Imagine_Maths_TM_Grade3

MATHEMATICS

Teacher Manual

MATHEMATICS

Master Mathematical Thinking

Grade 3

Foreword

Mathematics is not just another subject. It is an integral part of our lives. It shapes the very foundation of our understanding, personality and interaction with the world around us.

However, due to the subject’s abstract nature, the stress of achieving high academic scores and complex teaching methods, most children develop a fear of mathematics from an early age. This fear not only hinders their mathematical thinking, logical reasoning and general problem solving abilities, but also negatively impacts their performance in other academic subjects. This creates a learning gap which widens over the years.

The NEP 2020 has distinctly recognised the value of mathematical thinking among young learners and the significance of fostering love for this subject by making its learning engaging and entertaining. Approaching maths with patience and relatable real-world examples can help nurture an inspiring relationship with the subject. It is in this spirit that Uolo has introduced the Imagine Mathematics product for elementary grades (1 to 8). This product’s key objective is to eliminate the fear of mathematics by making learning exciting, relatable and meaningful for children. This is achieved by making a clear connection between mathematical concepts and examples from daily life. This opens avenues for children to connect with and explore maths in pleasant, relatable, creative and fun ways.

This product, as recommended by the NEP 2020 and the recent NCF draft, gives paramount importance to the development of computational and mathematical thinking, logical reasoning, problem solving and mathematical communication, with the help of carefully curated content and learning activities.

Imagine Mathematics strongly positions itself on the curricular and pedagogical approach of the Gradual Release of Responsibility (GRR), which has been highly recommended by the NEP 2020, the latest NCF Draft and other international educational policies. In this approach, while learning any new mathematical concept, learners first receive sufficient modelling, and then are supported to solve problems in a guided manner before eventually taking complete control of the learning and application of the concept on their own. In addition, the book is technologically empowered and works in sync with a parallel digital world which contains immersive gamified experiences, video solutions and practice exercises among other things. Interactive exercises on the digital platform make learning experiential and help in concrete visualisation of abstract mathematical concepts.

In Imagine Mathematics, we are striving to make high quality maths learning available for all children across the country. The product maximises the opportunities for self-learning while minimising the need for paid external interventions, like after-school or private tutorial classes.

The book adapts some of the most-acclaimed, learner-friendly pedagogical strategies. Each concept in every chapter is introduced with the help of real-life situations and integrated with children’s experiences, making learning flow seamlessly from abstract to concrete. Clear explanations and simple steps are provided to solve problems in each concept. Interesting facts, error alerts and enjoyable activities are smartly sprinkled throughout the content to break the monotony and make learning holistic. Most importantly, concepts are not presented in a disconnected fashion, but are interlinked and interwoven in a sophisticated manner across strands and grades to make learning scaffolded, comprehensive and meaningful.

As we know, no single content book can resolve all learning challenges, and human intervention and support tools are required to ensure its success. Thus, Imagine Mathematics not only offers the content books, but also comes with teacher manuals that guide the pedagogical transactions that happen in the classroom; and a vast parallel digital world with lots of exciting materials for learning, practice and assessment. In a nutshell, Imagine Mathematics is a comprehensive and unique learning experience for children.

On this note, we welcome you to the wonderful world of Imagine Mathematics. In the pages that follow, we will embark on a thrilling journey to discover wonderful secrets of mathematics—numbers, operations, geometry and measurements, data and probability, patterns and symmetry, algebra and so on and so forth. Wishing all the learners, teachers and parents lots of fun-filled learning as you embark upon this exciting journey with Uolo.

Key Elements of a Lesson—A Quick Glance

Clear and concise lessons that can be implemented through the academic year with each perfectly aligned to the topics covered in the Imagine Mathematics learners’ content book.

Place Value 1

Place Value 1

Place Value 1

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

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

Place Value 1

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

to check if students know how to read, write and show 2-digit and 3-digit numbers.

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

Vocabulary

Learning

Vocabulary

Alignment to NCF

C-1.1: Represents numbers using the place value structure of the Indian number system, compares whole

form:

of

of all the digits in a number round off: to write the closest 10 or 100 number instead of the actual number

Teaching Aids

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

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

QR Code: Access to digital solutions and other interactive resources.

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

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

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

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.

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 handson 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.

Place Value and Expanded Form of 4-digit Numbers

Reading 4-digit Numbers

Comparing Numbers

Forming 4-digit Numbers

Rounding off 3-digit Numbers

Revision

Addition by Expanding Numbers

Addition Without Regrouping

Addition With Regrouping

Adding Bigger Numbers

Estimating the Sum

Word Problems

Revision

Quick Subtraction

Subtraction Without Regrouping

Subtraction With Regrouping

Subtracting Bigger Numbers

Estimating the Difference

Word Problems

Revision

4.

5.

6.

7.

8.

9

Multiplication Facts

Table of 6

Table of 7

Table of 8

Table of 9

Tables of 10, 20, ..., 90

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

Multiplying by Expanding the Bigger Number

Multiplying by 1–digit Number Without Regrouping With Regrouping

Estimating the Product Word Problems

Revision

Equal Sharing

Division as Repeated Subtraction

Division and Multiplication Facts

8

Using Multiplication Tables

Properties of Division

Revision

Long Division Without Remainder

Division With Remainder

Word Problems

Revision

Features of 2-D Shapes

Symmetry in 2-D Shapes

Features of 3-D Shapes

View of Objects

Repeating Patterns

Rotating Patterns

Growing Patterns

Number Patterns

Tiling Patterns

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

Imagine Maths Page 3

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 then 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.

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 a rod of an abacus tells us the value of the digit.

Ask 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.

Th H T O

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 students to work in groups and use the place value blocks to show two 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. Finally, ask them to write the answer in their notebooks. Repeat the activity with two more numbers.

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 highest to lowest thus forming the largest number. Show them an abacus where the beads are arranged in descending order to form the number 7643. Ask students to form groups and take one 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. They will then draw the abacus for each number and write the numbers formed in their notebooks.

Imagine Maths Page 11

Th H T O

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 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.

Answers

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

Do It Together

Th H T O

4 3 1 9

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. Reading 4-digit Numbers

Do It Together

6000 + 400 + 30 + 4 six thousand thirty four four hundred

The number 6434 can be read as six thousand four hundred thirty-four.

3. 4-digit Numbers on Abacus

Do It Together

5 beads at the thousands place  4 beads at the tens place

2 beads at the hundreds place   1 bead at the ones place

Th H T O

5 2 4 1

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

4. Comparing Numbers

Do It Together

1765 4372 6145 4538 6 > 4 > 1

4372 4538 5 > 3

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

5. Forming 4-digit Numbers

Think and Tell

We have not placed 0 at the thousands place, because the number will become a 3-digit number.

Do It Together

Smallest number place the digits in ascending order: 3059

Th H T O

3 0 5 9

Largest 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

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.

Alignment to NCF

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.

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 sum

Teaching Aids

Small boxes; Green and blue marbles; Place value blocks of 100s, 10s and 1s; Straws in red, blue, yellow and white; Sheets with number lines drawn on them; Word problem written on a sheet of paper 6

Chapter: Addition of 3-digit Numbers

Properties of Addition

Learning Outcomes

Imagine Maths Page 20

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 two boxes of marbles with 4 green and 5 blue marbles in one box and 5 green and 4 blue marbles in another box to each group.

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. Ask them to now 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.

Ask them to now put 4 green marbles in one box. Ask them to add one more green marble and tell the sum. Explain that when we add 1 to any number, we get its successor. Ask the students to now 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

Learning Outcomes

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

Teaching Aids

Place value blocks of 10s and 1s

Activity

Imagine Maths Page 23

Instruct the students to work in groups. Distribute the place value blocks of 10s and 1s among the groups. Write a 2-digit addition problem on the board, like 23 + 12. Ask the students to show both the numbers using the place value blocks. Ask them to write the expanded form of the numbers in their notebooks.

Instruct them to combine the 1s and 10s blocks of both the numbers. Show them to write the total in the expanded form and then in standard form in their notebooks and make them practise more such problems mentally.

Addition Without Regrouping

Learning Outcomes

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

Teaching Aids

Straws in red, blue and white

Activity

Instruct the students to work in groups. Distribute the straws among the groups. Display an addition problem like 435 + 242 on the board. Introduce the column method by creating three columns (hundreds, tens and ones) and writing the digits of 435 and 242 in their corresponding columns. Specify that the red straws represent hundreds, the blue straws represent tens, and the white straws represent ones.

Imagine Maths Page 26

Instruct the students to copy the table and organise the straws based on the numbers: 435 with 4 red, 3 blue and 5 white straws; and 242 with 2 red, 4 blue and 2 white straws. Ask them to count the straws of each colour and record the total below its corresponding column.

Addition With Regrouping Imagine Maths Page 28

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 regroups 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 red straws represent thousands, blue straws represent hundreds, yellow straws represent tens, and 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 its corresponding column.

Estimating the Sum Imagine Maths Page

36

Learning Outcomes

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

Teaching Aids

Sheets with 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, let’s say 48 and 64, and ask the students to round them off to the nearest 10 using the number lines provided. 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.

Word Problems

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. Ask them to then 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

C Circle the numbers.

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

U Underline the question. B Box the key words.

E Evaluate/draw S Solve and check. 3

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 two months?

1. Properties of Addition

Answers

6. Regrouping Tens and Ones

Do It Together

2. Addition by Expanding Numbers

Think and Tell

The smallest 2-digit number is 10.

The largest 2-digit number = 99

So, the sum is 109. Do

7. Regrouping Hundreds

Do It Together

Do It Together Th H T O

8. Adding Bigger Numbers

Do It Together

3. Addition Without Regrouping

4. Regrouping Ones

5. Regrouping Tens

9. 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.

10. Word Problems

Do It Together

Number of girls = 480

Number of boys = 435

Total number of students = 480 + 435

Thus, 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 by a 3-digit number without regrouping.

subtract a 3-digit number by a 3-digit number with regrouping. subtract a 4-digit number by 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; Paper slips with numbers up to 50; Bowl; Operations stickers; Word problem sheets; Place value chart

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 different coloured counters 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.

Quick Subtraction

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

Imagine Maths Page 47

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 two numbers.

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

Subtraction Without Regrouping

Learning Outcomes

Imagine Maths Page 50

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 two 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 two methods.

Extension Idea

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

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

Subtraction With Regrouping

Learning Outcomes

Imagine Maths Page 52

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. Then, instruct them to solve the subtraction problem by writing the numbers one below the other and ask them to write the answers in their notebooks. Ask them 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?

Learning Outcomes

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

Teaching Aids

Place value chart

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 and cross out the number equivalent to the smaller number. Ask them the value of the remaining numbers on the place value chart.

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 two 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; Bowl; Place value blocks

Activity

Divide the class into groups.

Imagine Maths Page 60

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

Instruct them to round off the numbers to the nearest ten and then use the place value blocks to subtract the rounded-off numbers.

Encourage them to write the subtraction sentence in their notebooks.

Repeat the activity once more if time allows.

Learning Outcomes

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

Teaching Aids

A word problem written on a sheet of paper with space given 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

3. By Expanding the Smaller Number

2. By Counting Forward on a Number Line

4. Subtraction Without

35

The difference between 35 and 12 is 23.

5. Regrouping Tens

9. Estimating the Difference

Do It Together

32 is rounded off to 30

So, 532 – 204 = 328.     So, 643 – 328 = 315.

6. Regrouping Hundreds

Do It Together 1

7. Regrouping Twice

Do It Together

1

640 – 386 = 254.       954 – 867 = 87

8. Subtracting Bigger Numbers

Do

16 is rounded off to 20.

Estimated difference = 30 – 20 = 10. So, the estimated difference is 10.

10. 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 = ?

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

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 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 two 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

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 that 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 that any number multiplied by 0 gives 0. Discuss examples of 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.

Table of 6

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.

Imagine Maths Page 73

Ask the first student from each group to put one 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 two cups and put 6 straws inside each cup. Ask them to count the total number of straws in the two cups and write the multiplication sentence in their notebooks. Repeat the activity by asking the third student to put 6 straws each in three 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.

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 one 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 two cups and put 7 marbles inside each cup. Ask them to count the total number of marbles in the two cups and write the multiplication sentence in their notebooks. Repeat the activity by asking the third student to put 7 marbles each in three 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 7 + 7 + 7 + 7 + 7 = 5 × 7 = 35 books. So, there are 35 books in total.

Table of 8

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 into pairs.

Distribute the 100s grids to each pair.

Imagine Maths Page 75

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:

Table of 9

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 one more string with another 9 beads. Ask them to count the total number of beads on the two 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.

Imagine Maths Page 77

Ask them to put 1 bundle in front of them and write the multiplication sentence in their notebooks. Ask them to place one 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 two 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.

Ask them to now 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.

1. Multiplication Facts

1. 6 × 9 = 9 × 6

2. 14 × 1 = 14

3. 8 × 0 = 0

4. 18 × 1 = 18

2. Table

There are multiple patterns in the table. One pattern is the numbers shown diagonally shows the multiplication table of 9.

5

Multiplication by 2-digit Numbers

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.

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 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 two 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 by Expanding the Bigger Number

Learning Outcomes

Imagine Maths Page 85

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.

Multiplying by 1-digit Number

Learning Outcomes

Imagine Maths Page 88

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.

Without Regrouping

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.

With Regrouping

Learning Outcomes

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

Imagine Maths Page 92

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.

326

Instruct the students to pick one 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

Learning Outcomes

Imagine Maths Page 97

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 answ ers 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 with 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?

Answers

1. Multiplying by Expanding the Bigger Number

Do It Together

300

So, 122 × 3 = 366

2. Without Regrouping

Do It Together

Step 1

Multiply by the digit in the ones place.

Multiply by the digits in the tens place.

5. With Regrouping

Do It Together

4

3. With Regrouping

Do It Together

4. Without Regrouping

Do It Together

6. 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

7. Word Problems

Do It Together

Step 1

What do we know?

No. of beads in a necklace = 23

No. of necklaces to be made = 22.

Step 2

What do we need to find?

Total no. of beads required = 23 × 22.

Total beads required for 22 necklaces are 506

Division 6

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 out

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

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.

Imagine Maths Page 103

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 finished. 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 can’t be shared equally.

Imagine Maths Page 105

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’ve 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?

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. They will then 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

Imagine Maths Page 111

Ask the students if they can divide 48 ice cream sticks into 6 cups and how many sticks will there be 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.

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.

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

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

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

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

Do the same for the remaining two properties given below.

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

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

Answers

1. Equal Sharing

As

2. Division as Repeated Subtraction

Do It Together

2 4

6 1 8

Count

times.

