Imagine_Maths_CB_Grade3_Sample by Uolo

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

Imagine Mathematics

About This Book

MATHEMATICS

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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NEP 2020 based

NCF compliant

CBSE aligned

26/09/23 7:15 PM

MATHEMATICS Master Mathematical Thinking

Grade 3

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Fo re wo rd

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

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1 6-digits Let's Recall We know that numbers are basic units of mathematics and are used for counting, measuring and comparing quantities. We have also previously learned that each digit in a number has a value, which we call the place value. Let us take a 2-digit number as an example! The digit on the left is at ten’s place while the digit on the right is at one’s place.

K ey El emen t s o f a C hDivision apt easr— a Q u i c k G lanc e Repeated Subtraction

Similarly, in the number 2548, 5 represents 5 hundreds, or 500. However, in the number 56, 5 represents 5 tens, or 50. Therefore, even if a digit is same, its value always depends on where it is in the number.

Komal has 20 coins, and she wants to put 5 coins in each pouch. Let us help her to divide 20 by 5 using repeated subtraction.

4 Tens

8 Ones

2 Thousands 5 Hundreds

Step 1 Subtract 5 from 20 until we get 0.

Total number of coins = 20. Understanding Multiplication – Let's Warm-up Introductory Concept tiples Write the correct place value of the coloured numbers. Let’s take away 5. 1 Do It page with a introduction Find the first 5 multiples of 6. Check__________ by dividing if 92 and 96 are multiples of 6. 1 32 Together Number of remaining coins = 15. – ng holidays is always fun!quick You first decide on a place you want to visit, warm-up with a real life 2 548 __________ 1 2 Let’s take away 5 again. esearch what you can do there, and then finally make arrangements. 1 3 876 example __________ Number of remaining coins = 10. 4 4563 __________ s going to Ooty. The train departs every second day. – Let’s take away 5 again. 5 9958 __________ Real Life Connect

2 + 2 + 2 + 2 + 2 + 2 + 2 = 14

He has learnt 14 words already! Hurray!

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 +2 + 2 + 2 + 2……… This is too much! Sanju gets confused and asks his father to help.

6×1=6 8

6 × 2 = ____

9 16

TTh Th H T O Th Number of remaining coins =H 0. T +

=31 ×

multiplicand

TTh

multiplier

= 62

–

On multiplying a number by 1, the product is always the number itself.

On multiplying a number by 0, the product is always zero.

product

We can find the product of two numbers by placing them horizontally next to each other. Let us multiply 123 and 3. Step 1

Step 2

Step 3

Multiply by ones.

Multiply by tens.

Multiply by hundreds.

Multiply 3 and 3 ones.

Multiply 3 and 2 tens.

123 × 3 = __ __9

123 × 3 = __69

Did You Know?

Rinne Tsujikubo of Japan4 broke So, there are four 5s in 20. Hence, Komal requires pouches to keep the Guinness world record for fastest mental arithmetic on the coins. Let us start finding the total number

even number?

123 × 3 = 369

The product of 123 and 3 is 369.

Chapter 3 • Multiplication

of books step by step.

How many 7s are there in 21?

Example 2

n travel on the following dates - 2, 4, 6, 8, 10, 12, 14, 16 and so on. 6 92

Find the factors of 36 using the division method. Divide numbers by 36

What do we get?

Check the remainder

Are the numbers factors of 36?

36 ÷ 3

____

What do we know?

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January 17, 2023 by correctly adding 15 sets of three-digit numbers in 1.62 seconds.

1 total number of fiction books = 1219 96StepThe

The total number of non-fiction books = 1567 Subtract 7 from 21 until we get 0. What do we need to find?

dividing 92 by weby get 2 remainder. On dividing 96 by 6, we get ____ remainder. 36 ÷ 1 36 the number 0 ultiples of a number areOn the products we6,get multiplying by 1,Yes2, Think = The total number of fiction books 1 – and 7 Tell 36 ÷ 2 ____ 0 ____ nd so on. The total number of non-fiction books Do we need+of to go6. So, 92 _______________________________ of 6. So, 96 ___________________________

les of 3 can be found by using multiplication tables36as follows: ÷4 ____

We can multiply two numbers in any order. The product always remains the same.

Horizontal Method

9/11/2023 4:24:58 PM books and 1567 non-fiction books. How many books are there in total?

ing Multiples

We subtracted 5, four times. In the library, there are 1219 fiction to school the concept

Are the multiples of an even number always an

Do It Together

Story Sums

all the circled numbers

Think and Tellhave in common?

Count Fun the number of times 5 has been subtracted. fact, related

What do you think do

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Multiplication Rules

The number to be multiplied is multiplicand and the number by which we multiply is multiplier.

Do It Together

We know that the number obtained from multiplication is the product.

Add 12,344 and 1115. 6 × ____ = ____

StepSo, 2 of 5. + 1115 = _____________. Thinkofand Tell I scored out12,344 The first five multiples 6 are 6, ____, ____, 24, ____._________ 17

Multiplication by 1-digit Number

Let’s take away 5 again.

6 × ____ = 24

A quick-thinking

21 question 22

6 × ____ = ____

Sanju’s father helps him find the number of words using multiplication.

4 5 6 7Sunday 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Saturday Number of remaining coins = 5.

5 0

Sanju struggles to find how many words will he learn in whole January.

0 1 Friday 2 3 Thursday

He starts adding quickly.

y Tuesday Wednesday

1= 2= 3= 4= 5=

Sanju and his father play a newspaper game where he learns 2 new words each day. They have been playing this game for a week. Sanju is trying to find all the words he has learnt.

The total number of books in the library

We subtracted 1 2 1 9 seven 3 times. +

So, there are three 7s in 21. 2 7 8 6

beyond 6=to1219 find + 1567 more factors of 36?

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Step 2 Count how many times 7 has been subtracted.

Solve to find the answer.

– 7 out 36 ÷ 5 7 1 ____ 3 × 6 = An 18important So,Pointing the total number of books in the library is 2786. ____ 0 Yes It Yourself 5A 36 ÷ 6 7 keep in commonly made 3 × 7 = point 21 toDo Error Alert! The city NGO organised a two-day donation drive. Remember! Remember! On the first day of the drive, 1366 clothes were So, the factors of 36 are ___________________________________________________________________. 3 × 8 = mind 24 3 mistakes and – collected. 7 we add 1000 to a On the second day of the drive, 1000 Always countWhen how many times the A number is a multiple of itself too. 4-digit number, only the clothes were collected. How many clothes were 3 × 9 = 1 27Colour the balloons that are multiples of 2. avoid number has digit been not in thesubtracted, thousands 0howinto For example, multiples of 5 are 5, collected total? place changes. Do15, It Yourself the number itself. 3 × 10 = 30 10, 20, 25,5C 30 and so on! them

3 6 9 12 15

Round off each dividend to the nearest 10s and 100s and then divide. To the nearest 10s

Example 4

To the nearest 100s

a 1147 ÷ 2

b 4589 ÷ 3 c 6478 ÷ 6

d 8974 ÷ 7

4 6 5 8 7 Show 10 in different arrangements. Then, list the factors of 10.

Find the factors of the following numbers using multiplication.

What do we know?

ves no remainder

15 – 15 00

3 11

5 d 3916 e 340 18 13 – 17 15 Find the factors of the following numbers using division. 5 b 11 1 c 12 d 1301 e 15 9 leavesa remainder a 14

b 21

HOTS:

c 36

1 238 children went to a school camp. If one tent can be shared by 4 children, Total number of clothes collected = 1366 + 1000

g 48

f 12 questions k 17

b 8

g 13 l

c 9

d 10

h 14

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Which number has the greatest number of factors between 5 and 15?

What is the smallest number that has exactly three factors?

5 • Multiples and Factors

Points to Remember m

Word Problems

n 20

The place value table is divided into groups called periods.

•

5-digit numbers have 2 periods - Thousands Period and Ones Period.

•

Face value is the numerical value of the digit in a particular place in a number.

ways can she arrange the eggs?

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and fun

Chapter end

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summary

e 11 j

Place value Scavenger Hunt:

Divide the entire class into groups of 4.

classroom

Each group can be dedicated a particular category like City population, State population,

activity

Each group collects the data on their respective category from newspapers, magazines, or

Each groups’ data must include at least 5 numbers in their category.

