles? Say: We know that 5 groups of 300 marbles = 1500 marbles. As 5 groups of 300 make 1500, 5 jars are needed.

Answers

1. Properties of Multiplication

Do It Together

1. 6 × 9 = 9 × 6

2. 14 × 1 = 14

3. 8 × 0 = 0

4. 18 × 1 = 18

2. Table of 6

Do It Together

6 12 18 24

3. Table of 7

Do It Together

4. Table of 8

Do It Together

5. Table of 9 Do It Together

6. Tables of 10, 20, ..., 90

Do It Together 1. 5 × 10 = 50 2. 60 × 7 = 420 3. 80 × 8 = 640 4. 7 × 40 = 280

7. Tables of 100, 200, ..., 900 Do It Together 1.

Multiplication by 2-digit Numbers 5

Learning Outcomes

Students will be able to:

multiply 2- or 3-digit numbers by a 1-digit number by expanding the bigger number. multiply a 3-digit number by a 1-digit number using the vertical multiplication method. multiply a 3-digit number by a 2-digit number without regrouping. multiply a 3-digit number by a 2-digit number with regrouping. estimate the product of a 2-digit number and a 1- or 2-digit number. solve word problems on multiplying numbers up to 3 digits and 2 digits.

Alignment to NCF

C-4.3: Selects appropriate methods and tools for computing with whole numbers, such as mental computation, estimation, or paper pencil calculation, in accordance with the context

Let’s Recall

Recap to check if students know how to write multiplication facts. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary

product: the answer we get when we multiply 2 or more numbers

Teaching Aids

Number strips; Number cards; Display of items with price tags; Printout of the list of expense categories and their prices; Multiplication card puzzle; Word problem sheets

Chapter: Multiplication by 2-digit Numbers

Multiplying

Learning Outcomes

Students will be able to multiply 2- or 3-digit numbers by a 1-digit number by expanding the bigger number.

Teaching Aids

Number strips; Number cards

Activity

Begin by recalling the expanded form of 2- and 3-digit numbers. Demonstrate the multiplication of a 3-digit number by a 1-digit number (let’s say 425 × 8) by expanding the bigger number and discussing all the steps involved.

Write a problem, 38 × 5, on the board. Instruct the students to work in groups.

Distribute the number strips and the number cards among the groups.

Ask the students to use the number cards and place them over the strips to show the multiplication. Ask them to write the final product in their notebooks. This method of solving is called the Box Method. We can also solve the same problem using the Lattice method.

Multiplying by 1-digit Number

Learning Outcomes

Students will be able to multiply a 3-digit number by a 1-digit number using the vertical multiplication method.

Teaching Aids

Display of items with price tags

Activity

Demonstrate the vertical multiplication method on the board. Instruct the students to work in groups.

Set up a display of items with their prices written on them.

Ask the students to visit the displayed items. Ask them to note down the prices of the items and the number of items (in single digits) they want to buy. Ask them to find the amount they need to pay for each item by multiplying using the column method. Discuss the answers in class.

Learning Outcomes

Students will be able to multiply a 3-digit number by a 2-digit number without regrouping.

Teaching Aids

Printout of the list of expense categories and their prices

Activity

Demonstrate how to multiply a 3-digit number by a 2-digit number without regrouping on the board. Conduct a budgeting exercise for planning a school event. Distribute the budgeting sheet with expenses and price per child printed on it. Instruct the students to work in groups.

Ask the students to calculate the cost of food for 14 students and gifts for 13 children in their notebooks, and then discuss their answers within the group. Discuss the answers with the class.

Extension Idea

Ask: What is the total cost for buying 3 dresses and giving gifts to 3 students?

Expense Price

Dress �323 per child

Food �122 per child

Gifts �232 per child

Say: Cost of buying 3 dresses = ₹323 × 3 = ₹969 and cost of giving gifts to 3 students = ₹232 × 3 = ₹696. So, the total cost = ₹969 + ₹696 = ₹1665.

Learning Outcomes

Students will be able to multiply a 3-digit number by a 2-digit number with regrouping.

Teaching Aids

Multiplication card puzzle

Activity

Demonstrate how to multiply a 3-digit number by a 2-digit number with regrouping on the board.

Instruct the students to work in groups.

Distribute the multiplication puzzle cards among the groups, with questions written on some cards and their products on other cards.

Instruct the students to pick 1 card and do the multiplication in their notebooks. Ask them to look for the answer card and place it next to the question card. Ask them to arrange all the multiplication cards with their answers next to each other.

Estimating the Product

Learning Outcomes

Students will be able to estimate the product of a 2-digit number and a 1- or 2-digit number.

Activity

Begin by recalling the term estimation. Discuss some real-life scenarios where we use estimation. Give some 1- and 2-digit numbers and ask the students to round off the numbers to the nearest 10. Ask the students to round off the 2-digit number to the nearest 100 as well.

Write some 2-digit by 2-digit multiplication problems on the board. Ask the students to first round off both the numbers to the nearest 10 and multiply, and then to the nearest 100 and multiply. Ask them to now find the actual product. Ask them to compare the estimated product with the actual product.

Instruct the students to write the answers in their notebooks. Ask questions like: Which estimated product is nearest to the actual product?

Word Problems Imagine Maths Page 81

Learning Outcomes

Students will be able to solve word problems on multiplying numbers up to 3 digits and 2 digits.

Teaching Aids

Word problem sheets

Activity

Instruct the students to work in groups. Distribute the word problem sheets among the groups.

Ask them to read the problem: Sarah is making cartons of cookies for a bake sale. Each carton contains 189 cookies, and she wants to make 15 such cartons. How many cookies does she need in total? Ask them to note down what we know and what we need to find. Instruct the students to solve the problem in their notebooks. Discuss the answers in the class.

Extension Idea

Sarah is making cartons of cookies for a bake sale. Each carton contains 189 cookies, and she wants to make 15 such cartons. How many cookies does she need in total?

What do we know?

What do we need to find?

Solve to find the answer.

Instruct: Create your own word problem where you need to multiply 136 by 35. Say: There can be many such problems. One problem can be: A library has 136 books placed on a shelf. How many books are placed on 35 such shelves?

1. Using the Box Method

Do It Together

3 × 3 × 100 = 300 3 × 20 = 60 3 × 2 = 6

300 + 60 + 6 = 366

So, 122 × 3 = 366.

2. Using the Lattice Method

Do It Together

Answers

5. Multiplying by 2-digit Numbers without Regrouping

Do It Together

= 156

6. Multiplying by 2-digit Numbers with Regrouping

Do It Together

So, 523 × 5 = 2615.

3. Multiplying by 1-digit Numbers without Regrouping

Do It Together

121 × 4 = 484

4. Multiplying by 1-digit Numbers with Regrouping

Do It Together

4 2 2

237 × 6 = 1422

45 × 31 = 1395

7. Estimating the Product

Do It Together a 88 × 8

Round off the bigger number to the nearest 10. 88 is rounded to 90

Multiply the numbers.

90 × 8 = 720.

The estimated product of 88 and 8 is 720.

b 92 × 5 = 90 × 5 = 450.

The estimated product of 92 and 5 is 450.

8. Word Problems

Do It Together

No. of beads in a necklace = 23.

No. of necklaces to be made = 22.

Total no. of beads required = 23 × 22.

The total number of beads required for 22 necklaces is 506.

Learning Outcomes

Students will be able to:

divide a given number of things using equal sharing. divide a given number of things using repeated subtraction. write the division facts for the given multiplication facts and vice versa. divide a given number of things using multiplication tables. divide using the property of division by 1, 0 or by itself.

Alignment to NCF

C-1.3: Understands and visualises arithmetic operations and the relationships among them, knows addition and multiplication tables at least up to 10 × 10 (pahade), and applies the four basic operations on whole numbers to solve daily life problems

Let’s Recall

Recap to check if students know how to divide things into equal parts. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary

division: sharing things equally so everyone gets the same amount dividend: the big number that we are sharing divisor: the number of people or groups that are sharing quotient: the answer we get after sharing equally

Teaching Aids

Ice cream sticks; Paper cups

Chapter: Division

Equal Sharing

Learning Outcomes

Students will be able to divide a given number of things using equal sharing.

Teaching Aids

Ice cream sticks; Paper cups

Activity

Instruct the students to form groups. Distribute 15 ice cream sticks and 3 paper cups.

Instruct the students to place the 3 cups before them, and then put the ice cream sticks, one by one, in each cup till all the sticks are put in. Count the number of ice cream sticks that each cup has. Finally, ask the students to write the total number of ice cream sticks, then the division sign, followed by the number of paper cups, the equal to sign and then the number of ice cream sticks in each cup.

Discuss how the division is formed. Give the students 15 ice cream sticks and 5 paper cups. Ask them to share them equally among 5 cups and write the division sentence in their notebooks.

Extension Idea

Ask: Will you be able to distribute 15 ice cream sticks equally among 4 paper cups? Why or why not?

Say: No, 15 ice cream sticks cannot be shared equally among 4 paper cups. 3 ice cream sticks will be left over. When we try to distribute them, they cannot be shared equally.

Division as Repeated Subtraction

Learning

Outcomes

Students will be able to divide a given number of things using repeated subtraction.

Teaching Aids

Ice cream sticks; Paper cups

Activity

Instruct the students to form groups. Distribute the ice cream sticks and paper cups among the students. Instruct the students to take 12 ice cream sticks and distribute them by putting 4 sticks into each cup. While doing this, encourage them to write down a subtraction sentence to show the process in their notebooks. For example, they can write “12 – 4 = 8” for the first set of cups, “8 – 4 = 4” for the second set of cups and so on.

Once they have completed the task with the 12 ice cream sticks, ask them to count and note how many cups they used in total. Repeat the activity with 16 ice cream sticks and 8 ice cream sticks.

Ask questions like: Is it necessary to subtract the same number every time?

Writing Division Sentences;

Division and Multiplication Facts

Learning Outcomes

Students will be able to write the division facts for the given multiplication facts and vice versa.

Teaching Aids

Ice cream sticks; Paper cups

Activity

Instruct the students to form pairs.

Distribute some ice cream sticks and paper cups to the students.

Instruct them to make 2 groups of 8, which are 2 paper cups with 8 ice cream sticks in each cup, and then count the total number of ice cream sticks they used. Finally, they will write the multiplication fact (2 × 8 = 16) for them.

Then, they will put together all the ice cream sticks and distribute them equally in 8 cups. Ask the students to write the division fact (16 ÷ 8 = 2) for the same.

Ask questions like: Are there more multiplication or division facts that you can make with the 16 ice cream sticks?

Discuss how 1 more division and multiplication fact can be made.

Extension Idea

Instruct: Draw a picture to show the division fact and the corresponding multiplication fact.

Say:

Multiplication fact: 3 × 2 = 6

Division fact: 6 ÷ 3 = 2

Using Multiplication Tables

Learning Outcomes

Students will be able to divide a given number of things using multiplication tables.

Teaching Aids

Ice cream sticks; Paper cups

Activity

Ask the students if they can divide 48 ice cream sticks into 6 cups and how many sticks will be there in each cup. Ask the students to form groups for the activity. Select the multiplication table of 6 (or any other table).

Distribute 6 cups and 48 ice cream sticks to each group. Guide the students to distribute 48 sticks equally among 6 groups. Tell them that, as we needed to divide 48 sticks into 6 cups, we used the multiplication table of 6 and saw that 6 times 8 equals 48. Help them see that 6 groups of 8 sticks each give 48 ice cream sticks. Tell them that 8 ice cream sticks will be there in each cup.

Repeat the process for 45 sticks and divide the number of sticks in 5 cups equally.

Extension Idea

Ask: What is 60 ÷ 10; 70 ÷ 10 and 50 ÷ 10? Do you observe a pattern?

Say: 60 ÷ 10 = 6; 70 ÷ 10 = 7; 50 ÷ 10 = 5. Yes, there is a pattern that we see here. When you divide a 2-digit number by 10, the quotient is simply the digit in the tens place of the original number.

Properties of Division

Learning Outcomes

Students will be able to divide using the property of division by 1, 0 or by itself.

Teaching Aids

Ice cream sticks; Paper cups

Activity

Instruct the students to form groups.

Distribute the ice cream sticks and paper cups among the students.

Imagine Maths Page 93

Instruct the students to take ice cream sticks and paper cups. Ask them to distribute 2 sticks equally into 2 cups, and then count and write the number of sticks each cup holds, in their notebooks.

Say: When we divide any number by itself, the answer is always 1.

Now, instruct them to put those 2 sticks in 1 cup and ask them to count and write the number of sticks in that cup, in their notebooks.

Say: When we divide any number by 1, we get the same number.

Do the same for the remaining 2 properties given below.

When we divide 0 by any number, the answer is always 0

You cannot divide any number by 0. There’s no answer

1. Equal Sharing

Do It Together

4. Division and Multiplication Facts

Do It Together

As there are 6 groups of 5 stickers, Riya can put stickers on 6 gift boxes.

2. Division as Repeated Subtraction

Do It Together

Subtract 6 from 24 until we get 0. Count how many times 6 has been subtracted. We subtracted 6 four times.

So, there are four 6s in 24

3. Writing Division Sentences

Do It Together

Dividend = 50 Divisor = 5 Quotient = 10

Division sentence = 50 ÷ 5 = 10.

5. Using Multiplication Tables

Do It Together

6. Properties of Division

Do It Together 1.

÷ 0 = No answer

Division by 1-digit Numbers

Learning Outcomes

Students will be able to:

divide numbers up to 4 digits by 1-digit numbers (without remainder). divide numbers up to 4 digits by 1-digit numbers (with remainder). solve word problems on dividing numbers.

Alignment to NCF

C-4.1: Solve puzzles and daily-life problems involving one or more operations on whole numbers (including word puzzles and puzzles from ‘recreational’ areas, such as the construction of magic squares)

C-4.3: Selects appropriate methods and tools for computing with whole numbers, such as mental computation, estimation or paper-pencil calculation, in accordance with the context

Let’s Recall

Recap to check if students know how to form equal groups, such that each group contains the same number of items.

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

Vocabulary

dividend: the number that is to be divided divisor: the number that divides another number quotient: the number we get when we divide one number by another remainder: the number left after the division

Teaching Aids

Place value blocks for 1s, 10s and 100s; Imagine Mathematics Book; Word problem sheets

Chapter: Division by 1-digit Numbers

Long Division without Remainder

Learning Outcomes

Students will be able to divide numbers up to 4 digits by 1-digit numbers (without remainder).

Teaching Aids

Place value blocks for 1s, 10s and 100s; Imagine Mathematics Book

Activity

Begin by explaining division as the process of equally sharing items among groups. Introduce the problem 484 ÷ 4 to illustrate the concept.

Instruct the students to use the place value blocks to represent the dividend (484). They should lay out four 100s blocks (representing 400), eight 10s blocks (representing 80) and four 1s blocks (representing 4) to show a total of 484. Explain that the four 100s blocks, eight 10s blocks and four 1s blocks need to be divided equally into 4 groups.

Ask them to create these groups using 100s, 10s and 1s blocks ensuring each group has the same number of blocks. Finally, ask them to count the blocks in each group to find the quotient. Engage the students in discussing the process, emphasising how the blocks were divided equally among the groups, resulting in a clear division without any remainder. Explain the division steps shown in the Imagine Mathematics book page no. 100 and ask the students to calculate 484 ÷ 4 using this method, in their notebooks, and to verify their answer with the answer obtained using the place value blocks.

Extension Idea

Ask: Is it possible to equally divide 53 into 4 equal groups?

Say: You will have to trade one 10s block for ten 1s blocks to divide the blocks into 4 equal groups. After trading, you’ll now have four 10s blocks (representing 40) and thirteen 1s blocks, together representing the number 53. We will have 4 tens blocks and 3 ones blocks in each group. 1 ones block will be leftover. However, it is not possible to equally divide 53 into 4 equal groups as we will have a 1s block left over.

Learning Outcomes

Students will be able to divide numbers up to 4 digits by 1-digit numbers (with remainder).

Teaching Aids

Place value blocks for 1s, 10s and 100s; Imagine Mathematics Book

Activity

Write a division problem on the board, such as 325 ÷ 3.

Distribute the place value blocks among the students. Each student should then represent the dividend (325) using 100s, 10s and 1s blocks. Demonstrate how to make equal groups of 3 using the blocks. Show the students how to start with the 100s blocks, making groups of 3. They should trade or exchange blocks, as needed, to create full groups and count the remaining blocks. Finally, ask the students to write the answer in their notebooks. Now, explain the division done in the word problem, Kavya has a pack of 35 biscuits. given in the Imagine Mathematics book page no. 102 and ask the students to calculate 325 ÷ 3 using this method, in their notebooks, and to verify their answer with the answer obtained using the place value blocks.

Word Problems Imagine Maths Page 103

Learning Outcomes

Students will be able to solve word problems on dividing numbers.

Teaching Aids

Word problem sheets

Activity

Ask the students to form groups for the activity. Distribute the sheets with the word problem written on them.

Instruct the students to read the question on the sheet and find the answers by using the strategy: What do we know? What do we need to find? How to find?

A jug can hold 5 cups of juice. How many jugs are required to hold 515 cups of juice?

What do we know?

What do we need to find?

How to find?

Solve to find the answer.

Help the students when needed. Ask them to write the answers for each step in the rows provided in the table and solve using the long division method. Give a similar type of problem to the students. Example: 496 apples are packed in 4 boxes equally. How many apples are there in each box?

Extension Idea

Instruct: Create a word problem using the numbers 187 and 9. Say: You can make multiple word problems using the numbers 187 and 9. One such word problem could be: For a classroom activity, 187 markers are to be packed in boxes. If each box can hold 9 markers, then how many markers will not fit into the boxes?

Answers

1. Long Division without Remainder

Do It Together

3. Word Problems

Do It Together

Number of cups 1 jug holds = 7

Total cups of juice to be filled = 819

We need to find the number of jugs required to hold 819 cups of juice

Thus, 117 jugs are required to hold 819 cups of juice.

2. Division with Remainder

Think and Tell

No, the remainder cannot be greater than the divisor. When the number is divided, the remainder is what’s left after dividing as much as possible. If the remainder is bigger than the divisor, it means that it can still be further divided, which means the division is not complete yet.

Do It Together

Checking division:

(114 × 4) + 2 = 458

456 + 2 = 458

458 = 458

Checking division:

(800 × 6) + 1 = 4801

4800 + 1 = 4801

4801 = 4801

Shapes and Patterns

Learning Outcomes

Students will be able to:

list the properties of 2-D shapes and draw them on dot paper using the properties. identify lines of symmetry in 2-D shapes and draw them. identify and draw mirror images of shapes and figures. read a map by using directions and distances to go from one place to another. list the properties of 3-D shapes.

visualise 3-D shapes as 2-D shapes and draw their views and nets. identify the rule in a given repeating pattern and extend the pattern. identify the rule in a given rotating pattern and extend the pattern. identify the rule in a given growing pattern and extend the pattern. identify the rule in a given number pattern and extend the pattern. identify the shape that forms the tiling pattern and extend the pattern.

Alignment to NCF

C-1.4: Recognises, describes and extends simple number patterns such as odd numbers, even numbers, square numbers, cubes, powers of 2, powers of 10, and Virahanka–Fibonacci numbers

C-2.1: Identifies, compares, and analyses attributes of two- and three-dimensional shapes and develops vocabulary to describe their attributes/properties

C-2.3: Recognises and creates symmetry (reflection, rotation) in familiar 2-D and 3-D shapes

C-2.4: Discovers, recognises, describes and extends patterns in 2-D and 3-D shapes

Let’s Recall

Recap to check if students know how to distinguish between 2-D and 3-D shapes. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary

face: the surface of a 3-D shape edges: the line segments that form the shape line of symmetry: a line that divides the shape in equal halves

Teaching Aids

A4-size sheet of paper; Dot paper; Scissors; Cutouts of 2-D shapes such as circles, triangles and squares; Mirror; Grid paper(partially coloured); Crayons; Map of school marked with (classroom, playground, science lab and school entrance); Pencil; Wooden 3-D shapes; Disposable plates, glasses and bowls; Stickers of different shapes; Clock with movable hands; Paper cutouts of triangles with a dot on one corner; Paper cutouts of different colours; Unit blocks; Number grids; Ball; Square grids

Chapter: Shapes and Patterns

Features of 2-D Shapes

Learning Outcomes

Imagine Maths Page 110

Students will be able to list the properties of 2-D shapes and draw them on dot paper using the properties.

Teaching Aids

A4-size sheet of paper; Dot paper; Scissors

Activity

Instruct the students to work in groups. Distribute an A4-size sheet and dot paper to each group.

Ask one student from each group to volunteer and identify the shape of the sheet, and the sides and corners the sheet has. Discuss its sides and corners. Bring out the fact that sides are the line segments that form the shape and corners are the points where the sides meet.

Ask the students to form other 2-D shapes like squares and triangles by folding the paper and circles and ovals by drawing and cutting them from the sheet of paper. Discuss the properties of the shapes. Ask the students to use the dot paper to draw the shape using the properties discussed.

Extension Idea

Ask: What shape am I if I have 4 straight sides and 4 corners but all my sides are equal?

Say: A square has 4 sides and 4 corners and all its sides are equal.

Symmetry

Learning Outcomes

Students will be able to identify the lines of symmetry in 2-D shapes and draw them.

Teaching Aids

A4-size sheet of paper; Cutouts of 2-D shapes such as circles, triangles and squares

Activity

Imagine Maths Page 114

Begin by taking a sheet of paper, folding it in half and drawing a line along the crease. Ask the students if the shape appears to be the same on both sides of the line and if this makes the shape symmetrical.

Instruct the students to work in groups. Distribute the cutouts to the students, ask them to fold them in a way that makes the shapes symmetrical and then draw the line of symmetry.

Ask questions like: How many lines of symmetry did you draw in each shape?

Extension Idea

Ask: How can a line of symmetry be drawn on a square to get 2 different shapes?

Say: A vertical or horizontal line of symmetry splits the square into 2 rectangles. A diagonal line of symmetry splits the square into 2 triangles.

Learning Outcomes

Students will be able to identify and draw mirror images of shapes and figures.

Teaching Aids

Mirror; Grid paper (partially coloured); Crayons

Activity

Discuss how a mirror image is different from the actual image.

Ask the students to work in groups of 3. Distribute the coloured grid paper and mirror to each group.

Instruct one student to hold the mirror straight and ask the other student to hold the grid paper very close to the mirror.

Ask the third student to observe the image in the mirror and colour the image in the mirror.

Ask the students to take turns to colour the grid paper to complete the picture.

Ask questions such as: Did the mirror image look similar to the actual shape? Did the size of the image change?

Extension Idea

Ask: What is the word in the mirror text shown below? Where do we see it?

AMBULANCE

Say: It is the mirror image of the word AMBULANCE. We see it in emergency vehicles.

Simple Maps Imagine Maths Page 116

Learning Outcomes

Students will be able to read a map by using directions and distance to go from one place to another.

Teaching Aids

Map of school marked with (classroom, playground, science lab and school entrance); Pencil

Activity

Discuss what a map is and how maps are useful.

Divide the class into groups of 4. Distribute the map of school to each group. Discuss that to go from the classroom to playground, it is 7 steps straight.

Instruct the students to first draw the route from their classroom to the playground. Ask them to count the steps and note them in their notebooks.

Ask the students to draw the route from their classroom to the science lab and the route from their classroom to the school entrance. Ask them to note down the steps.

Playground

Ask questions such as: How many steps did it take from your classroom to the school entrance?

Features of 3-D Shapes

Learning Outcomes

Students will be able to list the properties of 3-D shapes.

Teaching Aids

Wooden 3-D shapes

Activity

Show a solid wooden shape to the students. Move your fingers around the shape to show its faces, edges and vertices. Instruct the students to work in groups.

Distribute 2 wooden objects each of different 3-D shapes to each group.

Imagine Maths Page 119

Instruct them to move their fingers along the sides of each shape and count the sides, move their hand around the surface of each shape and count the faces and then point out the corners of each shape. Ask the students to write the answers in their notebooks. Ask questions like: Did you identify any shape which did not have any corner or any vertex?

Extension Idea

Ask: What 2-D shapes can you see in a cuboid?

Say: A cuboid is usually formed using only rectangles or squares and rectangles. So, squares and rectangles are used to form a cuboid.

3-D Shapes as 2-D Shapes

Learning Outcomes

Students will be able to visualise 3-D shapes as 2-D shapes and draw their views and nets.

Teaching Aids

Wooden 3-D shapes; Disposable plates, glasses and bowls

Activity

Demonstrate different views of the same wooden 3-D objects to the students. Discuss with the students what the top, side and front views of an object are. Tell them that the parts of the object they see or those parts that are visible to their eyes are the different views of different objects.

Instruct the students to work in groups. Distribute a disposable plate, a glass, a bowl and one wooden 3-D shape to each group.

Ask them to first rotate and move the objects to draw different views of these items in their notebooks. Instruct them to exchange notebooks with other group members and compare their answers. Discuss how their views differ from each other. Ask them if the size of the items matters while drawing the views of similar objects. Now, ask them to place the wooden 3-D shape in front of them and visualise how would its net look. They will then draw the net on a sheet of paper, cut out the net, fold it to see if they get the same wooden shape.

Discuss how the faces of the 3-D shape helps in drawing its net.

Extension Idea

Ask: What is the same in the views and net of a cube?

Say: All the views of a cube show squares. To draw the net of a cube, we draw only squares. The views and net of a cube are dependent on the faces of a 3-D shape.