4. Using Multiplication Tables

Do

48 ÷ 6

56 ÷ 8

63 ÷ 9

72 ÷ 8

3. Division and Multiplication Facts

Do

6  ×  8  =  48

Therefore, 48 ÷ 6 =  8

8 ×  7  =  56

Therefore,  56  ÷ 8 =  7

9  ×  7  =  63

Therefore,  63  ÷ 9 =  7

8  ×  9  =  72

Therefore,  72  ÷  8  =  9

5. Properties of Division

Think and Tell

8735 ÷ 8735 = 1

Do It Together

81 ÷ 0

No answer

0 ÷ 99 0 ÷ 99 = 0

56 ÷ 1   56

96 ÷ 96     1

58 ÷ 0

No answer

0 ÷ 46     0

7

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-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-4.1: 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: a number that divides another number

quotient: the number we get when we divide one number by the other

remainder: number left after the division

Teaching Aids

Place value blocks for 1s, 10s and 100s; 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

Activity

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

Instruct 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.

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. 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

Activity

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

Distribute place value blocks among the students. Each student should then represent the dividend (325) using 100s, 10s and 1s blocks. Demonstrate making 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.

Word Problems

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 sheet with the word problem written on it.

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

Imagine Maths Page 122

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 one 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 boxes?

Answers

1. Long Division Without Remainder

Do It Together

Checking division:

Checking division:

2. Division With Remainder

Think and Tell

No. The remainder should be less than the divisor.

3. Word Problems

Do It Together

What do we know?

Checking division:

(Quotient × Divisor) + Remainder = Dividend

(14 × 3) + 2 = 44

42

4801

Number of cups one jug can hold = 7

Total cups of juice to be filled = 819

What do we need to find?  Number of jugs

How to find it? 819 ÷ 7 = ? Solve

find the answer.

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

Shapes and Patterns 8

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.

list the properties of 3-D shapes. draw the front, top and side view of objects. identify the rule in a given repeating pattern and extend the pattern.

Alignment to NCF

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.

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

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

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

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; Pair of scissors; Cutouts of 2-D shapes such as circles, triangles and squares; Clock with movable hands; Paper cutouts of triangles with a dot on one corner; Paper cutouts of different colours; Wooden 3-D shapes; Disposable plates, glasses and bowls; Stickers of different shapes; Unit blocks; Number grids; Ball; Square grids 37

Chapter: Shapes and Patterns

Features of 2-D Shapes

Learning Outcomes

Imagine Maths Page 129

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; Pair of scissors

Activity

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

Ask 1 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. Ask them to use the dot paper to draw the shapes using the properties.

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 sides equal.

Symmetry in 2-D Shapes

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 133

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 shape into 2 rectangles. A diagonal line of symmetry splits the shape into 2 triangles.

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.

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 vertices?

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.

View of Objects

Learning Outcomes

Students will be able to draw the front, top and side view of objects.

Teaching Aids

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

Activity

Imagine Maths Page 140

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 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 and a bowl to each group.

Ask them to 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.

Extension Idea

Ask: On drawing the views of which 3-D shape will you get only squares?

Say: On drawing the views of a cube, we get only squares.

Repeating Patterns

Learning Outcomes

Imagine Maths Page 143

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, etc.

Rotating Patterns

Learning Outcomes

Imagine Maths Page 143

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 next 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.

Learning Outcomes

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. Ask them about the similarities and differences in the pattern. Discuss growing patterns. Bring out the fact that in growing patterns, some unit is 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.

Number Patterns

Learning Outcomes

Imagine Maths Page 144

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.

Learning Outcomes

Students will be able to identify the shape that forms the 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

Think and Tell

6 sides and 6 corners. Yes, the shape has all straight sides.

4. View of Objects

5. Understanding Patterns

2. Symmetry in 2-D Shapes

3. Features of 3-D Shapes

Length, Weight and Capacity 9

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

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

Chapter: Length, Weight and Capacity

Units of Length

Learning Outcomes

Imagine Maths Page 153

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

Road Key Door

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 154

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 notebooks.

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.

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 a metre and a centimetre. Take the students to the playground and instruct them to work in two 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 a partner. Back in the classroom, ask the students to write the answers in their notebooks.

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

Imagine Maths Page 159

Learning Outcomes

Students will be able to solve word problems on length.

Teaching Aids

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 three 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 one 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 notebooks.

Ask the groups to pass their word problems to other groups to solve.

Units of Weight

Learning Outcomes

Imagine Maths Page 162

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

Imagine Maths Page 163

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

Distribute one set of number cards with weights written in grams to the first group and another set of number cards with 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 a partner.

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

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

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 given three types of fruits.

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

Ask one 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 notebooks.

Ask the groups to pass their word problem to other groups to solve.

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?

Units of Capacity

Learning Outcomes

Imagine Maths Page 167

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 various 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.

Cup Bucket Spoon

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 notebooks. Ask them to sort the things based on their units of measurement.

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 two groups.

Distribute the number cards with capacity written in millilitres to the first group and another set of number cards with the corresponding capacity 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 a partner. Ask the students to write the answers in their notebooks.

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.

Word Problems on Capacity

Learning Outcomes

Students will be able to solve word problems on capacity.

Teaching Aids

Cards with containers and their capacities

Activity

Imagine Maths Page 170

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

Instruct the students to frame a word problem using the capacities of the given three types of containers. (Note: If the students aren’t able to form a word problem, then provide them with a word problem.)

Ask one 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 notebooks.

Ask the groups to pass their word problem to the other groups to solve.

Answers

1. Units of Length

Do It Together

1 Length of the school grounds cm m km

2 Length of the bus cm m km

3 Length of a desk cm m km

4 Distance between a park and the house cm m km

5 Length of a shoe cm m km

6 Height of a street light pole cm m km

7 Length of a bat cm m km

8 Length of a saree cm m km

9 Height of a flagpole cm m km

10 Distance between a shop and the school cm m km

2. Measuring Length Using a Ruler

Do It Together

1 Ravi has two plants. The distance between the plants is 4 cm.

2  The length of the photo is 10 cm.

3 Ravi marked the length of a book on the ruler. The length is 12 cm.

4

3. Converting Units of Length

Do It Together

1

4

4. Word Problems on Length

Do It Together

Step 1: What do we know?

Distance travelled on Monday = 6 km

Distance covered on Tuesday = 12 km

Step 2: What do we need to find?

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.

5. Units of Weight

Do It Together

Cupcake        g kg

Tall Cake        g  kg

Pack of biscuits     g kg

Slices of Bread       g kg

Oven          g  kg

Cabinet       g  kg

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 A vendor sold 6 kg of tomatoes. He sold 6000 g of tomatoes.

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

7. Word Problems on Weight

Do It Together

Step 1: What do we know?

Weight of Bhanu’s suitcase = 15 kg

Weight of Vidya’s suitcase = 19 kg

Step 2: What do we need to find?

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.

It Together

10. Word Problems on Capacity

Do It Together

Step 1: What do we know?

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

Step 2: What do we need to find?

Total amount of petrol used to fill the 3 vehicles

= 79 L

10

Time

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 twelve multiples of 60; Bowl; Strips of paper; Year calendar; Story on a sheet of paper; Sample birth certificates

Chapter: Time

Read Time on a Clock

Learning Outcomes

Imagine Maths Page 176

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 the students 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 179

Demonstrate to the students the time intervals in which we write a.m. and p.m. Ask the students to look in 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 two 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

Imagine Maths Page 182

Clocks made on paper plates (without hands); Ice cream sticks; Small bags; Cards with digits from 1–12 and the first twelve 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 could match it with its correct pair with a student in group 2. After 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.

Estimating Time

Learning Outcomes

Imagine Maths Page 182

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

Teaching Aids

Bowl; Strips of paper

Activity

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

Distribute the strips of paper giving one 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 two groups. Discard the duplicate activities.

Conduct a quiz by picking a slip one by one and asking 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).

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 has to 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?

Ask questions like: On which day will your birthday fall?

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.)

Imagine Maths Page 190

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 he went to Kanyakumari in December.

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.

Reading a Birth Certificate Imagine

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 mock 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 parents of the person?; Where was the person born?

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

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

Extension Idea

Form Number

Government of ____________

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

Ask: If the date on Tanya’s birth certificate is January 10, 2020, then 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. Read Time on a Clock

Do It Together

2. Time as A.M. and P.M.

Think and Tell

Two times

Do It Together

3. Converting Time

Think and Tell

Answers may vary. Sample answer:

Approximately 6 hours.

Do It Together

a How many hours has Jenny spent doing the project?

The hour hand moved from 6 to _________ . It has moved by numbers, so hours have passed.

b  How many minutes has Jenny spent doing the project?

We know that 1 hour = 60 minutes.

So, hours = 60 minutes + minutes = minutes.

4. Estimating Time

Think and Tell

Answers may vary. Sample answer:

Two activities that may take days to complete can be camping and winter holidays.

Do It Together

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

January : 31 days February : 29 days

March : 31 days April : 30 days

May : 31 days June : 30 days

July : 31 days August : 31 days

September : 30 days October : 31 days

November : 30 days December : 31 days

6. Reading and Interpreting the Calendar

7. Making a Timeline

8. Reading a Birth Certificate

Do

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 the 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); Cards with pictures of ice cream flavours with price tags (e.g. Chocolate - ₹10.00, …); Envelopes with play money making up different amounts; Play money; Play money (in paise); Items with price tags in rupees; Semicircular puzzle cutouts with amounts in paise on one part and corresponding rupees on another part; Toy; Pack of stickers; Notebook

Chapter: Money

Rupee and Paise Amounts

Learning Outcomes

Imagine Maths Page 199

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 to the students. Take the students out to the playground. Instruct them to stand in two 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 200

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 counting 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 ₹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 one 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 204

Semicircular puzzle cutouts 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 two 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 cutouts with amounts in paise on one part and corresponding rupees on another part. Make sure that there are distractor cutouts too.

Ask the students to take the paise cutouts and look for their corresponding rupee conversion. Ask them to join the conversion cutouts 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 answers 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 find the answers 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

Imagine Maths Page 207

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

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

₹36.60 = thirty-six rupees sixty paise.

₹42.80 = forty-two rupees eighty paise.

₹61.03 = sixty-one rupees three paise.

2. Counting Money

Think and Tell

Yes, ₹20 + ₹1 + 50 paise = ₹21.50 + +

Do It Together

Step 1

Answers

4. Converting Paise into Rupees

Do It Together

12365 paise

Step 1: Remove the word ‘paise’ and put a dot after counting 2 numbers from the right of the given number.

8700 paise

Step 1: Remove the word ‘paise’ and put a dot after counting 2 numbers from the right of the given number.

Add the rupee notes and coins.

₹500 + ₹100 = ₹600.

₹600 + ₹20 = ₹620.

₹620 + ₹2 = ₹622

Step 2

Write the paise amount separated by a dot with the total rupee amount.

₹622 and 25 paise = ₹622.25 In figures = ₹622.25.

3. Converting Rupees into Paise

Do It Together

₹125.36 ₹56

Step 1: Remove the dot and ₹ sign.

₹125.36 =

Step 2: Write paise with the number.

Therefore, ₹125.36 = paise.

Remove the ₹ sign number and add 2 zeros after the 12536 12536

Step 1: _____________________ .

5600

₹56 = .

Step 2: _____________________

Write paise with the number

Therefore, ₹56 = paise.

5600

12365 paise = .

Step 2: Put the sign of ₹ before the number. Therefore, 12365 paise = ₹

123.65 123.65

Do It Together

Money with Anushka = ₹135.00. Money given by Mom = ₹42.50. Money given by Dad = ₹37.00.

8700 paise = .

87.00

Step 2: ______________________

Therefore, 8700 paise = ₹

Put the sign of ₹ before the number 87.00

5. Word Problems on Money

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

Yes, it will be the same.

The new total would be: ₹30 + ₹6.50 + ₹15.00 + ₹12.00 = ₹63.50.

Do It Together

Adarsh Departmental Store

The amount paid by Vishal = ₹171.50

Fractions 12

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; Coloured pencils; Crayons; Bangles; Sheet with circles drawn; Sheets with fraction circles drawn; One apple; Word problem cards

Chapter: Fractions

Parts of a Whole

Learning Outcomes

Imagine Maths Page 215

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; Coloured 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 coloured pencils.

Instruct students to work in their groups to fold the strips into halves, fourths and thirds. They will then shade to show the fractions one-half, one-fourth, one-third and two-thirds. Each student in the group should show one fraction. In their notebooks, they will then 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 219

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.

1 4 of 8 crayons = 2 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.

Writing

Learning Outcomes

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

Teaching Aids

One apple; Sheets with fraction circles drawn

Activity

Distribute 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.

Imagine Maths Page 227

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?

Say: There can be many such problems. One problem can be: Rohan has 45 bunches of f lowers. He sold 1 3 of the bunches. How many bunches of f lowers 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

Number of yellow balloons = 3

Total number of balloons = 7

Fraction of yellow balloons = Number of yellow balloons

Total number of balloons = 3 7

Number of green balloons = 4

Total number of balloons = 7

Fraction of green balloons = Number of green balloons

Total number of balloons = 4 7

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; Sheets with bar graphs showing the favourite sport of some children; Chart paper; Square cutouts; Glue sticks

Chapter: Data Handling

Data Tables

Learning Outcomes

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

Teaching Aids

Fruit stickers

Activity

Discuss with the students how to read the data given in a table.

Imagine Maths Page 234

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 of the favourite fruit of the whole class. In their notebooks, they will then make the 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 liked 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 238

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 take 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 the art class?

Say: 1 picture = 10 students, 3 and a half pictures = 30 + 5 = 35 students. So, 35 students went to the 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 students using 4 pictures, and since 1 picture shows 5 students, the art club will have 4 × 5 = 20 students.

Instruct the students to now 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.

Imagine Maths Page 241

Activity Club Number of Children Art

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? In their notebooks, they will then write the answers.

Drawing a Bar Graph

Learning Outcomes

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

Teaching Aids

Chart paper; Square cutouts; Glue sticks

Activity

Imagine Maths Page 246

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

Instruct the students to work in groups.

Distribute the chart paper, square cutouts 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. Ask them to now use the square cutouts and stick as many square cutouts as the number of marbles given in the table to make a tower.

Extension Idea

Ask: How many cutouts 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 cutouts 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 sport 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. We then 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?

1. Data Tables

Answers

2  Who purchased the most chocolates? How many?

Jennifer

The symbol of chocolates for is the most. The number of chocolates purchased =

Jennifer 8

4. Drawing a Bar Graph

Do It Together

y - axis

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

A B C 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 have made the pictograph difficult to read.

Do It Together

1 How many chocolates did Ahaan purchase?

Number of symbols of chocolates for Ahaan = 2 and

Scale: 1 division = 1 pencil

Number of Pencils Student x - axis

Ashutosh Akram   Vinay    Robin    Atif

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 between the hours spent on Maths homework and English homework = 9 – 6 = 3 hours.

2. English < Hindi < Science < Maths

Key: chocolates

2    4

Thus, Ahaan purchased chocolates.