Each group discusses and deduces the following for each number in their data:

The number being divided is called the dividend. The number by which we divide is called the divisor. The result of the division is called the quotient. The number left over after division is called the remainder.

•

To check if our answer after division is correct, we can use: Dividend = (Quotient × Divisor) + Remainder.

•

When a number is divided by 1, the quotient is always the number itself.

•

When a number is divided by itself, then the quotient is 1.

•

When 0 is divided by any number, then the quotient is always 0.

•

When a number is divided by 10, the digit at the ones place forms the remainder and the remaining digits form the quotient.

•

When a number is divided by 100, the digit in the ones place and tens place forms the remainder and the remaining digits form the quotient.

•

When a number is divided by 1000, the digits in the ones place, tens place and thousands place form the remainder and the remaining digits form the quotient. 77

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QR Code: Access

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to interactive

Setting: Groups of 4 1

•

Chapter 4 • Division

Rounding numbers is helpful when we need an estimate and when we want to convey 9/11/2023 4:26:02 PM numbers in an easier way.

Materials Required: Newspapers, Magazines, or the Internet

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Estimate the amount of money that each student gets.

15-09-2023 3.07.52 PM

of biscuits each packet. are possible? Numbers arranged in from the largest to theWhat smallestdifferent are said to bearrangements in a descending order.

Math Lab

multidisciplinary

₹5734 is distributed between 2 groups of students. Each group has 11 students.

Points to Remember

Raman, a baker, baked biscuits. He wants to place arranged from thehas smallest to the72 largest are said to be in an ascending order. the same number 2Numbers

mbers up to gits •

o 25

Tina bought 16 eggs. She wants to arrange them into a tray. In how many Chapter 5 • Multiples and Factors • 16-digit numbers have 3 periods - Lakhs Period, Thousands Period and Ones Period.

•

approximately how many tents will be needed for the camp?

•

20 30

viding 15 by 5, we get 0 remainder. On dividing 5,Explain we get remainder 1. Is of 6 a 16 factorby of 64? your answer. 7 Find the first five multiples the given numbers. 2 Applicative is a multiple of 5. So, 16 8is not multiple 5.10 have exactly TWO factors? Which a numbers betweenof 1 and a 7 and analytical

h 50

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Is 18 a factor of 126? Explain your answer.

115

Word Problems

What do we need to find?

19 f

people. About how many tables are needed?

Chapter 6 • Division

860 people have been invited to a banquet. The caterer is arranging tables. Each table can seat 10 Number of clothes collected during the 5first day of the drive = 1366

[Round off the dividend to the nearest hundred]. Number of clothes collected during the second day of the drive = 1000

Show 18 in different arrangements. list the factors of 18. 2 n also check if a number is a multiple of a number using division. If theThen, remainder Show 20 in different arrangements. Then, list the factors of 20. hen the bigger number is a multiple of the other3number. For example:

e 5555 ÷ 5

digital resources 9/11/2023 4:26:15 PM

Followers of celebrities, Number of speakers of a language, and Car and Bike prices. the internet.

Place value and face value of each digit. Correct number representation.

Correctly written number names. Correctly order the numbers in ascending and descending order Round off the numbers to the nearest 10s, 100s and 1000s.

iii

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G rad ual R e le ase of Re spon si bi li t y

The Gradual Release of Responsibility (GRR) is a highly effective pedagogical approach that empowers students to learn progressively by transitioning the responsibility from the teacher to the students. This method involves comprehensive scaffolding—including modelling, guided practice, and ultimately fostering independent application of concepts. GRR, endorsed and promoted by both the NEP 2020 and NCF, plays a pivotal role in equipping teachers to facilitate age-appropriate learning outcomes and enabling learners to thrive. The GRR methodology forms the foundation of the Imagine Mathematics product. Within each chapter, every unit follows a consistent framework: 1. I Do (entirely teacher-led)

2. We Do (guided practice for learners supported by the teacher) 3. You Do (independent practice for learners) GRR Steps

Unit Component

Snapshot

Numbers Beyond 9999 Ajay: Hello daddy, I found this letter, it is for you.

Real Life Connect

Father: Thank you. Ajay: The letter has your name and the address of our home. Father: Yes.

Real Life Connect

Ajay: But, what is this big number 781005?

From: Ajay Shukla, 12, Hathipol,

Guwahati - 781005

Father: It is a special code, also called the postal code. This code helps in finding the exact location in a city.

Theoretical explanation

Ajay: Okay daddy. But it has 6-digits, and I find it hard to read!

Facts about Multiples

• Every number is a multiple of 1 and the number itself.

ForAbout example, 55-digit × 1 = 5. Here, 5 is a multiple of 1 and 5. All Numbers!

• Every multiple is either greater than or equal to the number itself.

ToFor help Ajay understand 6-digit numbers, let's first learn about 5-digit numbers. example, the multiples of 8 are 8, 16, 24, 32, 40, … and so on. Here, each multiple is

to that or greater 8. thousand nine hundred ninety-nine is the greatest 4-digit Weequal know 9999than – nine • Every number has an unlimited number of multiples. number.

I do

For example, the multiples of 7 are 7, 14, 21, 28, 35, …, 70, 77, …, 7000, …, 70000, …,

Now, we add 1 to this, we unlimited. get 10000. and when so on. Here, multiples of 7 are Example 1

Find the 5 multiples of 4. 9999 + 1first = 10000

Remember!

We can find the multiples of 4 by using the number line showing jumps of 10000 4. is the smallest 5-digit

10000 is read as “Ten Thousand”. 1

Let us learn more about 5-digit numbers! 0

number. 99999 is the greatest 5-digit number.

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

Place Values and Expanded Form in 5-digit Numbers We can find the multiples of 4 by using multiplication tables as follows:

We4 know that a 4-digit number has 4 places on the place value chart - ones, tens, ×1= 4 hundreds and thousands. The place on the left to the Thousands place is called the Ten Did You Know? 4×2= 8 Leap years are always Thousands place. 4 × 3 = 12

Examples

multiples of 4. For example

× 4 take = 16a 5-digit number 13435. The place value chart Let4 us for this can be written the years 2016, number 2020, 2024, ... as:4 × 5 = 20 are all leap years. The five multiples TThfirstTh H T of 4Oare 4, 8, 12, 16 and 20. Example 2

Did You Know?

1 3 4 3 5 Find the first 5 multiples of 5. Check by dividing whether 95 is a multiple of 5. The number 4 is the 1 2 3 4 5 only number with the same number of Always remember that place value is the letters as its value in value of the digit in a number based on the English language. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 its0position in the given number.

The place 100 5= ×400. 5 ×value 1 = 5 of “4” 5 × in 2 =13435 10 5is × 34 =×15 4 = 20

5 × 5 = 25

The first five multiples of 5 are 5, 10, 15, 20 and 25. 5

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leaves remainder 0

95 – 95 00

19 On dividing 95 by 5, we get 0 remainder. So, 95 is a multiple of 5.

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Find the factors of 36 using the division method.

Do It Together

GRR Steps

Divide numbers by 36

Unit Component

What do we get?

Check the remainder

36 ÷ 1

36 ÷ 2

____

Yes

36 ÷ 4

____

Think and Tell Do we need to go

Find 20 and 30. Also, common factor of both 36 ÷ 3the common 12 factors of ____ ____ find the highest beyond 6 to find the numbers. more factors of 36?

Do It Together

Find the method. Step 1 factors7of 36 using1 the division 36 ÷ 5 ____

Do It Together

Factors of 20 36 ÷ 6 Divide numbers by 36

We do

Are the numbers

factors of 36? Snapshot

1 2 0 What do we get?

____

4 5 10 20 Yes Check the Are the numbers remainder factors of 36?

Step 2 So, the factors of 36 are ___________________________________________________________________.

Do It Together

36 ÷of130 Factors

Yes

Step363÷ 2

____

Common 36 ÷ 3Factors

____

Do It Yourself 5C

of 20 and 30 3610 ÷ in 4 different arrangements. ____ Show Then, list 0 the factors of 10. ____

Show Then, list 1 the factors of 18. ____ 3618 ÷ in 5 different arrangements. 7

Do we need to go beyond 6 to find more factors of 36?

The common factors of 20 and 30 are ____________________________________________________. Show 20 in different arrangements. Then, list the factors of 20.

3 4

Think and Tell

36 ÷ 6

____

Yes

Math Lab of the following Find the factorscommon numbers multiplication. The highest factor of 20 using and 30 is __________.