Repeating Patterns

Learning Outcomes

Imagine Maths Page 124

Students will be able to identify the rule in a given repeating pattern and extend the pattern.

Teaching Aids

Stickers of different shapes

Activity

Instruct the students to work in groups.

Distribute stickers of different shapes like stars, circles, etc. to each group.

Instruct the students to use stickers of one shape at a time on a sheet of paper followed by some other shape. Ask them to repeat this in order one more time and create a beautiful pattern. For example, ask the students to use a sticker of a star and then of a circle and repeat it.

Now, ask a student from each group to volunteer and come up to the front of the class to show their pattern. Discuss with the class their observations about the pattern and ask them to identify the repeating unit in the pattern and extend the pattern in their notebooks.

Extension Idea

Ask: If a square is added to the pattern you created, how do you think you would arrange the pattern?

Say: If a square is added to the pattern, then one of the ways a repeating pattern can be created would be: star, circle, square, star, circle, square.

Rotating Patterns

Learning Outcomes

Imagine Maths Page 124

Students will be able to identify the rule in a given rotating pattern and extend the pattern.

Teaching Aids

Clock with movable hands; Paper cutouts of triangles with a dot on one corner

Activity

Demonstrate forming a pattern on a clock with movable hands by rotating the minute hand from 12 to 3 to 6 to 9 in a clockwise and then in an anticlockwise direction. Discuss the similarities and the differences in the pattern shown to them. Bring out the fact that in rotating patterns, a unit changes direction with each step. The direction may be clockwise or anticlockwise; top, bottom, left or right.

Instruct the students to work in groups of 3.

Distribute the paper cutouts of triangles with a dot on one of the vertices to each group.

Ask each group to use them to form a pattern by rotating the triangles in different directions. Ask them how they formed the pattern and what they notice about it.

Growing Patterns

Learning Outcomes

Imagine Maths Page 124

Students will be able to identify the rule in a given growing pattern and extend the pattern.

Teaching Aids

Unit blocks

Activity

Instruct the students to work in groups of 5. Distribute the unit blocks to each group.

Instruct one of the students in the group to place one block in front of him/her. Ask the 2nd student to stack 3 blocks, one above the other. Ask the rest of the students to look at the difference of the blocks of the first and second student, and place as many blocks in front of them such that the difference remains the same. Ask them to repeat this till the last student in the group has placed a block. Ask them about the similarities and differences in the pattern. Discuss growing patterns. Bring out the fact that in growing patterns, the same number of units are added to every next unit.

Now, instruct them to use the same unit blocks and create some other growing pattern. Discuss with them how they formed the pattern and what they notice about it.

Learning Outcomes

Students will be able to identify the rule in a given number pattern and extend the pattern.

Teaching Aids

Number grids; Ball

Activity

Instruct the students to form groups of 6. Take the groups to the playground and ask them to form a circle. Tell them they are playing a game called ‘pass and pass’.

Give a ball to one student and ask him to say ‘1’. Say that each subsequent student will add the previous two numbers and say the result aloud before passing the ball. For example, student 1 says ‘1’, student 2 will add 0 and 1 and say ‘1’, student 3 will add 1 and 1 and say ‘2’, student 4 will add 1 and 2 and say ‘3’ and so on.

Then, as the students pass the ball and call out the numbers, ask the other students to observe the pattern and ensure the correct sequence is being followed.

Take the students back to the class. Write each number of the pattern on the board and discuss the number patterns. Bring out the fact that in the number patterns, a unit is repeated every time at a constant gap, based on addition, subtraction, multiplication or division.

Distribute the number grids among the groups. Ask them to shade the numbers to form a pattern until 5 numbers. Once the groups create a pattern, ask them to pass the grid to the next group to extend the pattern. Discuss the patterns created by various groups and the rules they applied.

Tiling Patterns Imagine Maths Page 126

Learning Outcomes

Students will be able to identify the shape that forms a tiling pattern and extend the pattern.

Teaching Aids

Paper cutouts of different colours; Square grids

Activity

Demonstrate how to form a tilling pattern by pasting square cutouts of two different colours next to each other. Bring out the fact that in tiling patterns, a unit of the same shape and size is repeated in such a way that no overlaps or gaps are there between the units and they can be extended horizontally or vertically.

Instruct the students to work in pairs. Distribute square grids among the pairs.

Ask them to colour the grids in such a way as to create a tilling pattern. Encourage them to make designs as well to make their pattern look different.

Extension Idea

Ask: Can we use a circle or an oval to make a tiling pattern? Why?

Say: No, we cannot use a circle or oval in a tiling pattern. If we use these two shapes, then there will be a lot of gaps while forming the tiling pattern. These shapes cannot be tiled to form a pattern.

1. Features of 2-D Shapes

Answers

Think and Tell the shape is a hexagon with 6 sides and 6 corners. Yes, the shape has all straight sides. Do It Together

2. Routes may vary. Sample route: Take 5 steps up. Take 5 steps left to the fair.

5. Features of 3-D Shapes

Do It Together

Triangle: 2 Circle: 1 Square: 2 Rectangles: 2

2. Symmetry

Do It Together 1 2 3

6. 3-D Shapes as 2-D Shapes

Do It Together

3. Mirror Image

Do It Together

7. Understanding Patterns

Do It Together

4. Simple Maps

Do It Together

1. a. The hospital to the fair is two steps.

b. The park to the hospital is two steps.

Length, Weight and Capacity

Learning Outcomes

Students will be able to:

estimate the correct unit that can be used to measure the length of an object. measure the length of an object using a ruler. convert between metres and centimetres. solve word problems on length. estimate the correct unit that can be used to measure the weight of an object.

Alignment to NCF

convert between kilograms and grams. solve word problems on weight. estimate the correct unit that can be used to measure the capacity of a container. convert between litres and millilitres. solve word problems on capacity.

C-3.1: Measures in non-standard and standard units and evaluates the need for standard units

C-3.2: Uses an appropriate unit and tool for the attribute being measured

C-3.3: Carries out simple unit conversions, within a system of measurement

C-3.5: Devises strategies for estimating the distance, length, time, perimeter weight, and volume

Let’s Recall

Recap to check if students know the basic idea of measuring lengths and weights. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary

weight: measurement of the heaviness of an object capacity: the amount that can be held in a particular space

Teaching Aids

Flash cards with pictures of different objects and distances; Imagine Mathematics book; Ruler; Metre and centimetre scale; Cards with corresponding lengths written in metres and centimetres; 2 sets of red, green and blue ribbons; Flash cards of objects of different weights; Cards with weights in g and kg; 2 sets of printed sheets with objects and their weights; Flash cards of containers with different capacities; Cards with capacities in L and mL; 2 sets of cards with containers and their capacities

Chapter: Length, Weight and Capacity

Units of Length

Learning

Outcomes

Imagine Maths Page 133

Students will be able to estimate the correct unit that can be used to measure the length of an object.

Teaching Aids

Flash cards with pictures of different objects and distances

Activity

Begin the class by discussing a few objects in the class that can be measured in centimetres or metres.

Divide the students into groups.

Provide each group with flash cards with pictures of a variety of distances and objects with different lengths, such as a road, key and door.

Instruct them to estimate the appropriate unit of measurement (centimetres, metres or kilometres) for each object and write it in their notebook. Ask them to sort the things based on their units of measurement.

Extension Idea

Ask: Name an object that can be measured both in metres and kilometres.

Say: We can measure the height of mountains both in metres and kilometres.

Measuring Length Using a Ruler

Learning Outcomes

Students will be able to measure the length of an object using a ruler.

Teaching Aids

Imagine Mathematics book; Ruler

Activity

Demonstrate to the students how to measure the length of an object using a ruler.

Imagine Maths Page 134

Divide the class into groups. Instruct the students to measure the lengths of various objects, like their Imagine Mathematics book, desks, pencils and pencil boxes.

Discuss how the measure of the Imagine Mathematics book and the desks will be the same for all students because the length is the same. Explain that the lengths of their pencil boxes and pencils will be different because the sizes are different. Ask the students to write the lengths of the objects in their notebook.

Extension Idea

Ask: Can you measure the length of a bangle using a ruler? Why or why not?

Say: The length of a bangle cannot be measured using a ruler because it does not have straight sides.

Road Key Door

Converting Units of Length

Learning Outcomes

Students will be able to convert between metres and centimetres.

Teaching Aids

Metre and centimetre scale; Cards with corresponding lengths written in metres and centimetres

Activity

Demonstrate measuring the length of the door using a metre scale and then measure the length of the same door using a centimetre scale. Help the students understand the relationship between metre and a centimetre. Take the students to the playground and instruct them to work in 2 groups.

Distribute the number cards, with lengths written in metres, to the first group, and another set of number cards, with the corresponding lengths written in centimetres, to the other group.

Instruct the students in both the groups to look at their cards and find their partner in the other group with the corresponding converted length. Instruct the students to stand in pairs once they find their partner.

Now, repeat this activity by exchanging the number cards between the groups and ask them to again find their partner. Back in the classroom, ask the students to write the answers in their notebook.

Extension Idea

Ask: Arrange the following lengths in descending order—12 m 45 cm, 1100 cm, 13 m.

Say: 12 m 45 cm = 1200 cm + 45 cm = 1245 cm, 13 m = 1300 cm. So, 13 m > 12 m 45 cm > 1100 cm.

Word Problems on Length

Learning Outcomes

Students will be able to solve word problems on length.

Teaching Aids

2 sets of red, green and blue ribbons

Activity

Divide the class into groups.

Take 3 ribbons of different colours and different lengths. (Make sure the lengths of the ribbons are complete numbers like 20 cm, 15 cm, 45 cm and the length is not told to the students as they have to measure the lengths.)

Instruct the groups to form a word problem using the 3 ribbons given to them. Distribute the 3 ribbons to each group.

(Example: Neha has red, green and blue ribbons with lengths of 20 cm, 15 cm and 45 cm, respectively. What is the total length of ribbons with her?)

Ask 1 student from each group to first measure the lengths of the ribbons, create a word problem and then read aloud the word problem that they made. Instruct the students to solve the word problem and write the answers in their notebook.

Distribute the next set of ribbons with different lengths and ask the students to repeat the same process of writing the word problem and finding the answer.

Units of Weight

Learning Outcomes

Students will be able to estimate the correct unit that can be used to measure the weight of an object.

Teaching Aids

Flash cards of objects of different weights

Activity

Begin by discussing the concept of weight and introducing various units of measurement for weight.

Ask the students to point out a few objects around them that can be measured in grams or kilograms.

Divide the students into groups.

Provide each group with flash cards showing pictures of objects of different weights, such as a cupcake, carrot, watermelon, etc.

Instruct the students to estimate the appropriate unit of measurement (grams or kilograms) for each object and write them in their notebook. Ask them to sort the things based on their units of measurement.

Converting Units of Weight

Learning Outcomes

Students will be able to convert between kilograms and grams.

Teaching Aids

Cards with weights in g and kg

Activity

Tell the students the relationship between kilograms and grams. Take the students to the playground and instruct them to work in 2 groups.

Distribute 1 set of number cards, with weights written in grams, to the first group and another set of number cards, with the corresponding weights written in kilograms, to the other group.

Instruct the students in both the groups to look at their cards and find their partner in the other group with the corresponding converted weight. Instruct the students to stand in pairs once they find their partner.

Now, repeat this activity by exchanging the number cards between the groups and ask them to again find their partner.

Back in the classroom, ask the students to write the answers in their notebook.

Extension Idea

Instruct: Arrange the following weights in descending order: 4 kg 400 g, 3 kg 300 g, 8 kg.

Say: 4 kg 400 g = 4000 g + 400 g = 4400 g, 3 kg 300 g = 3000 g + 300 g = 3300 g, 8 kg = 8000 g.

So, 8 kg > 4 kg 400 g > 3 kg 300 g.

Carrot Cupcake Watermelon

Word Problems on Weight

Learning Outcomes

Students will be able to solve word problems on weight.

Teaching Aids

2 sets of printed sheets with objects and their weights

Activity

Distribute sheets of paper (with a table drawn on each) among the groups. Divide the class into groups.

Object Oranges Apples Watermelons

Weight 2 kg 3 kg 6 kg

Instruct the students to frame a word problem using the weights of the 3 given types of fruits.

(Note: If the students aren’t able to form a word problem, provide them with a word problem.)

Ask 1 student from each group to read aloud the word problem that they made. Instruct the students to solve the word problem and write the answers in their notebook.

Distribute the next set of printed sheets with objects and their weights, and ask the students to repeat the same process of writing the word problem and finding the answer.

Extension Idea

Ask: Frame a word problem also including 1 kg of grapes.

Say: There can be many such word problems. One can be: Raju bought 4 types of fruits. He bought 2 kg of oranges, 3 kg of apples, 6 kg of watermelons and 1 kg of grapes. What is the total weight of the fruits that Raju bought?

Learning Outcomes

Students will be able to estimate the correct unit that can be used to measure the capacity of a container.

Teaching Aids

Flash cards of containers with different capacities

Activity

Begin by discussing the concept of capacity and introducing varioud units of measurement of capacity.

Ask the students to think of a few containers or vessels that can be measured in litres or millilitres. Discuss the same in the class.

Provide each student with flash cards showing pictures of containers of different capacities, such as a cup, a bucket, a spoon, etc.

Divide the students into groups.

Instruct the students to estimate the appropriate unit of measurement (millilitres or litres) for each object and write it in their notebook. Ask them to sort the things based on their units of measurement.

Cup Bucket Spoon

Converting Units of Capacity

Learning Outcomes

Students will be able to convert between litres and millilitres.

Teaching Aids

Cards with capacities in L and mL

Activity

Tell the students the relationship between litres and millilitres. Take the students to the playground and instruct them to work in 2 groups.

Distribute the number cards, with capacities written in millilitres, to the first group and another set of number cards, with the corresponding capacities written in litres, to the other group.

Instruct the students in both the groups to look at their cards and find their partner in the other group with the corresponding converted capacity. Instruct the students to stand in pairs once they find their partner.

Now, repeat this activity by exchanging the number cards between the groups and ask them to again find their partner.

Ask the students to write the answers in their notebook.

Extension Idea

Instruct: Arrange the following capacities in descending order: 8 L 725 mL, 5 L 850 mL, 9 L.

Say: 8 L 725 mL = 8000 mL + 725 mL = 8725 mL, 5 L 850 mL = 5000 mL + 850 mL = 5850 mL, 9 L = 9000 L. So, 9 L > 8 L 725 mL > 5 L 850 mL.

Learning Outcomes

Students will be able to solve word problems on capacity.

Teaching Aids

2 sets of cards with containers and their capacities

Activity

Divide the class into groups. Distribute the cards (with containers and their capacities written) to each group.

Type of Container

Capacity 500 mL 2 L 10 L 500 mL

Instruct the students to frame a word problem using the capacities of the 3 given types of containers.

(Note: If the students aren’t able to form a word problem, provide them with a word problem).

Ask 1 student from each group to read aloud the word problem that they made. Instruct the students to solve the word problem and write the answers in their notebook.

Distribute the next set of cards with containers and their capacities and ask the students to repeat the same process of writing the word problem and finding the answer.

1. Units of Length

Do It Together

1 Length of the school ground

2 Length of the bus

3 Distance between 2 countries

4 Length of a shoe

5 Height of a street light pole

6 Height of a flagpole

2. Measuring Length Using a Ruler

Do It Together

1 The length of the photo frame is 10 cm.

3. Converting Units of Length

Do It Together

Answers

5. Units of Weight

Do It Together

4. Word Problems on Length

Do It Together

Distance travelled on Monday = 6 km

Distance covered on Tuesday = 12 km

As we need to find the total distance covered, we will add the distances.

6 km + 12 km = 18 km

The total distance travelled by Soumya is 18 km.

6. Converting Units of Weight

Do It Together

1 The shopkeeper has 5 kg of apples. He has 5000 g of apples.

2 Riya bought 2 kg and 500 g of carrots. She bought 2500 g of carrots.

3 A bag of potatoes weighs 8 kg. The bag weighs 8000 g.

4 Meena puchased 3 kg and 450 g of bananas. She purchased 3450 g of bananas.

7. Word Problems on Weight

Do It Together

Weight of Bhanu’s suitcase = 15 kg

Weight of Vidya’s suitcase = 19 kg

Difference in weight = 19 – 15 = 4 kg

Therefore, Vidya’s suitcase is 4 kg heavier than Bhanu’s suitcase.

8. Units of Capacity

Do It Together

9. Converting Units of Capacity

Think and Tell

No, it will not be enough since a glass of juice is approximately 250–300 mL. So, 2 L of juice will be sufficient for around 8 people.

Do It Together

10. Word Problems on Capacity

Do It Together

Amount of petrol to fill the truck = 44 L

Amount of petrol to fill the car = 30 L

Amount of petrol to fill the bike = 5 L

Total amount of petrol used to fill the 3 vehicles = 44 L + 30 L + 5

Learning Outcomes

Students will be able to: read time on a clock to the nearest 5 minutes and write it as hh:mm and o’clock. understand the 24-hour clock and write time as a.m. or p.m. convert between hours and minutes. estimate whether an activity will take hours, minutes or seconds. read a calendar and answer questions based on it. read and make a timeline of festivals or life events. read a birth certificate and calculate the age based on it.

Alignment to NCF

C-3.2: Uses an appropriate unit and tool for the attribute (like length, perimeter, time, weight, volume) being measured

Let’s Recall

Recap to check if students know how to read, and have a basic understanding of how to read time. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary

birth certificate: identification document containing details such as name, date of birth, place of birth, etc. timeline: a graphical representation of a period in which important events are marked

Teaching Aids

Clocks made on paper plates (without hands); Ice cream sticks of 2 lengths; Sentence cards; Chart paper; Glue stick; Small bags; Cards with digits from 1–12 and the first 12 multiples of 60; Bowls; Strips of paper; Year calendars; Story on a sheet of paper; Sample birth certificates

Chapter: Time

Reading Time on a Clock

Learning Outcomes

Imagine Maths Page 150

Students will be able to read time on a clock to the nearest 5 minutes and write it as hh:mm and o’clock.

Teaching Aids

Clocks made on paper plates (without hands); Ice cream sticks of 2 lengths

Activity

Show a clock made on a paper plate and demonstrate reading the hours by counting forward by 1 and in minutes by skip counting by 5.

Instruct the students to make groups. Distribute the ice cream sticks and clocks made on paper plates (without hands) to each group. The paper plate should also show the multiples of 5 for students to count the time in 5 minutes. Instruct the students to skip count by 5 to find the time in minutes. Instruct the students to represent 10:20 by pasting the ice cream sticks on the paper plates to show the time. Instruct the students to write the time as hh:mm and o’clock. Instruct them to show some other time using the ice cream sticks and paper plates, and write the time in their notebooks.

Extension Idea

Ask: What time will the clock show if the hour and minute hands are interchanged at 3:45?

Say: The clock will show 9:15.

Time as a.m. and p.m.

Learning Outcomes

Students will be able to understand the 24-hour clock and write time as a.m. or p.m.

Teaching Aids

Sentence cards; Chart paper; Glue stick

Activity

Imagine Maths Page 152

Demonstrate to the students the time intervals in which we write a.m. and p.m. Ask the students to look at the Imagine Mathematics book to look at the timelines for a.m. and p.m. Make groups of students and distribute multiple sentence cards to them.

Going to school

Eating dinner

Going to play at park

Eating breakfast

Instruct the students to make 2 columns on the chart paper, labelling the first column as a.m. and the second column as p.m.

Ask the students to paste the sentence cards according to when the event occurs, on the chart paper, in their respective columns using a glue stick. For example, the sentence card with ‘Going to school’ will come in the column labelled a.m.

The group that correctly places all the sentence cards in the correct columns and in the least time wins.

Converting Time

Learning Outcomes

Students will be able to convert between hours and minutes.

Teaching Aids

Clocks made on paper plates (without hands); Ice cream sticks; Small bags; Cards with digits from 1–12 and the first 12 multiples of 60

Activity

Introduce the students to time conversion, by showing that 1 hour equals 60 minutes, using a paper plate and ice cream sticks. Make 2 groups of students and distribute 2 bags of cards—one with cards with the number of hours (2 hours, 3 hours, 4 hours, etc.) to one group and the other with the corresponding minutes (120 minutes, 180 minutes, 240 minutes) to the other group.

Ask the students of Group 1 to pick a card from the bag and read the time in hours and find the number of minutes in the given number of hours so that they can match it with its correct pair with a student in Group 2. Once all the students are done with this activity, switch the cards between the groups and repeat the activity. Ask the students to write the answers in their notebooks.

Extension Idea

Ask: Which is more: 2 hours 30 minutes or 160 minutes?

Say: 2 hours 30 minutes = 120 + 30 = 150 minutes. Hence, 160 minutes is a greater duration than 2 hours 30 minutes.

Learning Outcomes

Students will be able to estimate whether an activity will take hours, minutes or seconds.

Teaching Aids

Bowls; Strips of paper

Activity

Discuss 1 activity each that would take hours, minutes or seconds.

Distribute the strips of paper giving 1 to each student. Instruct the students to write the names of the activities that take hours, minutes or seconds on the strip of paper. The student should then put these strips of paper in a bowl.

Divide the entire class into 2 groups. Discard the duplicate activities.

Conduct a quiz by picking a slip, one by one, and asking the students to estimate whether the time taken for that activity is in seconds, minutes, hours, days or more. The groups will take turns, and the group that makes the most accurate estimations will win the game.

Discuss the activities for which different students answered differently (one student said this activity can be done in hours, while the other student said it can be done in minutes).

Reading a Calendar

Learning Outcomes

Students will be able to read a calendar and answer questions based on it.

Teaching Aids

Year calendars

Activity

First, demonstrate how to represent dates on the calendar and help the students understand it.

Divide the class into groups and distribute the year calendars to each group.

Ask each student to announce their birthday and instruct them to circle their birthday (for example, 28 January) on the calendar. Each group of students must represent their birthdays on the calendar. Repeat this process for all the students.

Ask the students a few questions, like: What is the day on February 24? How many months have 5 Sundays? Which month has the least number of days? On which day will your birthday be?

Making a Timeline

Learning Outcomes

Students will be able to read and make a timeline of festivals or life events.

Teaching Aids

Story on a sheet of paper

Activity

Demonstrate how to make a timeline for a given list of important events.

(For example, show a timeline for the list of festivals.)

Divide the class into small groups and provide each group with a specific story or event, such as “Family holidays” on a sheet of paper.

For example, Raj liked to go on holidays with his family. In January, he went to Kashmir; in April, he went to Rishikesh; in August, he went to Goa; and, in December, he went to Kanyakumari.

Ask the students to identify key moments or stages in the given event and create a visual timeline on a large sheet of paper. They can use drawings, labels or simple sentences to represent each stage of the event in order.

Encourage creativity and participation within the groups. After completing the timelines, have each group present their work to the class, explaining the sequence of events in the given story or event.

Learning Outcomes

Students will be able to read a birth certificate and calculate the age based on it.

Teaching Aids

Sample birth certificates

Activity

Discuss each detail, like name, date of birth, parent’s name, etc., which the students are required to fill out in the sample birth certificate.

Provide each student with a sample birth certificate, featuring details like name, date of birth, place of birth and other information. Ask the students to identify the necessary details. Ask questions like: In which year will the person be 25 years old?; What are the names of the person’s parents?; Where was the person born?

Instruct the students to write the answers to these questions in their notebooks.

Form Number

BIRTH CERTIFICATE

This is to certify that this information is taken from the original record of birth which is in the register for the year

Name:

Sex:

Date of Birth:

Place of Birth:

Name of Father:

Name of Mother:

Date of Registration: Registration Number: Date: Signature of issuing authority

Encourage discussions about the significance of the details and the purpose of a birth certificate.

Extension Idea

Ask: If the date on Tanya’s birth certificate is January 10, 2020, what will be her age on January 20, 2027. Say: Tanya’s age on January 20, 2027 will be 7 years and 10 days.

Answers

1. Reading Time on a Clock

Think and Tell

The hour hand points to a number in one day, two times. Do It Together a b c 4 o’clock 4:00 20 minutes past 5 5:20 5 minutes to 3 2:55

2. Time as a.m. and p.m. Do It Together Morning Noon and Evening Night

4. Estimating Time Do It Together

8:30 a.m. Brush teeth

Have breakfast

Play outdoors

3. Converting Time

Study

Think and Tell Answers may vary. Sample answer: Approximately 6 hours. Do It Together Start Time End Time Time Passed by 1 hour = 60 minutes 10 minutes

1 hour and 45 minutes = 60 + 45 = 105 minutes

2 hour and 15 minutes = 60 + 60 + 15 = 135 minutes

Putting on a T-shirt Playing a football match Putting on shoes Drinking a glass of water Celebrating a birthday

5. Units of Time on a Calendar

Do It Together

1. FYRADI - FRIDAY 2. SYUADN - SUNDAY 3. YAM - MAY 4. TCOBORE - OCTOBER

5. LAPIR - APRIL 6. TUHDYARS - THURSDAY

6. Interpreting a Calendar

Do It Together

1. The day of the week on 2 March: Saturday

2. The day of the week on 16 March: Saturday

3. The date on the first Monday: 4 March

4. The number of Sundays in the month: 5

5. The number of Saturdays in the month: 5

7. Making a Timeline Do It Together

8. Reading a Birth Certificate Do It Together

1. 8 Oct 2020 2. Sunita Lal 3. Raman Lal 4. 10

Think and Tell Individual answers.