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. 2356 b. 4111 c. 5431 d.  3344

2. a. 4746 b. 5625 c. 5241 d. 4047

3. a. 1932     b. 5358       c. 3041

Th H T O Th H T O Th H T O d. 7465       e. 9030       f. 4856

Th H T O Th H T O Th H T O

4. a. 3245 b. 5386 c. 7040 d. 6008 e. 2400 f. 8005  g. 9502  5. a. one thousand five hundred thirty-two   b. three thousand one hundred fifty-six c. four thousand eight hundred eleven d. six thousand five hundred eighteen e. seven thousand two hundred ninety-four

f. eight thousand forty-three g. seven thousand nine hundred h. nine thousand six hundred eighty-seven

6. a. 200 b. 5000 c. 4 d. 90 e. 8000 f. 9000 g. 600  h. 90  7. a. 3241 b. 5724 c. 7052 d. 6400 e. 8090

f. 9000 8. a. 2000 + 100 + 40 + 8

b. 4000 + 000 + 30 + 6 c. 6000 + 100 + 00 + 5

d. 7000 + 200 + 00 + 3 e. 8000 + 200 + 00 + 0

f. 6000 + 500 + 60 + 6 g. 7000 + 900 + 80 + 0

h. 9000 + 600 + 50 + 0

9. Value of the thousands place = 1000

Value of the hundreds place = 900

Value of tens place = 70

We get 1 + 9 + 7 + ____ = 20

= 1 + 9 +7 + 3 = 20

The year is 1973.

1B 1. a. 614 < 1700 b. 5092 < 7320 c. 2184 < 2357

d. 5720 > 5265 e. 4126 < 4510 f. 5271 > 5261

g. 4680 = 4680  2. a. 3205 4289 3526 3010

b. 4370 3740 7304 7403 c. 1080 1800 1008 8001  d. 1199 1999 9111 1991 e. 5022 2500 5477 4577  f. 9129 1299 9921 9291  3. a. 658 2168 6345 1265

b. 5882 3678 8249 8924 c. 6160 6061 6610 6110

d. 9911 9991 1119 9191 e. 4426 6244 4264 2644

f. 7567 6757 7067 7563

4. Ascending order a. 1765, 4390, 7430, 7935 b. 773, 2860, 7880, 9573 c. 392, 3067, 4853, 7943 d. 157, 6583, 8546, 9404 e. 1265, 3867, 8734, 8753 f. 3654, 6436, 8328, 9754

Descending order a. 7935, 7430, 4390, 1765

b. 9573, 7880, 2860, 773 c. 7943, 4853, 3067, 392

d. 9404, 8546, 6583, 157 e. 8753, 8734, 3867, 1265

f. 9754, 8328, 6436, 3654

5. Number of marbles with Simi = 245

Number of marbles with Eva = 236

Simi has more marbles as 245 > 236.

Number of marbles that could be with Dhwani = 230, 272 or 229. Dhwani has more marbles than Simi. So, Dhwani can have 272 marbles since only 272 is greater than 245.

1C 1. a. 512 b. 840 c. 6312 d. 9050 e. 710 f. 7400

2.

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

3. Smallest: a. 2467 b. 1367 c. 1025 d. 5068 e. 2089

f. 1057 g. 2578 h. 2489 Greatest: a. 7642 b. 7631

c. 5210 d. 8650 e. 9820 f. 7510 g. 8752 h. 9842

4. Odd numbers: 83, 91, 63, 149, 727, 923 Even numbers: 36, 78, 164, 348, 586, 860  5. 7908 1D 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. 59 is in between 50 and 60 but is closer to 60 d. 44 is in between 40 and 50 but is closer to 40 e. 123 is in between 120 and 130 but is closer to 120 2. a. 30 b. 70

c. 80 d. 140 e. 260 f. 320 g. 440 h. 550   3.

4. Number of apples with Ria and Sia = 632

Nearest tens of 632 = 630

5. Number of digits in the required number = 3

Options we have = 717, 752, 647

Number which will be round down = 752

Number which has odd tens digit = 752

The required number is 752.

Chapter Checkup 1. a. 1442 b. 3857 c. 4208 d. 5309 e. 6045

f. 5028 g. 8600 h. 9406

2. a. two thousand four hundred seventy-one

b. four thousand two hundred five

c. five thousand three hundred seventy-four

d. seven thousand three hundred eight

e. seven thousand five hundred sixty-four

f. eight thousand four hundred twenty-one

g. eight thousand seventy

h. nine thousand one hundred fifty-seven

3. a. 50 b. 10 c. 800 d. 8000 e. 7000 f. 90 g. 7000

h. 3  4. a. 2185 b. 3471 c. 8089 d. 5725 e. 4600

f. 6070 g. 8409 h. 9016 i. 5265  5. a. 1000 + 300 + 80 + 2

b. 3000 + 600 + 40 + 1 c. 5000 + 300 + 20 + 7

d. 6000 + 400 + 80 + 4 e. 7000 + 500 + 00 + 0

f. 8000 + 700 + 60 + 8 g. 9000 + 000 + 30 + 2

h. 2000 + 600 + 50 + 4  6. Smallest: a. 1023 b. 5068

c. 2458 d. 1047 e. 2347 f. 3068 g. 1479 h. 2057

Greatest: a. 3210 b. 8650 c. 8542 d. 7410 e. 7432

f. 8630 g. 9741 h. 7520

7. a. 860 < 2735 b. 4072 < 6650 c. 3184 > 3156

d. 6720 > 6265 e. 7126 > 4510 f. 6271 > 6261

g. 7680 = 7680 8. Ascending order a. 565, 730, 2390, 8935

b. 773, 880, 1860, 7573 c. 792, 5853, 6943, 7081

d. 657, 5683, 7846, 8704 e. 2265, 4867, 8734, 8753

f. 5436, 7354, 7428, 8754 g. 5789, 6454, 6789, 8480

h. 8521, 8634, 8820, 8845 Descending order

a. 8935, 2390, 730, 565 b. 7573, 1860, 880, 773

c. 7081, 6943, 5853, 792 d. 8704, 7846, 5683, 657

e. 8753, 8734, 4867, 2265 f. 8754, 7428, 7354, 5436

g. 8480, 6789, 6454, 5789 h. 8845, 8820, 8634, 8521

9. a. 60 b. 80 c. 100 d. 240 e. 390 f. 420 g. 550

10. Number of pencils come in 1 packet = 20

Number of crayons come in 1 packet = 25 25 is an odd number.

11. Number of beads with Sita = 76

Round off 76 nearest tens = 80

She should buy 80 beads to make the necklace.

12. 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)

i. 8426 ii. eight thousand four hundred twenty-six

iii. 8000 + 400 + 20 + 6

13. Greatest number = 9800

Smallest number = 7008

Chapter 2

Warm-up

1.

3.

2A

5.

Word Problem 1. Marbles Yash has: 6 red and 15 blue

Total marbles with Yash = 6 + 15

Marbles Sophie has: 15 red and 6 blue

Total marbles with Sophie = 15 + 6 6 + 15 = 15 + 6

Numbers can be added in any order. Their sum always remains the same.

So, both Yash and Sophie have an equal number of marbles.

5. We will skip tens 4 times to add 45 to 39 as 45 has 4 tens.

Word Problems 1. Number of stamps Raj collected = 34

Number of stamps Jatin collected = 51

Let’s expand these numbers to sum the total number of stamps: 3

They collected 85 stamps altogether.

2. The largest number formed with digits 4 and 6 is 64.

The smallest number formed with digits 1 and 2 is 12. Let’s expand 64 and 12 to find the sum:

The sum of the numbers formed is 76.

2C 1. a. H T O

2. a. 471 + 526 = 997. The sum is odd b. 148 + 111 = 259.

The sum is odd c. 123 + 321 = 444. The sum is even.

d. 145 + 541 = 686. The sum is even. e. 321 + 338 = 659.

The sum is odd. f. 873 + 122 = 995. The sum is odd.

3. a. True b. False c. False d. True

4. a. 171 + 324 = 495 b. 415 + 374 = 789 c. 456 + 111 = 567

d. 711 + 123 = 834 e. 232 + 463 = 695 f. 313 + 356 = 669

5. a. H T O

Word Problems 1. Money spent on repairing of pipelines: ₹542

Money spent on electrical repair: ₹256

Money spent in total:

So, Akshay’s landlord spent ₹798 in total.

2. Cars manufactured in January: 456

Cars manufactured in February: 512

Cars manufactured in both the months combined:

Thus, the company manufactured 968 cars in both months combined.

3. Students in grade 1: 145

Students in grade 2: 211

Students in grade 3: 242

Total number of students in the three grades combined:

So, there are 598 students in the three grades combined. 2D

4. a. 154 + 317 = 471 b. 187 + 381 = 568 c. 248 + 374 = 622

d. 647 + 451 = 1098 e. 717 + 313 = 1030 f. 828 + 373 = 1201

5. a. 539 and 614 will give a 4-digit sum.

539 + 614 = 1153

b. 286 and 614 when added will have 0 at the ones place. 286 + 614 = 900

c. 239 and 286 have a sum of 525. 239 + 286 = 525.

Word Problems 1. The number of puppets with Rucha = 109

The number of puppets Suhani has = 118 more than the puppets Rucha has That is, 109 + 118:

Thus, Suhani has 227 puppets.

2. Amount of money Jaspal has = ₹456

Amount of money his father gave him = ₹235

The total money Jaspal has now is: 456 + 235

Jaspal has ₹691 money in total.

3. Number of students who took admission in grade 2: 218

Number of students who took admission in grade 3: 317

Number of students who took admission in grade 4: 165

Total number of students in grades 2, 3, and 4 combined: Thus, the total number of students taking admission in all the grades combined is 700.

2E 1. a.

1234 more than 5145 is 6379 2174 more than 1211 is 3385

Word Problems 1. Number of stickers in one notebook = 1454

Number of stickers in another notebook = 2421

The total number of stickers:

1454 + 2421 = 3875

Thus, Shantanu has 3875 stickers in all.

2. Oranges in the first carton = 1245

Oranges in the second carton = 2311

Oranges in the third carton = 1421

Total number of oranges = 1245 + 2311 + 1421 = 4977

Thus, the farmer packed 4977 oranges in total.

2F 1. a. 17 rounded off to the nearest 10 = 20

34 rounded off to the nearest 10 = 30

Estimated sum = 20 + 30 = 50

b. 84 rounded off to the nearest 10 = 80

17 rounded off to the nearest 10 = 20

Estimated sum = 80 + 20 = 100

c. 15 rounded off to the next 10 = 20

54 rounded off to the nearest 10 = 50

Estimated sum = 20 + 50 = 70

d. 47 rounded off to the nearest 10 = 50

41 rounded off to the nearest 10 = 40

Estimated sum = 50 + 40 = 90

2. a. 18 is a smaller number than 21.

Rounding off 18 to the nearest 10 = 20

Estimated sum = 20 + 21 = 41

b. 42 is a smaller number than 54.

Rounding off 42 to the nearest 10 = 40

Estimated sum = 40 + 54 = 94

c. 36 is a smaller number than 64.

Rounding off 36 to the nearest 10 = 40

Estimated sum = 40 + 64 = 104

d. 43 is a smaller number than 57.

Rounding off 43 to the nearest 10 = 40

Estimated sum = 40 + 57 = 97

3. a. 47 is a bigger number than 22.

Rounding off 47 to the nearest 10 = 50

Estimated sum = 50 + 22 = 72

b. 58 is a bigger number than 41.

Rounding off 58 to the nearest 10 = 60

Estimated sum = 60 + 41 = 101

c. 19 is a bigger number than 14.

Rounding off 19 to the nearest 10 = 20

Estimated sum = 20 + 14 = 34

d. 34 is a bigger number than 15.

Rounding off 34 to the nearest 10 = 30

Estimated sum: 30 + 15 = 45

4. a. 41 rounded off to the nearest 10 = 40

47 rounded off to the nearest 10 = 50

Estimated sum = 40 + 50 = 90

Actual answer = 88

Thus, the estimated answer is close to the actual answer.

b. 58 rounded off to the nearest 10 = 60

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 rounded off to the nearest 10 = 10

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 rounded off to the nearest 10 = 20

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.

5. a. 48 rounded off to the nearest 10 = 50

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 rounded off to the nearest 10 = 40

57 rounded off to the nearest 10 = 60

Estimated sum = 40 + 60 = 100

The actual sum of the numbers = 92

Round off the actual sum to the nearest 10 = 90

Thus, the answer is not the same in both cases.

c. 52 rounded off to the nearest 10 = 50

19 rounded off to the nearest 10 = 20

Estimated sum = 50 + 20 = 70

The actual sum of the numbers = 71

Round off the actual sum to the nearest 10 = 70

Thus, the answer is not the same in both cases.

d. 11 rounded off to the nearest 10 = 10

Estimated sum = 10 + 10 = 20

The actual sum of the numbers: 21

Round off the actual sum to the nearest 10 = 20

Thus, the answer is not the same in both cases.

Word Problems 1. Money spent on notebooks: ₹54 and ₹28

Round off to the nearest 10 and add the money:

50 + 30 = 80

Thus, Rahul spent about ₹80 on notebooks.

2. Stamps collected by Amrish, Rajesh and Parthiv = 18 + 21 + 22

Round off the numbers to the nearest 10: 18 → 20; 21 → 20; 22 → 20

Total stamps collected = 20 + 20 + 20 = 60

They collected about 60 stamps in all.

2G 1. 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.

2. 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.

3. Starting number = 5415

Number exceeding 5415 by 2364 = 5415 + 2364 = 7779

4. 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.

5. a. Money spent on a hair dryer = ₹3015

Money spent on a quilt = ₹2155

The total money spent on both things = 3015 + 2155 = ₹5170

b. Money spent on a bottle of perfume = ₹900

Money spent on a bag = ₹1525

The total money spent on both things = ₹900 + ₹1525 = ₹2425

c. Money spent by Mr. Saxena if he bought all the 4 items = ₹2155 + ₹3015 + ₹900 + ₹1525 = ₹7595

Chapter Checkup

4. a. 15 + 16 + 17 = 48

The correct option is iv.

b. The sum of 48 and 22 is 70 Ones digit in the sum of 48 and 22 is 0.

The correct option is i.

c. 40 + 30 + 20 + 10 = 100

The correct option is iii.

d. 146 + 154 + 125 = 154 + 125 + 146

The correct option is ii.

0 5. a. 145 more than 456 = 456 + 145 = 601

H T O

c. 325 more than 481 = 481 + 325 = 806

H T O

e. 415 more than 871 = 871 + 415 = 1286

Th H T O

b. 847 more than 254 = 254 + 847 = 1101

Th H T O

d. 748 more than 369 = 369 + 748 = 1117

f. 78 more than 361 = 361 + 78 = 439

b. 25 + 52

25 rounded off to the next 10 = 30

52 rounded off to the nearest 10 = 50

Estimated sum = 30 + 50 = 80

c. 34 + 17

34 rounded off to the nearest 10 = 30

17 rounded off to the nearest 10 = 20

Estimated sum = 30 + 20 = 50

d. 36 + 63

36 rounded off to the nearest 10 = 40

63 rounded off to the nearest 10 = 60

Estimated sum = 40 + 60 = 100

9. a. 48 + 52 = 100

Rounding off the result to the nearest 10 is the same as the result: 100

b. 45 + 36 = 81

Rounding off the result to the nearest 10 = 80

c. 23 + 49 = 72

Rounding off the result to the nearest 10 = 70

d. 56 + 11= 67

Rounding off the result to the nearest 10 = 70

10. a. Largest 2-digit number = 99

Largest 3-digit number = 999

Sum of 99 + 999 = 1098

c. Largest 3-digit number = 999

b. Smallest 3-digit number = 100

Largest 3-digit number = 999

Sum of 100 + 999 = 1099

Second largest 3-digit number = 998

Sum of 999 + 998 = 1997

d. Smallest 4-digit number = 1000

Smallest 3-digit number = 100

Smallest 2-digit number = 10

Sum of 1000 + 100 + 10 = 1110

Word Problems 1. 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.