So,a the b 21 of 36c are d 39 e 40 f 42 g 48 h 50 i 77 14 factors 36 ___________________________________________________________________.

Board Game of Multiples

Find the factors of the following numbers using division.

Materials Required: Number grid asnumbers. shown below, dice, crayons Find the common factors of the following 1 18 Is a factor of 126? Explain your answer.

Do It Yourself 5D

Setting:bIn groupsc of 4 a 9

d 13

e 15

8, 10 of 64? Explainbyour 12, answer. 15 IsMethod: 6a a factor

c 13, 16

Do It Yourself 5C

d 14, 20

e 16, 18

10 different the factors of 10. 45 j 72, f numbers g h Then, i 54, 64 12 2681 Each player chooses their 20, 30 in 33, 10 44 35, 50list 1Show between 1 arrangements. and have colour. exactly TWO factors? 8 1 Which

number. 4 The common player chooses multiple that Also, find the lowest and the highest 3 Find factors ofathe pairsnumbers of of numbers. the factors of the following using multiplication. 4 3 Find the 18 20 22 48 Word common Problems number on Show the board and shades it with factors. it with a diagram. a 14 b 21 c 36 d 39 e 40 21 f 42 30 17g 4822 their colour.

Do It Yourself

a is6the b arrangements. c Then, d 3 40 8that has exactly 12 factors? number three Show 20smallest in different list the factors of 20. 50 e 436 10 3 What

Word Problems

a 16 and 24

a common factor of allyour the numbers. Isc 6 0aisfactor of 64? Explain answer. _______ d 15 and 25 havebetween a total of 1 3 and common factors. _______ Which numbers 10 have exactly TWO factors? e 6 is number a common factor 18, 30 and 66. _______ Which has theof greatest number of factors between 5 and 15?

f The lowest common factor of 20, 34, 39 and 42 is 1. _______ Chapter Checkup 10 What is the smallest number that has exactly three factors? 5

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Radhe says, “The number 14 has a greater number of factors than 45.” Is he correct? Verify your answer.

Word Find theProblems factors.

c 72 d 88 eggs. She wants to arrange them into a tray. iIn how many g 16 1201 Tina bought 156 200 h 180

ways can she arrange the eggs?

222

Raman, a baker, has baked 72 biscuits. He wants to place the same number 9/11/2023 4:26:19 PM

Which of these pairs of numbers have the common factor of 4? 92

a 5 and 20

b 20 and 100

c 12 and 36

d 60 and 200

c 15

d 23

Write the first 5 multiples. a 7

b 11

e 30

Write the smallest number which is a common multiple of the given number pairs.

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a 2 and 5

e 10 and 15

e 98 95

Find the common factors of the given pairs of numbers.

a 7 and 14 c 9arrangements of biscuits b in each packet. are possible? 24 and 30 What different and 12 d 20 and 25

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of biscuits in each packet. What different arrangements are possible?

aChapter 45 5 • Multiples andbFactors 66 2

13 have no common _______ aand factor ofwho 126? Explain factors. yourmost answer. The player colours the number of multiples on the board is the winner. 5Isb 1811

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f 818

92 8

Chapter Checkup

h 50 11 60

b 21 and 42 c 63 and 18 d 55 and 100 e 48 and 84 Tina bought 16 eggs. She wants to arrange them into a tray. In how many

Inthe case a player gets 1 on the dice, they 67 factors of the following numbers using division. 7 5 4 4Find ways can she arrange the eggs? Write if True or False. can choose any number on the board. b 11 c 72 dHe13 e is 15 9 12biscuits. 18 a baker, has baked wants to36 place samefnumber The biggest common factor of numbers 24 and 3.the _______ 2aa Raman, (Do you know why?)

You do

18 inhas different arrangements. Then, list the of number therolls greatest of factors between 5factors and 15?the One player the number diceare and sees Which of the following numbers factors ofthe 78 and 96? Circle correct 9 2 Which 5 18. 24 option. 15 Verify 42your answer. 25 35 2 2Show

b 3 and 7 f

10 and 25

c 5 and 8

g 11 and 22

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d 4 and 14

h 20 and 24

Find the following. a Multiples of 4 that are smaller than 30.

Pearson, P. D., & Gallagher, G. (1983). Contemporary Educational Psychology.

b Multiples of 6 that are smaller than 50.

Fisher, D., & Frey, N. (2021). Better learning through structured teaching: A framework for the gradual release of responsibility. c Multiples of 8 that are greater than 30 but smaller than 80.

Fisher, D., & Frey, N. (2014). Checking for understanding: Formative assessment techniques for your classroom.

Chapter 5 • Multiples and Factors

Gradual Release of Responsibility UM24CB_G4.indb 97

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C o nt e nt s

Place Value �� 1 • All About 4-digit Numbers • Comparing Numbers • Rounding off 3-digit Numbers

2 10 16

Division by 1-digit Numbers �� 127

Shapes and Patterns �� 138

Length, Weight and Capacity �� 162

Time �� 185

Money �� 208

Fractions �� 227

Data Handling �� 246

Addition of 3-digit Numbers �� 21 • Mental Addition • Adding 3-digit Numbers • Estimating the Sum • Word Problems

22 27 41 43

Subtraction of 3-digit Numbers �� 49 • Reviewing Subtraction • More on Subtraction • Estimating the Difference • Word Problems

50 56 69 72

Multiplication Tables �� 78 • Understanding Multiplication

Multiplication by 2-digit Numbers �� 93 • Multiplying Numbers • Estimating the Product • Word Problems

94 105 107

Division �� 112 • What Division Means • Division and Multiplication

113 118

• Dividing Numbers

• 2-D Shapes • 3-D Shapes • Patterns Around Us

128

139 146 152

• Length 163 • Weight 171 • Capacity 176

• Understanding Time 186 • Calendar 195

• Understanding Money • Making Bills

• Understanding Fractions

• Understanding Data

209 219

228

247

Answers �� 271

Place Value

Let’s Recall

We use numbers in our everyday lives.

Imagine you are at a grocery shop and you are buying various items. Different items have different prices. Let us say the price of a packet of cookies is ₹45. 45 can be understood as 45 = 40 + 5

45 is also the same as 4 tens + 5 ones. So this 2-digit number has 4 in the tens place and 5 in the ones place. T 4

O 5

We can therefore say that the place value in the ones place is 5. The place value in the tens place is 4 tens or 40.

Now, let’s say that the price of a bag of rice is ₹259 So, 259 = 200 + 50 + 9

H 2

T 5

O 9

Or, 259 = 2 hundreds + 5 tens + 9 ones

The place value in the ones place is 9 ones or simply 9. The place value in the tens place is 5 tens or 50. The place value on the hundreds place is 2 hundreds or 200.

Let’s Warm-up

Write the place value of the underlined digit. 1

893 =

_______________________

349 =

_______________________

864 =

_______________________

501 =

_______________________

123 =

_______________________ I scored ___________ out of 5.

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All About 4-digit Numbers Real Life Connect

Ajay has been collecting coins in his money bank for the past 2 years. Ajay: Dad! I’m collecting coins in my money bank. It is too heavy now. I wonder how many coins I have collected. Father: Why don’t you count the coins? Ajay: Great idea, Dad! Ajay starts counting and finds that he has 999 coins. Dad: Here, take this 1 coin as well, Ajay! Ajay: How much money do I have now, Dad? Father: Let’s find out!

Understanding 4-digit Numbers We have already learnt about 3-digit numbers. 999 is a 3-digit number. We can show 999 using the place value blocks as:

9 hundreds

9 tens

+ 9 ones

When we add 1 to 999, we get: adding 1 to 999

+ 9 hundreds

9 tens

9 ones

1 one

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9 hundreds

9 tens

9 hundreds

10 tens

10 ones = 1 ten 10 tens = 1 hundred

10 hundreds = 1 thousand or 1000

Place Value and Expanded Form of 4-digit Numbers The place value of a digit depends on its position in a number. We already know the places ones, tens and hundreds. The place to the left of the hundreds is called the ‘Thousands’ place. Thousands

Hundreds

Tens

Ones

↓

Let us understand more about place value using a 4-digit number 1536. The number can be written using the place value as: 1

Place value 5 3

Did You Know?

6 ones or 6

Numbers 1001; 1221; and 7337 can be read the same forwards and backwards. These are called palindromic 4-digit numbers.