Money 11

Learning Outcomes

Students will be able to: write a given amount in rupees and paise in figures and words. count the given amount of money and write as rupees and paise. convert the amount given in rupees to paise. convert the amount given in paise to rupees. solve word problems on adding and subtracting money amounts. make a bill to find the total amount to be paid.

Alignment to NCF

C-8.11: Performs simple transactions using money up to INR 100

Let’s Recall

Recap to check if students know how to count money in rupees. Ask students to solve the questions given in the Let’s Warm-up section.

Vocabulary

figures: the digits (0–9) used to write a number without using words conversion: changing the value from one form to another

Teaching Aids

Pairs of cards with money amounts written in words and in figures (e.g. 15.20 and fifteen rupees twenty paise); Envelopes with play money making up different amounts; Play money (in paise); Items with price tags in rupees; Semicircular puzzle cut-outs with amounts in paise on one part and corresponding rupees on another part; Play money; Toy; Pack of stickers; Notebook; Cards with pictures of ice cream flavours with price tags (e.g. Chocolate - ₹12.00, …)

Chapter: Money

Rupee and Paise Amounts

Learning Outcomes

Imagine Maths Page 170

Students will be able to write a given amount in rupees and paise, in figures and words.

Teaching Aids

Pairs of cards with money amounts written in words and in figures (e.g. 15.20 and fifteen rupees twenty paise)

Activity

Demonstrate the amounts in figures and words. Take the students out to the playground. Instruct them to stand in 2 rows.

Shuffle the money cards properly. Distribute the figure amount cards to the students in the first row and the word amount cards to the students in the second row.

Instruct the students to look for their partners as they get the “GO” instruction. Once they get to their partner, ask them to make a group of 6 that will have 3 pairs.

Extension Idea

Ask: Let us say you get a card that says ‘₹10.21’. Your friend gets a card that says ‘twenty-one rupees and ten paise’. Is the amount on both cards the same?

Say: No, the amount is not the same because ₹10.21 in words will be written as ten rupees and twenty-one paise.

Counting Money

Learning Outcomes

Imagine Maths Page 171

Students will be able to count the given amount of money and write it as rupees and paise.

Teaching Aids

Envelopes with play money making up different amounts

Activity

Demonstrate how to count money by showing play money of ₹500, ₹50, a ₹5 coin and a 25 paise coin.

Ask the students to add all the amounts in rupees as ₹500 + ₹50 + ₹5 = ₹555 and write the paise amount separated by a dot as ₹555.25. Instruct the students to work in pairs.

Distribute the envelopes with play money of different amounts to each pair. Ask the pairs to count the money inside the envelopes and write it as rupees and paise in their notebooks. Repeat the activity by asking the pairs to exchange their envelopes with other pairs.

Extension Idea

Ask: How can you make up the amount of ₹328 using notes and coins?

Say: There are many ways of making up ₹328 using notes and coins. One way can be: one ₹200 note + one ₹100 note + one ₹20 note + one ₹5 coin + one ₹2 coin + one ₹1 coin.

Converting Rupees into Paise

Learning Outcomes

Students will be able to convert the amount given in rupees to paise.

Teaching Aids

Play money (in paise); Items with price tags in rupees

Activity

Demonstrate the conversion of rupees into paise by writing a conversion problem, say ₹50.25, on the board. Discuss with the students that ₹1 = 100 paise and explain that to change rupees to paise, all they need to do is remove the dot and ₹ symbol and write paise after the figure.

Place a few items on the table, such as books, pencils, crayons, bags, etc., with price tags in rupees on them. Instruct the students to work in groups. Distribute the play money among the groups.

Begin by explaining the situation to the students: They are in a marketplace where the prices of items are in rupees, but they have money only in paise.

Instruct each group to come up to the table and choose any 1 item. Ask them to first convert the price of the item into paise, count the play money they need and write the answer in their notebooks.

Extension Idea

Ask: Is fifty-six rupees seventy-five paise less than or greater than 5680 paise? Say: Fifty-six rupees seventy-five paise is 5675 paise. Since 5675 < 5680, fifty-six rupees seventy-five paise < 5680 paise.

Converting Paise into Rupees

Learning Outcomes

Students will be able to convert the amount given in paise to rupees.

Teaching Aids

Imagine Maths Page 173

Semicircular puzzle cut-outs with amounts in paise on one part and corresponding rupees on another part Activity

Demonstrate the conversion of paise into rupees on the board. Explain that to change paise to rupees, they need to count 2 digits from the right, place a dot (.) and then write the rupee symbol (₹) before the amount. Instruct the students to work in groups.

Distribute the semicircular puzzle cut-outs with amounts in paise on one part and corresponding rupees on another part. Make sure that there are distractor cut-outs too. Ask the students to take the paise cut-outs and look for their corresponding rupee conversion. Ask them to join the conversion cut-outs to make circular shapes and write the answers in their notebooks.

Word Problems on Money

Learning Outcomes

Students will be able to solve word problems on adding and subtracting money amounts.

Teaching Aids

Play money; Toy; Pack of stickers; Notebook

Activity

Divide the class into groups. Distribute the play money to each group. Give the students a scenario:

‘Sara bought a colourful toy for ₹250 and a pack of stickers for ₹75. Sara’s sister bought a notebook for ₹50’. Arrange the items on the table, with the price tags, based on the given scenario.

Ask: How much did Sara and her sister spend in the toy store?

Let the students find the answer and note it down in their notebooks. Ask the students to count the same amount of play money and place it on their desks.

Next, ask: How much does Sara have left after paying with a ₹500 note? Explain that the remaining amount is ₹500 minus the total amount spent. Ask the students to write the answer in their notebooks.

Extension Idea

Instruct: Create a word problem where you need to add ₹15, ₹45 and ₹29.50.

Say: We can form many such word problems. One can be: Yashi went to a sweet shop and bought a candy for ₹15, a cupcake for ₹45 and a donut for ₹29.50. How much did she spend in total?

Making Bills

Learning Outcomes

Students will be able to make a bill to find the total amount to be paid.

Teaching Aids

Cards with pictures of ice cream flavours with price tags (e.g. Chocolate – ₹12.00, …)

Activity

Discuss with the students how to make a bill.

Instruct the students to work in groups.

Distribute single ice cream cards to each student in the group.

Ask the students to create a bill using the bill template in the book, based on the ice cream cards with them. For example, 3 students in the group can have chocolate flavour cards and 2 can have mango flavour cards.

Ask them to find the total bill amount.

Extension Idea

Ask: Rohan bought 6 orange ice creams for ₹120. What is the cost of 1 orange ice cream?

Say: Since the cost of 6 ice creams is ₹120, the cost of 1 ice cream will be ₹120 ÷ 6 = ₹20.

1. Rupee and Paise Amounts

Do It Together

1. ₹23.25 = twenty-three rupees twenty-five paise

2. ₹36.60 = thirty-six rupees sixty paise

3. ₹42.80 = forty-two rupees eighty paise

4. ₹61.03 = sixty-one rupees three paise

2. Counting Money

Think and Tell

Yes, ₹20 + ₹1 + 50 paise = ₹21.50 + +

Do It Together

₹500 + ₹100 = ₹600.

₹600 + ₹20 = ₹620.

₹620 + ₹2 = ₹622

₹622 and 25 paise = ₹622.25.

In figures = ₹622.25

3. Converting Rupees into Paise

Do It Together

1. ₹125.36 = . Therefore, ₹125.36 = paise.

Answers

5. Word Problems on Money

Do It Together

Money with Anushka = ₹135.00.

Money given by mom = ₹42.50.

Money given by dad = ₹37.00

We need to find the total money Anushka has; hence, we will add the money.

Add rupees and paise vertically separated by dot. Hence, Anushka has ₹214.50 in total.

6. Making Bills

Think and Tell

No the new total will not be the same. 6 pencils and 1 notebook would cost him ₹30 + ₹45 = ₹45.

Do It Together

paise.

4. Converting Paise into Rupees

Do It Together 12365 paise 8700 paise

1. 12365 paise = Therefore, 12365 paise = ₹ . 2. 8700 paise = Therefore, 8700 paise =

The amount paid by Vishal = ₹171.50

Learning Outcomes

Students will be able to: identify halves, thirds and fourths of a whole and shade pictures to show them. find the fraction of a collection of objects and shade to show the fraction. identify fractions of a whole and write them in their fraction form. solve word problems on fractions of a whole and collection.

Alignment to NCF

C-1.2: Represents and compares commonly used fractions in daily life (such as ½, ¼) as parts of unit wholes, as locations on number lines, and as divisions of whole numbers

Let’s Recall

Recap to check if students know that a whole can be divided into equal parts and that a fraction is a part of a whole.

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

Vocabulary

fraction: equal parts of a whole or a collection numerator: number of parts chosen denominator: total number of parts

Teaching Aids

Rectangular strips of paper; Colour pencils; Crayons; Bangles; Sheet with circles drawn; 1 apple; Sheets with fraction circles drawn; Word problem cards

Chapter: Fractions

Parts of a Whole

Learning Outcomes

Imagine Maths Page 184

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

Teaching Aids

Rectangular strips of paper; Colour pencils

Activity

Discuss with the students that a full or complete object is called a whole. For example, a whole chocolate. When a whole is divided into equal parts, fractions are formed. Let’s say a chocolate is divided into 2 equal parts, each part is one-half.

Instruct the students to form groups of 4.

Distribute the strips of paper and colour pencils.

Instruct the students to work in their groups to fold the strips into halves, fourths and thirds. Then, they will shade to show the fractions one-half, one-fourth, one-third and two-thirds. Each student in the group should show 1 fraction. Then, in their notebooks, they will draw and shade the fractions they have shown. Ask questions like: How did you show the fractions? How did you find the fractions?

Extension Idea

Ask: A circle is divided into 2 equal parts, with 1 part shaded. Another circle is divided into 4 equal parts, with 2 parts shaded. What do you notice?

Say: We see that the shaded part in both circles is the same and that one-half is equal to two-fourths.

Fractions of a Collection

Learning Outcomes

Imagine Maths Page 187

Students will be able to find the fraction of a collection of objects and shade to show the fraction.

Teaching Aids

Crayons; Bangles; Sheet with circles drawn

Activity

Instruct the students to work in groups.

Distribute 8 crayons and 4 bangles to each group. Ask them to put the crayons inside the 4 bangles such that each bangle has an equal number of crayons. Once the groups are done, ask them the number of crayons inside each bangle. Discuss how to write it as a fraction, 1 4 of 8 = 2 crayons. Ask them to find 1 2 of 8 crayons. Distribute sheets with 12 circles each in 3 rows drawn on them.

Ask the students to colour half of the circles in the first row, one-third of the circles in the second row and one-fourth of the circles in the third row.

1 4 of 8 crayons = 2 crayons

Writing

Learning Outcomes

Students will be able to identify fractions of a whole and write them in their fraction form.

Teaching Aids

1 apple; Sheets with fraction circles drawn

Activity

Distribute the sheets with fraction circles drawn on them among the students. Show an apple cut into 4 pieces to the students. Take out 1 piece and discuss that it can be written as 1 4 in fractions, with the upper number showing the number of parts chosen and the lower number showing the total number of parts.

Ask them to write and show the same fraction by shading a part of the circle on the sheet. Cut the apple further into 8 pieces and show 3 parts. Ask the students to write and show the same fraction by shading the circle. Repeat the same activity by showing 4 parts and then 6 parts of the apple.

Extension Idea

Ask: A circle is divided into 11 equal parts, with 8 parts shaded. How many more parts need to be shaded to make the fraction 9 11 ?

Say: 1 more part needs to be shaded. So, 9 parts out of 11 parts will give us the fraction 9 11 .

Word Problems

Learning Outcomes

Students will be able to solve word problems on fractions of a whole and collection.

Teaching Aids

Word problem cards

Activity

Discuss with the students that, to solve word problems on fractions, they need to read the problem and identify what is given, what they need to find and how they can find it.

Instruct the students to work in groups. Distribute the word problem cards among the groups. Instruct them to read the problem, write what is given, what they need to find and how to find the answer. Ask them to solve the problem. Discuss the answer in the class.

Extension Idea

Ask: Create your own word problem where you need to find 1 3 of 45.

Maths Page 191

Meena has 12 pens. 1 4 of her pens are blue. How many pens are blue?

What is given?

What do we need to find? How do we find?

Say: There can be many such problems. One problem can be: Rohan has 45 bunches of flowers. He sold 1 3 of the bunches. How many bunches of flowers did he sell?

Answers

1. Parts of a Whole

Think and Tell

An object can be divided into any number of equal parts. When a pizza is divided into 5 equal parts, each part is termed as one-fifth.

Do It Together

Total number of equal parts = 4

Number of parts shaded = 3

3 out of 4 parts are shaded, hence 3 4 fraction is shaded.

Number of parts not shaded = 1

1 out of 4 parts is not shaded, hence 1 4 fraction is not shaded.

2. Fractions of a Collection

Do It Together

Total number of balls = 8

Collection of balls we want to colour = 1 4 of 8 balls = 2 balls

2 balls can be coloured as:

3. Writing a Fraction

Do It Together

a. Number of yellow balloons = 3

Total number of balloons = 7

Fraction of yellow balloons = Number of yellow balloons

Total number of balloons = 3 7

b. Number of green balloons = 4

Total number of balloons = 7

Fraction of green balloons = Number of green balloons

4. Word Problems

Do It Together

Total number of roses = 15

Fraction of roses in the vase = 1 3

Total number of balloons = 4 7

Number of roses put in the vase = 1 3 × 15 = 5

Data Handling

Learning Outcomes

Students will be able to: organise the given data in a table. draw a pictograph using a scale for the given data. read a pictograph and answer questions on it. draw a bar graph using the given data. read a bar graph and answer questions on it.

Alignment to NCF

C-5.2: Selects, creates, and uses appropriate graphical representations (e.g., pictographs, bar graphs, histograms, line graphs, and pie charts) of data to make interpretations

Let’s Recall

Recap to check if students know how to read data in a table. 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 scale: a number that shows the units used

Teaching Aids

Fruit stickers; Smiley stickers; Sheet with a pictograph drawn on it; Chart paper; Square cut-outs; Glue sticks; Sheets with bar graphs showing the favourite sports of some children

Chapter: Data Handling

Data

Tables

Learning Outcomes

Students will be able to organise the given data in a table.

Teaching Aids

Fruit stickers

Activity

Imagine Maths Page 199

Discuss with the students how to read the data given in a table. Instruct the students to work in 2 groups. Ask the students in Group 1 to collect data from the whole class on their favourite fruit (banana, apple, mango, orange, etc.). Ask Group 2 to make a table on the collected data about the favourite fruit of the whole class. Then, in their notebooks, they will make a table, using the fruit stickers for the respective fruit, and write the answers. Ask questions like: Which is the most popular fruit?

Extension Idea

Ask: In the data collected, if 4 students changed their favourite fruit from banana to apple, how many people would now like both bananas and apples?

Say: If 4 students change their favourite fruit from banana to apple, the number of students who now like bananas will be 4 less than before and the number of people who now like apples will be 4 more than before.

Drawing a Pictograph

Learning Outcomes

Students will be able to draw a pictograph using a scale for the given data.

Teaching Aids

Smiley stickers Activity

Imagine Maths Page 202

Discuss with the students how data given as pictures is easier to understand. A pictograph helps us to show data using pictures or symbols. Instruct the students to work in groups. Distribute the smiley stickers and chart paper. Instruct the students to use the table created in the previous lesson to create a pictograph based on it. Ask them to use the key as 1 sticker = 2 students. Ask questions like: How many symbols will you draw for an odd number of students?

Extension Idea

Ask: Ramya drew 3 and a half pictures to show the number of students who went to art class. If the key used in the pictograph is 1 picture = 10 students, what is the total number of students who went to art class?

Say: 1 picture = 10 students, 3 and a half pictures = 30 + 5 = 35 students. So, 35 students went to art class.

Reading a Pictograph

Learning Outcomes

Students will be able to read a pictograph and answer questions to it.

Teaching Aids

Sheet with a pictograph drawn on it

Activity

Begin by drawing the given pictograph on the board. Discuss with the students that the key shows 1 picture = 5 students. Tell them that the art club shows 4 pictures, and since 1 picture shows 5 students, the art club will have 4 × 5 = 20 students.

Now, instruct the students to work in groups.

Distribute the same pictograph among the students by changing the key to 1 picture = 8 students. Instruct the students to read the pictograph and answer the questions.

Activity Club Number of Children

Sculpture Literary

Ask questions like: How many more students are there in the dance club than the sculpture club? What is the total number of students in the activity club? What fraction of students are there in the art club? Then, they will write their answers in their notebooks.

Drawing a Bar Graph

Learning Outcomes

Students will be able to draw a bar graph using the given data.

Teaching Aids

Chart paper; Square cut-outs; Glue sticks

Activity

Begin with a brief review of what a bar graph is. Discuss the x and y axes, their labelling and how to draw bars in a bar graph. Draw the table, as shown, on the board.

Name Priya Amit Arun Suhani

Number of marbles 7 9 5 8

Instruct the students to work in groups.

Distribute the chart paper, square cut-outs and glue sticks to each group. Ask the groups to make a bar graph on the chart paper by drawing the x-axis and y-axis and labelling them. Now, ask them to use the square cut-outs and stick as many square cut-outs as the number of marbles given in the table to make a tower.

Extension Idea

Ask: How many cut-outs will you stick for Suhani, if the scale is 1 division = 2 marbles?

Say: Suhani has 8 marbles and 1 division = 2 marbles. So, we will stick 4 cut-outs for Suhani.

Learning Outcomes

Students will be able to read a bar graph and answer questions on it.

Teaching Aids

Sheets with bar graphs showing the favourite sports of some children

Activity

Discuss with the students that to read data on a bar graph, we first find the bar for the category asked on the x-axis. Then, we look at the height of the bar and match it to the number on the y-axis. The corresponding number gives us the answer.

Instruct the students to work in groups. Distribute sheets with a bar graph drawn among the groups.

Instruct the students to read the bar graph and answer these questions: Which sport is the most popular? How many children like basketball? What is the total number of students surveyed?

Soccer Basketball Tennis Hockey

Number of Students Sport

Favourite Sport

1. Data Tables

Do It Together

Sport

Answers

2 Who purchased the most chocolates? How many? The number of symbols for is the most. The number of chocolates purchased =

4. Drawing a Bar Graph Do It Together

2. Drawing a Pictograph

Think and Tell

It is important to select a key to find the number of pictures to be drawn for each unit of data.

Do It Together

Section Number of Students

Section A

Section B

Section C

Section D

3. Reading a Pictograph

Think and Tell

If we change the key to 1 = 1 cm, we will have to draw 20 pictures for June, 25 pictures for July, 15 pictures for August and 10 pictures for September. This would make the pictograph difficult to draw and read.

Do It Together

1 How many chocolates did Aahan purchase?

Number of symbols of chocolates for Aahan = 2 and

5. Interpreting a Bar Graph Do It Together

1. Number of hours spent on Maths homework = 9

Number of hours spent on English homework = 6 Difference in the hours spent = 9 – 6 = 3 hours.

2. English < Hindi < Science < Maths

Key: chocolates

Thus, Aahan purchased chocolates.

Pencils

Solutions

Chapter 1

Let’s Warm-up

1. 893: 90 2. 349: 9 3. 864: 800

4. 501: 00 5. 123: 3

Do It Yourself 1A

1. a.

2 thousands 3 hundreds 5 tens 6 ones 2356

b. 4 thousands 1 hundreds 1 tens 1 ones 4111

3 thousands 3 hundreds 4 tens 4 ones 3344

d. 5 thousands 4 hundreds 3 tens 1 ones 5431

2. a. Count the number of beads on each rod.

4 beads at the thousands place

7 beads at the hundreds place

4 beads at the tens place

6 beads at the ones place

So, the number is 4746.

b. Count the number of beads on each rod.

5 beads at the thousands place

6 beads at the hundreds place

2 beads at the tens place

5 beads at the ones place

So, the number is 5625.

c. Count the number of beads on each rod.

5 beads at the thousands place

2 beads at the hundreds place

4 beads at the tens place

1 beads at the ones place

So, the number is 5241.

3. a. 1932 b. 5358

3041

4. a. 1532 - One thousand five hundred thirty-two

b. 3156 - Three thousand one hundred fifty-six

c. 4811 - Four thousand eight hundred eleven

d. 6518 - Six thousand five hundred eighteen

e. 7294 - Seven thousand two hundred ninety-four

f. 8043 - Eight thousand forty-three

5. a. 3215 - Place value = 200; Face value = 2

b. 5362 - Place value = 5000; Face value = 5

c. 7314 - Place value = 4; Face value = 4

d. 6892 - Place value = 90; Face value = 9

e. 8113 - Place value = 8000; Face value = 8

f. 9686 - Place value = 9000; Face value = 9

6. a. Three thousand two hundred forty-five = 3245

b. Five thousand three hundred eighty-six = 5386

c. Seven thousand forty = 7040

d. Six thousand eight = 6008

7. a. 2148 = 2000 + 100 + 40 + 8

b. 4036 = 4000 + 000 + 30 + 6

c. 6105 = 6000 + 100 + 00 + 5

d. 7203 = 7000 + 200 + 00 + 3

e. 8200 = 8000 + 200 + 00 + 0

f. 6566 = 6000 + 500 + 60 + 6

8. Length of NH44 = 4412 km

It can be written in words as four thousand one hundred twelve.

Challenge

1. Value of the thousands place = 1000

The hundreds place has the digit of the largest value - 9

Value of the hundreds place = 900

The tens place digit is 2 less than the hundreds place digit. 9 − 2 = 7. So, value of the tens place = 70

The sum of all the digits is 20. We get

1 + 9 + 7 + ____ = 20

17 + ___ = 20

___ = 20 − 17

___ = 3

= 1 + 9 + 7 + 3 = 20

The year is 1973.

Do It Yourself 1B

1. The numbers ending with 1, 3, 5, 7 and 9 are odd numbers.

Odd numbers: c. 83, d. 91, e. 63, g. 149

The numbers ending with 0, 2, 4, 6 and 8 are even numbers.

Even numbers: a. 36, b. 78, f. 164, h. 348

2. a. 614 < 1700

614 is a 3-digit number and 1700 is a 4-digit number

A 4-digit number is greater than a 3-digit number.

So, 614 < 1700

b. 5092 < 7320

Compare digits at the thousands place 5 < 7.

So, 5092 < 7320

c. 2184 < 2357

Compare digits at the thousands place 2 = 2. Since the digits are the same, compare the digits at the hundreds place.

The digits at the hundreds place, 1 < 3.

So, 2184 < 2357

d. 5720 > 5265

Compare digits at thousands place, 5 = 5. Since the digits are the same, compare the digits at the hundreds place.

The digits at the hundreds place, 7 > 2.

So, 5720 > 5265

e. 4126 < 4510

Compare digits at the thousands place, 4 = 4. Since the digits are the same, compare the digits at the hundreds place.

The digits at the hundreds place, 1 < 5.

So, 4126 < 4510

f. 5271 > 5261

Compare digits at thousands place, 5 = 5. Since the digits are the same, compare the digits at the hundreds place.

The digits at the hundreds place, 2 = 2. Since the digits are the same, compare the digits at the tens place.

The digits at tens place, 7 > 6.

So, 5271 > 5261

3. Ascending order

a. Compare the digits at the thousands place, 1 < 4 < 7. Since the digits in the thousands place of 7430 and 7935 are the same, compare the digits at the hundreds place 4 < 9.

So, 1765 < 4390 < 7430 < 7935 1765, 4390, 7430, 7935

b. A 3-digit number is less than a 4-digit number 773 is the smallest number

Compare the digits in the thousands place of 2860, 7880 and 9573, 2 < 7 < 9.

So, 773 < 2860 < 7880 < 9573 773, 2860, 7880, 9573

c. A 3-digit number is less than a 4-digit number.

392 is the smallest number

Compare the thousands digit of 3067, 4853 and 7943, 3 < 4 < 7.

So, 392 < 3067 < 4853 < 7943

392, 3067, 4853, 7943

d. A 3-digit number is less than a 4-digit number 157 is the smallest number.

Compare the digits at thousand place of numbers 6583, 8546 and 9404, 6 < 8 < 9.

So, 157 < 6583 < 8546 < 9404 157, 6583, 8546, 9404

Descending order

a. The digits at the thousands place of 7935 and 7430 are the same, compare the digits at the hundreds place: 9 > 4. 7935 > 7430

The digits in the thousands place of 4390 is greater than the digit at the thousands place of 1765.

4390 > 1765

So, 7935 > 7430 > 4390 > 1765

7935, 7430, 4390, 1765

b. Compare the digits in the thousands place of the given numbers—9573, 7880, 2860, 773

9 > 7 > 2

So, 9573 > 7880 > 2860 > 773 9573, 7880, 2860, 773

c. Compare the digits in the thousands place of the given numbers—7943, 4853, 3067 and 392

7 > 4 > 3

So, 7943 > 4853 > 3067 > 392 7943, 4853, 3067, 392

d. Compare the digits in the thousands place of the given numbers—9404, 8546, 6583, 157

9 > 8 > 6

9404 > 8546 > 6583 > 157 9404, 8546, 6583, 157

4. To form the smallest number, the digits from the thousands place to the ones place should be in ascending order.

Smallest:

a. 2 < 4 < 6 < 7, smallest number = 2467

b. 1 < 3 < 6 < 7, smallest number = 1367

c. 0 < 1 < 2 < 5, a 4-digit number cannot start with 0. Smallest number = 1025

d. 0 < 5 < 6 < 8, 4-digit number cannot start with 0. Smallest number = 5068

e. 0 < 2 < 8 < 9, a 4-digit number cannot start with 0. Smallest number = 2089

f. 0 < 1 < 5 <7, a 4-digit number cannot start with 0.