2. People living in the first block of the society = 87

People living in the second block of the society = 98

People living in the third block of the society = 117

Total number of people living in the society = 87 + 98 + 117 = 302

Thus, there are 302 people in the society.

3. 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.

4. Number of tazos with Vishwa = 47

Number of tazos Ishan had 2 weeks earlier = 47 + 18 = 65

Number of tazos collected by Ishan in 2 weeks = 37

Total number of tazos with Ishan = 65 + 37 = 102

Thus, Ishan has 102 tazos.

Chapter 3

Let’s Warm-up

Do It Yourself

3A 1. a. 72 − 72 = 0 b. 27 – 0 =

d. 87 – 87 = 0 e. 19 − 0 = 19 f. 56 – 1 = 55 2. a. 93

b. 25 c. 44 d. 85 e. 92 f. 66   3. a. True b. True

c. False d. True e. False f. False

4. The predecessor of 500 is 499.

5.  Word Problems

1. Number of pens bought by Jacob = 12

Number of pens he gave to Akshay = 1

Number of pens left with Jacob =12 – 1 = 11

Jacob is left with 11 pens.

2. Number of cookies baked by Suresh = 26

Number of cookies left after party = 0

Number of cookies eaten at the party = 26 – 0 = 26

There were 26 cookies eaten in the party.

3. Weight of the cake = 44 ounces

Weight of cake eaten by guests = 44 ounces

Ounces of cake left after the party = 44 – 44 = 0

No cake is left after the party.

3B 1. a. 76 – 59

Count forward to 76

Adding the jumps

1 + 10 + 6 = 17

76 – 59 = 17

b. 56 – 27

Adding the jumps

3 + 10 + 10 + 6 = 29

56 – 27 = 29

c. 21 – 13

Adding the jumps

7 + 1 = 8

21 – 13 = 8

d. 72 – 57

Adding the jumps

3 + 10 + 2 = 15

72 – 57 = 15

e. 33 – 15

Adding the jumps

5 + 10 + 3 = 18

33 – 15 = 18

f. 45 – 36

Adding the jumps

4 + 5 = 9

45 – 36 = 9

2. 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. 32 – 13 =

Breaking the smaller number into tens and ones

Subtracting the tens from the bigger number

32 – 10 = 22

Subtracting the ones from 22

22 – 3 = 19

32 – 13 = 19

d. 46 – 17

Breaking the smaller number into tens and ones

Subtracting the tens from the bigger number

46 – 10 = 36

Subtracting the ones from 36

36 – 7 = 29

46 – 17 = 29

e. 93 – 45

Breaking the smaller number into tens and ones

Subtracting the tens from the bigger number

93 – 40 = 53

Subtracting the ones from 53

53 – 5 = 48

93 – 45 = 48

f. 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

3.  15 20 30

40 43

There are two jumps of tens when 15 is subtracted from 43. 4.

+4 +10 +1

46 50 60 61

There is one jump of tens when 46 is subtracted from 61. 1 jump of tens will be drawn toward the right of the number line.

5.

+10 +10 +3

46 56 66 69

Total of jumps taken by Dan = 10 + 10 + 3

Dan is subtracting from = 46 + 10 + 10 + 3 = 69

Dan is subtracting 46 from 69.

Word Problems

1. Number of pumpkins in the patch = 85

Number of pumpkins left = 48

Number of pumpkins picked = 85 – 48 = 37

There were 37 pumpkins picked.

2. Number of sandwiches sold by me = 72

Number of sandwiches sold by Alec = 57

Number of sandwiches sold by Navin = 38

a. Number of more sandwiches sold by me than Navin = 72 – 38                            = 34

I have sold 34 more sandwiches than Navin

b. Number of fewer sandwiches sold by Navin than Alec = 57 – 38 = 19

Navin has sold 19 fewer sandwiches than Alec.

3. Number of tickets sold by Sam = 59

Number of tickets sold by Sana = 85

Number of tickets sold by Anna = 47

Number of more tickets Sold by Sana than Anna = 85 – 47 = 38

Sana has sold 38 more tickets than Anna.

3C 1.

a. Subtract the ones Subtract the tens Subtract the hundreds

b. Subtract the ones Subtract the tens Subtract the hundreds

4. Number of computers in stock = 265

Number of computers sold = 142

Number of computers left = 123 123 computers are left in the stock.

5. a. Number of more stamps Rahul has than Gyan = 789 – 245 = 544 b. Ravi has more stamps. Number of more stamps Ravi has than Gyan = 545 – 245 = 300

Word Problems

1. Number of tickets sold by Vinay = 594

Number of tickets sold by Arvind = 273

Number of more tickets sold by Vinay than Arvind = 594 – 273   = 321

Vinay has sold 321 more tickets than Arvind.

2. 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.

3. Number of points scored by Bhakti = 265

Number of points scored by Gauri = 142

Number of more points Bhakti scored than Gauri = 265 – 142 = 123

Bhakti has scored 123 more points than Gauri.

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

Number of tickets sold by Akhil = 460 – 159 = 301

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

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

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

Prasad needs to sell 19 more tickets to reach 350.

Word Problems 1. Number of computers sold in sale = 257

Number of more computers sold this week than the week before the sale = 172

Number of computers sold the week before the sale = 257 – 172 = 85

85 computers were sold the week before the sale.

2. Number of muffins sold by Darshana = 336

Number of muffins sold by Bharti = 287

Number of more muffins sold by Darshana than Bharti = 336 – 287 = 49

49 more muffins were sold by Darshana than Bharti. 3E 1. a.

4. Number of students = 2740

Number of girls = 1430

Number of boys = 2740 – 1430 = 1310

There are 1310 boys in the college.

5. 1227 must be added to 5860 so that the sum is 6987.

Word Problems

1. Number of clocks sold in 2022 = 7407

Number of clocks sold in 2023 = 8638

Number of more clocks he sold in 2023 than in 2022 = 8638 – 7407 = 1231

He sold 1231 more clocks in 2023 than in 2022.

2. Money Liza had = ₹5275

Money she spent = ₹3142

Money left with Liza = ₹5275 – ₹3142 = ₹2133

₹2133 is left with Liza.

3F 1. a. 43 – 31

Estimated

f.

3G

3. Price of pen = ₹78

Round off the price = ₹80

Money Anand already has = ₹37

Rounding off saved money = ₹40

Estimated more money he needs to buy the pen: ₹80 – ₹40 = ₹40

4. Number of seashells Ajay collected = 42

Rounding off number of seashells with Ajay we have = 40

Number of seashells he gave to Vijay = 23

Rounding off number of seashells with Vijay, we 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.

5. No, Arun did not estimate correctly as round off of 43 is 40 instead of 50: 40 – 20 = 30

Word Problems

1. Number of houses in the village previously = 32

Rounding off 32 to nearest tens, we have = 30

Number of houses in the village now = 67

Rounding off 67 to nearest ten, we have = 70

Estimated difference = 70 – 30 = 40

About 40 houses were newly built in the village.

2. Number of stickers Ashok has = 83

Rounding off 83 to nearest tens, we have = 80

Number of stickers Madan has = 56

Round off 56 to nearest tens, we have = 60

Estimated number of more stickers Ashok has than Madan = 80 – 60 = 20

Ashok has 20 more stickers than Madan.

3. Number of chocolates in the bowl = 96

Rounding off 96 to nearest tens, we have = 100

Number of chocolates Naveen took = 15

Rounding off 15 to nearest tens, we have = 20

Estimated remaining chocolates = 100 – 20 = 80

Number of chocolates remaining after Darshana took some of the chocolates = 68

Rounding off 68 to nearest tens, we have = 70

Number of estimated chocolates taken by Darshana = 80 – 70 = 10

About 10 chocolates were taken by Darshna.

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. Number of people invited to the party = 500

Number of people who could not come = 230

Number of people who came to the party = 500 – 230 = 270 270 people came to the party.

3. Number of books he sold on opening day = 487

Number of fewer books sold by him the next day = 189

Number of books he sold the next day = 487 – 189 = 298

There were 298 books sold the next day.

4. 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.

5. 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.

6. 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.

7. Number of chocolate cookies baked = 50

Number of oatmeal cookies baked = 900

Total Number of cookies = 50 + 900 = 950

Number of cookies sold = 765

Number of cookies remained = 950 – 765  = 185

Mrs. Jones is left with 185 cookies.

8. Greatest 3-digit number using 6, 4 and 3 = 643

Smallest 3-digit number using 6, 4 and 3 = 346

Difference between the smallest and the greatest = 643 – 346 = 297

Difference between the greatest 3-digit number and smallest 3-digit number using 6, 4 and 3 is 297

Word Problems 1. Number of cardboard rolls collected = 915

Number of cardboard rolls used in first exhibition = 268

Number of cardboard rolls used in second exhibition = 380

Total Number of cardboard rolls used = 268 +380 = 648

Number of cardboard rolls left = 915 – 648 = 267

Artist is left with 267 cardboards.

2. Number of stamps with Amit = 467

Number of stamps his father has given = 133

Total 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.

3. 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.

Chapter Checkup

d.

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 4. a.

5. a. 96 – 12

Estimated

c. 61 – 44

Estimated difference:

b. 82 – 29

Estimated difference:

T O 6 0 –

Word Problems 1. 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.

2. Number of pages in the book = 978

Number of pages read by Renuka = 829

Number of pages still to be read = 978 – 829 = 149 149 pages are still remaining to be read.

3. 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 = 120 120 people watched the whole match.

4. 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

124 kg potatoes are remaining.

5. Price of speakers = ₹672

Money saved by musician in two months = ₹224 + ₹224 = ₹448

Money he still needs to save = 672 – 448 = ₹224

Musician still needs to save ₹224.

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

2. a. True b. False c. 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. Total number of trees Raghu is planting at his farm = 15

Number of trees planted in each row = 5

Number of row formed: 5 + 5 + 5 = 15

OR 3 × 5 = 15

Thus, there are 3 rows with 5 trees in each.

Word Problem 1. 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. Order of multiplication doesn’t matter as the product always remains the same.

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

2. a. 8 × 8 = 64

8 × 8 > 60

c. 4 × 99 = 396

b. 9 × 10 = 90 and 100 × 1 = 100 9 × 10 < 100 × 1

4 × 99 < 400 d. 6 × 7 = 42

3. a. 8 × 9 = 72

b. 80 × 3

Add one zero at the end and multiply 8 with 3:

80 × 3 = 240

c. 700 × 10

Add 3 zeroes at the end and multiply 7 with 1:

700 × 10 = 7000

d. 6 × 8 = 48

e. 90 × 4

Add 1 zero at the end and multiply 9 with 4:

90 × 4 = 360

f. 4 × 40

Add 1 zero at the end and multiply 4 with 40:

4 × 40 = 160

g. 10 × 10

Add 2 zeroes at the end and multiply 1 with 1:

10 × 10 = 100

4. a. 8 × 8 = 64 b. 7 × 80 = 560 c. 100 × 4 = 400

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.

Word Problems 1. 1 century = 100 runs

The player has hit 5 centuries.

5 centuries = 5 × 100

Add 2 zeroes at the end and multiply 5 and 1.

5 × 100 = 500

Thus, the player has hit 500 runs by centuries.

2. Runs made by first cricketer = 5 sixes = 5 × 6 = 30

Runs by another cricketer = 8 fours = 8 × 4 = 32

Total runs made by both cricketers = 30 + 32 = 62

Chapter Checkup 1. a. True b. True c. False d. True e. True f. True g. False

2. a.

6.  a.  b.

7. 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.

8. 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

9. Number of boxes to pack = 900

Towels in each box = 9

Total number of towels altogether = 900 × 9 = 8100

Hence, there are 8100 towels in total.

Chapter 5

3. a. 8, 16, 24, 32,

c. 30, 40, 50, 60, 70, 80, 90, 100 d. 18,

e. 14, 28, 42, 56, 70, 84, 98, 112 f. 200, 400, 600, 800, 1000, 1200, 1400, 1600 4.

4. Number of boxes sold = 230

Number of cupcakes in each box = 5

Total number of cupcakes sold = 230 × 5 1150 cupcakes are sold.

5. Word Problem 1. Number of shelves in the library = 8.

Number of books each shelf can hold = 120

Total number of books = 120 × 8 There are 960 books in the library.

4. Greatest 2-digit number = 99

Smallest 2-digit number = 10 99 × 10 = 990

5. Number of candies in each packet = 15

Number of packets = 39

Total number of candies = 39 × 15

There are 585 candies in all.

Word Problem 1. 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.

5D 1. a. The digit at unit place is 5. Hence, 45 is rounded up to 50.

b. The digit at unit place is more than 5

Hence, 36 is rounded up to 40

c. The digit at unit place is more than 5

78 is rounded up to 80

d. The digit at unit place is less than 5

91 is rounded down to 90

e. The digit at unit place is less than 5

52 is rounded down to 50

f. The digit at unit place is less than 5. 83 is rounded down to 80.

g. The digit at unit place is less than 5. 44 is rounded down to 40

h. The digit at unit place is more than 5

27 is rounded up to 30

2. a. Rounding off 44 to 40 40 × 5 = 200

c. Rounding off 26 to 30 30 × 4 = 120

e. Rounding off 98 to 100 100 × 9 = 900

b. Rounding off 32 to 30 30 × 6 = 180

d. Rounding off 81 to 80 80 × 2= 160

f. Rounding off 43 to 40 40 × 7 =280

3. a. Rounding off 66 to 70    Actual product

Comparing:

b. Estimated product

Rounding off 18 to 20      Actual product

Comparing:

c. Estimated product

Rounding off 45 to 50  Actual product  Comparing: 50 × 2 = 100

d. Estimated product

Rounding off 33 to 30  Actual product    Comparing:

e. Estimated product

Rounding off 99 to 100  Actual product  Comparing:

100 × 1 = 100       99 × 1 = 99

f. Estimated product       Actual Product

Rounding off 67 to 70

Comparing:

4. Rounding off 37 to 40

Rounding off 13 to 10

40 × 10 = 400

5.

Word Problem 1. Number of

Number

Estimated bangles packed:

Rounding off 45 to 50 and 24

Rhea

5E

There

2. Number of packets = 54

Number of balloons = 45

Total number of balloons = 54 × 45

There will be 2430 balloons.

3. Cost of 1 table = ₹100

Number of tables = 12

Cost of 12 tables = 100 × 12 = ₹1200

The cost of 12 tables will be ₹1200

4. 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.