3 tens or 30

5 hundreds or 500

1 thousands or 1000

Expanded Form of 4-digit Numbers We already know that when we write a number as the sum of the values of its digits, the number is said to be in expanded form. Let us write the expanded form of 4257. The place value chart of 4257 is:

Chapter 1 • Place Value

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Th 4

H 2

T 5

O 7

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The expanded form can be written as: Th 4

H 2

T 5

O 7

7 × 1 = 7 or 7 ones

5 × 10 = 50 or 5 tens

2 × 100 = 200 or 2 hundreds

4257

= 4000 + 200 + 50 + 7

Standard form 4 × 1000 = 4000 or 4 thousands Example 1

Expanded form

Write the place value of each digit of the number “2175”. Also, write the number in its expanded form. Let us write the number 2175 using place value. Th 2

H 1

T 7

O 5

5 ones or 5

7 tens or 70

1 hundred or 100

2 thousands or 2000

We can also write the number in an expanded form in the following way: Th 2

H 1

T 7

O 5

5 × 1 = 5 or 5 ones

7 × 10 = 70 or 7 tens

1 × 100 = 100 or 1 hundred

2 × 1000 = 2000 or 2 thousands So, 2175 = 2000 + 100 + 70 + 5 Do It Together

Write the place value of each digit of the number “4319”. Also, write the number in the expanded form. Let us write the number 4319 using place value. Th 4

____

T 1

____ 9 ones or 9

_____ tens or _____

3 hundreds or _____ _____ or 4000

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Now let’s write the number in its expanded form: Th 4

H 3

T 1

O 9

_____ × 1 = 9 or 9 _____ 1 × _____ or 1 _____

3 × _____ or 3 hundreds

4 × 1000 = _____ or 4 _____

Reading 4-digit Numbers Let us learn how to read a 4-digit number. Look at the place value blocks shown below.

Step 1: Count the number of blocks. 2 thousands

2 hundreds

3 tens

8 ones

Step 2: Write the number of blocks in standard and expanded form. 2238 = 2000 + 200 + 30 + 8 Step 3: Read each part of the expanded form. Two thousand

2000 + 200 + 30 + 8

Two hundred

Eight

Thirty

Therefore, the number 2238 can be read as two thousand two hundred thirty-eight. Example 2

Read and write the number formed by the blocks.

Chapter 1 • Place Value

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Step 1: Count the number of blocks. 7 thousands

1 hundred

1 ten

6 ones

Step 2: Write the number of blocks in standard and expanded form. 7116 = 7000 + 100 + 10 + 6

Step 3: Read each part of the expanded form. Seven thousand

7000 + 100 + 10 + 6 sixteen

One hundred Note: 10 + 6 will be read as sixteen and not ten six.

The number 7116 can be read as seven thousand one hundred sixteen. Do It Together

Read and write the number formed by the blocks.

Step 1: Count the number of blocks. ________ thousands

4 ________

________ tens

4 ________

Step 2: Write the number of blocks in the standard and expanded form. 6434 = ________ + 400 + ________ + 4

Step 3: Read each part of the expanded form. ____________

6000 + 400 + 30 + 4

Four hundred

four

____________

The number 6434 can be read as _____________________________________.

Error Alert! Do not use ‘and’ while writing seven thousand eight the number names. hundred and forty-two

seven thousand eight hundred forty-two

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4-digit Numbers on Abacus We have seen that blocks are useful when reading and writing numbers. We can also read numbers using an Abacus. An abacus can have any number of rods. Here we will be using an abacus that has 4 rods. The first rod from the right is for the ones, second is for the tens, the third is for hundreds and the last rod is for the thousands place.

Let us look at the steps to read a number on an abacus. Step 1: Count the number of beads in each rod. There are 2 beads at the thousands place, 3 beads at the hundreds place, 5 beads at the tens place, and 4 beads at the ones place.

Step 2: Write the corresponding number of beads in the place value table. Th 2

H 3

T 5

O 4

The number on the abacus is 2354. The number is read as two thousand three hundred fifty-four. Example 3

Which number is formed by the beads on the abacus. Step 1: Count the beads in each rod. 4 beads at the thousands place 0 beads at the hundreds place 5 beads at the tens place 7 beads at the ones place

Step 2: Write the number of beads in the place value chart. Th 4

H 0

T 5

O 7

The number is 4057. The number is read as four thousand fifty-seven.

Chapter 1 • Place Value

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Do It Together

Count the beads in the abacus to find the number. Fill in the blanks. Step 1: Count the beads on each rod. _______ beads at the thousands place

2 beads at the _______ place

_______ beads at the tens place

1 bead at the _______ place

Step 2: Write the number of beads in the place value chart. Th

H 2

____

O 1

The number is ________.

The number is read as five thousand ________ hundred ________ one.

Do It Yourself 1A 1

Write the numbers by counting the blocks. a

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Count the beads. Read and write the number. a

Th H 3

T O

1932

Th H d

Th H

T O

5358

Th H e

T O

9030

T O

Th H

T O

Th H

T O

4856

Th H

3041

T O

Write the numerals. a

three thousand two hundred forty-five

five thousand three hundred eighty-six

seven thousand forty

six thousand eight

two thousand four hundred

eight thousand five

nine thousand five hundred two

Write the numbers in words. a

1532

3156

4811

6518

7294

8043

7900

9687

Write the place value of the underlined digit. a

3215

5362

7314

6892

8113

9686

8657

7590

Chapter 1 • Place Value

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T O

7465

Th H

Show the numbers on the abacus. a

23-09-2023 11:38:26

Write the numbers in standard form. a

3000 + 200 + 40 + 1

5000 + 700 + 20 + 4

7000 + 50 + 2

6000 + 400 + 0 + 0

8000 + 000 + 9 + 0

9000 + 000 + 00 + 0

7000 + 800

9000 + 500 + 2

Write the numbers in expanded form. a

2148

4036

6105

7203

8200

6566

7980

9650

6053

5998

Read the hints to find the year.

• The value of the thousands place is 1000. • The hundreds place has the digit of the largest value. • The tens place digit is 2 less than the hundreds place digit. • The sum of all the digits is 20.

Comparing Numbers Real Life Connect

Sam and Jim are at their school library. Both of them are looking at the books available in the library. Sam: Look Jim! This book has 1235 pages. Jim: My dad also has two books like this! Sam: How many pages do those books have? Jim: I saw that one of the books has 885 pages and the other has 1145 pages. Sam: Wow! I wonder which book has more pages. We have learnt in our previous class that a number with more digits is greater than the number with fewer digits.

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As 1235 and 1145 are 4-digit numbers and 885 is a 3-digit number, 1235 and 1145 are greater than 885. 1235 > 885 and 1145 > 885 Now let us see which is greater between 1235 and 1145. Step 1: Write the numbers in the place value chart. Step 2: Compare the digits at the thousands place. Both the digits are the same. 1235

Th 1

H 2

1145

T 3

O 5

Step 3: Compare the digits at the hundreds place. 1235

1145

(2 > 1)

Remember! Always compare the digits from the left to right.

Since 2 > 1, 1235 > 1145 We now know that 1235 > 1145 and 1235 > 885. We also know that 1145 > 885.

Let us now learn to arrange these numbers in ascending and descending order. When numbers are arranged from the highest to the lowest it is called descending order. When numbers are arranged from the lowest to the highest it is called ascending order. Descending order: 1235 > 1145 > 885 Ascending order: 885 < 1145 < 1235 Example 4

Compare the numbers 3174 and 3147. Both numbers have the same number of digits. Step 1: Write the numbers in the place value chart. Step 2: Check the digit at the thousands place. 3174

3147

Both the digits are the same; 3 = 3

Chapter 1 • Place Value

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Th 3 3

H 1 1

T 7 4

O 4 7

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Step 3: Check the digit at the hundreds place. 3174

3147

Both the digits are the same; 1 = 1

Step 4: Check the digit at the tens place. 3174

3147

(as 7 > 4)

The digit 7 in 3174 is greater than the digit 4 in 3147; 7 > 4 Therefore, 3174 > 3147 Example 5

Arrange the numbers in ascending and descending order. 510, 2168, 1321, 6344

We need to first check the number of digits of all the numbers.

Step 1: Check whether the numbers have the same number of digits. 510 is a 3-digit number and 2168, 1321 and 6344 are 4-digit numbers. 510 is the smallest number among the given set of numbers.