Smallest number = 1057

g. 2 < 5 < 7 < 8, smallest number = 2578

h. 2 < 4 < 8 < 9, smallest number = 2489

To form the greatest number, the digits from the thousands place to the ones place should be in descending order.

Greatest:

a. 7 < 6 > 4 > 2. Greatest number = 7642

b. 7 > 6 > 3 > 1. Greatest number = 7631

c. 5 > 2 > 1 > 0. Greatest number = 5210

d. 8 > 6 > 5 > 0. Greatest number = 8650

e. 9 > 8 > 2 > 0. Greatest number = 9820

f. 7 > 5 > 1 > 0. Greatest number = 7510

g. 8 > 7 > 5 > 2. Greatest number = 8752

h. 9 > 8 > 4 > 2. Greatest number = 9842

5. A 9999

B 1000

C 9876

D 1023

Smallest 4-digit number

Greatest 4-digit number

Smallest 4-digit number using different digits

Greatest 4-digit number using different digits

6. Length of river Nile = 6650 km

Length of river Amazon = 6575 km

The digit at the hundreds place of 6650 is greater than the digit at hundreds place of 6575. (6 > 5 )

So, the length of river Nile is greater than river Amazon.

7. The digits are 7, 3, 2 and 5.

To form the largest number, the digits from the thousands place to the ones place should be in descending order

7 > 5 > 3 > 2.

The largest number possible using the same digits is 7532.

Challenge

1. The largest number written by Anahita can be 9999. The largest number written by Hetal can be 9876. Since digits at the thousands place of 9999 and 9876 are the same, compare the digits at the hundreds place: 9 > 8. 9999 > 9876

So, the 4-digit number written by Anahita is the largest number.

Do It Yourself 1C

1. a. There are 38 students in my class. 38 can be rounded off to 40.

b. There are 73 trees in a park. 73 can be rounded off to 70.

c. 44 is in between 40 and 50 but is closer to 40.

d. 123 is in between 120 and 130 but is closer to 120

2. a. 32 is less than 35. So, 32 is rounded off to 30.

b. 67 is greater than 65. So, 67 is rounded off to 70.

c. 81 is less than 85. So, 81 is rounded off to 80.

d. 137 is greater than 135. So, 137 is rounded off to 140.

e. 256 is greater than 255. So, 256 is rounded off to 260.

f. 321 is less than 325. So, 321 is rounded off to 320.

g. 442 is less than 445. So, 442 is rounded off to 440.

h. 547 is greater than 545. So, 547 is rounded off to 550.

4. Rina and Sia served food to 632 people. 632 is less than 635. So, 632 can be rounded off to 630. Hence, Rina and Sia served about 630 people.

5. Number of trains in Delhi Metro = 268 trains

Number of stations = 256 stations

268 trains rounded off to the nearest tens = 270 trains

256 stations rounded off to the nearest tens = 260 stations

Challenge

1. Number of digits in the required number = 3

Options we have = 718, 752 and 648

718 is greater than 715. So,718 is rounded off to 720. 752 is less than 755. So, 752 is rounded off to 750. 648 is greater than 645. So, 648 is rounded off to 650. So, numbers which can be round down is 752. Number which has odd tens digit = 752 Hence, the required number is 752. Thus option b is correct.

Chapter Checkup

1. a. One thousand four hundred forty-two = 1442

b. Three thousand eight hundred fifty-seven = 3857

c. Four thousand two hundred eight = 4208

d. Five thousand three hundred nine = 5309

e. Six thousand forty-five = 6045

f. Five thousand twenty-eight = 5028

2. a. 2471 = Two thousand four hundred seventy-one

b. 4205 = Four thousand two hundred five

c. 5374 = Five thousand three hundred seventy-four

d. 7308 = Seven thousand three hundred eight

e. 7564 = Seven thousand five hundred sixty-four

f. 8421 = Eight thousand four hundred twenty-one

3. a. 1056, Place value = 50

b. 3814, Place value = 10

c. 5807, Place value = 800

d. 8379, Place value = 8000

e. 7291, Place value = 7000

f. 9092, Place value = 90

4. a. 2000 + 100 + 80 + 5 = 2185

b. 3000 + 400 + 70 + 1 = 3471

c. 8000 + 80 + 9 = 8089

d. 5000 + 700 + 20 + 5 = 5725

e. 4000 + 600 + 0 = 4600

f. 6000 + 0 + 70 + 0 = 6070

5. a. 1382 = 1000 + 300 + 80 + 2

b. 3641 = 3000 + 600 + 40 + 1

c. 5327 = 5000 + 300 + 20 + 7

d. 6484 = 6000 + 400 + 80 + 4

e. 7500 = 7000 + 500 + 00 + 0

f. 9032 = 9000 + 000 + 30 + 2

6. To form the smallest number, the digits of the number are arranged in ascending order from the thousands place to the ones place.

Smallest number:

a. 0 < 1 < 2 < 3, 4-digit number cannot start with 0. Smallest number = 1023

b. 0 < 5 < 6 < 8, 4-digit number cannot start with 0. Smallest number = 5068

c. 2 < 4 < 5 < 8. Smallest number = 2458

d. 0 < 1 < 4 < 7, 4-digit number cannot start with 0. Smallest number = 1047

e. 2 < 3 < 4 < 7. Smallest number = 2347

f. 0 < 3 < 6 < 8, 4-digit number cannot start with 0. Smallest number = 3068

To form the greatest number, the digits of the number are arranged in descending order from thousands place to ones place.

Greatest number:

a. 3 > 2 > 1 > 0, Greatest number = 3210

b. 8 > 6 > 5 > 0, Greatest number = 8650

c. 8 > 5 > 4 > 2, Greatest number = 8542

d. 7 > 4 > 1 > 0, Greatest number = 7410

e. 7 > 4 > 3 > 2, Greatest number = 7432

f. 8 > 6 > 3 > 0, Greatest number = 8630

7. a. 860

3184

Th H T O

b. 4072 Th H T

d. 4856

Th H T O

e. 9030

Th H T O

f. 7465

Th H T O

8. Ascending order

a. Compare the digits in the hundreds place of the 3-digit numbers 565 and 730, 5 < 7.

Next, compare the digits in the thousands place of the 4-digit numbers 2390 and 8935, 2 < 8.

So, 565 < 730 < 2390 < 8935 565, 730, 2390, 8935

b. Compare the digits at the hundreds place of the 3-digit numbers 773 and 830, 7 < 8.

Next compare the digits in the thousands place of the 4-digit numbers 1860 and 7573, 1 < 7.

So, 773 < 880 < 1860 < 7573 773, 880, 1860, 7573

c. A 3-digit number is less than a 4-digit number

Compare the digits in the thousands place of the numbers 5853, 6943 and 7081, 5 < 6 < 7

So, 792 < 5853 < 6943 < 7081 792, 5853, 6943, 7081

d. A 3-digit number is less than a 4-digit number.

Compare the digits in the thousands place of the numbers 5683, 7846, 8704, 5 < 7 < 8

So, 657 < 5683 < 7846 < 8704 657, 5683, 7846, 8704

e. Compare the digits in the thousands place of the numbers 2 < 4 < 8.

The digits in the thousands place and the hundreds place of 8734 and 8753 are the same. Compare the tens digit of the number, 3 < 5.

So, 2265 < 4867 < 8734 < 8753 2265, 4867, 8734, 8753

f. Compare the digits in the thousands place of the numbers 5436, 7354, 7428, 8754, 5 < 7 < 8.

The digits in the thousands place of numbers 7354 and 7428 are same, compare the hundreds place 3 < 4. So, 5436 < 7354 < 7428 < 8754 5436, 7354, 7428, 8754

Descending order

a. Compare the digits in the thousands place of numbers 8935, 2390, 8 > 2.

Compare the digits in the hundreds place of 730 and 565, 7 > 5.

So, 8935 > 2390 > 730 > 565 8935, 2390, 730, 565

b. Compare the digits at the thousands place of numbers 7573 and 1860, 7 > 1.

Compare the digits at the hundreds place of numbers 880 and 773, 8 > 7.

So, 7573 > 1860 > 880 > 773

7573, 1860, 880, 773

c. Compare the digits at the thousands place of the number 7081, 6943 and 5853, 7 > 6 > 5.

A 4-digit number is greater than a 3-digit number.

So, 7081 > 6943 > 5853 > 792 7081, 6943, 5853, 792

d. Compare the digits at thousands place of numbers 8704, 7846 and 5683, 8 > 7 > 5.

A 4-digit number is greater than a 3-digit number.

So, 8704 > 7846 > 5683 > 657 8704, 7846, 5683, 657

e. Compare the thousands digit of the numbers, 8 > 4 > 2. The digit at the thousands and hundreds place of the numbers 8753 and 8734 are the same.

Compare the digits at tens place 5 > 3.

So, 8753 > 8734 > 4867 > 2265

8753, 8734, 4867, 2265

f. Compare the digits at the thousands place of numbers, 8 > 7 > 5.

The digits at thousands place of the number 7428 and 7354 are the same, compare the digit at hundreds place 4 > 3.

So, 8754 > 7428 > 7354 > 5436

8754, 7428, 7354, 5436

9. a. 64 is less than 65. So, 64 is rounded off to 60.

b. 97 is greater than 95. So, 97 is rounded off to 100.

c. 393 is less than 395. So, 393 is rounded off to 390.

d. 421 is less than 425. So, 421 is rounded off to 420.

10. Number of types of hornbills in the world = 62

62 is less than 65. So, 62 is rounded off to 60.

Rounded-off number = 60

So, there are about 60 types of hornbills in the world.

11. Answer may vary. Sample answer:

Anna saved ₹5500 and Divya saved ₹4510. Who saved more money?

Challenge

1. a. Number of legs a spider has = 8 (thousands place)

b. Number of wheels in a car = 4 (hundreds place)

c. Number of wings a bird has = 2 (tens place)

d. Number of faces in a cube = 6 (ones place)

The number is: 8426

Number name: Eight thousand four hundred twenty-six Expanded form: 8000 + 400 + 20 + 6

2. 43 is smallest of all the given numbers. So, 43 will come on the top circle.

905 is the greatest among all the given numbers. So, 905 will come on bottom circle.

284 and 168 are greater than 43 and less than 905. So, they will come on the circles on the right and left side.

Case Study

1. Mount Everest—8848 m

K2—8611 m

Annapurna—8041 m

Mount Kailash—6638 m

Compare the digits at the thousands place of numbers, 8 > 6 and the digits in the thousands place of 8848, 8041 and 8611 is the same. So, compare the digits at the hundreds place 0 < 6 < 8.

So, Mount Everest is the highest peak. Thus, option c is the correct answer.

2. Mount Everest—8848 m

K2—8611 m

Annapurna—8041 m

Mount Kailash—6638 m

Kedarnath—3583 m

Compare the digits in thousands place of numbers 3583, 6638, 8041, 8611, 8848, 3 < 6 < 8.

The digit in the thousands place are the same in 8848, 8611, 8041. Compare the digits in hundreds place—0 < 6 < 8. So, 3583 < 6638 < 8041 < 8611 < 8848

Mountain peaks in ascending order is—Kedarnath, Mount Kailash, Annapurna, K2, Mount Everest

3. We see that Kedarnath has the least mountain peak. Kedarnath – 3583 m = 3000 m + 500 m + 80 m+ 3 m

In words: Three thousand five-hundred eighty-three

4. Answers may vary

Chapter

2 Let’s Warm-up

Do It Yourself 2A

1. a. 36 + 1 = 37

37 > 35

So, 36 + 1 > 35

b. 87 + 0 = 87

87 < 98

So, 87 + 0 < 98

c. 789 + 5 = 794

5 + 789 = 794

789 + 5 = 5 + 789

d. 6 + 4 = 10

4 +

4. Students can expand any one number.

1 7 → 10 + 7

9 → 50 + 9

9 ← 80 + 9 e. 5 7 → 50 + 7 2 2 → 22

9 ← 72 + 7

6 3 → 60 + 3

5 → 25 8 8 ← 85 + 3

5. There are 3 tens and 7 ones in 37.

Jump 3 tens from 41 which is 71. From 71 jump 7 ones to the right, which is 78.

6. Number of butterfly species = 48

Number of species added to the park = 30

Total species in Bannerghatta National Park = 48 + 30 = 78

4 8 → 40 + 8

3 0 → 30

7 8 ← 70 + 8

So, there are 78 species in Bannerghatta National Park.

Challenge

1. No, it is not solved correctly.

Smallest number, using the digits 3 and 4 = 34

Greatest number, using the digits 3 and 4 = 43

We should add 43 + 34 and not 43 + 43.

There are 3 tens and 4 ones in 34.

We should jump 3 tens below from 43, we will reach 73. We should jump 4 ones from 73, which is 77.

Do It Yourself 2B

1. a. H T O

4 5 6 + 2 3 2 6 8 8 b. H T O 7 4 1 + 2 5 6 9 9 7

c. H T O 1 4 7 + 5 4 1 6 8 8

2. a. True, the sum of 144 and 215 is 359.

b. False, the sum of 121 and 212 is 333.

c. False, the sum of 541 and 145 is 686.

d. True, the sum of 614 and 314 is 928.

3. H T O

3 4 7 + 3 2 1 6 6 8

4. a. H T O 1 1 6 1 6 + 1 8 4 8 0 0 b. H T O 1

c. Th H T O

3 2 1 4 + 6 1 4 5 9 3 5 9 d. Th H T O 7 1 5 1 + 2 1 2 6 9 2 7 7

6. a. To find 1234 more than 5145, add 1234 and 5145.

Th H T O

5 1 4 5

+ 1 2 3 4

6 3 7 9 1234 more than 5145 is 6379.

b. To find 2174 more than 1211, add 2174 and 1211.

Th H T O

1 2 1 1

+ 2 1 7 4

3 3 8 5 2174 more than 1211 is 3385.

7. Amount spent on the raincoat = ₹456

Amount spent on the umbrella = ₹235

Total amount spent by Jaspal = ₹456 + ₹235 = ₹691

8. 209 can be drawn as: 108 can be shown as:

2 hundreds + 1 hundreds = 3 hundreds + =

9 ones and 8 ones = 17 ones = 1 tens and 7 ones + = =

So the sum is 209 + 108 = 317

9. Number of oranges in the first carton = 1245

Number of oranges in the second carton = 2311

Number of oranges in the third carton = 1421

Total number of oranges = 1245 + 2311 + 1421 = 4977

Thus, the farmer packed 4977 oranges in total. Number of oranges as in the thousands place (4) are shown as:

Challenge

1. a. The two largest numbers will have the largest sum. Compare the hundreds digit of the numbers, 6 > 5 > 2.

So, 614 > 539 > 286 > 239

539 and 614 are the two largest numbers.

So, let us add 539 and 614.

539 and 614 will give a 4-digit sum.

539 + 614 = 1153

Th H T O 1

5 3 9 + 6 1 4 1 1 5 3

b. Add the digits at the ones place and check if the answer is 10.

9 + 6 = 15 ≠ 10

9 + 4 = 13 ≠ 10

9 + 9 = 18 ≠ 10

6 + 4 = 10

So, add 286 and 614

286 + 614 = 900 H T O 1 1

2 8 6 + 6 1 4

9 0 0

c. Add the digits at the ones place and check which two numbers have 5 at the ones place.

9 + 6 = 15

So, add 239 and 286 239 + 286 = 525

1 2 3 9 + 2 8 6 5 2 5

Do It Yourself 2C

1. a. 17 is greater than 15. So, 17 rounded off to the nearest 10 = 20

34 is less than 15. So, 34 rounded off to the nearest 10 = 30

Estimated sum = 20 + 30 = 50

b. 84 is less than 85. So, 84 rounded off to the nearest 10 = 80 17 is greater than 15. So, 17 rounded off to the nearest 10 = 20

Estimated sum = 80 + 20 = 100

c. 15 is equal to 15. So, 15 rounded off to the nearest 10 = 20

54 is less than 55. So, 54 rounded off to the nearest 10 = 50

Estimated sum = 20 + 50 = 70

d. 47 is greater than 45. So, 47 rounded off to the nearest 10 = 50

41 is less than 45. So, 41 rounded off to the nearest 10 = 40

Estimated sum = 50 + 40 = 90

2. a. 31 is less than 35. So, 31 rounded off to the nearest 10 = 30

36 is greater than 35. So, 36 rounded off to the nearest 10 = 40

Estimated sum = 30 + 40 = 70

Actual answer = 67

Thus, the estimated answer is close to the actual answer.

b. 58 is greater than 55. So, 58 rounded off to the nearest 10 = 60

23 is less than 25. So, 23 rounded off to the nearest 10 = 20

Estimated sum = 60 + 20 = 80

Actual answer = 81

Thus, the estimated answer is close to the actual answer.

c. 12 is less than 15. So, 12 rounded off to the nearest 10 = 10

17 is greater than 15. So, 17 rounded off to the nearest 10 = 20

Estimated sum = 10 + 20 = 30

Actual answer = 29

Thus, the estimated answer is close to the actual answer

d. 21 is less than 25. So, 21 rounded off to the nearest 10 = 20

47 is greater than 45. So, 47 rounded off to the nearest 10 = 50

Estimated sum = 20 + 50 = 70

Actual answer = 68

Thus, the estimated answer is close to the actual answer

3. Number of cookies made = 43

43 is less than 45. So, rounded-down number of cookies = 40

Number of puff pastries = 66

66 is greater than 65. So, rounded-up number of puff pastries = 70

Estimated number of items = 40 + 70 = 110

Thus, Ria made a total of 110 food items.

4. Number of star fishes found by Nisha = 78

78 is greater than 75. So, rounded-up number of fishes = 80

Number of star fishes found by Rohit = 52

52 is less than 55. So, rounded-down number of star fishes = 50

Total number star fishes found by Nisha and Rohit = 80 + 50 = 130

Thus, Nisha and Rohit found 130 star fishes in total.

5. a. 48 is greater than 45. So, 48 rounded off to the nearest 10 = 50

32 is less than 35. So, 32 rounded off to the nearest 10 = 30

Estimated sum = 50 + 30 = 80

The actual sum of the numbers = 80

Thus, the answer is the same in both cases.

b. 35 is equal to 35. So, 35 rounded off to the nearest 10 = 40

57 is greater than 55. So, 57 rounded off to the nearest 10 = 60

Estimated sum = 40 + 60 = 100

The actual sum of the numbers = 92

Rounding off the actual sum to the nearest 10 = 90

Thus, the answer is not the same in both cases.

c. 52 is greater than 55. So, 52 rounded off to the nearest 10 = 50

19 is greater than 15. So, 19 rounded off to the nearest 10 = 20

Estimated sum = 50 + 20 = 70

The actual sum of the numbers = 71

Rounding off the actual sum to the nearest 10 = 70

Thus, the answer is the same in both cases.

d. 11 is less than 15. So, 11 rounded off to the nearest 10 = 10

Estimated sum = 10 + 10 = 20

The actual sum of the numbers: 21

21 is less than 25. So, rounding down the actual sum to the nearest 10 = 20

Thus, the answer is the same in both cases.

Challenge

1. Score in round 1 = 35

35 is equal to 35. So, rounded-up score in round 1 = 40

Score in round = 48

48 is greater than 45. So, rounded up score in round 2 = 50

Sum of scores in round 1 + round 2 = 40 + 50 = 90

Total estimated score = 170

Rounded-off total in round 3 should be 80 to get 170 points. The score of round 3 should be between 75 and 84 to get 80 points.

Do It Yourself 2D

1. Number of toys sold in the month of January = 134

Number of toys sold in the month of February = 217

Total toys sold in January and February = 134 + 217 = 351

Thus, the total number of toys sold in both months are 351.

2. The cost of a bicycle = ₹4231

The cost of a music system = ₹4566

The total cost of both things = 4231 + 4566 = 8797

Thus, the total cost of both the bicycle and music system is ₹8797.

3. Number of seeds the first packet contains: 28

Number of seeds the second packet contains: 35

Number of seeds in total: 28 + 35 = 63

Thus, the total seeds are 63.

4. Number of students enrolled in Grade 2 = 218 students

Number of students enrolled in Grade 3 = 317 students

Number of students enrolled in Grade 4 = 165 students

Total number of students enrolled = 218 + 317 + 165 = 700 students

Thus, 700 students have enrolled altogether.

5. Length of Sankesula Barrage = 1300 m

Length of Nagarjuna Sagar Dam = 1300 + 250 = 1550 m

Thus, the length of Nagarjuna Sagar Dam is 1550 m.

6. a. Money spent on the hair dryer = ₹3015

Money spent on the quilt = ₹2150

The total amount of money spent on both things = ₹3015 + ₹2150 = ₹5165

Thus, ₹5165 was spent in total.

b. Money spent on a bottle of perfume = ₹900

Money spent on a bag = ₹220

Total money spent on both of the things = ₹900 + ₹220 = ₹1120

Thus, ₹1120 was spent in total.

c. Money spent by Mr Saxena if he bought all the 4 items = ₹5165 + ₹1120 = ₹6285

Thus, ₹6285 was spent in total.

7. Answer may vary. Sample answer:

Uma has collected 726 red roses and 492 yellow roses. How many roses has Uma collected in all?

Challenge

1. Number of beads with Nisha = 3 green + 4 red + 3 blue = 3 hundreds + 4 tens + 3 ones = 343

Number of beads with Ria = 5 green + 6 red + 2 blue = 5 hundreds + 6 tens + 2 blue = 562

Total number = 343 + 562

The beads will make the number 905.

Chapter Checkup

1. a. 45 + 1 = 46

Any number added to 1, the sum is the successor

b. 14 + 0 = 14

Any number added to 0, the sum is number itself.

c. 87 + 48 = 48 + 87

Number can be added in any order, sum will be the same.

d. 5 + 3 = 3 + 5

Number can be added in any order, sum will be the same.

e. 1 + 83 = 84

Any number added to 1, the sum is the successor.

f. 0 + 18 = 18

Any number added to 0, the sum is the number itself.

a. 84 + 8

84 is less than 85. So, 84 rounded off to the nearest 10 = 80

8 is greater than 5. So, 8 rounded off to the nearest 10 = 10

Estimated sum = 80 + 10 = 90

b. 34 + 17

34 is less than 35. So, 34 rounded off to the nearest 10 = 30

17 is greater than 15. So, 17 rounded off to the nearest 10 = 20

Estimated sum = 30 + 20 = 50

c. 25 + 52

25 is equal to 25. So, 25 rounded off to the next 10 = 30

52 is less than 55. So, 52 rounded off to the nearest 10 = 50

Estimated sum = 30 + 50 = 80

5. a. 56 + 11 = 67

67 is greater than 65. So, rounding off the result to the nearest 10 = 70

b. 23 + 49 = 72

72 is less than 75. So, rounding off the result to the nearest 10 = 70

c. 45 + 36 = 81

81 is less than 85. So, rounding off the result to the nearest 10 = 80

7. a. 78 more than 361 = 361 + 78 = 439 b. 145 more than 456 = 456 + 145 = 601

c. 847 more than 254

Number of tazos collected by Ishan in 2 weeks = 37

Total number of tazos with Ishan = 65 + 37 = 102

carry 1 1 6 5 + 3 7

1 0 2

Thus, Ishan has 102 tazos.

11. Answer may vary. Sample answer:

Akil has made 1230 candles, and Anu has made 528 more candles than Akil. How many candles have they made in total?

Challenge

1. 100 + 70 + 130 = 300

130 + 50 + 120 = 300

100 + 80 + 120 = 300

H T O 1 1 1 2 5 4 + 8 4 7 1 1 0 1

e. 748 more than 369 = 369 + 748 = 1117

H T O 1 1 1 3 6 9 + 7 4 8 1 1 1 7

2 5

6 = 254 + 847 = 1101

f. 415 more than 871 = 871 + 415 = 1286

8. Number of mathematics books = 1025

Number of science books = 987

Number of Hindi books = 689

The total number of books in the library = 1025 + 987 + 689 = 2701

Thus, the total number of books in the library is 2701.

9. a. Boys in the Carnival = 1023

Girls in the Carnival = 1988

Total boys and girls in the Carnival = 1023 + 1988 = 3011

Thus, a total number of 3011 boys and girls went to the Carnival.

b. Men in the Carnival = 1547

Women in the Carnival = 2048

Total men and women in the Carnival = 1547 + 2048 = 3595

Thus, a total number of 3595 men and women went to the Carnival.

c. Boys in the Carnival = 1023

Girls in the Carnival = 1988

Men in the Carnival = 1547

Women in the Carnival = 2048

Total number of people in the Carnival = 1023 + 1988 + 1547 + 2048 = 6606

Thus, a total of 6606 people went to the carnival.

10. Number of tazos with Vishwa = 47

Number of tazos Ishan had 2 weeks earlier = 47 + 18 = 65

carry 1 4 7 + 1 8

6 5

2. Estimated sum of 2 numbers = 30

The first number = 23

23 is less than 25. So, 23 rounded off to nearest 10 is 20. The second rounded-off number = 30 − 20 = 10

The 1-digit numbers that can be rounded off to 10 are the digits which are equal to 5 or greater than 5. These are 5, 6, 7, 8 and 9.

Case Study

1. Number of leopards in Bihar = 32

32 is less than 35. So, 32 rounded off gives 30.

Number of leopards in Goa = 71

71 is less than 75. So, 71 rounded off gives 70.

So, the estimated number of leopards in Bihar and Goa = 30 + 70 = 100

Hence, option c is correct.