5. Number of trips in a day = 14

Number of seats in the car = 6

Total number of people travelled = 14 × 6

84 people travelled in the car.

Word Problem 1.

a. Price of 45 candles = 45 × ₹12

The price of 45 candles is ₹540.

c. Price of 45 bells = ₹45 × 45

b. Price of 25 stars = ₹50 × 25

The price of 25 stars is ₹1250

i. 80 9

4 × 4 × 80 = 320

×

= 36  Product: 320 + 36 = 356

b. 45 × 1 = 0 False    c. 57 × 0 = 0 True

45 × 1 = 45

d. 25 × 25 = 625 True   e. 89 × 12 = 1289 False

8. a. Rounding off 54 to 50   b. Rounding off 49 to 50

50 × 6 = 300           50 × 7 = 350

c. Rounding off 34 to 30 30 × 3 = 90

d. 12 will be 10     10 × 6 = 60

e. Rounding off 38 to 40     f. Rounding off 91 to 90

40 × 2 = 80            90 × 3 = 270

g. Rounding off 34 to 30     h. Rounding off 44 to 40

34 × 4 = 120           40 × 2 = 80

i. Rounding off 66 to 70

70 × 4 = 280

9. 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 travelled in the bus.

10. Number of crates = 12

Number of apples in each crate = 45

Total number of apples = 12 × 45

There are 540 apples in the crates.

Word Problems

1. Number of sheets = 56

Number of stickers in each sheet = 56

Total number of stickers = 56 × 56

There are 3136 stickers in total.

2. Number of pages in each book = 340

Number of books = 6

Total number of pages = 340 × 6 There are 2040 books.

3. 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.

4. Number of children = 36

Amount of money paid by each child = ₹30

Total amount paid = ₹30 × 36 ₹1080 was paid at the entrance.

5. 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.

6. 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

1700 people can watch the movie in one time. Number of people who can watch the movie two times = 1700 × 2

3400 people can watch the movie in 2 times.

7.

c. 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 1’s in 9.

d. Subtract 3 from 9 until we get zero. Count how many times 3 has been subtracted. We subtracted 3 for 3 times. So, there are three 3’s in 9.

e. 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.

f. Subtract 6 from 36 until we get zero. Count how many times 6 has been subtracted. We subtracted 6 for 6 times. So, there are six 6’s in 36.

Chapter

6

Let’s Warm-up 1. True

True

False

True Do It Yourself

6A 1. a. 4 people

b. 2 people

c. 7 people d. 9 people

e. 4 people

f. 5 people

g. 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.

h. Subtract 7 from 28 until we get zero. Count how many times 7 has been subtracted. We subtracted 7 for 4 times. So, there are four 7’s in 28.

2. a. Subtract 5 from 15 until we get zero. Count how many times 5 has been subtracted. We subtracted 5 for 3 times. So, there are three 5’s in 15.

b. 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.

3.

7 balloons of each colour:

4. Total number of apples = 18

Number of apples in each basket = 6

Number of baskets = 3

5. 24 has  8 groups of 4

32 has 9 groups of 9

56 has 4 groups of 6

81 has 8 groups of 7

Word Problems

1. 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.

2. Total number of pencils: 16

Number of pencils Vijay and Sunita each get = 16 ÷ 2

Each of them will get 8 pencils.

3. 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

2. a. Division facts of

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 =

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

3. 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

4. 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 any number by 1, we get the same number back. Thus, 7 ÷ 1 = 7.

f. When we divide any number by itself, the answer is always 1. Thus, 100 ÷ 100 = 1.

g. When we divide 0 by any number, the answer is always 0. Thus, 0 ÷ 3 = 0.

h. We cannot divide any number by 0. There is no answer. Thus, 15 ÷ 0 = No answer.

5. Dividend Divisor Quotient

Word Problems 1. Total cupcakes at the party = 18

Cupcake each child gets = 1

Number of children at the party = 18 ÷ 1 = 18

There are 18 children in the party.

2. Number of apples with Maya = 45

Number of friends among which apples are divided = 9

Number of apples each friend gets = 5

So, the multiplication fact for this is: 9 × 5 = 45

3. Number of marbles with Ravi = 36

Number of bags he wants to divide 36 into = 4

4 × 9 = 36. Therefore, 36 ÷ 4 = 9

Thus, Ravi will keep 9 marbles in each bag.

Chapter Checkup 1. a. 3 people

b. 8 people

c. 6 people

d. 2 people

e. 4 people

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.

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,

f. We divide 9 seven times from 63 until we get zero. Thus, 63 ÷ 9

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

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. Total number of cupcakes = 32

Number of friends = 4

Number of cupcakes each friend will get = 32 ÷ 4

We know, 4 × 8 = 32. Therefore, 32 ÷ 4 = 8

Thus, Ruma’s each friend will get 8 cupcakes.

8. Number of marbles with Arushi = 24

The number of cousins among whom she wants to divide marbles = 6

Number of marbles each cousin will get = 24 ÷ 6

Let’s divide by repeated subtraction. Subtract

6 from 24 until we get zero.

Count the number of times 6 has been subtracted.

We subtracted 6 four times. There are four sixes in 24.

g. We divide 9 six times from 54 until we get zero. Thus, 54 ÷ 9 =

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 72 ÷ 9 = 8 is 8 × 9 = 72.

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

Thus, each cousin will get 4 marbles.

9. Number of pencils with the teacher = 30

Number of students = 10

Number of pencils each student will get = 30 ÷ 10

Let’s divide by repeated subtraction. Subtract

10 from 30 until we get zero.

Count the number of times 10 has been subtracted.

We subtracted 10 three times. Thus, each student will get 3 pencils.

10. Number of apples with the fruit vendor = 36

Number of baskets with the vendor = 6

Number of apples in each basket = 36 ÷ 6

Let’s 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, each basket will have 6 apples.

Word Problem 1. 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.

Chapter 7

3. (Quotient × Divisor) + Remainder = Dividend

(Q × D) + R = (20 × 2) + 1 = 40 + 1 = 41 = Dividend

(Q × D) + R = (13 × 5) + 3 = 68 = Dividend

(Q × D) + R = (12 × 7) + 5 = 89 = Dividend

d. 4 4

(Q × D) + R = (44 × 3) + 0 = 132 = Dividend

(Q × D) + R = (64 × 3) + 4 = 324 = Dividend

(Q × D) + R = (284 × 9) + 6 = 2562 = Dividend

1

4 0 1 (Q × D) + R = (515 × 8) + 1 = 4121 = Dividend

(Q × D) + R = (90 × 6) + 1 = 541 = Dividend

2 –

0

– 2 4 0 (Q × D) + R = (854 × 6) + 0 = 5124 = Dividend

4. a. (7 × 5) + 3  44

b. (12 × 4) + 1  41

c. (9 × 6) + 5  47

d. (5 × 8) + 4  38

e. (20 × 2) + 1  79

f. (15 × 3) + 2  49

g. (11 × 7) + 2  59

5. a. Cost of 1 shirt of Brand A = 360 ÷ 3 1 2 0

b. Cost of 1 shirt of Brand B = 475 ÷ 5

c. Cost of 1 shirt of Brand C = 128 ÷ 2

0 0

∴ ₹120

Word Problems

0

₹95

1. Total number of toys = 945 Number of toys in each box = 5

Number of boxes required = 945

₹64

So, brand C is cheaper.

2. Total number of people in the theatre = 7385

Number of people in each row = 7

Number of rows filled completely = 7385 ÷ 7

189 boxes are needed to keep the toys in boxes of 5.

1055 rows are filled completely.

3. 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

There are 3 puppies without a doghouse.

4. Method: What do we know? What do we need to find?

How to find?

a. Number of flower seeds = 3548

Number of rows = 6

Number of seeds left after planting = 3548 ÷

b. Number of cups = 74

Number of cups in each tray = 8

Number of trays needed = 74 ÷ 8

c. Number of storybooks = 513

Number of storybooks each classroom gets = 9

Number of classrooms = 513

So, 2 seeds are left.

Chapter Checkup 1.

– 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.

So, 57 classrooms will receive the storybooks.

g.

(Q × D) + R = (307 × 6) + 0 = 1842 = Dividend

5.

(Q × D) + R = (982 × 8) + 0 = 7856 = Dividend

(Q × D) + R = (1407 × 7) + 5 = 9854 = Dividend

a. (13 × 4) + 2  153 d. (3041 × 2) + 1  981

b. (128 × 3) + 5  54 e. (122 × 8) + 5  1189

c. (21 × 7) + 6  389 f. (297 × 4) + 1  6083

6. (Quotient × Divisor) + Remainder = Dividend

a. (10 × 4) + ___ = 43

1 0

4 4 3 – 4 3

Remainder = 3 (10 × 4) + 3 = 43

d. (7 × 9) + ___ = 64

7 9 6 4 – 6 3 1 (7 × 9) + 1 = 64

b. (_____ × 2) + 1 = 49 2 4

2 4 9 – 4 9 – 8 1 (24 × 2) + 1 = 49

e. (___ × 3) + 1 = 352 1 1 7

3 3 5 2 – 3 5 – 3 2 2 – 2 1 1

(117 × 3) + 1 = 352

c. (____ × 6) + 2 = 50 8

6 5 0 – 4 8 2

(8 × 6) + 2 = 50

f. (42 × 5) + ___ = 214 4 2

2 1

g. (___ × 8) + 6 = 94

7. Number of beads for crafting = 800

Number of beads required in a necklace = 8

Number of necklaces that can be made = 800 ÷ 8

0 0 8 8 0

8. Number of marbles = 126

Number of bags = 9

Number of marbles in each bag = 126

Number of booklets need to be prepared = 5245 ÷ 5

So, there will be 14 marbles in each bag.

9. Number of tickets to be sold = 5245

So, 1049 booklets need to be prepared.

10. Let us divide 156 ÷ 7

Remainder = 2

We know that 2 + 5 = 7

Let us add 5 to 156 and then divide the number by 7.

156

161

161

So, 5 needs to be added to 156.

Word Problems 1. Number of cookies = 84

Number of cookies in a box = 4

Number of boxes required = 84 ÷ 4

So, 21 boxes are required for the cookies.

2. Number of pencils in a box = 720

Number of pencils each student received = 3

Number of students = 720 ÷ 3

So, 240 students will receive the pencils.

3. Number of cups = 156

Number of cups one tray can hold = 10

Number of cups outside the tray = 156 ÷ 10

So, 100 necklaces can be made with the help of 800 beads.

Number of tickets in each booklet = 5

So, 6 cups will remain outside the tray.

3.  a. Shapes Corners 1

b. 8

2. 3.

4.

Do It Yourself

8A 1. a. The bread is in the shape of a square. b. This disc is in the shape of a circle. c. A chocolate bar is in the shape of a rectangle.

2.  a. Shapes Sides 0

b. 3 c. 4

3. Square =  2 , Rectangle =  2 , Triangle =  1 , Circle =  6

4. a. False  b. True c. True d. True

5.

8B 1. b. d.

2. a. The line does not divide the rectangle such that the two halves are exact copies.

3. a. b. c. 4. a.

b. c. 5. a. b.

c. d.

Word Problem 1. Yes, the standing and sleeping lines Ratna found on the rectangular paper are the lines of symmetry. standing line of symmetry sleeping line of symmetry 8C 1.

c. 0

4. 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

5. a. A cuboid has 12 straight edges. b. A sphere has no edge.

c. A cone has 1 curved edge. d. A cylinder has 2 curved edges.

e. A cube has 12 straight edges.

8D 1. View B 2. View C

3. Drawings may vary. Sample drawings:

a. b. 4. a. Front view Side view

b. Front view Side view c. Front view Side view

5. Drawing may vary. Sample drawing: Top view Side view We get a rectangular shape in the drawings of the top and sides of the textbook.

8E 1. a.

b.

e. 28, 32, 36, 40, 44 , 48 f. 35, 45, 55, 65, 75 , 85

g. 45, 47, 49, 51,  53 ,  55 ,  57

2. a. Cube b. Cylinder c. Sphere d. Cone

4. e. and f.   are not tiling patterns.

5. a. JTJHJE JCJA JR JIJS JRJE JD – THE CAR IS RED b. ATBHCE

DSEKFY GIHS IBJLKULE – THE SKY IS BLUE c. 1I 2L3I4K5E

6D7O8S9A – I LIKE DOSA

Chapter Checkup 1. a. Square = 1, Rectangle = 7, Triangle = 2, Circle = 5 b.

2. a. b.

3. a. b. c. d.

4. Drawings may vary. Sample drawings:

Chapter 9

Let’s Warm-up 1. False  2. True  3. True

Do It Yourself

9A 1. a. Metres b. Centimetres c. Kilometres d. Metres

e. Centimetres f. Centimetres  2. a. 8 cm b. 11 cm

c. 10 cm d. 15 cm e. 7 cm f. 4 cm   3. a. 6 m = 6 ×

100 cm = 600 cm b. 2 m 52 cm = 2 × 100 + 52 cm = 252 cm

c. 8 m = 8 × 100 cm = 800 cm d. 4 m 15 cm = 4 × 100 + 15 cm = 415 cm e. 9 m 9 cm = 9 × 100 + 9 cm = 909 cm f. 7 m 26 cm =

7 × 100 + 26 cm = 726 cm g. 9 m = 9 × 100 = 900 cm

h. 5 m 55 cm = 5 × 100 + 55 cm = 555 cm

4. a. 700 cm = 100 cm + 100 cm + 100 cm + 100 cm + 100 cm +

100 cm + 100 cm = 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m = 7 m

b. 600 cm = 100 cm + 100 cm + 100 cm+ 100 cm + 100 cm +

100 cm = 1 m + 1 m + 1 m + 1 m + 1 m + 1 m = 6 m

c. 400 cm = 100 cm + 100 cm + 100 cm + 100 cm = 1 m + 1 m +

1 m + 1 m = 4 m

d. 800 cm = 100 cm + 100 cm + 100 cm + 100 cm + 100 cm +

100 cm + 100 cm + 100 cm = 1 m + 1 m + 1 m + 1 m + 1 m + 1 m +

1 m + 1 m = 8 m

e. 500 cm = 100 cm + 100 cm + 100 cm + 100 cm + 100 cm =

1 m + 1 m + 1 m + 1 m + 1 m = 5 m

f. 900 cm = 100 cm + 100 cm + 100 cm + 100 cm + 100 cm +

100 cm + 100 cm + 100 cm + 100 cm = 1 m + 1 m + 1 m + 1 m +

1 m + 1 m + 1 m + 1 m + 1 m = 9 m

5. a.

b.

6. a.

b.

c.

d.

e.

Top:  Side:  Front:

7. a. 12, 16, 20, 24, 28, 32, 36, 40 b. 48, 56, 64, 72, 80, 88, 96

c. 32, 37, 42, 47, 52, 57, 62 d. 29, 32, 35, 38, 41, 44, 47

e. 56, 61, 66, 71, 76, 81, 86 f. 80, 82, 84, 86, 88, 90, 92 8. a. b.