Step 2: Compare the digits at the thousands place for the rest of the 3 numbers. 2168

1321

6344

1<2<6

The numbers can be arranged in ascending order as: 510 < 1321 < 2168 < 6344

The descending order of the numbers can be given as: 6344 > 2168 > 1321 > 510 Do It Together

Ordering Numbers

Arrange the numbers in ascending and descending order. 1765, 4372, 6145, 4538

As all the numbers have 4 digits, we will start comparing from the thousands place. 1765

4372

6145

4372

4538

_____ > _____

4538

6 > _____ > _____

Numbers 4372 and 4538 have the same digit at the thousands place, comparing the hundreds place of these 2 numbers gives: The ascending order is: 1765, _______, _______, 6145.

The descending order is: 6145, _______, _______, _______. 12

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Do It Yourself 1B 1

Compare the following numbers using the symbols >, <, = a

614 _____ 1700

5092 _____ 7320

2184 _____ 2357

5720 _____ 5265

4126 _____ 4510

5271 _____ 5261

4680 _____ 4680

Circle the smallest number in the group. a

3205

4289

3526

3010

4370

3740

7304

7403

1080

1800

1008

8001

1199

1999

9111

1991

5022

2500

5477

4577

9129

1299

9921

9291

Circle the greatest number in the group. a

658

2168

6345

1265

5882

3678

8249

8924

6160

6061

6610

6110

9911

9991

1119

9191

4426

6244

4264

2644

7567

6757

7067

7563

Arrange the following numbers in ascending and descending order. a

1765, 4390, 7430, 7935

773, 7880, 9573, 2860

4853, 7943, 392, 3067

8546, 9404, 157, 6583

8753, 1265, 8734, 3867

8328, 3654, 9754, 6436

7554, 7580, 7689, 7589

Simi has 245 marbles. Eva has 236 marbles. Who has more marbles? Dhwani has a greater number of marbles than Simi. Could Dhwani have 230, 272, or 229 marbles? Explain how you know.

Forming 4-digit Numbers

Do you know that we can form the smallest and greatest 4-digit numbers, using all the digits without repetition? Let us learn how to form 4-digit numbers.

Let us use the digits 3, 5, 1, and 7 to form the smallest and the largest number. To form the smallest number, place the given digits in ascending order in the place value chart. Th 1

H 3

T 5

Chapter 1 • Place Value

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O 7 13

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Similarly, to form the greatest number, place the given digits in descending order in the place value chart. Th 7

H 5

T 3

O 1

Therefore, 1357 is the smallest and 7531 is the greatest 4-digit number formed using the digits 3, 5, 1 and 7. Example 6

Form the smallest and the greatest number using the following digits – 4, 0, 8, 7. Smallest number → place the values in ascending order. Th 4

H 0

T 7

O 8

Think and Tell Why have we not placed 0 at the thousands place?

Largest number → place the values in descending order. Th 8

H 7

T 4

O 0

Therefore, 4078 is the smallest and 8740 is the greatest 4-digit number formed using the digits 4, 0, 8, 7. Do It Together

Form the smallest and the greatest number using the following digits – 3, 5, 9, 0. Smallest number → place the digits in __________ order. Th

____ ____

T 5

____

Largest number → place the digits in __________ order. Th 9

____ ____

O 0

Therefore, __________ is the smallest and __________ is the greatest 4-digit number formed using the digits 3, 5, 9, 0. Even and Odd Numbers Numbers that have 0, 2, 4, 6, 8 in their ones place are called even numbers. 24, 36, 78, 592, 5240, 4318 are even numbers.

Remember! Even numbers of things can be put in pairs. (Groups of 2)

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Numbers that have 1, 3, 5, 7, 9 in their ones place are called odd numbers. 13, 77, 681, 179, 4525, 5297 are odd numbers

Remember! Odd numbers have one left over when you put the odd number of things in pairs.

Do It Yourself 1C 1

Tick the 4-digit numbers. a

512 b 840 c 6312

9050

710 f 7400

Match the following. A

9999

Smallest 4-digit number

1000

Greatest 4-digit number

9876

Smallest 4-digit number using different digits

1023

Greatest 4-digit number using different digits

Form the smallest and the greatest numbers using the given digits. a

4, 2, 7, 6

6, 1, 3, 7

5, 0, 2, 1

8, 6, 0, 5

2, 0, 9, 8

1, 5, 0, 7

2, 5, 7, 8

4, 2, 8, 9

Group the numbers as even and odd numbers. a

164 g 149 h 348

586 j 860 k 727 l 923

Write the number for the smallest 4-digit number from 7, 8, 9, 0 having 9 at the hundreds place without repeating the digits.

Chapter 1 • Place Value

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Rounding off 3-digit Numbers Real Life Connect

Lina goes to the market with her mother to buy return gifts for her birthday. Mother: Take out the list of guests, Lina. Lina: I’m so sorry Mumma! I forgot to bring the list. Mother: No problem, Lina! I remember that there were about 30 names in the list. When they get home, Lina finds that there were 27 names in the list. Did you notice the word ‘about’ before the number 30? The number 30 is not the exact number but close to the exact number. The number 30 is the rounded off number. Rounding off a number is a method used when we do not know the exact number but come close to the actual number. Let us see how Lina’s mother rounded off 27 to 30. Step 1: Draw the number line and write the numbers between 20 and 30.

20 21 22 23 24 25 26 27 28 29 30

Step 2: Look for the nearest 10 of the number. 27 is between 20 and 30 but is closer to 30. Therefore, the number 27 is rounded up to 30. Example 7

Round off 83 to the nearest 10. Step 1: Draw the number line.

80 81 82 83 84 85 86 87 88 89 90

Step 2: Look for the nearest 10 of the number. 83 is between 80 and 90 but is closer to 80. Therefore, 83 is rounded down to 80. 16

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Example 8

Round off 123 to the nearest 10. Step 1: Draw the number line. 120 121 122 123 124 125 126 127 128 129 130

Step 2: Look for the nearest 10 of the number.

123 is between 120 and 130 but is closer to 120. Therefore, 123 is rounded down to 120. Do It Together

Round off 286 to the nearest 10.

Remember!

Step 1: Draw the number line.

If the number is exactly in between, it is rounded off to the higher ten.

280 281 282 283 284 285 286 287 288 289 290

Step 2: Look for the nearest 10 of the number. 286 is between __________ and 290 but is closer to __________. Therefore, it is rounded off to __________.

Do It Yourself 1D 1

Fill in the blanks. a

There are 38 students in my class. 38 can be rounded off to ________.

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

59 is between 50 and 60 but is closer to ________.

44 is between 40 and 50 but is closer to ________.

123 is between 120 and 130 but is closer to ________.

Round off the numbers to the nearest 10. a

256 f 321 g 442 h 547

Chapter 1 • Place Value

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137

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Draw an arrow to match each number to its nearest 10.

273

830

827

470

270

358

360

Rina and Sia had 632 apples to distribute. To the nearest tens, about how many apples did they have?

I am a 3-digit number.

If you round me off to nearest 10, I round down and not up. My tens digit is odd, but I am even. Who am I? 717

752

647

Points to Remember • A 4-digit number always has 4 digits – thousands, hundreds, tens and ones. • The smallest 4-digit number is 1000 and the largest 4-digit number is 9999. • The place value of a digit depends on the position that it occupies in a number. • Expressing a number as a sum of the value of its digits is called the expanded form of a number.

• The number with more digits is the greater number. When comparing numbers from the left, the number with the greater digit in the same place value is the greater number. • In ascending order, the numbers are arranged from smallest to greatest and in descending order the numbers are arranged from greatest to smallest. • Odd numbers end with 1, 3, 5, 7 or 9 as the digit at the ones place. Even numbers end with 0, 2, 4, 6 or 8 as the digit at the ones place.

• While rounding off the numbers, if the digit in the ones place is 0, 1, 2, 3 or 4, then round off the number to the smaller ten. • If the digit in the ones place is 5, 6, 7, 8 or 9, then round off the number to the higher ten.

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Math Lab Mystery Number Hunt Setting: In groups of 4

Materials Required: Prepare a set of clue cards, each with a hint about a specific 4-digit number as mentioned below: The year India got Independence. The year in which COVID spread.

Smallest number with the digits 5, 0, 1, 7. Largest number with the digits 7, 2, 9, 5. Method: Distribute the clue cards to each team. The teams need to find the 4-digit number for each of the four hints. The team that correctly identifies the mystery numbers wins!