2. Number of leopards in Kerela = 472

Number of leopards in Andhra Pradesh = 343

Total leopards in Kerela and Andhra Pradesh = 472 + 343 = 815

Thus, there are 815 leopards in total.

3. Number of leopards in Chhattisgarh = 846

Total leopards in Kerela and Andhra Pradesh = 815

Since the digits in the hundreds place of 846 and 815 are the same, compare the digits at the tens place. 4 > 1, so 846 > 815.

The total leopards in Kerela and Andhra Pradesh are less than the number of leopards in Chhattisgarh.

4. Answers may vary.

Chapter 3

Let’s Warm-up

Do It Yourself 3A

1. a. True, a number subtracted from 0 is the number itself.

b. True, a number subtracted from itself is zero.

c. False, a number subtracted from 0 is the number itself.

d. True, 1 subtracted from a number is the predecessor.

e. False, a number subtracted from itself is zero.

f. False, a number subtracted from 0 is the number itself.

2. a. 21 − 13

Adding the jumps

7 + 1 = 8

21 − 13 = 8

b. 45 − 36

Adding the jumps

4 + 5 = 9

45 − 36 = 9

c. 56 − 27

Adding the jumps

3 + 10 + 10 + 6 = 29

56 − 27 = 29

3. a. 41 − 17

Breaking the smaller number into tens and ones:

Subtracting the tens from the bigger number,

41 − 10 = 31

Subtracting the ones from 31,

31 − 7 = 24

41 − 17 = 24

b. 63 − 26

Breaking the smaller number into tens and ones:

Subtracting the tens from the bigger number,

63 − 20 = 43

Subtracting the ones from 43, 43 − 6 = 37

63 − 26 = 37

c. 71 − 24

Breaking the smaller number into tens and ones:

Subtracting the tens from the bigger number,

71 − 20 = 51

Subtracting the ones from 51, 51 − 4 = 47

51 − 24 = 47

4. Number of species of fish = 43

Number of species of fish shifted = 15

Number of species of fish left = 43 − 15

15 20 30 40 43 +5 +10 +10 +3

There are two jumps of tens when 15 is subtracted from 43.

5. Number of roses Jaya had = 61

Number of roses Jaya gave her sister = 46

Number of roses left with Jaya = 61 − 46

+10

There is 1 jump of tens when 46 is subtracted from 61.

Jeny will have 15 roses left with her. 6. 46 56 66 69 +10 +10 +3

The total of jumps taken by Dan = 10 + 10 + 3

Dan is subtracting from 46 + 10 + 10 + 3 = 69

Dan is subtracting 46 from 69.

Challenge

1. Outer triangle:

58 − 29 = 29

75 − 29 = 46

75 − 58 = 17

Inner triangle: 29 − 17 = 12

9 14

4. Number of bottles Yukti collected = 469

Number of fewer bottles Priya collected than Yukti = 227

Number of bottles Priya collected = 469 − 227 = 242

Priya has collected 242 bottles.

5. a. Number of tickets sold by Joginder = 282

Number of tickets sold by Mohan = 178

Number of fewer tickets sold by Akhil than Joginder and Mohan = (282 + 178) − 159 carry 1 1 2 8 2 + 1 7 8 4 6 0

Number of tickets sold by Akhil = (282 + 178) − 159 = 460 − 159 = 301

5 10

4 6 0 1 5 9

3 0 1

Akhil has sold 301 tickets.

b. Number of tickets sold by Joginder = 282

Number of more tickets he needs to sell to reach 350 = 350 − 282 = 68 14

2 5 10

3 5 0 2 8 2 0 6 8

Joginder needs to sell 68 more ticket to reach 350.

Number of tickets sold by Mohan = 178

Number of more tickets he needs to sell to reach 350 = 350 − 178 = 172 14

2 4 10

3 5 0 1 7 8 1 7 2

Mohan needs to sell 172 more ticket to reach 350.

Number of tickets sold by Prasad = 331

Number of more tickets he needs to sell to reach 350 = 350 − 331 = 19

4 10

3 5 0

3 3 1

0 1 9

Prasad needs to sell 19 more tickets to reach 350.

6. Number of bones in deer = 327

Number of bones in cat = 235

Difference in number of bones = 327 − 235 = 92

To verify the answer, add the difference to 235 = 235 + 92 = 327 H T O 1 2 3 5 + 9 2 3 2 7

Challenge

1. To form the largest number, the digits 5, 8 and 2 are arranged in descending order from hundreds place to ones place. 8 > 5 > 2. So, the largest number using the digits 5, 8 and 2 = 852

To form the smallest number, the digits 5, 8 and 2 are arranged in ascending order from hundreds place to ones place. 2 < 5 < 8. So, the smallest number using the digits 5, 8 and 2 = 258

Difference between the numbers = 852 − 258 = 594 H T O 14

Thus, the difference between the numbers is 594.

Do It Yourself 3C

1. a. 3468 − 5 = 3463 b. 5296 − 40 = 5256

H T O

4 6

c. 6807 − 600 = 6207 d. 8547 − 7000 = 1547

Compare the digits at thousands place of the numbers 3331, 3011, 8100 and 8815, 3 < 8

Since the digits in the thousands place is the same in 3331, 3011, compare the digits at hundreds place of 3331 and 3011, 0 < 3

Since the digits in the thousands place is the same in 8100 and 8815, compare the digits at hundreds place of 8100 and 8815, 1 < 8 So, 3011 < 3331 < 8100 < 8815

The numbers in ascending order are: 3011, 3331, 8100, 8815

4. Number of government schools in Mizoram = 3872

Number of government schools in Nagaland = 2702

There are 1170 more schools in Mizoram than Nagaland.

Th H T O

3 8 7 2 – 2 7 0 2

1 1 7 0

5. Amount needed by Amit = ₹6987

Amount arranged by Amit = ₹5860

Amount needed by Amit = ₹6987 − ₹5860 = ₹1127

Th H T O

6 9 8 7 – 5 8 6 0 1 1 2 7

Challenge

1. THAR = 9869 DOWN = 3423

Th H T O

9 8 6 9 – 3 4 2 3

6 4 4 6

6 is equal to A, and 4 is equal to O. 6446 = AOOA

Thus, 6446 is equal to AOOA.

Do It Yourself 3D

2. a. 43 – 31

Estimated difference:

58 – 36

3. Number of seashells Ajay collected = 42

Rounding off the number of seashells Ajay have = 40

Number of seashells he gave to Vijay = 23

Rounding off the number of seashells Vijay have = 20

Number of seashells Ajay has after giving to Vijay = 40 − 20 = 20

Rounding off to the nearest ten, Ajay now has about 20 seashells.

4. No, Arun had rounded off incorrectly.

43 is less than 45, so 43 will be rounded off to 40 and not 50. 19 is greater than 15, so 19 will be rounded off to 20.

Difference = 40 − 20 = 20

5. Total number of chocolates = 96

96 is greater than 95, so 96 can be rounded off to 100

Number of chocolates distributed by Navin = 17 17 is greater than 15, so 17 will be rounded off to 20.

Number of chocolates left = 68

68 is greater than 65, so 68 can be rounded off to 70.

Number of chocolates distributed by Darshana = Total chocolates − (Number of cholates distributed by Navin + Number of chocolates left) = 100 − (20 + 70) = 100 − 90 = 10

Thus, Darshana distributed about 10 chocolates.

Challenge

1. The smallest possible 2-digit number using any 2 digits from 5, 9, 8, 1 can be formed by arranging the smallest digits in the tens and ones places. 1 < 5 < 8 < 9.

Smallest 2-digit number = 15

Rounded-off number = 20

The greatest possible 2-digit number using any 2 digits from 5, 9, 8, 1 can be formed by arranging the largest digits in the tens and ones places. 9 > 8 > 5 > 1.

Greatest 2-digit number = 98

Rounded-off number = 100

Estimated sum of numbers = 20 + 100 = 120

Estimated difference of numbers = 100 − 20 = 80

Do It Yourself 3E

1. Number of stickers with Ravi = 478

Numbers of stickers with Shashi = 689

Shashi has more stickers.

Number of more stickers with Shashi = 689 − 478 = 211

Shashi has 211 more stickers than Ravi.

2. Runs scored by Team A = 435

Lesser runs scored by Team B = 146

Runs scored by Team B = 435 − 146 = 289

Team B scored 289 runs.

3. Amount with Amisha = ₹700

Amount spent by Amisha = ₹592

Amount left with Amisha = ₹108

4. Number of wheat bags in the warehouse = 5397

Number of wheat bags taken out = 3075

Number of wheat bags remained in warehouse = 5397 − 3075 = 2322

There are 2322 wheat bags remaining in the warehouse.

5. Number of shoes Nikhil bought in January = 5788

Number of shoes left on 1st February = 1475

Number of shoes Nikhil sold in January = 5788 − 1475 = 4313

Nikhil sold 4313 shoes in January

6. Number of stamps with Amit = 467

Number of stamps his father has given = 133

Total number of stamps = 467 + 133 = 600

Number of stamps Amit wants = 800

Number of more stamps Amit needs to collect = 800 − 600 = 200

Amit requires 200 more stamps.

7. Number of packages with Narendra = 442

Number of packages delivered by Narendra = 174

Remaining packages with Narendra = 442 − 174 = 268

Number of packages with David = 464

Number of packages delivered by David = 188

Remaining packages with Narendra = 464 − 188 = 276

Narendra is closer to finishing his deliveries.

8. Money Laila had = ₹5275

Money, she spent = ₹3142

Money left with Laila = ₹5275 − ₹3142 = ₹2133

Laila is left with ₹2133.

Th H T O

5 2 7 5 – 3 1 4 2

2 1 3 3

9. Answer may vary. Sample answer: Manju scored 794 points in a game and Raju scored 831 points. How many more points did Raju score more than Manju?

Challenge

1. Answers may vary. Sample answer:

To get a difference of 60, one rounded-off number can be 90 and the other rounded-off number can be 30.

Estimated difference = 90 − 30 = 60

To get 90 as rounded-off number, the actual number can be between 85 and 94.

To get 30 as rounded-off number, the actual number can be between 25 and 34.

Thus, the numbers are 93 and 32.

Chapter Checkup

1. a. 64 − 64 = 0

When the number is subtracted from itself the difference is 0.

b. 59 − 0 = 59

When 0 is subtracted from a number, the difference is number itself.

c. 93 − 1 = 92

When 1 is subtracted from a number, the difference is the predecessor.

d. 23 − 23 = 0

When the number is subtracted from itself the difference is 0.

e. 16 − 0 = 16

When 0 is subtracted from a number, the difference is number itself.

f. 75 − 1 = 74

When 1 is subtracted from a number, the difference is the predecessor.

2. a. 52 − 29

Adding the jumps

1 + 10 + 10 + 2 = 23

52 − 29 = 23

b. 61 − 46

Adding the jumps

4 + 10 + 1 = 15

61 − 46 = 15

c. 64 − 35

Adding the jumps

5 + 10 + 10 + 4 = 29

64 − 35 = 29

d. 92 − 67

Adding the jumps

3 + 10 + 10 + 2 = 25

92 − 67 = 25

e. 43 − 24

Adding the jumps

6 + 10 + 3 = 19

43 − 24 = 19

f. 71 − 42

Adding the jumps

8 + 10 + 10 + 1 = 29

71 − 42 = 29

3. a. 52 − 27

Breaking the smaller number into tens and ones:

Subtracting the tens from the bigger number,

52 − 20 = 32

Subtracting the ones from 32, 32 − 7 = 25

52 − 27 = 25

b. 84 − 55

Breaking the smaller number into tens and ones:

Subtracting the tens from the bigger number,

84 − 50 = 34

Subtracting the ones from 34, 34 − 5 = 29

84 − 55 = 29

c. 76 − 29

Breaking the smaller number into tens and ones:

Subtracting the tens from the bigger number,

76 − 20 = 56

Subtracting the ones from 56, 56 − 9 = 47

76 − 29 = 47

d. 23 − 14

Breaking the smaller number into tens and ones:

Subtracting the tens from the bigger number, 23 − 10 = 13

Subtracting the ones from 13, 13 − 4 = 9

23 − 14 = 9

e. 68 − 49

Breaking the smaller number into tens and ones:

Subtracting the tens from the bigger number,

68 − 40 = 28

Subtracting the ones from 28, 28 − 9 = 19

68 − 49 = 19 f. 62 − 21

Breaking the smaller number into tens and ones:

Subtracting the tens from the bigger number,

62 − 20 = 42

Subtracting the ones from 42, 42 − 1 = 41

62 − 21 = 41

6. Number of pages kept for printing = 678

Number of pages have been printed = 259

Number of pages left for printing = 678 − 259 = 419

419 pages are left for printing.

7. Number of people who came to watch the match = 985

Number of people who left 1 hour into the match = 197

Remaining number of people = 985 − 197 = 788

Number of people who left before the half-time = 668

Remaining people who watched the whole match = 788 − 668 = 120

Thus, 120 people watched the whole match.

8. Potatoes bought by vendor from the market = 925 kg

Potatoes which are rotten = 123 kg

Remaining potatoes = 925 − 123 = 802 kg

Potatoes sold by vendor = 678 kg

Remaining potatoes with him = 802 − 678 = 124 kg

Thus, 124 kg potatoes are remaining.

9. First crewed landing on moon happened in 1969. Last crewed moon landing happened in 1972.

Difference = 1972 − 1969 = 3

The last crewed moon landing happened 3 years after the first crewed landing on moon happened.

10. Number of cardboard rolls collected = 915

Number of cardboard rolls used in the first exhibition = 268

Number of cardboard rolls used in the second exhibition = 380

Total Number of cardboard rolls used = 268 + 380 = 648

Number of cardboard rolls left = 915 − 648 = 267

Therefore, the artist is left with 267 cardboards.

11. Answer may vary. Sample answer:

There are 8567 books in a library. 1245 books were sent for binding. How many books were left in the library?

Challenge

1. Difference between 962 and 473 = 962 − 473 = 495

Difference between 609 and 473 = 609 − 473 = 136

Difference between 962 and 609 = 962 − 609 = 353

609 and 473 will have the least difference = 136 962 and 473 will have the highest difference = 495

Case Study

1. Option c

Number of post office in Goa = 258

Number of post office in Nagaland = 330

Difference = 330 − 258 = 72

We should jump 7 tens in the left of the line.

2. a. There are 82 fewer post offices in Nagaland than in Mizoram. True

Number of post offices in Nagaland = 330

Number of post offices in Mizoram = 412

Difference = 412 − 330 = 82

Thus, there are 82 fewer post offices in Nagaland.

H T O

3 11

4 1 2 –

3 3 0 8 2

b. There are 154 more post offices in Goa than in Mizoram. False

Number of post offices in Goa = 258

Number of post offices in Mizoram = 412

Difference in the number of offices = 412 − 258 = 154

H T O 10

3 0 12

4 1 2

– 2 5 8

1 5 4

Thus, there 154 less post offices in Goa than Mizoram.

3. Number of post offices in Haryana = 2689

Number of post offices in Jammu & Kashmir = 1684

Th H T O

2 6 8 9 – 1 6 8 4 1 0 0 5

There are 1005 more post offices in Haryana than in Jammu & Kashmir.

4. Number of post offices in Nagaland = 330

Number of post offices in Haryana = 2689

Th H T O

2 6 8 9 –

3 3 0

2 3 5 9

2359 is the difference in the number of post offices in Nagaland and Haryana.

5. Answers may vary.

Chapter 4

Let’s Warm-up

1. 3 + 3 + 3 + 3 = 4 × 3 = 12 2. 5 + 5 + 5 + 5 = 4 × 5 = 20

3. 10 + 10 + 10 = 3 × 10 = 30 4. 4 × 6 = 24 5. 6 × 8 = 48

Do It Yourself 4A

1. a. 3 + 3 + 3 + 3 + 3 = 5 × 3 b. 8 + 8 + 8 = 3 × 8

c. 2 + 2 + 2 + 2 = 4 × 2 d. 13 + 13 + 13 + 13 + 13 = 5 × 13

2. a. When you multiply any number by 1, you get the same number. True

b. When you multiply a number by 0, you always get 1. False

c. Order matters when multiplying numbers. False

3. 8 added 9 times is:

8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 9 × 8

Option b is correct.

4. a. 9 × 3 = 3 × 9 b. 2 × 0 = 0 c. 1 × 7 = 7 d. 5 × 8 = 8 × 5

e. 47 × 94 = 47 × 94 f. 123 × 1 = 123

5. Number of elephants in each row = 15

Total number of rows = 2

Repeated addition = 15 + 15 = 30

Multiplication sentence = 2 × 15 = 30

6. 3 batches of 4 cookies will make: 3 × 4 = 12 cookies

4 cookies in 3 batches will make: 4 × 3 = 12 cookies

So, the total number of cookies will be the same whether Sophie multiplies 3 by 4 or 4 by 3. The order of multiplication doesn’t matter as the product always remains the same.

Challenge

1. Number of dots in each row = 5

Number of rows = 4

Total number of dots = 5 × 4 = 20

Number of dots removed = 4

New number of dots = 20 – 4 = 16

Multiplication sentence = 4 × 4 = 16

After removing the dots Rearrangement

Do It Yourself 4B

1. a. 1 week = 7 days

9 weeks = 9 × 7 = 63 days

9 weeks = 63 days b. 1 day = 24 hours

5 days = 5 × 24 = 120 hours

5 days = 120 hours

c. 1 hour = 60 minutes d. 1 week = 7 days So, 10 weeks = 10 × 7 days = 70 days

10 weeks = 70 days

a 8 × 8 = 64

8 × 8 > 60

b. 9 × 10 = 90 and 100 × 1 = 100 9 × 10 < 100 × 1

c. 4 × 99 = 396 4 × 99 < 400 d. 6 × 7 = 42

3. a. 8 × 9 = 72

b. 10 × 10

Add 2 zeroes at the end and multiply 1 with 1: 10 × 10 = 100

c. 4 × 40

Add 1 zero at the end and multiply 4 with 4: 4 × 40 = 160

d. 80 × 3

Add one zero at the end and multiply 8 with 3: 80 × 3 = 240

e. 90 × 4

Add 1 zero at the end and multiply 9 with 4: 90 × 4 = 360

f. 700 × 10

Add 3 zeroes at the end and multiply 7 with 1: 700 × 10 = 7000

4. a. 8 × 8 = 64

b. Add one zero at the end and multiply 7 with 9 7 × 90 = 630

c. 560 7 = 80

7 × 80 = 560

d. 5400 6 = 900

6 × 900 = 5400

e. 400 4 = 100

100 × 4 = 400

f. 3600

6 = 600

600 × 6 = 3600

5. Number of friends = 9

Number of candies given to each friend = 6

Total candies distributed = 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6

Or, 9 × 6 = 54

So, Raj distributed 54 candies among his friends.

6. 1 century = 100 runs

The player has scored 5 centuries. 5 centuries = 5 × 100

Add 2 zeroes at the end and multiply 5 and 1. 5 × 100 = 500

Thus, the player has scored 500 runs by centuries.

7. Answers may vary. Sample answer: The cost of a book is ₹45. What is the cost of 20 such books?

Challenge

1. Number of fours hit by Gautam Gambhir = 7

Total runs = 4 × 7 = 28

Number of sixes hit by Sachin Tendulkar = 3

Total runs = 6 × 3 = 18

Total runs scored by both through fours and sixes = 28 + 18 = 46

Chapter Checkup

1. a. 45 × 8 = 8 × 45 True, because the order does not matter when two numbers are multiplied by each other.

b. 4 × 6 = 24 True

c. 89745 × 0 = 89745 False, because when a number is multiplied by 0, the product is always 0.

d. 5 × 8 = 40 True

e. 9 × 8 = 72 True

f. 6 × 600 = 3600 True

2. a.

3. a. Pattern: Each number increases by 8. 8, 16, 24, 32, 40, 48, 56, 64

b. Pattern: Each number increases by 13. 13, 26, 39, 52, 65, 78, 91, 104

c. Pattern: Each number increases by 10. 30, 40, 50, 60, 70, 80, 90, 100

d. Pattern: Each number increases by 9. 18, 27, 36, 45, 54, 63, 72, 81

e. Pattern: Each number increases by 14. 14, 28, 42, 56, 70, 84, 98, 112

f. Pattern: Each number increases by 200. 200, 400, 600, 800, 1000, 1200, 1400, 1600

c. 44 × 100 = 4400 4400 < 4444

44 × 100 < 4444 d. 5 × 60 =

e. 48975 × 1 = 48975 48975 × 1 > 0

6. Total cookie boxes with Rajesh = 10 Cookies in each box = 7

Total cookies Rajesh has = Number of cookie boxes × Cookies in each box

= 10 × 7 = 70

Thus, Rajesh has a total of 70 cookies. Boxes are shown by rectangles and cookies are shown by circles.

7. Number of petals in a wild rose = 5

Number of wild roses = 6

Total number of petals = 5 × 6 = 30 petals

So, there are 30 petals in the bouquet.

8. Number of puppies in a litter = 8

Number of German Sheperd in the shelter house = 3

Total number of puppies = 8 × 3 = 24 puppies

9. Number of chocolates Vivan bought = 9

The price of each chocolate = ₹6

Total price of 9 chocolates = 9 × ₹6 = ₹54

Money Vivan paid to the shopkeeper = ₹100

Money he should get in return = ₹100 – ₹54 = ₹46

Challenge 1. 9 × 4 = 36 5 × 5 = 25

2. Number of layers in a fruit dessert = 9

Number of fruits in each layer = 8

Even numbers = 2, 4, 6 and 8. So, there are 4 even number layers.

Total number of grapes = 4 × 8 = 32

Odd numbers = 1, 3, 5, 7, and 9. So, there are 5 odd number layers.

Total number of blueberries = 5 × 8 = 40

Case Study

1. A wooden stacker toy has 6 rings. There are 2 such toys. The multiplication sentence for the number of rings is 6 × 2 = 12

2. Number of wheels for each wooden dog toy = 4

Total number of dog toys = 7

Total number of wheels for 7 dog toys = 4 × 7 = 28

Thus, option b is correct.

3. Cost of one wooden rattle = ₹90

Cost of 4 wooden rattle = 4 × ₹90

4 × 9 = 36

4 × ₹90 = ₹360

4. Number of plates = 2

Number of tumblers = 2

Number of spoons = 2

Number of pans = 2

Number of baskets = 2

Number of pots = 2

Total number of pieces = 2 + 2 + 2 + 2 + 2 + 2 = 6 × 2 = 12

5. Answers may vary.

Chapter 5

Warm-up

3. 100 20 3

3 × 3 × 100 = 300 3 × 20 = 60 3 × 3 = 9

300 + 60 + 9 = 369 2 tens are multiplied by 3.

4. 423 × 8 = 423 3384 × 8 = 3384 =

5. 333 × 3 = 999 3 0 9 0 9 0 9 9 3 9 9 9 0 9 9 3 3 0 The cabin travels 999 metres after 3 trips on the Rajgir ropeway.

Challenge

1. The error that Samir did are marked below:

Correct method to solve:

2 × 321 = 600 + 40 + 2 = 642

Do It Yourself 5B

2. a. 3 4

4. The error that Daniel did are circled below.

6. 1 hour in Venus = 243 earth hours

7 hours in Venus = 243 × 7 = 1701 earth hours

Challenge

1. Number of sides in a square = 4

So, the number of walls required to build a pet house = 4

Number of bricks in each wall = 120

Number of bricks required for 4 walls = 120 × 4 = 480

Do It Yourself 5C

3. Amount of sugar required for 1 cotton candy = 14 g

Number of cotton candy = 21

Amount of sugar required for 21 cotton candies = 14 × 21 = 294 g 21 cotton candies need 294 g of sugar

5. Number of cloth pieces for each layer = 230

Number of layers in quilt = 5

Total

4. Number of rows = 23

Number of trees in each row = 5

Number of trees in the garden = 23 × 5

There are 115 trees in total.

Challenge

1. Greatest 2-digit number = 99

Smallest 2-digit number = 10

99 × 10 = 990

Do It Yourself 5D

1. a. The digit at the unit place is 5. Hence, 45 is rounded up to 50.

b. The digit at the unit place is more than 5. Hence, 36 is rounded up to 40

c. The digit at the unit place is more than 5. Hence, 78 is rounded up to 80

d. The digit at the unit place is less than 5. Hence, 91 is rounded down to 90.

e. The digit at the unit place is less than 5. Hence, 52 is rounded down to 50

f. The digit at the unit place is less than 5. Hence, 83 is rounded down to 80

g. The digit at the unit place is less than 5. Hence, 44 is rounded down to 40.

h. The digit at the unit place is more than 5. Hence, 27 is rounded up to 30

2. a. 44 × 5

The digit at the unit place is less than 5. Hence, rounding-off 44 to 40.

Add one zero at the end and multiply 4 with 5: 40 × 5 = 200

c. 26 × 4

The digit at the unit place is more than 5. Hence, rounding-off 26 to 30.

Add one zero at the end and multiply 3 with 4: 30 × 4 = 120

b. 32 × 6

The digit at the unit place is less than 5. Hence, rounding-off 32 to 30.

Add one zero at the end and multiply 3 with 6: 30 × 6 = 180

d. 81 × 2

The digit at the unit place is less than 5. Hence, rounding-off 81 to 80.

Add one zero at the end and multiply 8 with 2: 80 × 2 = 160

3. a. Rounding-off 66 to 70 Actual product

b. Estimated product Rounding-off 18 to 20 Actual

c. Estimated product Rounding off 45 to 50 Actual

d. Estimated product Rounding-off 33 to 30 Actual

5. Number of boxes = 45

Number of bangles in each box = 24

Estimated bangles packed: Rounding-off 45 to 50 and 24 to 20 Riya packed around 1000 bangles.