9. The table would look like a rectangle when seen from the sides. It would look like a circle when seen from the top.

10. a. Colouring may vary

b. Individual drawings.

Side Top

9B

5. Manu has a rope of length 3 m 55 cm. How long is the rope in cm?

We know that 1 m = 100 cm

Length of the rope = 3 m 55 cm = 3 × 100 + 55 cm = 355 cm

So, the rope is 355 cm long.

Word Problems 1. Bobby should use centimetres.

2. Length of the rope = 6 m + 50 cm

6 m 50 cm = 600 cm + 50 cm = 650 cm

So, the length of the rope in cm is 650 cm.

3. Length of the pipe = 700 cm = 100 cm + 100 cm + 100 cm + 100 cm + 100 cm + 100 cm + 100 cm = 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m = 7 m

So, the pipe is 7 m long.

1. Total length of 2 ribbons = 50 cm + 30 cm = 80 cm

2. Difference between the lengths of the wire and the rope = 5 m – 2 m = 3 m

3. Total length of the two clothes = 14 m + 22 m = 36 m

4. Total distance travelled = 4 km + 9 km = 13 km

5. Difference between the length of pencil and crayon = 15 cm – 11 cm = 4 cm

Word Problems 1. Total distance travelled in 5 hours = 25 km + 18 km = 43 km

2. Length of the Copper wire = 1 m 50 cm = 100 cm + 50 cm = 150 cm

Length of the silver wire = 2 m = 2 × 100 cm = 200 cm

So, the total length of the two wires = 150 cm + 200 cm = 350 cm

3. Length of the orange thread = 4 m = 4 × 100 cm = 400 cm

Length of the blue thread = 350 cm

The orange thread is longer than the blue thread by how much = 400 cm – 350 cm = 50 cm

So, the orange thread is longer than the blue thread by 50 cm.

9C 1. a. grams b. kilogram c. grams d. kilogram  e. kilogram f. kilogram g. grams h. grams

2. The shopkeeper will measure the weight in kg.

3. The pencil is measured in g.

4. a. 8 kg = 8 × 1000 g = 8000 g

b. 1 kg 500 g = 1 × 1000 g + 500 g = 1500 g

c. 9 kg = 9 × 1000 g = 9000 g

d. 4 kg 200 g = 4 × 1000 g + 200 g = 4200 g

e. 7 kg 750 g = 7 × 1000 g + 750 g = 7750 g

f. 3 kg 300 g = 3 × 1000 + 300 g = 3300 g

g. 6 kg 460 g = 6 × 1000 + 460 g = 6460 g

h. 2 kg 250 g = 2 × 1000 g + 250 g = 2250 g

5. Weight of bag in kg = 5 kg

Weight of bag in g = 5 × 1000 g = 5000 g

The weight of the bag in grams is 5000 g.

Word Problems 1. Weight of Sara’s pet = 3 kg 300 g

Weight of the pet in grams = 3 × 1000 + 300 g = 3300 g

So, the weight of the pet in gram is 3300 g

2. Weight of Mohit’s computer = 8 kg and 750 g.

Weight in grams = 8 × 1000 + 750 g = 8750 g

So, the weight of the computer in grams is 8750 grams.

3. Weight of the basket = 9 kg and 250 grams.

Weight of the basket in grams = 9 × 1000 + 250 g = 9250 g

So, the weight of the basket in grams is 9250 grams.

9D 1. Weight of the box of chocolates = 500 g

Weight of the box of candies = 750 g

Total weight of the boxes = 500 g + 750 g = 1250 g = 1000 g + 250 g = 1 kg 250 g

So, the total weight of the boxes is 1 kg 250 g.

2. Weight of vegetables = 4 kg

Weight of fruits = 5 kg

How much more fruits than vegetables:

5 kg – 4 kg = 1 kg

So, Shalu bought 1 kg more fruits than vegetables.

3. Weight of Tina’s backpack = 10 kg

Weight of items added in backpack = 3 kg

Total weight of the backpack = 10 kg + 3 kg = 13 kg

So, the total weight of the backpack is 13 kg.

4. Weight of the watermelon = 5 kg

Weight of one of the pieces = 2 kg

Weight of the other piece = 5 kg – 2 kg = 3 kg.

So, the weight of the other piece is 3 kg.

5. Weight of Aman’s cake = 1200 g

Weight of Seema’s cake = 1900 g

Difference in the weight of the cakes = 1900 g – 1200 g = 700 g

So, the difference in the weight of the baked cakes is 700 g. Word Problems

1. Weight of newspapers sold = 4 kg and 200 g = 4 × 1000 grams + 200 grams = 4200 grams

Weight of magazines = 700 grams.

Total weight of the articles = 4200 grams + 700 grams = 4900 grams

So, the total weight of the articles sold = 4900 grams.

2. Weight of the fruit basket = 2 kg = 2 × 1000 g = 2000 g

Weight of the banana = 100 g

Weight of the apple = 150 g

Total weight of banana and apple = 100 g + 150 g = 250 g

The weight of the fruit basket after taking out a banana and an apple = 2000 g – 250 g = 1750 g

So, the weight of the fruit basket is 1750 grams.

9E 1. Items

a. Cough Syrup COUGH SYRUP

b. Syringe

c. Tub of water d. Glass of milk

e. Bucket of water f. Hand sanitizer

g. Barrel of water h. Spoon of oil

2. 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 + 500 mL = 4500 mL

e. 9 L 200 mL = 9 × 1000 mL + 200 mL = 9200 mL

f. 5 L 850 mL = 5 × 1000 + 850 mL = 5850 mL

g. 8 L 725 mL = 8 × 1000 + 725 mL = 8725 mL

h. 7 L 355 mL = 7 × 1000 + 355 mL = 7355 mL

3. Quantity of water Rohan needs in litre = 3 L

Quantity of water Rohan needs in millilitre = 3 × 1000 mL = 3000 mL

So, Rohan will need 3000 mL of water.

4. Amount of oil Priya used = 1 L and 500 mL

1 L 500 mL = 1 × 1000 mL + 500 mL = 1500 mL

So, Priya used 1500 mL of oil.

5. Amount of water fish tank can hold = 8 L 650 mL

8 L + 650 mL = 8 × 1000 + 650 mL = 8650 mL

So, Neha needs 8650 mL of water to fill in the tank.

Word Problem 1. Quantity of water Nihal poured onto his plants =

6 L 250 mL

6 L 250 mL = 6 × 1000 + 250 mL = 6250 mL

So, Nihal poured 6250 mL of water.

9F

1. Amount of cooking oil shopkeeper sold in one week = 23 L

Amount of cooking oil shopkeeper sold in another week = 31 L

Total amount of oil shopkeeper sold = 23 L + 31 L = 54 L

The shopkeeper sold 54 L of cooking oil in total.

2. Amount of water in the tub = 5 L 600 mL

5 L 600 mL = 5 × 1000 + 600 mL = 5600 mL

There is 5600 mL of water in the tub.

3. Amount of water filled in the water bottle = 500 mL

Quantity of water used to water the plants = 3 × 500 mL = 1500 mL = 1000 mL + 500 mL = 1 L 500 mL

So, Mohan filled 1 L 500 mL of water in all.

4. Amount of milk Aditya sold = 8 L 750 mL

8 L 750 mL = 8 × 1000 + 750 mL = 8750 mL

So, Aditya sold 8750 mL of milk.

5. Amount of water Raju poured in the jug = 4 L = 4 × 1000 mL = 4000 mL

Amount of water Raju transferred = 750 mL

Amount of water left in the jug = 4000 mL – 750 mL = 3250 mL = 3000 mL + 250 mL = 3 L 250 mL

So, 3 L 250 mL of water is left in the jug.

Word Problem 1. Quantity of water in the tank = 5 L 550 mL = 5 × 1000 mL + 500 mL = 5500 mL

Quantity of water filled in later = 3 L 300 mL = 3 × 1000 + 300 mL = 3300 mL

Total quantity of water in the tank = 5500 mL + 3300 mL = 8800 mL

So, the water tank has 8850 mL of water.

Objects

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

e. The height of a house f. The length of a room

g. The length of a wallet h. The length of a needle

2. a. 12 cm b. 4 cm

c. 7 cm d. 8 cm

e. 4 cm f. 12 cm

3. 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. 6 m 890 cm = 6 × 100 + 890 cm = 1490 cm

e. 8 m 50 cm = 8 × 100 + 50 cm = 850 cm

f. 4 m 900 cm = 4 × 100 + 900 cm = 1300 cm

g. 8 m 300 cm = 8 × 100 + 300 cm = 1100 cm

h. 7 m 250 cm = 7 m = 7 × 100 + 250 cm = 950 cm

4. a. 500 cm = 100 cm + 100 cm + 100 cm + 100 cm + 100 cm = 1 m + 1 m + 1 m+ 1 m + 1 m = 5 m

b. 300 cm = 100 cm + 100 cm + 100 cm = 1 m + 1 m + 1 m = 3 m

c. 1100 cm = 100 cm + 100 cm + 100 cm + 100 cm + 100 cm +

100 cm + 100 cm + 100 cm + 100 cm + 100 cm + 100 cm = 1 m + 1 m +

1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m = 11 m

d. 200 cm = 100 cm + 100 cm = 1 m + 1 m = 2 m

e. 1200 cm = 100 cm + 100 cm + 100 cm + 100 cm + 100 cm + 100 cm +

100 cm + 100 cm + 100 cm + 100 cm + 100 cm + 100 cm = 1 m + 1 m +

1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m = 12 m

f. 1300 cm = 100 cm + 100 cm + 100 cm + 100 cm + 100 cm +

100 cm + 100 cm + 100 cm + 100 cm + 100 cm + 100 cm + 100 cm + 100 cm = 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m + 1 m = 13 m

5. Objects

a. An empty box b. A banana

c. A bag of rice d. A cylinder

e. Candy f. Two watermelons

g. A bag of flour h. Two apples

6. 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

g. 5 kg 500 g = 5 × 1000 + 500 g = 5500 g

h. 1 kg 278 g = 1 × 1000 g + 278 g= 1278 g

7. Objects

a. Tank of water b. Cup of tea

c. Barrel of water d. Spoonful of oil

e. Bottle of shampoo f. 3 jugs of lemonade

g. Petrol Tank h. Glass of juice

8. 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

g. 7 L 450 mL = 7 × 1000 + 450 mL = 7450 mL

h. 9 L 100 mL = 9 × 1000 mL + 100 mL = 9100 mL

9. Length of the red string = 30 cm

Length of the purple string = 86 cm

Total length = 30 cm + 86 cm = 116 cm = 100 cm + 16 cm = 1 m 16 cm

The total length of the two strings is 1 m 16 cm.

10. Weight of the bag of sand = 4 kg 500 g

4 kg 500 g = 4 × 1000 g + 500 g = 4500 g

So, the weight of the bag is 4500 g

Word Problems 1. Length of the wire = 5 m 66 cm

5 m 66 cm = 5 × 100 + 66 cm = 566 cm

So, the length of the wire in centimetres is 566 cm.

2. Capacity of the tub = 7 L 500 mL

7 L 500 mL = 7 × 1000 mL + 500 mL = 7500 mL

So, the capacity of the tub in mL is 7500 mL.

3. Amount of orange juice in the big jug = 850 mL

Amount of orange juice poured = 500 mL

Amount of orange juice remaining in the jug = 850 mL – 500 mL = 350 mL

So, the amount of orange juice remaining is 350 mL

4. Weight of the box = 6 kg 450 g = 6 × 1000 + 450 g = 6450 g

Weight added to the box = 2 kg 250 g = 2 × 1000 + 250 g = 2250 g

Total weight in grams = 6450 g + 2250 g = 8700 g

The total weight of the box is 8700 g.

5. Quantity of water in the tub = 5 L 500 mL =

5 × 1000 + 500 mL = 5500 mL

Quantity of water used from the tub = 3 L 200 mL = 3 × 1000 mL + 200 mL = 3200 mL

Amount of water left in the tub = 5500 mL – 3200 mL = 2300 mL = 2000 mL + 300 mL = 2 L 300 mL

So, 2 L 300 mL of water is left in the tub.

6. Length of the cloth with the tailor = 600 cm

Length of the cloth the tailor cut = 3 m = 3 × 100 cm = 300 cm

Length of the cloth left with the tailor = 600 cm – 300 cm = 300 cm

So, 300 cm of cloth is left with the tailor.

Chapter 10

Let’s Warm-up

1.

Half past 4

2. 5:00

3. 6:30

4. 12:00 Do It Yourself

10A 1. A shows the hour hand and B shows the minute hand.

2. a.

b.

c.

d.

B Minute hand

Half past 4

Quarter to 3

25 minutes to 8

25 minutes past 11

3. 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

4. a. Sam wakes up at 7 a.m. in the morning. b. He reaches school by 9 a.m. in the morning. c. Sam comes back from school at 1 p.m. at noon. d. He goes to play with his friends at 6 p.m. in the evening. e. Sam eats dinner and goes to bed by 9 p.m. at night.

5. a. 5 minutes past 2 b. 20 minutes to 4

c. Half past 10 d. Quarter past 1

Word Problems 1. On the alarm, the hour hand is at 7 and the minute hand is at 12.

Thus, Niru woke up at 7 o’clock or 7 a.m. today.

2. The minute hand is at 10 and the hour hand is about to reach 2.

So, Meera reached her dance class at around 1:50 or 10 minutes to 2.

She reached about 10 minutes early.

3. Half past eleven 11:30 is before noon and 12:30 is afternoon.

Thus, the show starts at 11:30 a.m. and ends at 12:30 p.m. 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. c. There are 60 minutes in 1 hour.

2. a. The hour hand moved from 3 to 4. It has moved by 1 number. So, 1 hour has passed. b. The hour hand moved from 4 to 7. It has moved by 3 numbers. So, 3 hours have passed. c. The hour hand moved from 10 to 12. It has moved by 2 numbers. So, 2 hours have passed. d. The hour hand moved from 12 to 4. It has moved by 4 numbers. So, 4 hours have passed. e. Between 1:20 to 2:20, the hour hand has moved 1 number. So, 1 hour has passed. f. Between 3:30 to 5:30, the hour hand has moved 2 numbers. So, 2 hours have passed. g. Between 7:15 to 11:15, the hour hand has moved 4 numbers. So, 4 hours have passed.

3. a. Filling a glass of milk will take some minutes.

b. Boiling water will take a few minutes. c. Eating a banana will take a few minutes. d. Watering a plant will take some minutes e. Washing, ironing, and folding some clothes will take an hour or more.

4. 1 day = 24 hours

1 hour = 60 minutes

So, minutes in 24 hours = 60 × 24 = 1440 minutes

Thus, there are 1440 minutes in a day.

Word Problems 1. Between 3 o’clock and 5 o’clock, the hour hand has moved 2 numbers. Thus, Anuj has spent 2 hours in his swimming class.

2. From 9 o’clock to 10 o’clock, the hour hand has moved 1 number. So, 1 hour has passed. We know that 1 hour = 60 minutes. Thus, Vibhu’s test was 60 minutes long.