Chapter Checkup 1

Write the numerals. a

one thousand four hundred forty-two

three thousand eight hundred fifty-seven

four thousand two hundred eight

five thousand three hundred nine

six thousand forty-five

five thousand twenty-eight

eight thousand six hundred

nine thousand four hundred six

Write the numbers in words. a

2471

4205

5374

7308

7564

8421

8070

9157

Write the place value of the underlined digit. a

1056

3814

5807

8379

7291

9092

7952

6153

Write the standard form of the numbers. a

2000 + 100 + 80 + 5

3000 + 400 + 70 + 1

8000 + 80 + 9

5000 + 700 + 20 + 5

4000 + 600 + 0

6000 + 0 + 70 + 0

8000 + 400 + 9

9000 + 16 + 0

5000 + 200 + 60 + 5

Chapter 1 • Place Value

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Write the expanded form of the numbers. a

1382

3641

5327

6484

7500

8768

9032

2654

Form the smallest and the greatest numbers using the following digits. a

2, 0, 3, 1

8, 6, 0, 5

5, 4, 2, 8

4, 1, 0, 7

3, 4, 2, 7

3, 6, 0, 8

1, 9, 7, 4

5, 2, 7, 0

Compare the numbers using the symbols >, <, or =. a

860

2735

4072

6650

3184

3156

6720

6265

7126

4510

6271

6261

7680

Arrange the numbers in ascending and descending order. a

565, 2390, 730, 8935

773, 880, 7573, 1860

5853, 6943, 792, 7081

7846, 8704, 657, 5683

8753, 2265, 8734, 4867

7428, 7354, 8754, 5436

6454, 8480, 6789, 5789

8634, 8820, 8845, 8521

Round off the numbers to the nearest ten. a

393

421

547

236

Pencils come in packets of 20. Crayons come in packets of 25. Which number of the two is an odd number?

If Sita needs 76 beads to make a necklace. About how many beads should she buy? [Round off the number to the nearest 10.]

Sam is looking for a 4-digit number. Help him to find the number. These clues will help you.

The thousands place is equal to the number of legs a spider has.

The hundreds place is equal to the number of wheels in a car.

The tens place is equal to the number of wings a bird has.

The ones place is equal to the number of faces of a cube. i

Write the number ______________.

Write the number in words ______________.

iii

The expanded form of the number is ______________.

What is the difference between the greatest and the smallest 4-digit number that can be formed using the digits 8, 0, 7 and 9, using each digit only once?

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Addition of 3-digit Numbers

Let’s Recall Mother and father brought fruit from the market! They are so nice and fresh! They brought a bag of pears. How many pears are there? There are 4 pears! They brought a bag of oranges. How many oranges are there? There are 5 oranges! How much fruit is there altogether? Let’s put them together and count to see! + These are 9 items of fruit altogether! Putting objects together and counting them is Addition! We can write this as: 4 + 5 = 9 or

Let’s Warm-up

4 +5 9

Match the following. 1

3 4

16 7

I scored ____________ out of 4.

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Mental Addition Real Life Connect

Sam and his friend Max enjoyed going to the seashore. They collected seashells! Sam collected 5 blue seashells and 4 red seashells while Max collected 4 blue seashells and 5 red seashells.

Properties of Addition How many seashells did each of them collect?

Total number of seashells with Sam = 5 blue seashells + 4 red seashells = 9 seashells 5 blue seashells

4 red seashells

Total number of seashells with Max = 4 blue seashells + 5 red seashells = 9 seashells 4 blue seashells

5 red seashells

So, both the boys collected the same number of seashells. 5+4=4+5=9 Order property of Addition

Numbers can be added in any order. Their sum always remains the same. For example, 2 + 3 = 5. This is the same as 3 + 2 = 5. We know that Sam has 9 seashells. He found an orange-coloured seashell lying around. How many seashells does he have? 9 seashells + 1 seashell = 10 seashells Addition by 1

When 1 is added to a number, the sum is the number after. This next number is called the successor. For example, 10 is the successor of 9. 22

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Sam collected his 10 seashells and put them in a bucket. He had one empty bucket. How many seashells does he have in total? The empty bucket has no shells. So, there are 0 shells. What happens when Sam puts his shells in? Total number of seashells = 10 seashells + 0 seashells = 10 seashells. Addition with 0

When 0 is added to a number, the sum is the number itself. For example, 10 + 0 = 10.

Remember! When a number is added to another then the sum is always bigger than both the numbers. The only exception to this rule is when one of the numbers is 0.

For example, 4 + 5 = 9. 9 is greater than both 4 and 5. But 4 + 0 remains 4. Fill in the blanks.

Example 1

Do It Together

Example 2

Find the sum.

7 + 11 = 11 + ___

45 + 1 = 46

14 + 19 = 19 + 14

17 + 0 = 17

Find the missing number. 1

6 + 9 = ____ + 6

____ + 1 = 14

8 + ____ = 8

18 + 1 = ____

Do It Yourself 2A 1

Fill in the blanks. a

4 + 1 = ____

8 + 9 = ____ + 8

178 + 871 = 871 + ____

8794 + 0 = ____

0 + 1 = ____

1 + ____ = 156

Chapter 2 • Addition of 3-digit Numbers

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Write if true or false.

When you add 1 to any number, you get the same number.

When you add 0 to a number, you always get the successor.

Order does not matter while adding two numbers.

On adding two numbers, the sum is always greater than the two numbers.

Put the correct symbol >, <, =.

36 + 1

789 + 5

5 + 789

Match the following.

87 + 0

6+4

4+8

24 + 1

65 + 0

47 + 45

45 + 47

86 + 6

1 + 17

0 + 29

6 + 86

Add and complete the crossword.

7 +

+ + +

= 72

Word Problem 1

Yash has 6 red marbles and 15 blue marbles. Sophie has 15 red marbles and 6 blue marbles. Who has more marbles? Write your answer without actual calculation.

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Addition by Expanding Numbers Expanding Both the Numbers Remember Sam and Max collected seashells. They are now collecting marbles from the sand. Sam collects 45 marbles and Max collects 34 marbles. How many marbles do they collect in total? Let us add by expanding the 2 numbers.

Total marbles = 45 marbles + 34 marbles Add by expanding numbers.

Step 2: Add the ones.

Step 1: Expand both the numbers.

5 ones + 4 ones = 9 ones

45  4 tens + 5 ones = 40 + 5 34  3 tens + 4 ones = 30 + 4 4

3 7

5 4

→ 40 → 30

← 70

Step 3: Add the tens.

Step 4: Add the tens and ones to get the sum.

40 + 30 = 70

70 + 9 = 79

Expanding Only One Number Let us see how can we solve the same problem by expanding only 1 number. Total marbles = 45 marbles + 34 marbles 45 can be written as 45. Expand 34 → 30 + 4

Step 1: Add the tens in 34 to 45. 45 + 30 = 75

Chapter 2 • Addition of 3-digit Numbers

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30 + 4 75 + 4 = 79

Step 2: Add the ones in 34 to the answer. 75 + 4 = 79

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Numbers can also be added mentally. Skip count by 2 tens

Now, let us add 52 and 26 mentally.

Step 1: Keep the bigger number in mind, 52. Step 2: Skip count by the same number of tens as the tens in the second number 26. 26 has 2 tens. 52 → 62, 72

52 52 + 26 62 72 73 74 75 76 77 78 Count forward by 6 ones

Count forward by the same number of ones as in the second number 26. 26 has 6 ones. 72 → 73, 74, 75, 76, 77, 78 So, 52 + 26 = 78.

Think and Tell

What is the sum of the smallest 2-digit number and the largest 2-digit number?

Find the sum of the numbers.

Example 3

Add 47 and 12 by expanding both the numbers.

47 → 40 + 7 (Split 47 into 40 and 7)

Thus, 47 + 12 = 59.

12 → 10 + 2 (Split 12 into 10 and 2) 2

48 → 40 + 8

Thus, 48 + 31 = 79. Find the sum of 41 and 36 mentally. Skip count by 3 tens

7 2 9

Add 48 and 31 by expanding only one number.

Expand 48.

Example 4

→ 40 + → 10 + ← 50 +

30 + 1 78 + 1 = 79 Do It Together

Add the given numbers by expanding them. 1

41 41 + 36 = 77 51 61 71 72 73 74 75 76 77 Count forward by 6 ones

15 + 53

15 → 10 + 5

44 + 35

53 → 50 + ____ 1

→ 10 → ___

+ +

___

___ ___ ← ___

___

5 3

Thus, 15 + 53 = ____. 26

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Do It Yourself 2B Find the sum by expanding both the numbers.