Challenge

1. Numbers rounded off to 50 are: 45, 46, 47, 48, 49, 50, 51, 52, 53, 54.

Products of the digit = 15 = 3 × 5 or 5 × 3

Hence, the number is 53.

Do It Yourself 5E

1. Number of boxes = 12

Number of erasers in each box = 13

Total number of erasers = 12 × 13

There are 156 erasers.

2. Cost of 1 notebook = ₹100

Number of notebooks = 12

Cost of 12 notebooks = 100 × ₹12 = ₹1200

The cost of 12 notebooks will be ₹1200

3. Number of apple trees in a row = 64

Number of rows = 7

Number of apples in the orchard = 64 × 7

There are 448 apple trees in all.

4. Number of scouts and guides leader in school = 12

Number of students under each leader = 26

Total number of students = 12 × 26 = 312

O 1 1 2 × 2 6

2 + 2 4 0 3 1 2

5. Number of packets = 54

Number of balloons in each packet = 45

Total number of balloons = 54 × 45

There will be 2430 balloons.

6. a. Price of 1 candle = ₹12

Price of 45 candles = 45 × ₹12

The price of 45 candles is ₹540.

4 5 × 1 2

0 + 4 5 0 5 4 0

c. Price of 1 bell = ₹45

Price of 45 bells = ₹45 × 45

Price of 45 bells is ₹2025.

b. Price of 1 star = ₹50

Price of 25 stars = ₹50 × 25

The price of 25 stars is ₹1250.

381 × 7 = 2667 3

7. Answer may vary. Sample answer:

There are 35 students in each section of grade 3. How many students are there in Grade 3, if there are 5 sections?

Challenge

1. Length of the swimming pool = 50 m

Deepak swims twice the same length = 2 × 50 m = 100 m Deepak practices swimming for 6 days.

Length covered in 6 days = 6 × 100 m = 600 m So, Deepak covered 600 m in 6 days.

Chapter Checkup

1. a. 62 × 0 = 0 T, because on multiplying a number by 0, the product is always 0.

b. 1 × 55 = 56 F, because on multiplying a number by 1, the product is always the number itself.

c. 1 × 91 = 92 F, because on multiplying a number by 1, the product is always the number itself.

d. 88 × 0 = 0 T, because on multiplying a number by 0, the product is always 0.

2. a. 10 2

4 × 4 × 10 = 40 4 × 2 = 8 Product: 40 + 8 = 48

b. 20 9

3 × 3 × 20 = 60 3 × 9 = 27 Product: 60 + 27 = 87

6. a. 12 will be 10 10 × 6 = 60

b. Rounding-off 34 to 30

30 × 4 = 120

c. Rounding-off 34 to 30

30 × 3 = 90

d. Rounding-off 44 to 40

40 × 2 = 80

7. Number of trips made by the bus = 16

Number of people seated in the bus = 76

Number of people travelled in the bus = 76 × 16

1216 people travelled in the bus.

8. Number of crates = 12

Number of apples in each crate = 45

Total number of apples = 12 × 45

There are 540 apples in 12 crates.

9. Number of chocolates = 6

Number of boxes = 15

Cost of each box = ₹9

Money needed to buy the chocolates = ₹9 × 15

Raj will need ₹135 to buy the chocolates.

10. Number of pages in the Constitution of India = 234

Number of books = 6

Total number of pages in 6 books = 234 × 6 = 1404 pages

11. Number of sheets = 56

Number of stickers in each sheet = 56

Total number of stickers = 56 × 56

There are 3136 stickers in total.

12. Number of buses = 39

Number of children who could sit in the bus = 25

Total number of children who went to picnic = 39 × 25

975 children went to the picnic.

13. Number of children = 36

Amount of money paid by each child = ₹50

Total amount paid = ₹50 × 36 ₹1800 was paid at the entrance.

14. Number of auditoriums = 4

Number of people who can sit in the auditorium = 425

Total number of people who can watch movie at one time = 425 × 4 = 1700

Total number of people who can watch the movie two times in the multiplex theatre = 2 × 1700 = 3400

15. Answer may vary. Sample answer:

The cost of 1 pencil box is ₹15. What is the cost of 25 pencil boxes?

Challenge

1. The sum of two numbers = 17

The numbers can be = 0 + 17; 1 + 16; 2 + 15; 3 + 14; 4 + 13; 5 + 12; 6 + 11; 7 + 10

The product of 9 × 8 = 72, 10 × 7 = 70, 11 × 6 = 66, 12 × 5 = 60, 13 × 4 = 52, 14 × 3 = 42, 15 × 2 = 30, 16 × 1= 16, 17 × 0 = 0

12 × 5 = 60

So, the numbers are 12 and 5.

2. 22 × 3 = 66

66 × 4 = 264

264 + 12 = 276

22 × 3 × 4 + 12 = 276

Case Study

1. ₹60 × 2 = ₹120

Hence, option d is correct.

2. ₹80 × 3 = ₹240 T O 8 0 × 3 2 4 0

3. Cost of toll at Nashri = ₹165

Number of cars = 7

Total cost = ₹165 × 7 = ₹1155 H T O 4 3 1 6 5 × 7 1 1 5 5

4. Cost of toll at Manavasi = ₹60

Cost of toll at Debra = ₹80

Cost of toll for 10 cars at Manavasi = ₹60 × 10 = ₹600

Cost of toll for 10 cars at Debra = ₹80 × 10 = ₹800

Total cost = ₹800 + ₹600 = ₹1400

5. Answers may vary

Chapter 6 Let’s Warm-up

Number of marbles = 6

1. The marbles can be distributed equally among 6 friends. True

Since, 6 ÷ 6 = 1

2. The marbles can be distributed equally among 2 friends. True

Since, 6 ÷ 2 = 3

3. The marbles can be distributed equally among 4 friends. False

Since, 6 is not divisible by 4. 4. The marbles can be distributed equally among 3 friends. True Since, 6 ÷ 3 = 2

Do It Yourself 6A

1. a. Number of cups = 8

Number of people = 4

Number of cups shared equally among 4 people = 8 ÷ 4 = 2 cups

b. Number of buttons = 21

Number of people = 7

Number of buttons shared equally among 7 people = 21 ÷ 7 = 3 buttons

c. Number of crayons = 18

Number of people = 9

Number of crayons shared equally among 9 people = 18 ÷ 9 = 2

2. There are 21 balloons.

Total number of colours = 3

Number of balloons of each colour = 21 ÷ 3 = 7

7 balloons of each colour:

Total number of apples = 18

Number of baskets = 3

Number of apples in each basket = 18 ÷ 3 = 6

4. a. Subtract 1 from 9 until we get zero. Count how many times 1 has been subtracted. We subtracted 1 for 9 times. So, there are nine

b. Subtract 11 from 22 until we get zero. Count how many times 11 has been subtracted. We subtracted 11 for 2 times. So, there are two 11’s in 22.

2 2 – 1 1 1 1 – 1 1 0 1 2

c. Subtract 9 from 27 until we get zero. Count how many times 9 has been subtracted. We subtracted 9 for 3 times. So, there are three 9’s in 27.

5. Total number of rotis made by Karthik = 15

Number of people in the house = 5

Number of rotis each person gets = 15 ÷ 5

Thus, each member will get 3 rotis.

6. Total number of matchsticks = 36

Number of matchsticks used every day = 3

Subtract 3 from 36 until we get zero. It will take 12 days to finish all the matchsticks. 3

Challenge

1. 63 7 9 9 = 10

We try division because 10 is a small number, 63 ÷ 7 = 9 9 ÷ 9 = 1

1 + 9 = 10

Hence, the correct mathematical symbol to make the statement correct is: 63 ÷ 7 ÷ 9 + 9 = 10

Do It Yourself 6B

1. a. When we divide any number by 1, we get the same number back. Thus, 25 ÷ 1 = 25.

b. We cannot divide any number by 0. There is no answer. Thus, 12 ÷ 0 = No answer.

c. When we divide 0 by any number, the answer is always 0. Thus, 0 ÷ 5 = 0.

d. When we divide any number by itself, the answer is always 1. Thus, 9 ÷ 9 = 1.

e. When we divide 0 by any number, the answer is always 0. Thus, 0 ÷ 3 = 0.

d. Subtract 8 from 32 until we get zero. Count how many times 8 has been subtracted. We subtracted 8 for 4 times. So, there are four 8’s in 32.

f. We cannot divide any number by 0. There is no answer. Thus, 15 ÷ 0 = No answer

2. a. 6 × 10 = 60 Therefore, 60 ÷ 6 = 10

b. 4 × 9 = 36 Therefore, 36 ÷ 4 = 9

c. 7 × 8 = 56 Therefore, 56 ÷ 7 = 8

d. 2 × 14 = 28 Therefore, 28 ÷ 2 = 14

e. 3 × 9 = 27 Therefore, 27 ÷ 3 = 9

f. 4 × 8 = 32 Therefore, 32 ÷ 4 = 8

3. a. Division facts of 7 × 4 = 28 are: 28 ÷ 7 = 4 and 28 ÷ 4 = 7

b. Division facts of 5 × 9 = 45 are: 45 ÷ 5 = 9 and 45 ÷ 9 = 5

c. Division facts of 3 × 6 = 18 are: 18 ÷ 3 = 6 and 18 ÷ 6 = 3

d. Division facts of 8 × 2 = 16 are: 16 ÷ 8 = 2 and 16 ÷ 2 = 8

e. Division facts of 10 × 3 = 30 are: 30 ÷ 10 = 3 and 30 ÷ 3 = 10

f. Division facts of 6 × 7 = 42 are: 42 ÷ 6 = 7 and 42 ÷ 7 = 6

4. Dividend Divisor Quotient

a. 20 ÷ 2 = 10

b. 42 ÷ 6 = 7

c. 30 ÷ 6 = 5

d. 63 ÷ 9 = 7

5. Total cream rolls at the party = 18

Cream rolls each child gets = 1

Remember, the property of division: When you divide any number by 1, the answer is always a number itself.

Number of children in the party = 18 ÷ 1 = 18

There are 18 children in the party.

6. Number of notebooks with the teacher = 45

Number of students among which the notebooks are to be distributed = 9

Number of notebooks each student will get = 5

So, the multiplication fact for this is: 9 × 5 = 45

7. Number of trash pieces collected in an hour = 36

Number of bags they wanted to keep the trash into = 4

Chapter Checkup

1. a. Number of things = 15

Number of people = 3

Number of things shared equally among 3 people = 15 ÷ 3 = 5 things

b. Number of dice = 24

Number of people = 8

Number of dice shared equally among 8 people = 24 ÷ 8 = 3 dice

c. Number of coins = 12

Number of people = 6

Number of coins shared equally among 6 people = 12 ÷ 6 = 2 coins

d. Number of balls = 14

Number of people = 2

Number of balls shared equally among 2 people = 14 ÷ 2 = 7 balls

2. a. We divide 3 eight times from 24 until we get zero. Thus, 24 ÷ 3 = 8

b. We divide 6 six times from 36 until we get zero. Thus, 36 ÷ 6 = 6

Therefore, 36 ÷ 4 = 9

Thus, the group will keep 9 pieces of trash in each bag.

8. Answer will vary. Sample answer: Rahul bought 55 roses to put in vases in a party hall. If he put 5 roses in each vase, how many vases did he use?

Multiplication fact: 11 × 5 = 55

c. We divide 9 five times from 45 until we get zero. Thus, 45 ÷ 9 = 5

d. We divide 8 nine times from 72 until we get zero. Thus, 72 ÷ 8 = 9

e. We divide 7 eight times from 56 until we get zero. Thus, 56 ÷ 7 = 8

f. We divide 9 seven times from 63 until we get zero. Thus, 63 ÷ 9 = 7

6. Answers may vary. Sample answers:

a. Example 1: 25 ÷ 1= 25; Example 2: 43 ÷ 1 = 43

b. Example 1: 15 ÷ 15 = 1; Example 2: 32 ÷ 32 = 1

c. Example 1: 0 ÷ 17 = 0; Example 2: 0 ÷ 23 = 0

d. Example 1: 20 ÷ 0 = No answer; Example 2: 14 ÷ 0 = No answer

7. Number of toy cars = 20

Number of children = 20

Number of toy cars each child will receive = 20 ÷ 20

Remember, the property of division: When you divide any number by itself, the answer is always 1.

Thus, 20 ÷ 20 = 1

So, each child will get 1 car.

8. Total number of cupcakes = 32

Number of children = 4

Number of cupcakes each child will get = 32 ÷ 4

g. We divide 9 six times from 54 until we get zero. Thus, 54 ÷ 9 = 6

h. We divide 8 ten times from 80 until we get zero. Thus, 80 ÷ 8 = 10

3. a. Multiplication fact for 36 ÷ 3 = 12 is 12 × 3 = 36

b. Multiplication fact for 88 ÷ 4 = 22 is 22 × 4 = 88

c. Multiplication fact for 96 ÷ 8 = 12 is 12 × 8 = 96

d. Multiplication fact for 40 ÷ 5 = 8 is 8 × 5 = 40

e. Multiplication fact for 25 ÷ 5 = 5 is 5 × 5 = 25

f. Multiplication fact for 60 ÷ 6 = 10 is 10 × 6 = 60

g. Multiplication fact for 48 ÷ 6 = 8 is 8 × 6 = 48

h. Multiplication fact for 36 ÷ 9 = 4 is 4 × 9 = 36

4. a. Division facts of 9 × 5 = 45 are: 45 ÷ 9 = 5 and 45 ÷ 5 = 9

b. Division facts of 4 × 8 = 32 are: 32 ÷ 4 = 8 and 32 ÷ 8 = 4

c. Division facts of 5 × 3 = 15 are: 15 ÷ 5 = 3 and 15 ÷ 3 = 5

d. Division facts of 7 × 2 = 14 are: 14 ÷ 7 = 2 and 14 ÷ 2 = 7

e. Division facts of 4 × 6 = 24 are: 24 ÷ 4 = 6 and 24 ÷ 6 = 4

f. Division facts of 9 × 8 = 72 are: 72 ÷ 9 = 8 and 72 ÷ 8 = 9

g. Division facts of 2 × 10 = 20 are: 20 ÷ 2 = 10 and 20 ÷ 10 = 2

h. Division facts of 3 × 7 = 21 are: 21 ÷ 3 = 7 and 21 ÷ 7 = 3

5. a. 9 × 3 = 27. Therefore, 27 ÷ 9 = 3

b. 5 × 9 = 45. Therefore, 45 ÷ 5 = 9

c. 7 × 9 = 63. Therefore, 63 ÷ 7 = 9

d. 5 × 7 = 35. Therefore, 35 ÷ 5 = 7

e. 6 × 7 = 42. Therefore, 42 ÷ 6 = 7

f. 9 × 6 = 54. Therefore, 54 ÷ 9 = 6

g. 3 × 9 = 27. Therefore, 27 ÷ 3 = 9

h. 8 × 10 = 80. Therefore, 80 ÷ 8 = 10

Therefore, 32 ÷ 4 = 8

Thus, each child will get 8 cupcakes.

9. Number of people who visited Taj Mahal = 36

Number of people in a group = 6

Number of groups = 36 ÷ 6

Let us divide by repeated subtraction.

Subtract 6 from 36 until we get zero.

Count the number of times 6 has been subtracted.

We subtracted 6 six times.

Thus, there will be 6 groups of 6 people.

Challenge

1. By using any two numbers from the box the division sentence on the caterpillar is:

2. Answers may vary Sample answer:

24 ÷ 6 = 4

2 ÷ 2 = 1

12 ÷ 3 = 4

24 ÷ 2 = 12

6 ÷ 2 = 3

4 ÷ 1 = 4

Case Study

1. Total number of fish = 27

Number of tanks = 3

Number of fish in each tank = 27 ÷ 3

Let us divide by repeated subtraction.

Subtract 3 from 27 until we get zero.

Count the number of times 3 has been subtracted.

We subtracted 3 twelve times. Hence, the number of fish in each tank = 12

Hence, option c is correct.

4. Total number of fish = 18

Number of tanks = 3

Number of fish in each tank = 18 ÷ 3

Let us divide by repeated subtraction.

Subtract 3 from 18 until we get zero.

Count the number of times 3 has been subtracted.

We subtracted 3 six times. Hence, the number of fish in each tank = 6

Hence, True.

5. Answer may vary

Chapter 7

Let’s Warm-up 1. 16 ÷ 4 15

3 × 5

Do It Yourself 7A

We subtracted 3 nine times.

Hence, the number of fish in each tank = 9

Hence, option d is correct.

2. The division sentence for the number of fish in each tank is 27 ÷ 3 = 9

3. Total number of fish = 36

Number of tanks = 3

Number of fish in each tank = 36 ÷ 3

Let us divide by repeated subtraction.

Subtract 3 from 36 until we get zero.

Count the number of times 3 has been subtracted

c. 235 ÷ 4

5 8

4 2 3 5 – 2 0 3 5 – 3 2 3

Quotient = 58

Remainder = 3 d. 412 ÷ 5 8 2 5 4 1 2 – 4 0 1 2 – 1 0 2

Quotient = 82

Remainder = 2

3. (Quotient × Divisor) + Remainder = Dividend

a. 41 ÷ 2

2 0

2 4 1 – 4 0 1

(Q × D) + R = (20 × 2) + 1 = 40 + 1 = 41 = Dividend b. 132 ÷ 3 4 4 3 1 3 2 – 1 2 1 2 – 1 2 0 (Q × D) + R = (44 × 3) + 0 = 132 = Dividend

c. 324 ÷ 5 6 4 5 3 2 4 – 3 0 0 2 4 – 2 0 4

(Q × D) + R = (64 × 5) + 4 = 324 = Dividend d. 2562 ÷ 9 2 8 4 9

(Q × D) + R = (284 × 9) + 6 = 2562 = Dividend

4. a. (7 × 5) + 3 44

b. (12 × 4) + 1 41

c. (9 × 6) + 5 38

d. (5 × 8) + 4 49

e. (20 × 2) + 1 59

5. Total number of puppies in a shelter = 57

Number of puppies each dog house can have = 9

Number of puppies left without a doghouse = 57 ÷ 9 6 9 5 7 – 5 4 3

There are 3 puppies without a doghouse.

6. Number of flower seeds = 3548

Number of rows = 6

Number of seeds left after planting = 3548 ÷ 6 5 9 1

6 3 5 4 8 – 3 0 5 4 – 5 4 0 8 – 6 2

So, 2 seeds are left.

7. Number of cups = 74

Number of cups in each tray = 8

Number of trays needed = 74 ÷ 8 9 8 7 4 – 7 2 2

9 trays will hold 72 cups.

There are 2 extra cups, we would need an extra tray to hold them.

So, the total number of trays required: 9 + 1 = 10 trays

8. Number of storybooks = 513

Number of storybooks each classroom gets = 9

Number of classrooms = 513 ÷ 9

9 5

5 7

So, 57 classrooms will receive the storybooks.

9. Cost of 3 shirts of Brand A = ₹360

Cost of 5 shirts of Brand B = ₹475

Cost of 2 shirts of Brand C = ₹128

a. Cost of 1 shirt of Brand A = 360 ÷ 3 1 2 0 3 3 6 0 – 3 0 6 – 6 0 0

b. Cost of 1 shirt of Brand B = 475 ÷ 5

So, brand C is cheaper.

Challenge

1. The number divided by 7 gives 560.

Therefore, number ÷ 7 = 560 or number 560 7 =

To find the number, multiply 7 on both sides of equation number 75607 7 ×=×

number = 3920

Now, divide 3920 by 56 = 3920 ÷ 56

Hence, by dividing 3920 by 56 we get 70.

Chapter Checkup

3. (Quotient × Divisor) + Remainder = Dividend

a. 91 ÷ 4 2 2 4 9 1 – 8 1 1 – 8 3 (Q × D) + R = (22 × 4) + 3 = 91 = Dividend b. 125 ÷ 6 2 0 6 1 2 5 – 1 2 0 5 (Q × D) + R = (20 × 6) + 5 = 125 = Dividend

c. 645 ÷ 8 8 0 8 6 4 5 – 6 4 0 5

(Q × D) + R = (80 × 8) + 5 = 645 = Dividend

d. 1842 ÷ 6 3 0 7 6 1 8 4 2 – 1 8 0 4 2 – 4 2 0 (Q × D) + R = (307 × 6) + 0 = 1842 = Dividend

4. (Quotient × Divisor) + Remainder = Dividend

a. (10 × 4) + = 43 1 0 4 4 3 – 4 3 (10 × 4) + 3 = 43 b. ( × 2) + 1 = 49 2 4 2 4 9 – 4 9 – 8

d. (7 × 9) + = 64 7 9 6 4 – 6 3 1 (7 × 9) + 1 = 64

× 5) + 4 = 214

× 3) + 1 = 352

5. Number of tickets to be sold = 5245

Number of tickets in each booklet = 5

Number of booklets need to be prepared = 5245 ÷ 5 1 0 4 9 5 5 2 4 5 – 5 0 2 4 – 2 0 4 5 – 4 5 0

So, 1049 booklets need to be prepared.

6. Number of firefighters = 720

Number of groups = 3

Number of firefighters in each group = 720 ÷ 3 2 4 0 3 7 2 0 – 6 1 2 – 1 2 0 0 – 0 0

So, 240 firefighters will be there in a group.

7. Number of packets of pulses = 156

Number of packets given to each family = 10

Number of families who received the packets = 156 ÷ 10

So, 15 families received the packets.

Challenge

1. To find the number that needs to be added to 156 so that it can be divided by 7 without a remainder, we find the remainder when 156 is divided by 7.

2 2 7 1 5 6

Since the remainder is 2, we need to add enough to make the total divisible by 7. The next multiple of 7 after 154 is 161. Difference between 161 and 156 = 161 − 156 = 5 Therefore, the number that needs to be added to 156, so that it can be divided by 7 without a remainder is 5.

2. 88 cm Total height 256 cm

Total length 600 cm Number of steps = 16

a. Total height of the staircase = 256 cm

Height of each step = Total height ÷ Number of steps = 256 ÷ 16 = 16 cm

b. Total length of the staircase = 600 cm

Length of the staircase = 600 − 88 = 512 cm

Length of each step = Length of the staircase ÷ Number of steps

512 ÷ 16 = 32 cm

Case Study

1. Total weight of the stone = 56 ton Number of workers = 8

Weight each worker has to move = 56 ÷ 8 = 7 ton

Thus, option c is correct.

2. Total weight of the stone = 56 ton Number of workers = 4

Weight

So, twice as heavy would each worker ’s load be compared to having 8 workers.

Hence, option a is correct.

3. Dividing the weight of the stone by the number of workers makes the stone lighter. False

4. The fewer workers they have, the less each worker needs to carry. False

5. Answer may vary. Sample answer: Everyone needs to know exactly when to push or pull the levers together to move the block safely and avoid accidents.

Chapter 8

Let’s Warm-up

1. Objects having similar shapes.

3. Square = 2

Rectangle = 2

Triangle = 1

Circle = 6

4. a. A triangle has 3 curved sides. False

b. The opposite sides of a rectangle are equal in length. True

c. An oval has 0 sides and 0 corners. True

d. The 4 sides of a square are straight sides. True

5. Figures may vary. Sample figure:

Challenge

1. The given figure is made up of 6 squares.

Do It Yourself 8B

1. a. Figure a does not show symmetry along the dotted line.

b. Figure b shows symmetry along the dotted line.

c. Figure c does not show symmetry along the dotted line.

d. Figure d shows symmetry along the dotted line.

5. a. Go 4 steps up from the house and then 1 step to left then you will reach the park

b. Go 2 steps up and 2 steps right from the school and you will reach the hospital

c. Answers may vary. Sample answer:

A way to go from the park to the fire station without crossing the hospital, go 5 steps to the right then go 1 step up.

6. Answers may vary. Sample answer:

Challenge

1. These are called lines of symmetry. There are 4 lines of symmetry in the given rangoli.

Do It Yourself

2. a. 6 plane rectangular faces Cube

b. Only 1 curved face Cone

c. 1 plane and 1 curved face Cylinder

d. 6 plane square faces Cuboid

e. 2 plane faces and 1 curved face Sphere

3. Number of clay balls used = 8

Number of toothpicks used = 12

The clay balls will act as corners and the toothpicks will act as edges of the solid shape.

The length of all the toothpicks is equal. So, all the sides of the solid shape are the same.

The solid shape formed is a cube.

4. Answers may vary. Sample answer: A box, book or eraser when traced will give a rectangle.

2. a. b. c. d.

3. a. b. c.

1. a. Cube b. Cylinder

c. Sphere d. Cone

Challenge

1. 5 cubes when placed one over the another forms a cuboid.

When we trace the solid figure, we get a rectangle and a square.

Do It Yourself 8D

1. a. View B is the side view of the doughnut. View B

b. View B is the side view of the wooden box. View B

2. Images may vary a. , b. , c. ,

3. Drawings may vary a. b.

4. Drawings may vary. Sample drawings:

, The front view and the top view of the book are shown. We get a rectangle in each case.

The net of a book looks like as shown:

Challenge

1. A cuboid has a net where all its faces are rectangular in shape. Left Front Top Base Right Back

Do It Yourself 8E

1. a. The repeating unit is red hat, blue hat, brown hat.

b. The repeating unit is banana, apple, orange

c. The repeating unit is smiling face, neutral face, sad face

d. The repeating unit is red rocket, yellow rocket, blue rocket and again blue rocket

2. a. The pattern is pink balloon, yellow balloon, blue balloon.

b. The pattern is blue fish, yellow fish, red fish.