3. The hour hand has moved 8 numbers from 10 o’clock last night to the next 6:10 morning. So, 10 p.m. to 6 a.m. is 8 hours. So, 8 hours have passed.

Anju woke up at 6:10, that is, 10 minutes past 6. Thus, Anju slept for 8 hours and 10 minutes.

10C 1. a. 2024  Day of the week

b  January  Month

c  26th  Year

d. Friday  Date of the month

2. a. There are 7 days in a week.  b. A year is divided into 12 months c. A year has 365 days, if it is not a leap year.

3. a. False.  b. True.  c. False.  d. True.

4. Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday are the days in a week.

5. 1 month = 30 days.

2 months = 30 × 2 = 60 days.

Thus, there will be 60 days in two months.

Word Problems 1. 1 week = 7 days. So, 2 weeks = 7 + 7 OR 7 × 2 = 14 days. Thus, Anand has practiced his dance performance for 14 days.

2. Number of months with 31 days: 7

Number of days in these 7 months = 7 × 31 = 217 days

Number of months with 30 days: 4

Number of days in these 4 months = 4 × 30 = 120 days

Number of days in February = 29

Total number of days in this year: 217 + 120 + 29 = 366 days

10D 1. a. The calendar shows the year 2034.   b. There are 31 days in this month.

2. a. There are 4 Sundays in this month. b. The month starts from a Monday c. On 25 May, the day is Thursday

d. The next day of 18 May is a Friday e. 2 May is a Tuesday. The next Tuesday will be on 9 May. f. 30 May is the last Tuesday of the month. g. The month is ending on 31 May. It is on Wednesday. h. In this month, Saturdays are on dates

6, 13, 20, and 27. i. In this year, month of June is starting from Thursday.

3.

A Hour hand Ram Navami Dusshera Diwali Bhai Dooj Guru Nanak Jayanti

4.

29 October 31 October 20 November 22 November 5 December Cricket match Basketball match Tug-of-war match Football match Kho-Kho match

February August October November December

5. a. Rina was born in the year 2010. b. Rina’s baby sister was born in 2017. Rina was born in 2010. So, when her sister was born, Rina was: 2017 – 2010 = 7 years old. c. Rina was born in 2010. She won a dance competition in 2025. She was: 2025 – 2010 = 15 years old when she won the dance competition. d. Rina was born in 2010. Rina’s age in 2034: 2034 – 2010 = 24.

Rina will be 24 years old in 2034.

Word Problems 1. Seema was born on 17 April 2018.

Number of years passed from 2018 to 2022 = 2022 – 2018 = 4

So, Seema was 4 years old in the year 2022.

2. Aaru was born on 05 July 2010.

The number of years that will pass by 2025: 2025 – 2010 = 15 years

Aaru will be 15 years old on 05 July 2025.

3. Date of birth of Tinu: 31 July 2015; Date of birth of Mittu: 31 July 2021

Both Tinu and Mittu were born on the same date in the same month. The year they were born was different. Therefore, the difference in their age, 2021 – 2015 = 6 years.

Thus, Tinu is older than Mittu by 6 years.

Chapter Checkup 1. a. 1:50 OR 10 minutes to 2 b. 1:30 OR half past 1 c. 10:45 OR quarter to 11 d. 12:05 OR 5 minutes past 12  e. 5:40 OR 20 minutes to 6 f. 11:35 or 25 minutes to 12   2. a. 4 o’clock b. 9 o’clock

c. 10 minutes past 12 d. 20 minutes past 9

e. Half past 1 f. Quarter to 7

3. a. Between 2 o’clock to 5 o’clock, the hour hand has moved 3 numbers. So, 3 hours have passed. b. Between 7 o’clock to 10 o’clock, the hour hand has moved 3 numbers. So, 3 hours have passed. c. Between 9 o’clock to 3 o’clock, the hour hand has moved 6 numbers. So, 6 hours have passed. d. Between 5:20 and 7:20, the hour hand has moved 2 numbers. So, 2 hours have passed. e. Between 9:15 and 11:15, the hour hand has moved 2 numbers. So, 2 hours have passed. f. 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. 3 o’clock in the afternoon is after 12 o’clock in the noon but before midnight 12 o’clock. So, it is 3:00 p.m.

c. 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. d. 9 o’clock at night is after 12 o’clock in the noon but before midnight 12 o’clock. So, it is 9:00 p.m.  e. 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. f. 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. e. Baking two cakes and some cookies will take hours.

6.

a. Day before Monday  2024

b. Day after Monday  February

c. Month before March  Sunday

d. Month after March  2021

e. Year before 2022  April

f. Year after 2023  Tuesday

7. a. If it is not a leap year, there are 365 days in the year.

b. The date on the last day of the year is always 31 December.

c. The date on the first day of the year is always 1 January.

d. If today is 30 April 2023, the date tomorrow will be 1 May, 2023

e. If today is 12 June 2023, yesterday’s date was 11 June, 2023

f. If today is Monday, 1 June 2023, the date after a week will be Monday, 8 June 2023 g. Sia’s birthday is on Friday, 20 May. The date, a week before Sia’s birthday would be Friday, 13 May.

8. Republic day Earth day Independence day Gandhi Jayanti Children’s day

26 January 22 April 15 August 2 October 14 November

9. If this is 2024:

a. The next year will be 2025.

2024 + 1 = 2025

b. 2 years back, the year was 2022.

2024 – 2 = 2022

c. After 5 years, the year will be 2029.

2024 + 5 = 2029

10. The drawing of the calendar for the month of July will vary. Sample drawing:

a. There are 5 Sundays in the month. b. The date on 2nd Saturday is 14 July. c. Mondays are on 2, 9, 16, 23 and 30.

d. i. Wednesday  ii. Thursday  iii. Wednesday   iv. Monday Word Problems 1. 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.

9 o’clock at night is after noon and before midnight 12 o’clock. So, Rama slept at 9 p.m.  2. In between 8 to 10, the hour hand has moved by 2 numbers. Thus, 2 hours have passed.

3. Atul’s date of birth: 02 March 2015

10 years from Atul’s birth year: 2015 + 10 = 2025

So, Atul will turn 10 years old on 02 March 2025.

4. 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.

5. Diya’s date of birth: 12 August 2003

Diya’s age in the year 2020 was: 2020 – 2003 = 17

Thus, Diya was 17 years old on her birthday in 2020.

6. 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.

Chapter 11

Let’s Warm-up 1. We can get two ₹10 notes or coins for ₹20.  2. We can get six ₹5 coins for ₹30.  3. Seven ₹2 coins and one ₹1 coin make ₹15.  4. Ten ₹2 coins make ₹20. Do It Yourself

11A 1. a. Twenty-eight rupees fifty paise b. Thirty-six rupees twenty-five paise c. Forty-nine rupees seventy paise

d. Fifty-seven rupees thirty-five paise e. Sixty-five rupees thirty-seven paise f. Seventy-one rupees seventy-five paise.

g. Eighty-eight rupees sixty-two paise h. Ninety-two rupees forty-eight paise  2. a. ₹56.70 b. ₹29.88 c. ₹35.57

d. ₹68.50 e. ₹73.22 f. ₹15.66 g. ₹88.78

3. a. ₹32.50 b. ₹45.25 c. ₹160.50 d. ₹252.50

e. ₹530.25   4. a. ₹22.25  b. ₹30.50  c. ₹55.50

d. ₹75  e. ₹70.50  f. ₹32.25  g. ₹53.25  5. ₹56.08

11B 1. a. 2500 paise b. 3200 paise c. 4100 paise

d. 11256 paise e. 22925 paise f. 35837 paise

g. 47435 paise h. 58620 paise  2. a. ₹56.00 b. ₹42.00

c. ₹36.52 d. ₹62.41 e. ₹75.23 f. ₹85.62 g. ₹123.56  h. ₹562.14  3. 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

4. ₹1 = 100 paise

So, ₹76 = 7600 paise

5. Cost of the eraser in rupee = ₹5

Cost of the eraser in paise = 500 paise (₹1 = 100 paise)

Siya will pay 500 paise

11C

1. Money given to Vaibhav = ₹50.50

Money given to Neeraj = ₹75.00

Money given altogether

= (₹50.50 + ₹75.00) = ₹125.50

Mother gave ₹125.50 to Vaibhav and Neeraj altogether.

2. Price of lunch box = ₹85.50

Amount of money Priya has = ₹72

Amount of money Priya needs

= (₹85.50 – ₹72.00) = ₹13.50

Priya needs ₹13.50 more to buy the lunch box.

3. Cost of English book = ₹130.00

Cost of Hindi book = ₹129.50

Cost of Math book = ₹142.00

Total cost of the books = (₹130.00 + ₹129.50 + ₹142.00) = ₹401.50

The total cost of the books are ₹401.50

4. Price of cricket bat = ₹235.50

Price of cricket ball = ₹45.00

Total cost = ₹235.50 + ₹45.00 = ₹280.50

The total cost of the bat and ball is ₹280.50

5. Money with Suhani = ₹238.50

Money Suhani gave to her mother = ₹153.00

Money left with Suhani = ₹238.50 – ₹153.00 = ₹85.50

Suhani is left with ₹85.50.

6. Money spent by Divya on Sunday = ₹238.00

Money spent by Divya on Monday = ₹125.50

Money spent by Divya in total = ₹238.00 + ₹125.50 = ₹363.50

Divya spent ₹363.50 in all.

7. 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.

8. Amount given to 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 11D 1.

Vipin needs to pay ₹96.50.

2. The bill is not correct.

The correct bill is:

Total amount -

3.             Total amount4. 5.

Total:

6. Amount with Sahil - ₹200.   Let us prepare the bill for Sahil

9.

Total:

Yes, Sahil will be able to purchase all the fruits.

Chapter Checkup 1. a. Fifty-two rupees thirty-six paise.

b. Sixty-five rupees fourteen paise. c. Seventy-one rupees five paise.  2. a. ₹38.65 b. ₹29.55 c. ₹59.09  3. a. ₹35.50

Thirty-five rupees fifty paise. b. ₹22.25 Twenty-two rupees

Twenty-five paise. c. ₹62.50 Sixty-two rupees fifty paise.

d. ₹45.25 Forty-five rupees twenty-five paise.

e. ₹82.25 Eighty-two rupees twenty-five paise.

4.

5. a. 2515 paise b. 5225 paise c. 23548 paise

6. a. ₹32.56 b. ₹152.36 c. ₹523.64

7. Correct bills:

8.

Divya has to pay ₹188.50

Amount customer paid to Sam = ₹200.00

Amount Sam will return = ₹200 – ₹130 = ₹70

10. Amount spent on the doll = ₹152.00

Amount spent on a toy = ₹58.50

Total amount spent = ₹152.00 + ₹58.50   Sam spent ₹210.50 in all.

Word Problems 1. Amount of the pen = ₹23.00

Amount given to the shopkeeper = ₹50

Change received = ₹50 – ₹23.00 = ₹27 Kavya will receive ₹27 from the shopkeeper.

2. Amount for school fees = ₹535.50

Amount with Reena = ₹425.00

Amount she needs = ₹535.50 – ₹ 425.00 = ₹110.50 She needs ₹110.50 more

3. Amount John has = ₹125.50

Amount of money Tanya has more than John = ₹52.00

Amount with Tanya = ₹125.50 + ₹52.00 = ₹177.50 Tanya has ₹177.50 with her.

4. Amount Seema has = ₹136.50

Amount spent on notebook = ₹55

Amount spent on crayons = ₹136.50 – ₹55 = ₹81.50. Seema spent ₹81.50 on crayons.

Chapter 12

   1 2    of the shape may vary. Sample answers: a. b. c. d.

3. Shaded one-fourth    1 4    of the shape may vary. Sample answers:

a. b. c. d.

4. 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 d. One-fourth or 1 4

Half

One-fourth

Three-fourths

6. Shaded one-third or 1 3 of the shape may vary. Sample answers:

a. b. c. d.

Word Problem 1. Total apple pie available = 1. Number of friends = 4. Pie given to each friend = 1 ÷ 4 = 1 4

Thus, each friend gets 1 4 of apple pie.

12B 1. The coloured part of the collection may vary. Sample answers: a. 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

b. Total number of cats = 8. Part of the collection we want to colour = half or 1 2 . Half or 1 2 of the collection = 8 ÷ 2 = 4

c. 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

c. Total number of bowls = 24. Part of the collection we want to colour = one-third or 1 3 . One-third or 1 3 of the collection = 24 ÷ 3 = 8

d. Total number of leaves = 22. Part of the collection we want to colour = half or 1 2 . Half or 1 2 of the collection = 22 ÷ 2 = 11

d. Total number of tomatoes = 30. Part of the collection we want to colour = one-third or 1 3 . One-third or 1 3 of the collection = 30 ÷ 3 = 10

3. The coloured part of the collection may vary. Sample answer: a. Total number of fish = 8. Part of the collection we want to colour = one-fourth or 1 4 . One-fourth or 1 4 of the collection = 8 ÷ 4 = 2

2. The coloured part of the collection may vary. Sample answer: a. 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

b. Total number of caps = 12. Part of the collection we want to colour = one-fourth or 1 4 . One-fourth or 1 4 of the collection = 12 ÷ 4 = 3

c. Total number of flowers = 20. Part of the collection we want to colour = one-fourth or 1 4 . One-fourth or 1 4 of the collection = 20 ÷ 4 = 5

b. Total number of parrots = 15. Part of the collection we want to colour = one-third or 1 3 . One-third or 1 3 of the collection = 15 ÷ 3 = 5

d. 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

4. a. True b. False c. False

5. a. To find 1 2, we divide the number by 2: 6 ÷ 2 = 3.

b. To find 1 3, we divide the number by 3: 9 ÷ 3 = 3. c. To find 1 4, we divide the number by 4: 8 ÷ 4 = 2. d. To find 1 2, we divide the number by 2: 18 ÷ 2 = 9.  e. To find 1 3, we divide the

number by 3: 12 ÷ 3 = 4.  f. To find 1 4, we divide the number by 4: 16 ÷ 4 = 4 g. To find 1 3, we divide the number by 3: 21 ÷ 3 = 7. h. To find 4, we divide the number by 4: 12 ÷ 4 = 3

Word Problem 1. Total number of plants = 12. Number of plants that were put in the living room = 1 3 of total plants = 1 3 of 12 = 12 ÷ 3 = 4 plants. Thus, Ramya put 4 plants in the living room.

12C 1. a. Numbers of shaded parts: 4. Total number of parts in the figure = 9. The fraction of shaded parts: Number of shaded parts

Total parts in the figure = 4 9 b. Numbers of shaded parts: 4. Total number of parts in the figure = 8. The fraction of shaded parts: Number of shaded parts

Total parts in the figure = 4 8 c. Numbers of shaded parts: 5. Total number of parts in the figure = 9. The fraction of shaded parts: Number of shaded parts

Total parts in the figure = 5 9 . d. Numbers of shaded parts: 7. Total number of parts in the figure = 16. The fraction of shaded parts: Number of shaded parts

Total parts in the figure = 7 16 e. Numbers of shaded parts: 4. Total number of parts in the figure = 9. The fraction of shaded parts:

Number of shaded parts

Total parts in the figure = 4 9 f. Numbers of shaded part: 1

Total number of parts in the figure = 2. The fraction of shaded parts: Number of shaded parts

Total parts in the figure = 1 2 2. Shaded parts may vary. Sample answers:

3 4

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

Total parts = 3 9 Number of uncoloured parts = 6. 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

Total parts = 6 11 . Number of uncoloured parts = 5. 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

Total parts = 6 13 . Number of uncoloured parts = 7. Fraction of uncoloured part:

Number of uncoloured parts

Total parts = 7 13 .