14 + 41

46 + 23

27 + 11

24 + 55

64 + 33

35 + 33

Find the sum by expanding only one number.

17 + 32

44 + 21

71 + 10

30 + 59

57 + 22

63 + 25

Add the numbers mentally.

43 + 26 = ____

32 + 13 = ____

78 + 21 = ____

41 + 52 = ____

54 + 43

Find the sum by expanding the smaller number.

36 + 12

22 + 47

14 + 53

How many times will you skip count by tens to add 45 to 39?

Word Problems 1

Raj and Jatin were fond of collecting stamps. Raj collected 34 stamps and Jatin collected 51 stamps. How many stamps did they collect altogether?

Rajitha was picking numbers from a bag. She picked 4 and 6 and formed the largest number from these digits. She picked 1 and 2 the second time and formed the smallest number using these digits. What is the sum of the numbers formed?

Adding 3-digit Numbers Real Life Connect

Sam and Max now started collecting pebbles. After collecting different coloured pebbles, they put the pebbles in their buckets. Sam: I collected 234 pebbles. Max: I collected 313 pebbles.

Chapter 2 • Addition of 3-digit Numbers

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Addition Without Regrouping Sam: How many pebbles did we collect altogether? Max: We should add the number of pebbles each of us collected. Add each digit individually. Let us now add 234 and 313.

Always add from right to left – Add the ones, then the tens, and finally the hundreds.

Step 1: Add the ones in the two numbers.

Step 2: Add the tens in the two numbers.

Step 3: Add the hundreds in the two numbers.

4+3=7

3+1=4

2+3=5

Write 7 in the ones column.

Write 4 in the tens column.

Write 5 in the hundreds column.

Example 5

Remember!

2 3

4 7

2 3

3 4

3 7

Thus, 183 + 604 = 787.

Do It Together

Thus, 417 + 512 = 929. What is the sum of 183 and 604?

Step 1: Add the ones: 7 + 2 = 9

Example 6

Add 417 and 512.

Step 3: Add the hundreds: 4 + 5 = 9

2 3

Step 2: Add the tens: 1 + 1 = 2

7 9

Add 654 and 321. H

6 3

___ ___

4 5

654 + 321 = ________

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Do It Yourself 2C Find the sum.

456 + 232

741 + 256

222 + 666

325 + 473

147 + 541

Without actual addition, state whether the sum is odd or even.

471 + 526

148 + 111

123 + 321

145 + 541

321 + 338

873 + 122

Write if true or false.

The sum of 144 and 215 is 359.

The sum of 121 and 212 is 313.

The sum of 541 and 145 is 786.

The sum of 614 and 314 is 928.

Fill in the blanks.

171 + 324 = _______

415 + 374 = _______

456 + 111 = _______

711 + 123 = _______

232 + 463 = _______

313 + 356 = _______

Find the missing numbers.

1 3

4 ___ ___

+ ___ 2

6 ___ ___

4 1

O 6

6 ___

___ ___ 9

+ ___ 2

6 ___ ___

Word Problems 1

Akshay’s landlord spent ₹542 on repairs of pipelines and ₹256 on electrical repairs. How much did he spend in total?

A company manufactured 456 cars in the month of January and 512 cars in the month of February. How many cars did the company manufacture in the two months combined?

In a school, there are 145 students in Grade 1, 211 students in Grade 2 and 242 students in Grade 3. How many students are there in the three grades combined?

Chapter 2 • Addition of 3-digit Numbers

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Addition With Regrouping Sam had 234 pebbles and he found 4 more pebbles. Sam: Hey Max! I have 238 pebbles now. How many pebbles do we have now? Max: Let us add 238 marbles and 313 marbles. Regrouping Ones Step 1: Add 238 and 313. Add the ones. 8 ones + 3 ones = 11 ones Regroup 11 ones as 1 ten and 1 ones.

Remember! When there are more than 9 ones, regroup 10 ones into 1 ten.

Carry 1 to the tens column. Write 1 in the ones place. H 2

Step 2: Add the tens. 1 + 3 + 1 (carried from the ones) = 5 Write 5 in the tens place. H 2

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Step 3: Add the hundreds. 2+3=5

Write 5 in the hundreds place. H

So, 238 + 313 = 551. Example 7

Add 156 and 325. Step 1: Add the ones. 6 ones + 5 ones = 11 ones

11 ones = 1 ten + 1 ones

Carry 1 into tens column.

Step 2: Add the tens.

Step 3: Add the hundreds.

Write 8 in the tens place.

Write 4 in the hundreds place.

5 tens + 2 tens + 1 ten (Carried from the ones) = 8 tens

1 hundreds + 3 hundreds = 4 hundreds

Write 1 in the ones place. H 1

So, 156 + 325 = 481. Example 8

Add 248 and 124. O

So, 248 + 124 = 372. Chapter 2 • Addition of 3-digit Numbers

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Add 786 and 107.

Do It Together

___ ___

786 + 107 = _________ 31

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Remember! When there are more than 9 tens, then regroup 10 tens into 1 hundred.

Regrouping Tens Let us now add 453 and 361. Step 1: Add the ones.

3 ones + 1 one = 4 ones

Write 4 in the ones place.

1 4

Step 2: Add the tens.

5 tens + 6 tens = 11 tens

11 tens = 1 hundred + 1 ten

Carry 1 to the Hundreds column. Write 1 in the tens place. H

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Step 3: Add the hundreds.

4 hundreds + 3 hundreds + 1 hundred (carried from the tens) = 8 hundreds Write 8 in the hundreds place. H

So, 453 + 361 = 814. Example 9

Add 353 and 374. Step 1: Add the ones.

Step 2: Add the tens.

Step 3: Add the hundreds.

3 ones + 4 ones = 7 ones

5 tens + 7 tens = 12 tens

Write 7 in the ones place.

12 tens = 1 hundred + 2 tens

3 hundreds + 3 hundreds + 1 hundred (Carried from the tens) = 7 hundreds

Carry 1 to the Hundreds column.

Write 7 in the hundreds place.

Write 2 in the tens place.

So, 353 + 374 = 727.

Do It Together

Find the sum of 152 and 383. 152 + 383 = _________

Chapter 2 • Addition of 3-digit Numbers

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___ ___

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Regrouping Tens and Ones Let us add 455 and 368. Step 1: Add the ones.

5 ones + 8 ones = 13 ones. 13 ones = 1 ten + 3 ones

Carry 1 to the tens column. Write 3 in the ones place. H 4

Step 2: Add the tens.

5 tens + 6 tens + 1 ten (carried from the ones) = 12 tens 12 tens = 1 hundred + 2 tens

Carry 1 to the hundreds column. Write 2 in the tens place. H

1 5

Step 3: Add the hundreds.

1 hundred (carried from the tens) + 4 hundreds + 3 hundreds = 8 hundreds Write 8 in the hundreds place. H

1 5

So, 455 + 368 = 823 34

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Example 10

Find the sum of 368 and 489. Step 1: Add the ones.

8 ones + 9 ones = 17 ones 17 ones = 1 ten + 7 ones Carry 1 to the tens column.

Write 7 in the ones place. H 3

Step 2: Add the tens.

Step 3: Add the hundreds.

15 tens = 1 hundred + 5 tens

Write 8 in the hundreds place.

6 tens + 8 tens + 1 ten (Carried from the ones) = 15 tens

Carry 1 to the hundreds column.

Write 5 in the tens place. H

1 6

+ So, 368 + 489 = 857. Do It Together

3 tens + 4 tens + 1 hundred (Carried from the tens) = 8 tens

What is the sum of 512 and 188? 512 + 188 = _________

1 6

___ ___

Regrouping Hundreds Let us add 743 and 514. Step 2: Add the tens.

Step 1: Add the ones.

Write 5 in the tens place.

Write 7 in the ones place.

3 ones + 4 ones = 7 ones

4 tens + 1 ten = 5 tens Step 3: Add the hundreds.

7 hundreds + 5 hundreds = 12 hundreds

11 hundreds = 1 thousand + 2 hundreds

Write 1 in the thousands place and 2 in the hundreds place. So, 743 + 514 = 1257. Chapter 2 • Addition of 3-digit Numbers

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7 35

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Let us now add 786 and 546 with regrouping of ones, tens, and hundreds. Step 1: Add the ones.