3. a. The pattern is one circle is adding each time.

b. The pattern is smiley are rotated anticlockwise and brown smiley, blue smiley, purple smiley, yellow smiley.

c. The pattern is figure is rotating clockwise.

d. The pattern is 1 outer circle is added each time.

e. Pattern: Each number increases by 4. 28, 32, 36, 40, 44, 48, 52

f. Pattern: Each number decreases by 10. 95, 85, 75, 65, 55, 45, 35

4. Option a, b and c show the tiling pattern. Option d does not show the tiling pattern since it has gaps between the circles. Thus, option d is correct.

5. a. JTJHJE JCJAJR JIJS JRJEJD

Here, letter ‘J’ is repeated before each alphabet

The secret message is ‘THE CAR IS RED’.

b. 1I 2L3I4K5E 6D7O8S9A

Here digits 1, 2, 3, 4, 5, 6, 7, 8, 9 appear before every alphabet.

The secret message is ‘I LIKE DOSA’.

6. Figures may vary. Sample figure:

Challenge 1.

Answer may vary. Sample answer: If the name is RAJ. It will be written as:

Chapter Checkup

1. a. The given shape as Square = 1

Rectangle = 7

Triangle = 2

Circle = 5

b. Drawing may vary Sample drawing:

Challenge

1. She can do it in 12 different ways. She will get only a cuboid.

2. 4 triangles can be made but 8 triangles can be seen.

7. a. Pattern: Each number increases by 4. 12, 16, 20, 24, 28, 32, 36, 40

b. Pattern: Each number increases by 8. 48, 56, 64, 72, 80, 88, 96

c. Pattern: Each number increases by 5. 32, 37, 42, 47, 52, 57, 62

d. Pattern: Each number increases by 3. 29, 32, 35, 38, 41, 44, 47

8. a. b.

Case Study

1. The ‘+’ sign shows the hospital. 2.

3. The (H) sign shows the hotel. Thus, option b is correct. 4. Step out on MG Road, turn to the right and walk straight. The house is on the left.

5. The top view of the parking area is given in the map.

Chapter 9 Let’s Warm-up

1. The book is 7 forearms long. False

Do It Yourself 9A

2. The watermelon is heavier than the pen True

3. The capacity of each glass is less than that of the jug True

1. a. The distance between two cities: Kilometres b. A pipe: Metres

2. a. b. c. d.

3. a. Cone b. Cube c. Cylinder d. Cuboid

9. Side: Rectangle Top: Circle

10. a. Colouring may vary

c. A phone: Centimetres

d. The length of hands of a person: Centimetres

2. a. The scissors start at 0 cm and ends at 8 cm. So, the length of the scissors is 8 cm.

b. The pen starts at 0 cm and ends at 11 cm. So, the length of the pen is 11 cm.

c. The nail starts at 0 cm and ends at 10 cm. So, the length of the nail is 10 cm.

d. The straw starts at 0 cm and ends at 15 cm. So, the length of the straw is 15 cm.

3. 1 m = 100 cm

a. 6 m = 6 × 100 cm = 600 cm

b. 8 m = 8 × 100 cm = 800 cm

c. 9 m 9 cm = 9 × 100 + 9 = 900 + 9 = 909 cm

d. 4 m 15 cm = 4 × 100 + 15 = 400 + 15 = 415 cm

e. 7 m 26 cm = 7 × 100 + 26 = 700 + 26 = 726 cm

f. 2 m 52 cm = 2 × 100 + 52 = 200 + 52 = 252 cm

4. 1 cm = 1 ÷ 100 m

a. 700 cm = 700 ÷ 100 = 7 m

b. 600 cm = 600 ÷ 100 = 6 m

c. 400 cm = 400 ÷ 100 = 4 m

d. 800 cm = 800 ÷ 100 = 8 m

e. 500 cm = 500 ÷ 100 = 5 m

f. 900 cm = 900 ÷ 100 = 9 m

5. Height of the building on which the tower is installed = 22 m

Height of the tower = 14 m

Total height of the tower from the ground = 22 m + 14 m = 36 m

6. Length of the monitor lizard = 2 m

Length of the python = 6 m

We know that, 6 > 2

So, Python is longer than monitor lizard.

Difference between the lengths of monitor lizard and python = 6 m – 2 m = 4 m

Thus, Python is longer than monitor lizard by 4 m.

Challenge

1. Here, 2 boxes show 10 cm.

We need to shade 1 m 30 cm

1 m 30 m = 1 m + 30 cm = 100 cm + 30 cm = 130 cm 10 cm is already shaded.

The centimetres on the metre scale that still has to be shaded = 130 cm − 10 cm = 120 cm

Since 2 boxes represent 10 cm, or 10 cm = 2 boxes 1 cm = 2 ÷ 10 boxes

120 cm will be represents by shading 120 10 × 2 = 24 blocks.

100 cm

30 cm

Do It Yourself 9B

1. a. Feather: Grams

b. Car: Kilograms

c. Pillow: Grams

1 Metre

d. Chair: Kilograms

e. Pan: Grams

f. Television: Kilograms

2. 1 kg = 1000 g

a. 8 kg = 8 × 1000 g = 8000 g

b. 9 kg = 9 × 1000 g = 9000 g

c. 1 kg 500 g = 1 × 1000 + 500 = 1000 + 500 = 1500 g

d. 4 kg 200 g = 4 × 1000 + 200 = 4000 + 200 = 4200 g

e. 3 kg 300 g = 3 × 1000 + 300 = 3000 + 300 = 3300 g

f. 7 kg 750 g = 7 × 1000 + 750 = 7000 + 750 = 7750 g

3. Weight of Farah’s pet cat = 3 kg 600 g

Weight of the pet cat in grams = 3 × 1000 + 600 = 3000 + 600 = 3600 g

Thus, the weight of Farah’s pet cat in grams is 3600 g.

4. Weight of the vegetables bought = 4 kg

Weight of the fruit bought = 5 kg

Difference between the weights of fruit and vegetables = 5 kg – 4 kg = 1 kg

Thus, Shalu purchased 1 kg more fruit than vegetables.

5. Weight of the watermelon = 5 kg

Weight of one cut piece of the watermelon = 2 kg

Weight of the other cut piece of the watermelon = 5 kg – 2 kg = 3 kg

Thus, the weight of the other piece was 3 kg.

6. Weight of the newspapers sold = 4 kg 200 g = 4 × 1000 + 200 = 4000 + 200 = 4200 g

Weight of the magazines sold = 700 g

Total weight of the scrap sold = 4200 g + 700 g = 4900 g = 4000 g + 900 g = 4 kg 900 g

Thus, the total weight of the articles was 4 kg 900 g.

Challenge

1. First weigh blocks A and B.

If the pan with block A goes down, A is heavier.

If the pan with block B goes down, B is heavier.

If A is heavier, weigh blocks A and C to find the heavier block. If B is heavier, weigh blocks B and C to find the heavier block.

Do It Yourself 9C

1. Items

a. Cough syrup

b. Syringe c. Tub of water

d. Bucket of water e. Hand sanitizer f. Barrel of water

2. 1 L = 1000 mL

a. 2 L = 2 × 1000 mL = 2000 mL

b. 6 L = 6 × 1000 mL = 6000 mL

c. 9 L = 9 × 1000 mL = 9000 mL

d. 4 L 500 mL = 4 × 1000 mL + 500 mL = 4000 mL + 500 mL = 4500 mL

e. 9 L 200 mL = 9 × 1000 mL + 200 mL = 9000 mL + 200 mL = 9200 mL

f. 5 L 850 mL = 5 × 1000 mL + 850 mL = 5000 mL + 850 mL = 5850 mL

3. Amount of water required by Rohan to make lemonade = 3 L

Amount of water required by Rohan to make lemonade in millilitres = 3 × 1000 mL = 3000 mL

4. Quantity of each water bottle = 500 mL

Number of times the water bottle is filled = 3

Total quantity of water used = 500 mL × 3 = 1500 mL = 1000 mL + 500 mL = 1 L 500 mL

Thus, Mohan used 1 L 500 mL of water.

5. Quantity of water poured in the jug = 4 L = 4 × 1000 mL = 4000 mL

Quantity of water transferred into a glass = 750 mL

Quantity of water left in the jug = 4000 mL – 750 mL = 3250 mL = 3000 mL + 250 mL = 3 × 1000 mL + 250 mL = 3 L 250 mL

Thus, 3 L 250 mL of water is left in the jug.

6. Capacity of the fuel tank of Mohit’s car = 38 L

Capacity of the fuel tank of Soham’s car = 45 L

Total capacity of the tanks of two cars

= 38 L + 45 L = 83 L

Thus, the total capacity of both tanks is 83 L.

Challenge

1. He first uses the 6 L jar to get 6 L of milk. He pours half the milk from the 6 L jar to make it 3 L of milk in total.

Chapter Checkup

1. a. Tank of water b. Spoonful of oil c. Cough syrup

d. A jug of lemonade e. Petrol tank f. Glass of juice

2. a. The length of a spoon b. The height of a tree

c. The width of a book d. The length of a swimming pool

3. a. An empty box b. A banana

c. A cylinder d. A lollipop

e. A bag of flour f. Two apples

4. a. The zip starts at 0 cm and ends at 12 cm. So, the length of the zip is 12 cm.

b. The paper clip starts at 0 cm and ends at 4 cm. So, the length of the paper clip is 4 cm.

c. The pencil starts at 0 cm and ends at 7 cm. So, the length of the pencil is 7 cm.

d. The screwdriver starts at 0 cm and ends at 8 cm. So, the length of the screwdriver is 8 cm.

5. 1 m = 100 cm

a. 5 m = 5 × 100 cm = 500 cm

b. 2 m = 2 × 100 cm = 200 cm

c. 9 m = 9 × 100 cm = 900 cm

d. 8 m 50 cm = 8 × 100 cm + 50 cm = 800 cm + 50 cm = 850 cm

e. 4 m 900 cm = 4 × 100 cm + 900 cm = 400 cm + 900 cm = 1300 cm

f. 6 m 890 cm = 6 × 100 cm + 890 cm = 600 cm + 890 cm = 1490 cm

6. 1 cm = 1 ÷ 100 m

a. 200 cm = 200 ÷ 100 = 2 m

b. 300 cm = 300 ÷ 100 = 3 m

c. 1000 cm = 1000 ÷ 100 = 10 m

d. 1100 cm = 1100 ÷ 100 = 11 m

e. 1200 cm = 1200 ÷ 100 = 12 m

f. 1300 cm = 1300 ÷ 100 = 13 m

7. 1 kg = 1000 g

a. 8 kg = 8 × 1000 g = 8000 g

b. 9 kg = 9 × 1000 g = 9000 g

c. 7 kg 450 g = 7 × 1000 + 450 g = 7450 g

d. 2 kg 999 g = 2 × 1000 + 999 g = 2999 g

e. 3 kg 760 g = 3 × 1000 + 760 g = 3760 g

f. 4 kg and 640 g = 4 × 1000 + 640 g = 4640 g

8. 1 L = 1000 mL

a. 2 L = 2 × 1000 mL = 2000 mL

b. 7 L = 7 × 1000 mL = 7000 mL

c. 4 L = 4 × 1000 mL = 4000 mL

d. 5 L 800 mL = 5 × 1000 + 800 mL = 5800 mL

e. 6 L 550 mL = 6 × 1000 + 550 mL = 6550 mL

f. 8 L 900 mL = 8 × 1000 + 900 mL = 8900 mL

9. Weight of a fully grown goliath frog = 3 kg 250 g

e. The height of a house f. The length of a room

Weight of the frog in grams = 3 × 1000 + 250 = 3000 + 250 = 3250 g

Thus, the weight of a fully grown goliath frog is 3250 grams.

10. Water used by Ahana = 5 L 500 mL = 5 × 1000 mL + 500 mL = 5000 mL + 500 mL = 5500 mL

Water used by Sameer = 1 L 200 mL = 1 × 1000 mL + 200 mL = 1000 mL + 200 mL = 1200 mL

Water saved by Sameer = 5500 mL – 1200 mL = 4300 mL = 4000 mL + 300 mL = 4 L 300 mL

Thus, Sameer saves 4 L 300 mL of water.

Challenge

1. When a ribbon is cut into 4 equal parts then 3 cuts are made. Cut 1

Cut 2 Cut 3

3 m 3 m 3 m 3 m 3 m

The distance between the either ends of the trees will be 15 m.

Case Study

1. Yash uses 10 g of nuts in a mango smoothie. Thus, option (a) is correct.

2. Quantity of milk used in banana smoothie = 225 mL

Quantity of milk used in mango smoothie = 225 mL

Total quantity of milk used in both the smoothies = 225 mL + 225 mL = 450 mL

3. Weight of sugar used in the banana smoothie = 50 g

Weight of sugar used in the mango smoothie = 20 g

Total weight of the sugar used = 50 g + 20 g = 70 g

Total weight of sugar available with Yash = 1 kg = 1000 g

Total weight of sugar left with Yash after making both the smoothies = 1000 g – 70 g = 930 g

4. Answers may vary

Chapter 10

Let’s Warm-up

Half past 4

Do It Yourself 10A

1. A shows the hour hand, and B shows the minute hand. B Minute hand A Hour hand

2. a. 12:00 or 12 o’ clock b. 10:15 or Quarter past 10

c. 2:30 or Half past 2

d. 12:20 or 20 minutes past 12

3. a. Sai wakes up at 7 a.m. in the morning.

b. He reaches school by 9 a.m. in the morning.

c. Sai comes back from school at 1 p.m. after noon.

d. He goes to play with his friends at 6 p.m. in the evening.

4. a. 5 minutes past 2

c. Half past 10

b. 40 minutes to 3

Quarter past 1

5. Time at which August Kranti Rajdhani Express runs between Delhi and Mumbai = 5:30 p.m.

Time at which it reaches Mumbai Central = Half past 10 in the morning

Half past 10 = 10:30

Morning means a.m.

Thus, the train reaches Mumbai Central at 10:30 a.m.

Challenge

1. Time at which Sneha reaches the lunch room = 5 minutes before 12

The time is before noon, so it will be written as 11:55 a.m.

Time at which Veena reaches the lunch room = 5 minutes after 12

The time is after noon, so it will be written as 12:05 p.m.

Thus, Sneha’s time is written as a.m., and she reached the lunch room at 11:55 a.m.

Do It Yourself 10B

1. a. The minute hand in a clock completes one round in 60 minutes.

b. The hour hand in a clock completes one round in 12 hours.

2. a. The hour hand moved from 3 to 4. It has moved by 1 number.

Since, when the hour hand moves from one number to another, the minute hand moves around the clock.

1 number = 1 hour.

So, 1 hour has passed.

b. The hour hand moved from 4 to 7. It has moved by 3 numbers.

Since, when the hour hand moves from one number to another, the minute hand moves around the clock.

1 number = 1 hour

3 numbers = 1 × 3 hour = 3 hours

So, 3 hours have passed.

c. The minute hand moved from 9 to 12. It has moved by 3 numbers.

Since, when the minute hand moves from one number to another, 5 minutes will have passed.

1 number = 5 minutes

3 number = 3 × 5 = 15 minutes

So, 15 minutes have passed.

d. The hour hand moved from 3 to 5. It has moved by 2 numbers.

The minute hand moved from 9 to 12. It has moved by 3 numbers.

So, 2 hours and 15 minutes have passed.

3. a. Filling a glass of milk will take some minutes.

b. Watering a plant will take some minutes.

c. Eating a banana will take a few minutes.

d. Washing, ironing and folding clothes will take an hour or more.

4. Time taken to complete the marathon = 2 hours

We know that, 1 hour = 60 minutes

Number of minutes taken to complete the marathon = 2 × 60 minutes = 120 minutes

Thus, Eliud Kipchoge completed the marathon in around 120 minutes at the Berlin Marathon.

5. Start time of Shatabdi Express from Delhi = 6:45 a.m.

Time at which Shatabdi Express reached Meerut = 8:00 a.m.

From 6:45 a.m. to 8:00 a.m., the hour hand has moved 1 number and the minute hand moved 3 numbers. So, 1 hour and 15 minutes has passed.

We know that 1 hour = 60 minutes

Thus, Vibhu took 60 + 15 = 75 minutes to reach to Meerut from Delhi.

Challenge

1. Given that, = 1 hour and = 10 minutes

We need to represent 160 minutes using these symbols. 160 minutes = 120 minutes + 40 minutes

We know that, 1 hour = 60 minutes

120 minutes = 120 ÷ 60 = 2 hours

So, 160 minutes = 2 hours + 40 minutes

Using the symbols, 160 minutes can be represented as .

Do It Yourself 10C

1. a. 2024 Day of the week

b. January Month

c. 26th Year

d. Friday Date of the month

2. a. Sunday is a month. False, because Sunday is a day.

b. December is a month. True

c. May is the first day of the week. False, because May is a month not a day and it is the fifth month of the year.

d. A leap year has 29 days in February True

3. a. There are 4 Sundays in this month.

b. The month starts from a Monday

c. On 25 May, the day is Thursday

d. 2 May is a Tuesday. The next Tuesday will be on 9 May.

e. In this month, Saturdays are on dates 6, 13, 20 and 27

4. We know that, 1 week = 7 days

So, 2 weeks = 7 + 7 OR 2 × 7 = 14 days

Thus, Anand has practiced his dance performance for 14 days.

6. Date on which Constitution of India was adopted by the Constituent Assembly = 26 November, 1949

Date on which Constitution of India was implemented = 26 January, 1950

Number of months taken for the implementation of Constitution of India = 2 months

26 November 1949 26 December 1949 26 January 1950 1 month 1 month

Challenge

1. We need to find the number of leap years between 2014 and 2058.

The first leap year after 2014 is 2016.

A leap year comes after every 4 years. The leap years will be 2016, 2020, 2024, 2028, 2032, 2036, 2040, 2044, 2048, 2052 and 2056.

Thus, there are 11 leap years between 2014 and 2058.

Do It Yourself 10D

1. Navratri

Starts Dusshera Diwali Bhai Dooj Guru Nanak Jayanti

3 October 12 October 1 November 3 November 27 November

2. Cricket match Basketball match Tug-of-war match Football match Kho-Kho match

February August October November December

3. a. Rina was born in the year 2000.

b. The year in which Rina was born = 2000

Year in which Rina’s sister was born = 2007

Rina’s age at the time of her sister’s birth = 2007 – 2000 = 7 years

Thus, Rina was 7 years at the time of her sister ’s birth.

c. The year in which Rina won the dance competition = 2015

Age of Rina when she won the dance competition = 2015 – 2000 = 15 years

Thus, Rina was 15 years old when she won the dance competition.

d. Age of Rina in 2034 = 2034 – 2000 = 34 years

Thus, Rina will be 34 years old in 2034.

4. Birthdate of Tinu = 31 July 2015

Birthdate of Mitu = 31 July 2021

Since, 2015 < 2021, Tinu was born earlier, he is older than Mitu.

Difference between the ages of Tinu and Mitu = 2021 – 2015 = 6 years

Thus, Tinu is older than Mitu by 6 years.

Challenge

1. Suppose Seema’s brother’s age = B

Seema’s age = 2 times the brother’s age = 2 × B

Seema’s age = 10 + Brother’s age = 10 + B

10 + B = 2 × B

10 = 2 × B − B

10 = B

So, B = 10

Seema's age = 2 × B = 2 × 10 = 20

Thus, Seema’s age is 20 years and her brother’s age is 10 years.

Chapter Checkup

1. a.

50 minutes past 1 or 1:50 or 10 minutes to 2

b. Half past 1 or 1:30

c. Quarter to 11 or 10:45

2. a. 10 minutes past 12

b. Half past 1

c. Quarter to 7

3. a. Between 5:20 and 7:20, the hour hand has moved 2 numbers.

So, 2 hours have passed.

b. Between 9:15 and 11:15, the hour hand has moved 2 numbers.

So, 2 hours have passed.

c. Between 2:10 and 4:10, the hour hand has moved 2 numbers.

So, 2 hours have passed.

4. a. 7:30 in the morning is after midnight and before noon.

So, it is 7:30 a.m.

b. 6:15 in the evening is after 12 o’ clock in the noon but before midnight 12 o’ clock.

So, it is 6:15 p.m.

c. 5 minutes to 12 midnight can be written as 11:55. It is before 12 o’ clock midnight. So, it is 11:55 p.m.

d. 5 minutes after 12 midnight can be written as 12:05. It is after midnight 12 o’ clock.

So, it is 12:05 a.m.

5. a. Making tea will take some minutes.

b. Washing a shirt will take some minutes.

c. Blinking eyes 5 times will take less than a minute.

d. A picnic day will take hours.

6. a. The date on the last day of the year is always 31 December.

b. If today is 30 April 2023, the date tomorrow will be 1 May, 2023, because April has 30 days.

c. If today is 12 June 2023, yesterday’s date was 11 June, 2023.

d. If today is Monday, 1 June 2023, the date after a week will be Monday, 8 June 2023, because 1 week = 7 days. So, 1 + 7 = 8

7. Born in Delhi Played for Delhi U-15 U-19 England Tour Won U-19 World Cup Won ODI World Cup

8. Sun Mon Tues Wed Thurs Fri

a. There are 5 Sundays in the month.

b. The date on the 2nd Saturday is 14.

c. The dates of all the Mondays are 2, 9, 16, 23, 30.

9. Time at which Rama woke up = 7 o’ clock in the morning 7 o’ clock in the morning is after 12 o’ clock midnight but before noon 12 o’ clock.

So, Rama woke up at 7 a.m.

Time at which Rama slept = 9 o’ clock in the night

9 o’ clock at night is after noon and before midnight 12 o’ clock.

So, Rama slept at 9 p.m.

10. Aditi’s age on 28 August 2007: 7 years.

7 + 7 = 14

Thus for 14 years, we add more 7 years to the date: 2007 + 7 = 2014

Thus, Aditi was 14 years old on 28 August 2014.

Challenge

1. Today’s date: 17 April 2023

As the month and year will remain the same, the date from 5 days from now will be 17 + 5 = 22 April 2023

Today is Monday. It will be Saturday after 5 days.

Thus, Arun’s uncle will come on Saturday, 22 April 2023.

2. Number of times hour hand minute hand coincide between 3 p.m. and 4 p.m. = 1 time

Number of times hour hand minute hand coincide between 4 p.m. and 5 p.m. = 1 time

Number of times hour hand minute hand coincide between 5 p.m. and 6 p.m. = 1 time

Thus, the hour hand and the minute hand coincide 3 times between 3 p.m. and 6 p.m.

Case Study

1. The train was delayed by 50 minutes.

2. When Priya reached the station, the clock was showing 3:00 p.m.

When Priya reached there were still 50 minutes for her train to leave.

So, the actual time of Priya’s train was 3:50 p.m.

Thus, option b is correct.

3. The train got delayed by 50 minutes. The original time of arrival was 3:50 p.m.

The time at which the train arrived = 3:50 p.m. + 50 minutes = 4:40 p.m.

Thus, the train arrived at 4:40 p.m.

4. The train was delayed by 50 minutes. So, it was not delayed by an hour. Since 1 hour = 60 minutes

5. Time taken by sweeper to clean the platform = 1 hour 1 hour = 60 minutes

So, the sweeper cleaned the platform in 60 minutes. Answer may vary.

Chapter 11

Let’s Warm-up

1. We can get two ₹10 notes or coins for ₹20, since 2 × ₹10 = ₹20

2. We can get six ₹5 coins for ₹30, since 6 × ₹5 = ₹30

3. Seven ₹2 coins and one ₹1 coin make ₹15, since 7 × ₹2 + 1 × ₹1 = ₹14 + ₹1 = ₹15

4. Ten ₹2 coins make ₹20, since 10 × ₹2 = ₹20

Do It Yourself 11A

1. a. ₹28.50 - Twenty-eight rupees fifty paise

b. ₹36.25 - Thirty-six rupees twenty-five paise

c. ₹49.70 - Forty-nine rupees seventy paise

d. ₹57.35 - Fifty-seven rupees thirty-five paise

e. ₹65.37 - Sixty-five rupees thirty-seven paise

f. ₹71.75 - Seventy-one rupees seventy-five paise

g. ₹88.62 - Eighty-eight rupees sixty-two paise

h. ₹92.48 - Ninety-two rupees forty-eight paise

2. a. Fifty-six rupees seventy paise = ₹56.70

b. Twenty-nine rupees eighty-eight paise = ₹29.88

c. Thirty-five rupees fifty-seven paise = ₹35.57

d. Sixty-eight rupees fifty paise = ₹68.50

e. Seventy-three rupees twenty-two paise = ₹73.22

f. Fifteen rupees sixty-six paise = ₹15.66

3. a.

₹32.50

4. a. ₹25.36 = 2536 paise

b. 802 paise = ₹8.02

c. 2125 paise = ₹21.25

d. ₹125.36 = 12536 paise

e. 36125 paise = ₹361.25

f. ₹358.80 = 35880 paise

5. Price of petrol in Mumbai as of July 2024 = ₹103.44 ₹103.44 as words is one hundred three rupees forty-four paise.

6. Mahi’s Gullak: One note of ₹50, one note of ₹20, coins of ₹10, ₹5 and ₹5

Total amount in Mahi’s Gullak = ₹50 + ₹20 + ₹10 + ₹5 + ₹5 = ₹90

Meher ’s Gullak: Three notes of ₹20 and one coin of ₹10

Total amount in Meher’s Gullak = 3 × ₹20 + ₹10 = ₹60 + ₹10 = ₹70

Mahi’s Gullak has ₹20 more than Meher’s Gullak. Half of this money should be transferred to Meher’s Gullak so that they have the same amount of money.