4. Coloured part of the collection may vary. Sample answer: a. 4 7 b. 5 9

c. 6 10 d. 9 13

5. 4 parts out of 5 is equal to 16. Thus, 5 parts will be 20. Thus, there are 20 buses in total.

Word Problem 1. Total number of marbles = 24. Fraction of marbles in one-third set = 1 3 . Number of marbles in one-third set = 1 3 of 24 = 24 ÷ 3 = 8 marbles. Thus, there are 8 marbles in one-third of the set.

12D 1. 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 2  Total number of marbles in the bag = 24. Fraction of green marbles = 1 3 1 3 of the total marbles = 24 ÷ 3 = 8. Thus, 8 marbles are green inside the bag. 3. 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.  4. Number of crayons given by Sunil to his sister = 8. Total number of crayons Sunil had = 15. Fractions of crayons given by Sunil to his sister = Number of crayons given

Total number of crayons = 8

15.  5. Total pairs of shirts Vishal owns = 12. Fraction of shirts which are blue = 1

4 . Number of blue shirts = 1 4 of 12 = 12 ÷ 4 = 3. Thus, Vishal has 3 blue shirts.  6. Total number of building blocks in the bag = 25. Number of blocks used by Ravi = 16. Number of unused blocks = 25 – 16 = 9. Fractions of unused blocks = Number of unused block

Total number of blocks = 9 25 7. Number of books with Rani = 27. Fraction of books donated = 1 3 . Number of books donated = 1 3 of 27 = 27 ÷ 3 = 9 Number of books left = 27 – 9 = 18. Thus, 18 books are left with Rani.

Word Problem 1. Number of pages read by Suhani = 11. Total number of pages in the book = 24. Fractions of pages read by Suhani = Number of pages read

Total number of pages in the book = 11 24

Chapter Checkup 1. a. Numbers of coloured parts in the figure: 4.

Total number of parts in the figure = 6. The fraction of coloured parts: Number of coloured parts

Total parts in the figure = 4 6 b. Numbers of coloured parts in the figure: 8 Total number of parts in the figure = 9.

The fraction of coloured parts: Number of coloured parts

Total parts in the figure = 8 9 c. Numbers of coloured parts in the figure: 1. Total number of parts in the figure = 3. The fraction of coloured parts: Number of coloured parts

Total parts in the figure = 1 3 2. Coloured part of the figures may vary. Sample answers:

a.  4 9     b. 3 5     c.  2 7

3. a. Total number of brinjals = 15. Part of the collection we want to colour = one-third or 1 3 1 3 of the collection = 15 ÷ 3 = 5

b. Total number of kites = 18. Part of the collection we want to colour = half or 1 2 1 2 of the collection = 18 ÷ 2 = 9

6. a. To find 1 2, we divide the number by 2: 12 ÷ 2 = 6. b. To find 1 3, we divide the number by 3: 15 ÷ 3 = 5. c. To find 1 4, we divide the number by 4: 4 ÷ 4 = 1. d. To find 1 2, we divide the number by 2: 8 ÷ 2 = 4

7. Total parts of the cake = 5. Cake is divided among 4 friends and Tim. Each of them gets 1 part then the fraction each get = 1 5

8. Total number of flowers Meena bought = 9.

Fraction of flowers that were tulips = 1 3

1 3 of the total flowers = 9 ÷ 3 = 3. Thus, 3 flowers were tulips.

9. Total number of pencils Sunita has = 25.

Number of red pencils = 12.

Fractions of red pencils = Number of red pencils

Total pencils = 12 25

10. Total number of apples in the basket = 24.

c. Total number of cups = 20. Part of the collection we want to colour = one-fourth or 1 4 1 4 of the collection = 20 ÷ 4 = 5

d. Total number of balls = 21. Part of the collection we want to colour = one-third or 1 3 1 3 of the collection = 21 ÷ 3 = 7

Fraction of rotten apples = 1 4

1

4 of the total apples in the basket = 24 ÷ 4 = 6. 6 apples are rotten.

Remaining apples that are still good = Total apples – Rotten apples 24 – 6 = 18.

Thus, 18 apples are still good.

Word Problems 1. Total number of plants Manya planted = 6. Number of rose plants = 2.

Fractions of rose plants = Number of rose plants

Total plants = 2 6

2. Total number of invitations Raj sent for the party = 18. Number of friends who are unable to attend the party = 3. Number of friends who attended the party= 18 – 3 = 15.

Fractions of friends who attended the party = Friends who attended the party

Total invitations sent = 15 18

4. a. Half = 1 2 b. One-third = 1 3 c. Three-fourth = 3 4

d. One-fourth = 1 4 e. Fraction = Numerator Denominator = 5 8

f. Fraction = Numerator Denominator = 7 12

5. 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

b. Total stars in the collection = 17.

Number of pink stars = 9

Total capsicum = 7 12

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

c. Total crayons in the collection = 15.

Number of blue crayons = 6

Fraction of blue crayons = Number of blue crayons

Total number of crayons = 6 15

Number of yellow crayons = 9.

Fraction of yellow crayons = Number of yellow crayons

Total number of crayons = 9 15

Chapter 13

Let’s Warm-up 1. Tuesday  2. Friday  3. Monday and Wednesday  4. Thursday Do It Yourself

13A 1. c. Both the statements are true.  2. a. False b. True  c. False. Organizing the collected data makes it easy to understand. d. True. We later organize data collected from surveys in meaningful ways such as in tables.  3. Data of marks obtained in Math out of 100, organised from highest to lowest: 99, 98, 89, 83, 80, 78, 77, 70, 65, 58, 45.

4. Let’s put the data in the table form: From the table, we can tell that bananas and grapes are the two fruits that are liked by an equal number of students.

5. a. Number of people who eat Barley are 3. b. Number of people who eat Ragi are less than those who eat rice. c. Most of the people eat rice as a main food. Word Problems 1. Section B has the highest strength. The number of students in Section B = 52. Section G has the least strength. The number of students in Section G = 36. Difference in the number of students in section B and G = 52 – 36 = 16. Thus, 16 more students are there in the section

with the highest strength than the one with the least strength. 2. a. Roll number 5 scored maximum marks in both Math and Science. b. Total marks scored by Roll no. 1 = 67 + 78 = 145. Total marks scored by Roll no. 2 = 57 + 81 = 138. Total marks scored by Roll no. 3 = 78 + 69 = 147. Total marks scored by Roll no. 4 = 75 + 87 = 162. Total marks scored by Roll no. 5 = 84 + 89 = 173. So, none of the students scored equal number of marks combined.

13B 1. a. True b. True c. True  2. 1 symbol = 10 animals. A total of 5 such symbols = 10 × 5 = 50 animals.

3. 2 represents 10 snowflakes. That is: = 10 snowflakes. = 5 snowflakes. 20 snowflakes = 4 × 5 snowflakes. Thus, 4 symbols will represent 20 snowflakes.

4.

Flavours Number of Ice Creams

Vanilla

Strawberry

Chocolate Mango

5 = 2 children. If we break the given number in multiples of 2:

Favourite Swings Favourite Swings

6. 1 fruit = 1 unit a. There are 5 apples. b. Oranges are the maximum in number. There are 9 oranges. c. Banana is the minimum in number. There are just 4 bananas.

7. Each = 10 books a. Number of symbols used to show Math books sold = 10. So, Math books sold = 10 × 10 = 100. 100 math books are sold. b. Number of symbols used to show Hindi books sold = 6. So, Hindi books sold = 6 × 10 = 60. 60 Hindi books are sold. c. Maximum symbols are given for Math books. Thus, Math books were sold the maximum. Minimum symbols are given for Hindi books. Thus, Hindi books were sold the least. d. Number of keys used to show Computer books sold = 8. So, Computer books sold = 8 × 10 = 80. 80 Computer books are sold.

Word Problems 1.  = 1 student a. In the table there are six symbols for Science. So, 6 students’ favourite subject is Science. b. In the table there are three symbols for English. So, 3 students’ favourite subject is English. c. Maximum symbols are given for Mathematics. Thus, Mathematics is liked by the greatest number of students.

2. = 2 students a. In the table, the number of symbols given for Wednesday are = 4. So, the number of books borrowed on Wednesday = 4 × 2 = 8. 8 books were borrowed on Wednesday. b. In the table, the number of symbols given for Monday are = 5. So, the number of books borrowed on

Monday = 5 × 2 = 10. 10 books were borrowed on Monday. c. In the table, the maximum symbols are given for Saturday:

If = 2 students, then  = 1 student. So, = (6 × 2) + 1 = 12 + 1 = 13. Thus, the maximum number of 13 books were borrowed on Saturday. d. In the table, the minimum symbols are given for Thursday: . We know that = 2 students. So = 3 × 2 = 6. Thus, the minimum number of 6 books were borrowed on Thursday. e. The number of books borrowed on Tuesday = . If = 2 students, then  = 1 student. So, = (3 × 2) + 1 = 6 + 1 = 7. The number of books borrowed on Thursday = . We know that = 2 students. So = 3 × 2 = 6. Books borrowed on Tuesday – Books borrowed on Thursday: 7 – 6 = 1. Thus, the difference in the number of books borrowed on Tuesday and Thursday is 1 book. f. The number of books borrowed on Monday: , that is 5 × 2 = 10. The number of books borrowed on Tuesday: that is, (3 × 2) + 1 = 6 + 1 = 7. The number of books borrowed on Wednesday: , that is 4 × 2 = 8. The number of books borrowed on Thursday = , that is = 3 × 2 = 6. The number of books borrowed on Friday: that is, (5 × 2) + 1 = 10 + 1 = 11. The number of books borrowed on Saturday: = (6 × 2) + 1 = 12 + 1 = 13. Thus, the total books borrowed in the week = 10 + 7 + 8 + 6 + 11 + 13 = 55 books 13C 1.

Different Modes of Transport used by People Scale: 1 division = 1 person

Bus   Train Bicycle  Bike  Auto

Modes of Transport

Favourite Colours Scale: 1 division = 1 student

Red     Green    Black   Yellow Number of Students Colours

3. a. 4 children like sports. b. 5 children like adventure.

c. Cartoon channel is the favourite. 9 children like it.

d. 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.

e. 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.

4. a. Nimisha slept the maximum number of hours.

b. Both Raghav and Eric slept for 7 hours, which is the minimum number of hours on the graph.

c. Nimisha slept for 9 hours. Rajat slept for 8 hours. Number of hours by which Nimisha slept more than Rajat = 9 – 8 = 1 hour. Thus, Nimisha slept 1 hour more than Rajat.

d. Shoaib slept for 8 hours. Raghav slept for 7 hours. Number of hours by which Raghav slept less than Shoaib = 8 – 7 = 1 hour. Thus, Raghav slept 1 hour less than Shoaib.

Word Problem 1.  First, put the data in the table form. Then, prepare a bar graph.

English     Hindi     Maths     GK

Favourite Subject

a. Math, Hindi and GK are the most favourite subjects among the students. They are all of the highest value of 9 students per subject.

b. English is the least favourite subject among the students. 8 students selected it.

c. 8 students like English. d. 9 students like Maths.

e. Yes, Maths, Hindi and GK are equally liked by the students. Chapter Checkup 1.

c. Motor bikes are parked the most in the parking lot. There are 112 motorbikes. d. Number of motor bikes parked: 112. Number of scooters parked: 84. 112 – 84 = 28. Thus, 28 more bikes are parked than scooters in the parking lot.

3. First, put the data in the table form:

Favourite Hobbies Number of Students Favourite Hobbies Number of Students

Singing 7 Singing

Dancing 9 Dancing

Sports 10 Sports

Watching TV 9 Watching TV

Reading 5 Reading

Then, replace the number with the key  = 1 student.

4.  = 2 students. a. In the table, there are 10 shown for coffee. The number of children who like coffee: 2 × 10 = 20. 20 children like coffee. b. Milk is liked the least. c. In the table, there are 9 shown for tea. The number of children who like coffee: 2 × 9 = 18. 18 children like coffee. d. Number of children who like coffee: 2 × 10 = 20. Number of children who like milk: 2 × 8 = 16. 20 – 16 = 4. Thus, 4 children like coffee more than milk.

5.

Scale: 1 division = 1 student

2. a. 12 jeeps are parked in the parking lot.

b. 10 buses are parked in the parking lot.

Raj  Ronit  Zayn   Rhea Venkatesh Riddhi Preeti

6. a. Only 1 run is scored in the 5th over. b. 6 runs are scored in the 7th over. c. Maximum runs were scored in the 6th over. There are 10 runs in the over. d. List and add the runs scored in each over by the 10th over: 4 + 8 + 9 + 3 + 1 + 10 + 6 + 8 + 9 + 5 = 63. 63 runs are scored in 10 overs.

Word Problems 1. a. Rohit took the maximum number of wickets.  b. Number of wickets Rohit took = 10. Number of wickets George took = 9. 10 – 9 = 1. So, Rohit took 1 more wicket than George. c. Sanjeev and Goerge took the same number of wickets. They both took 9 wickets each. d. Wasim took the minimum number of wickets out of 4 bowlers. He took 8 wickets. 2. = 2 tomatoes a. There are 5 shown in the table against Ramesh.  = 2 tomatoes, thus Ramesh harvest 2 × 5 = 10 tomatoes. b. There are 5 and 1  shown in the table against Suresh. A total of tomatoes. If = 2 tomatoes, then = 1 tomato. Thus, Suresh harvested: (2 × 5) + 1 = 11 tomatoes. c. Tarachand harvested the least number of tomatoes. There are 4 shown in the table against his name. Thus, he harvested: 2 × 4 = 8 tomatoes. d. Number of tomatoes Suresh harvested = 11. Number of tomatoes Tarachand harvested = 8. 11 – 8 = 3. Thus, Suresh harvested 3 more tomatoes than Tarachand.

About the Book

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

Key Features

• Let’s Recall: Helps to revisit students’ prior knowledge to facilitate learning the new chapter

• Real Life Connect: Introduces a new concept by relating it to day-to-day life

• Examples: Provides the complete solution in a step-by-step manner

• Do It Together: Guides learners to solve a problem by giving clues and hints

• Think and Tell: Probing questions to stimulate Higher Order Thinking Skills (HOTS)

• Error Alert: A simple tip off to help avoid misconceptions and common mistakes

• Remember: Key points for easy recollection

• Did You Know? Interesting facts related to the application of concept

• Math Lab: Fun cross-curricular activities

• QR Codes: Digital integration through the app to promote self-learning and practice

About Uolo

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

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