Thus, ₹20 ÷ 2 = ₹10 should be transferred.

Mahi can transfer two coins of ₹5 or one coin of ₹10 to Meher’s Gullak.

Challenge

1. We need to make ₹639 with the help of 3 notes and 4 coins. We can take 1 of ₹500, 1 note of ₹100 and 1 note of ₹20; 1 coin of ₹10, 1 coin of ₹5 and 2 coins of ₹2. ₹500 + ₹100 + ₹20 + ₹10 + ₹5 + (2 × ₹2) = ₹639

Do It Yourself 11B

1. Price of the lunch box = ₹85.50

Amount of money Priya has = ₹72

More money required by Priya to buy the lunch box = ₹85.50 − ₹72 = ₹13.50

2. Money saved by Vaibhav = ₹50.50

Money saved by Neeraj = ₹75.00

Total money saved by Vaibhav and Neeraj = ₹50.50 + ₹75.00 = ₹125.50

3. Price of the cricket bat = ₹235.50

Price of the ball = ₹45.00

Total price of the bat and the ball = ₹235.50 + ₹45.00 = ₹280.50

4. Cost of snake plant = ₹238

Cost of money plant = ₹125.50

Total money spent = ₹238 + ₹125.50 = ₹363.50

5. Amount of money John has = ₹284.50

Amount of money Maria has = ₹156.00

Amount of money Richa has = ₹284.50 – ₹156.00 = ₹128.50

Richa has ₹128.50 with her

6 Amount given to the shopkeeper = ₹100 Amount received back = ₹28.50 Cost of pencil box = ₹100 – ₹28.50 = ₹71.50 The cost of the pencil box is ₹71.50.

Do It Yourself 11C

1. Fruits and Veggies Store

Vipin needs to pay ₹96.50.

2. The bill is not correct. The correct bill is:

4. Ravi Buys Joe Buys Tanya Buys 2 bananas for ₹10.00

Total:

Yes, Sahil will be able to purchase all the fruits.

Chapter Checkup

1. a. ₹52.36 = Fifty-two rupees thirty-six paise

b. ₹65.14 = Sixty-five rupees fourteen paise

c. ₹71.05 = Seventy-one rupees five paise

2. a. Thirty-eight rupees sixty-five paise = ₹38.65

b. Twenty-nine rupees fifty-five paise = ₹29.55

3. To convert rupee amount to paise amount, remove the dot and ₹ sign then write paise with the number.

a. ₹25.15 = 2515 paise

b. ₹52.25 = 5225 paise

c. ₹235.48 = 23548 paise

4. To convert the paise amount to rupee amount, remove the word 'paise' and put a dot after counting 2 numbers from the right of the given number then put the sign of ₹ before the number.

a. 3256 paise = ₹32.56

b. 15236 paise = ₹152.36

c. 52364 paise = ₹523.64

5. Remove the dot and ₹ sign then write paise with the number. In rupees In paise

a. ₹2.35 348 paise

b. ₹3.48 3480 paise

c. ₹23.56 235 paise

d. ₹34.80 2356 paise

6. Correct bills:

Challenge

1. Amount with Sahil—₹200 Let us prepare the bill for Sahil. Super Market Item Quantity Rate per Item Amount Apples 4 ₹20.00 ₹80.00

Divya has to pay ₹188.50.

8. Cost of a pack of cupcake = ₹136.50

Cost of sugar used in the cupcake = ₹55

Cost of other ingredients used in the cupcake

9. Money that has to be paid by Reena for school fees = ₹535.50

Money with Reena = ₹425

More money required by Reena = ₹535.50 – ₹425 = ₹110.50

10. Amount donated at a mall = ₹152.00

Amount donated outside the temple = ₹58.50

Total amount donated = ₹152.00 + ₹58.50 = ₹210.50

Challenge

1. Store

Amount customer paid to Sam = ₹200.00

Amount Sam will return = ₹200 – ₹130 = ₹70

2. Money with Ajay = ₹2 + ₹1 + 50 paise + 50 paise + 50 paise = ₹3 + ₹1 + 50 paise = ₹4 and 50 paise = ₹4.50

Money with Rahul = ₹2 + ₹2 + ₹1 + 50 paise = ₹5 and 50 paise = ₹5.50

Difference between the amount of money with Ajay and Rahul = ₹5.50 – ₹4.50 = ₹1

Thus, Rahul has ₹1 more than Ajay in his pocket.

Case Study

1. 1 rupee = 100 paise

1 paisa = 10 kauri

1 rupee = 100 × 10 kauri

= 1000 kauri

Thus, option d is correct.

2. Cost of a toy = 10 paise

10 paise as kauri = 10 × 10 kauri

= 100 kauri

Thus, the toy costs 100 kauri.

3. 1 rupee = 100 paise

5 rupees = 5 × 100 paise

= 500 paise

Thus, 5 rupees is the same as 500 paise.

4. Answers may vary.

Chapter 12

Let’s Warm–up

Do It Yourself 12A

1. a. Since 1 out of 2 parts are shaded, the fraction for the shaded portion is 1 2

b. Since 1 out of 3 parts are shaded, the fraction for the shaded portion is 1 3

c. Since 1 out of 4 parts are shaded, the fraction for the shaded portion is 1 4

2. The coloured part of the whole may vary. Sample answers:

a. Half or 1 2 b. Three-fourth or 3 4 c. One-third or 1 3

One-fourth or 1 4 e. Two-thirds or 2 3 f. Three-fourths or 3 4

4. To shade 1 3 of a shape, any one part of 3 parts is to be shaded. Sample figures: a. b. c.

5. Total cups of water that was boiled = 4 cups Cups of water that got evaporated = 2 cups Fraction of water that turned into water vapour = 2 4

Challenge

1. Rajiv folded the paper in half three times. Each time you fold a paper in half, the number of equal parts doubles.

First fold: The paper is folded in half, so there are 2 equal parts.

Second fold: The paper is folded in half again, doubling the parts to 4 equal parts.

Third fold: The paper is folded in half once more, doubling the parts again to 8 equal parts.

After unfolding the paper, it will be divided into 8 equal parts. Since Rajiv coloured each part differently, the fraction representing each part is 1 8

Thus, each of the 8 equal parts represents 1 8 of the whole sheet.

Do It Yourself 12B

1. a. To shade 1 2 of the total objects, any half of the total number of objects can be shaded.

Sample answer:

Total number of pumpkins = 16

Part of the collection we want to colour = half or 1 2

Half or 1 2 of the collection = 16 ÷ 2 = 8

b. To shade 1 2 of the total objects, any half of the total number of objects can be shaded.

Sample answer:

Total number of bats = 14

Part of the collection we want to colour = half or 1 2

Half or 1 2 of the collection = 14 ÷ 2 = 7

c. To shade 1 3 of the total objects, any one-third of the total number of objects can be shaded.

Sample answer:

Total number of mangoes = 18

Part of the collection we want to colour = one-third or 1 3

One-third or 1 3 of the collection = 18 ÷ 3 = 6

d. To shade 1 4 of the total objects, any quarter of the total number of objects can be shaded.

Sample answer:

Total number of apples = 16

Part of the collection we want to colour = one-fourth or 1 4

One-fourth or 1 4 of the collection = 16 ÷ 4 = 4

2. a. 1 4 of 16 = 16 ÷ 4 = 4. So, the statement is true.

b. 1 2 of 10 = 10 ÷ 2 = 5. So, the statement is false.

c. 1 3 of 6 = 6 ÷ 3 = 2. So, the statement is false.

d. 1 3 of 18 = 18 ÷ 3 = 6; 2 3 of 18 = 2 × 6 = 12. So, the statement is false.

3. a. To find 1 2, we divide the whole by 2.

1 2 of 18 = 18 ÷ 2 = 9

b. To find 1 3, we divide the whole by 3.

1 3 of 9 = 9 ÷ 3 = 3

c. To find 1 3, we divide the whole by 3.

1 3 of 21 = 21 ÷ 3 = 7

d. To find 1 4, we divide the whole by 4.

1 4 of 12 = 12 ÷ 4 = 3

4. Total number of plants = 12

Fraction of plants that were put in the living room = 1 3

Number of plants that were put in the living room = 1 3 of 12 = 12 ÷ 3 = 4

Thus, 4 plants were put in the living room.

5. Figures may vary. Sample figure:

Fraction = 8 16

8 parts out of 16 parts are shaded, so the fraction is 8 16

Challenge

1. Total number of bears in the zoo = 12

Fraction of bears which are brown = 1 3

Number of brown bears in the zoo = 1 3 of 12 = 12 ÷ 3 = 4

Number of black bears in the zoo = 2 × 4 = 8

Number of black bears and brown bears in the zoo

= 4 + 8 = 12

= Total number of bears in the zoo. Thus, there are no other colour bears in the zoo.

Do It Yourself 12C

1. a. Total number of parts = 8

Number of shaded parts = 4

Fraction of shaded parts = Number of shaded parts

b. Total number of parts = 9

Number of shaded parts = 5

Total number of parts = 4 8

Fraction of shaded parts = Number of shaded parts

c. Total number of parts = 9

Number of shaded parts = 4

Total number of parts = 5 9

Fraction of shaded parts = Number of shaded parts

d. Total number of parts = 16

Total number of parts = 4 9

Number of shaded parts = 7

Fraction of shaded parts = Number of shaded parts

Total number of parts = 7 16

2. a. 8 out of 14 parts are to be shaded.

8 14

b. 4 out of 10 parts are to be shaded.

4 10

c. 6 out of 10 trees are to be shaded. 6 10

d. 5 out of 9 tomatoes are to be shaded. 5 9

3. a. Total parts in the collection = 9

Number of coloured parts = 4

Fraction of coloured part: Number of coloured parts

Total parts = 4 9

Number of uncoloured parts = 5

Fraction of uncoloured part:

Number of uncoloured parts

Total parts = 5 9

b. Total parts in the collection = 9

Number of coloured parts = 3

Fraction of coloured part: Number of coloured parts

Number of uncoloured parts = 6

Total parts = 3 9

Fraction of uncoloured part: Number of uncoloured parts

Total parts = 6 9

c. Total parts in the collection = 11

Number of coloured parts = 6

Fraction of coloured part: Number of coloured parts

Number of uncoloured parts = 5

Total parts = 6 11

Fraction of uncoloured part: Number of uncoloured parts

Total parts = 5 11

d. Total parts in the collection = 13

Number of coloured parts = 6

Fraction of coloured part: Number of coloured parts

Number of uncoloured parts = 7

Total parts = 6 13

Fraction of uncoloured part: Number of uncoloured parts

Total parts = 7 13

4. Number of red roses = 8

Total number of roses in the vase = 17

Fractions of red roses in the vase = Number of red roses

Total number of roses = 8 17

5. Number of bottles thrown away as waste = 24

Fraction of bottles which were plastic = 1 2

Number of bottles which were plastic = 1 2 of 24 = 24 ÷ 2 = 12

Thus, there were 12 plastic bottles.

6. Total number of shirts with Vishal = 12 shirts

Fraction of shirts which were blue = 1 4

Number of shirts which were blue = 1 4 of 12 = 12 ÷ 4 = 3

Thus, Vishal had 3 blue shirts.

7. Total number of building blocks in the bag = 25

Number of blocks used by Ravi to build a house = 16

Number of blocks which remain unused = 25 – 16 = 9

Fraction of building blocks which remain unused =

Number of unused blocks

Total number of blocks = 9 25

8. Total number of books with Rani = 27

Fraction of books donated by Rani = 1 3

Number of books donated by Rani = 1 3 of 27 = 27 ÷ 3 = 9

Number of books left with Rani = 27 – 9 = 18

Thus, Rani is left with 18 books.

Challenge

1. 4 parts out of 5 is equal to 16.

Thus, 5 parts will be 20.

Thus, there are 20 buses in total.

The figure below shows the groups of buses and buses in each group.

2. Let us divide the shape into equal parts as shown in the figure.

Total number of equal parts = 10

Total number of shaded parts = 2

Total number of unshaded parts = 8

Fraction of the shape left unshaded = 8 10

Chapter Checkup

1. a. Half = 1 2

b. One-third = 1 3

c. Three-fourths = 3 4

d. Numerator: 5; Denominator: 8 = 5 8

e. One-fourth = 1 4

f. Numerator: 7; Denominator: 12 = 7 12

2. a. Total capsicum in the collection = 12

Number of green capsicum = 5

Fraction of green capsicum = Number of green capsicum

Total capsicum = 5 12

Number of yellow capsicum = 7

Fraction of yellow capsicum = Number of yellow capsicum

Total capsicum = 7 12

b. Total stars in the collection = 17

Number of pink stars = 9

Fraction of pink stars = Number of pink stars

Total number of stars = 9 17

Number of blue stars = 8

Fraction of blue stars = Number of blue stars

Total number of stars = 8 17

3. The coloured part of the whole may vary.

a. 3 5

b. 2 7

c. Total kites = 18; Fraction of the kites to be shaded = 1 2 of the total kites = 1 2 of 18 = 18 ÷ 2 = 9

So, we will shade 9 kites.

d. Total balls = 21; Fraction of balls to be shaded = 1 3 of the total balls = 1 3 of 21 = 21 ÷ 3 = 7

So, we will shade 7 balls.

4. a. To find 1 2 of 12, we divide the number by 2: 12 ÷ 2 = 6

b. To find 1 3 of 15, we divide the number by 3: 15 ÷ 3 = 5

c. To find 1 4 of 4, we divide the number by 4: 4 ÷ 4 = 1

d. To find 1 2 of 8, we divide the number by 2: 8 ÷ 2 = 4

5. Total number of people = 4 friends + Tim = 5 friends

Number of equal parts cake is divided = 5

Since the cake is divided into 5 equal parts and there are 5 people, each person gets one part of the cake.

So, the number of pieces each friend gets = 1

Fraction of cake that each friend gets =

Number of parts each friend gets

Total number of parts = 1 5

Thus, each friend gets 1 5 of a cake.

6. Total number of flowers bought by Meena = 9

Fraction of flowers that were tulips = 1 3

Number of flowers that were tulips = 1 3 of 9 = 9 ÷ 3 = 3 tulips

Thus, Meena bought 3 tulips.

7. Total number of plants planted by Manya = 6 plants

Number of plants which were rose = 2 plants

Fraction of plants which were rose = 2 6

8. Total number of apples = 24

Fraction of apples that were rotten = 1 4

Number of apples that were rotten = 1 4 of 24 = 24 ÷ 4 = 6

Number of apples which are still good = 24 – 6 = 18

Thus, 18 apples are still good.

9. Number of invitations sent = 18

Number of friends who were not able to attend the birthday party = 3

Number of friends who attended the birthday party = 18 – 3 = 15

Fraction of friends who attended the birthday party = 15 18

Thus, 15 18 friends attended the birthday party.

Challenge

1. Clue: I am less than 2 and a half wholes. I am more than a whole. You can make me out of 4 halves.

4 halves is the same as 2 wholes.

In option A, we can see two wholes.

Thus, the correct answer is A.

2. Answers may vary. Sample figures:

Case Study

1. Total parts = 8

Parts for fruits and vegetables = 3

Fraction filled with fruits and vegetables = 3 8

Thus option c is correct.

2. Total parts = 8

Parts for proteins = 3

Fraction of proteins in the plate = 3 8

3. Grains cover 2 8 of the plate. True 3 4 of the plate is proteins. False

4. Total parts = 8

Parts of the plate that are protein = 3

Parts of the plate that are not protein = 8 − 3 = 5

Fraction of the plate that is not protein = 5 8

5. Answers may vary.

Chapter 13 Let’s Warm-up

1. Tuesday 2. Friday

3. Monday and Wednesday 4. Thursday

Do It Yourself 13A

1. a. Raw data is an organised form of data. False

b. Writing the numbers in ascending or descending order makes it easier to find the greatest or smallest from the data. True

c. Collecting data makes it easy to understand. False

d. The data collected from surveys is called raw data. True

2. Data of marks obtained out of 100 in Maths, organised from highest to lowest: 99, 98, 89, 83, 80, 78, 77, 70, 65, 58, 45

3. Let us put the data in the table form: Apple, Orange, Banana, Mango, Apple, Grapes, Banana, Grapes, Apple, Grapes, Banana, Mango, Apple, Grapes, Mango, Apple, Banana, Grapes, Mango, Banana, Apple, Orange, Mango, Orange, Grapes, Banana, Orange, Mango.

4. a. The number of people who eat barley is 3

b. The number of people who eat ragi is less than those who eat rice.

c. The most people eat rice as their main food.

Challenge

1. a. Number of cutlets sold by shop A in Week 5

= Half the number of cutlets sold in Week 4

= 1 2 × 40 = 40 ÷ 2 = 20

Thus, shop A sold 20 cutlets in Week 5.

b. Number of cutlets sold by shop B in Week 2 if it sells 10 more cutlets = 40 + 10 = 50

Number of cutlets sold by shop B in Week 3 if it sells 10 more cutlets = 30 + 10 = 40

Total number of cutlets sold by shop B in Week 2 and Week 3 = 50 + 40 = 90

Total number of cutlets sold by shop A in Week 2 and Week 3 = 50 + 20 = 70

Difference between the number of cutlets sold by shop A and shop B in Week 2 and Week 3 = 90 – 70 = 20

Thus, shop B sold 20 more cutlets than shop A in these Weeks.

Do It Yourself 13B

1. a. A pictograph represents data using pictures and objects. True

b. In a pictograph, more pictures mean a bigger number.

True

c. Pictographs help us understand and interpret the data.

True

2.  = 2 children. We can break the given numbers in the multiplication tables of 2.

Favourite Swings Number of Children Favourite Swings Number of Children

2 × 6 = 12

2 × 5 = 10

2 × 4 = 8

3. Given that, = 2 books

Thus,

a. In the table, the number of symbols given for Wednesday = 4

Number of books borrowed on Wednesday = 4 × 2 = 8 books

b. The day on which there are maximum number of symbols = Friday

Number of symbols on Friday = Five and a half

Number of books borrowed on Friday = 5 × 2 + 1 2 × 2

= 10 + (2 ÷ 2) = 10 + 1 = 11

c. Number of symbols on Tuesday = Three and a half

Number of books borrowed on Tuesday = 3 × 2 + 1 2 × 2

= 6 + 1 = 7

Number of symbols on Thursday = 3

Number of books borrowed on Thursday = 3 × 2 = 6

Difference between the number of books borrowed on Tuesday and Thursday = 7 – 6 = 1

4. Flavour Number of Ice Creams

Vanilla

Strawberry

Chocolate

Mango

Key: = 1 ice cream

5. Given that, Key: 1 bin = 1 unit

a. Number of symbols for wet waste = 5

Number of households who segregate wet waste = 5 × 1 = 5 households

Number of symbols for e-waste = 4

Number of households who segregate e-waste = 4 × 1 = 4 households

Difference between the number of households who segregate wet waste and e-waste = 5 – 4 = 1

Thus, 1 more household segregate wet waste compared to e-waste.

b. Number of symbols for wet waste = 5

Number of households who segregate wet waste = 5 × 1 = 5 households

If 3 more households start segregating wet waste then the number of households who segregate wet waste = 5 + 3 = 8 households

c. Answers may vary

6. Answers may vary. Sample answer: On how many households was the survey conducted?

Challenge

1. a. Here, 1 = 10 animals or 10 animals = 1

1 animal = 1 ÷ 10

50 animals = 1 10 × 50 = 5

So, pictures will represent 50 animals.

So, if = 10 animals, 5 pictures will be drawn for 50 animals.

b. Here, 2 = 10 snowflakes

So, = 10 ÷ 2 = 5 snowflakes

20 snowflakes = 5 snowflakes × 4

So, will represent 20 snowflakes.

So, if 2 = 10 snowflakes, 4 pictures will be drawn for 20 snowflakes.

3. a. The least number of glasses of water were drank by Raghav and Eric.

The most number of glasses of water were drank by Nimisha.

b. Number of glasses of water which Nimisha drank = 9

Number of glasses of water which Rajat drank = 8

Difference between the number of glasses of water drank by Nimisha and Rajat = 9 – 8 = 1

Thus, Nimisha drank 1 more glass of water than Rajat.

c. Number of glasses of water which Raghav drank = 7

Number of glasses of water which Shoaib drank = 8

Difference between the number of glasses of water drank by Raghav and Shoaib = 8 – 7 = 1

Thus, Raghav drank 1 less glass of water than Shoaib.

4. a. 4 children like sports.

b. Cartoon channel is the favourite. 9 children like it.

c. Number of children who like adventure = 5

Number of children who like sports = 4

The difference between the number of children who like sports and the number of children who like adventure = 5 – 4 = 1 child

d. Number of children who like comedy = 8

Number of children who like sports = 4

Number of children who like cartoons = 9

Number of children who like adventure = 5

Total number of children in the survey = 8 + 4 + 9 + 5 = 26 children

5. Answers may vary. Sample answer: How many more students like comedy than adventure?

Challenge

1. a. Number of students who read ‘Red Riding Hood’ = 4

If 2 more students read ‘Red Riding Hood’ then the number of students who read this book = 4 + 2 = 6

The book which is read by 6 students according to the given bar graph = ‘Town Mouse and Country Mouse’

Thus, if 2 more students read the story, ‘Red Riding Hood’ then ‘Red Riding Hood’ and ‘Town Mouse and Country Mouse’ will show the same bars.

b. Given that, new 1 division = 2 books.

Earlier 1 division = 1 book

Number of books for ‘Beauty and the Beast’ = 10 books

When 1 division = 2 books, then 10 books will be represented by 10 ÷ 2 = 5 divisions.

Thus, if the scale shows 1 division = 2 books, then we will show 5 divisions for ‘Beauty and the Beast’.

Chapter Checkup

1. Favourite Fruit Number of Students

Number of People in a Household

2. Favourite Hobby Number of Students Singing Dancing Sports Watching TV Reading

3. Given: 1 CINEMA TICKET... = 2 students

a. Number of symbols for musical films = 10

Number of children whose favourite genre is musical = 10 × 2 = 20 children

b. The genre which has the least number of symbols = Action

Thus, action films is liked by the least number of children.

c. Number of symbols for musical films = 10

Number of children whose favourite genre is musical = 10 × 2 = 20 children

Number of symbols for action films = 8

Number of children whose favourite genre is action = 8 × 2 = 16 children

Difference between the number of children who like musical films and those who like action films = 20 – 16 = 4 children

Thus, 4 more children like musical films than action films.

4. a. Only 1 run is scored in the 5th over.

b. Maximum runs were scored in the 6th over.

c. List and add the runs scored in each over till the 10th over: 4 + 8 + 9 + 3 + 1 + 10 + 6 + 8 + 9 + 5 = 63

63 runs are scored in 10 overs.

Challenge

1. As there are 4 pictures of squirrel and 1 picture of squirrel = 2 squirrels then 4 pictures = 4 × 2 = 8 squirrels

Thus, 8 squirrels visited Meher’s garden on Sunday.

2. a. Number of symbols of tomatoes for Suresh = 5 and a half If 2 tomatoes are removed then the number of symbols of tomatoes for Suresh = 3 and a half

Number of tomatoes with Suresh = 3 × 2 + 1 2 × 2 = 6 + 1 = 7 tomatoes

Thus, if 2 pictures of tomatoes are removed from Suresh’s row, then 7 tomatoes were used by him.

b. New key: 1 picture = 4 tomatoes

Old key: 1 picture = 2 tomatoes

Number of tomatoes with Tarachand as per old key = 4 × 2 = 8 tomatoes

Number of pictures of tomatoes for Tarachand as per new key = 8 tomatoes ÷ 4 = 2 pictures

Thus, if the key changes to 1 picture = 4 tomatoes, then 2 pictures should be drawn for Tarachand.

Case Study

1. The highest rainfall is in the month of February. Thus, the correct answer is option (c).

2. The bar for June is the lowest. June shows the lowest rainfall.

3. April has the second highest length of the bar in the bar graph. Thus, April shows the second highest rainfall.

4. Answers may vary.

About the Book

The Imagine Mathematics teacher manuals bridge the gap between abstract mathematics and real-world relevance, offering engaging activities, games and quizzes that inspire young minds to explore the beauty and power of mathematical thinking. These teacher manuals are designed to be indispensable companions for educators, providing well-structured guidance to make teaching mathematics both effective and enjoyable. With a focus on interactive and hands-on learning, the lessons in the manuals include teaching strategies that will ensure engaging lessons and foster critical thinking and problem-solving skills. The teaching aids and resources emphasise creating an enriched and enjoyable learning environment, ensuring that students not only grasp mathematical concepts but also develop a genuine interest in the subject.

Key Features

• Alignment with Imagine Mathematics Content Book: Lesson plans and the topics in the learners’ books are in sync

• Learning Outcomes: Lessons designed as per clear, specific and measurable learning outcomes

• Alignment to NCF 2022-23: Lessons designed in accordance with NCF recommendations

• Built-in Recaps: Quick recall of pre-requisite concepts covered in each lesson

• Supporting Vocabulary: Systematic development of mathematical vocabulary and terminology

• Teaching Aids: Resources that the teachers may need to facilitate the lesson

• Activity: Concise and organised lesson plans that outline each activity

• Extension Ideas: Analytical opportunities upon delivery of each lesson

• Detailed Solutions: Solutions to all types of questions in the Imagine Mathematics Content Book

• Digital Assets: Access to supplementary interactive resources

About Uolo

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ISBN 978-81-984519-7-2

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