Step 2: Add the tens.

6 ones + 6 ones = 12 ones

8 tens + 4 tens + 1 ten (carried from the ones) = 13 tens

12 ones = 1 ten + 2 ones

13 tens = 1 hundred + 3 tens

Carry 1 to the tens column.

H 7

Write 1 in the thousands place and 3 in the hundreds place.

Write 3 in the tens place. Th

1 8

7 hundreds + 5 hundreds + 1 hundred (Carried from the tens) = 13 hundreds

13 hundreds = 1 thousand + 3 hundreds

Carry 1 to the hundreds column.

Write 2 in the ones place.

Step 3: Add the hundreds.

Th 1

1 8

Error Alert! ALWAYS remember to add the carryover. H 1

Example 11

Add 487 and 647.

Step 1: Add the ones. Th

H 4

So, 487 + 647 = 1134.

2 3 5

1 3 9 2

4 8

Step 2: Add the tens. Th

1 8

2 6

Step 3: Add the hundreds. Th 1

1 8

4 .

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Th Do It Together

___ ___ ___

H 2

Add 876 and 129.

H 8

876 + 129 = _________

Do It Yourself 2D 1

Add the numbers by regrouping ones. a

H T O

+ 2

___ ___ ___

Find the sum. Fill in the boxes. a

H 6

___ ___ ___

Chapter 2 • Addition of 3-digit Numbers

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Add the numbers by regrouping the hundreds. a

Add the numbers by regrouping the tens. a

H 4

___ ___ ___

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+ 5

H 1

___ ___ ___

Fill in the blanks. a 154 + 317 = ____________

248 + 374 = ____________ 717 + 313 = ____________

239

286

___ ___ ___

187 + 381 = ____________ 647 + 451 = ____________ 828 + 373 = ____________

Read the numbers and answer the questions.

539

614

Find the pair of numbers that will give a 4-digit sum.

Which two numbers when added will have 0 at the ones place?

Which two numbers have a sum of 525?

Word Problems 1

Rucha has a collection of 109 puppets. Suhani has 118 more puppets than Rucha. How many puppets does Suhani have?

Jaspal had ₹456 with him. His father gave him ₹235 more. How much money does he have now?

218 students took admission in Grade 2, 317 students took admission in Grade 3 and 165 students took admission in Grade 4. How many students took admission for all the grades combined?

Adding Bigger Numbers Sam and Max put all the pebbles in their buckets. Sam: Max! I have a total of 1543 pebbles. Max: I have a total of 2014 pebbles.

Sam: How many pebbles did we collect? Max: Let us add the numbers. 38

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Total pebbles = 1543 pebbles + 2014 pebbles

Let us add 1543 and 2014 to find the total number of pebbles. Step 1: Add the ones. 3+4=7 Th

4 7

5+0=5

4+1=5

Step 3: Add the hundreds. Th

Step 2: Add the tens.

O 4

Step 4: Add the thousands. 1+2=3

3 7

H 5

3 7

1543 + 2014 = 3557

So, Max and Sam collected 3557 pebbles. Example 12

Add 1234 and 8765. Step 1: Add the ones.

4 ones + 5 ones = 9 ones Th

5 9

2 hundreds + 7 hundreds = 9 hundreds H

3 tens + 6 tens = 9 tens

Step 3: Add the hundreds.

Step 2: Add the tens.

4 9

Step 4: Add the thousands. 1 thousand + 8 thousands = 9 thousands

4 9

H 2

4 9

So, 1234 + 8765 = 9999. Chapter 2 • Addition of 3-digit Numbers

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Do It Together

Find the sum of 1454 and 2323.

1454 + 2323 = _________

___ ___ ___

4 7

Do It Yourself 2E Add.

1111 + 2222

1254 + 2141

Fill in the blanks.

a c

4156 + 2111 = _________ 7142 + 1644 = _________

b d

1454 + 6121

7151 + 2126

2314 + 3275

1471 + 2416 = _________ 3733 + 4162 = _________

Use the column method to find the sum.

3214 + 6145

3417 + 4371

1341 + 8422

Find the sum.

Th H T O

+ c

+ d

___ ___ ___ ___

What is 1234 more than 5145?

___ ___ ___ ___ Th

Answer the questions.

Th 4

___ ___ ___ ___

Th H T O

___ ___ ___ ___

What is 2174 more than 1211?

Word Problems 1

Shantanu collected stickers. He had pasted 1454 stickers in one notebook and 2421 stickers in another notebook. What is the total number of stickers Shantanu has?

A farmer packs 1245 oranges in the first carton, 2311 oranges in the second carton and 1421 oranges in the third carton. How many oranges does he pack in total?

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Estimating the Sum Real Life Connect

Sam and Max collected coloured stones from the seashore. Sam collected 37 stones and Max collected 42 stones.

Sam: So, we have about 80 stones altogether! Max: How did you find that out so fast! Let us find out!

Step 1: Round off both numbers to the nearest 10. 37 → 40

42 → 40

Step 2: Add the rounded off numbers. 40 + 40 = 80

Thus, the estimated sum of 37 + 42 is 80.

Check how close the estimated answer is to the actual answer.

37 + 42

8 3

37 + 42 = 79

79 is close to 80.

0 0

7 9

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

Error Alert!

Remember! An estimate is a smart guess about something. Estimation is used to find quick answers that are very close to the actual answer.

Chapter 2 • Addition of 3-digit Numbers

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While rounding off to the nearest ten, we round up when the digit at the ones place is 5 or more.

55 → 50

55 → 60 41

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Example 13

Estimate the sum of 36 and 53 by rounding off to the nearest 10. Also, check how close the estimated answer is to the actual answer. Step 1: Round off the numbers to the nearest 10. 36 → 40. 53 → 50. Step 2: Add the rounded off numbers 40 and 50. 40 + 50 = 90

Step 3: Check the actual answer.

36 + 53

36 + 53 = 89

Thus, the estimated answer is close to the actual answer. Do It Together

6 9

Find the estimated sum of 24 and 78. Compare with the actual sum. 24 rounded off to the nearest 10 is __________. 78 rounded off to the nearest 10 is __________.

So, the estimated sum of 24 and 78 is __________.

Do It Yourself 2F 1

Find the estimated sum of the numbers by rounding off both numbers to the nearest 10. a

15 and 54

47 and 41

18 and 21

54 and 42

36 and 64

43 and 57

47 + 22

41 + 58

14 + 19

15 + 34

Round off the numbers to the nearest 10 and find the sum. Check whether the answer is close to the actual answer. a

84 and 17

Find the estimated sum of the numbers by rounding off the bigger number to the nearest 10. a

Find the estimated sum of the numbers by rounding off the smaller number to the nearest 10. a

17 and 34

41 + 47

58 + 23

12 + 17

21 + 47

Round off the numbers to the nearest 10 and find the sum. Also find the sum of the numbers and then round off the sum to the nearest 10 to check whether the answer is the same in both the cases. a

48 + 32

35 + 57

52 + 19

11 + 10

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Word Problems 1

Rahul purchased two notebooks for ₹54 and ₹28. About how much did he spend on the notebooks?

Amrish, Rajesh and Parthiv collected stamps. They collected 18, 21, and 22 stamps, respectively. About how many stamps did they collect altogether?

Word Problems Real Life Connect

Sam and Max were collecting driftwood to build a sandcastle. Sam collected 15 pieces of wood. Max collected 12 pieces of wood. How many pieces of wood did they collect altogether? We can solve a word problem in different ways. Let’s use the CUBES method to find the answer. CUBES C: Circle the numbers. U: Underline the question. B: Box the key words. E: Evaluate/draw S: Solve and check.

Circle the numbers.

Sam collected 15 pieces of wood. Max collected 12 pieces of wood. How many pieces of wood did they collect altogether ?

Box the key words.

Underline the question.

Evaluate: 15 pieces of wood + 12 pieces of wood = 15 + 12 Solve. So, Sam and Max collected 27 pieces of wood altogether.

Chapter 2 • Addition of 3-digit Numbers

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Check using order property of addition. 12 + 15

Example 14

Thus, the answer is correct.

There are 654 cherry trees and 256 plum trees on Joseph’s farm. How many trees are there in total? Let us apply the CUBES method to solve the word problem. CUBES C: Circle the numbers.

U: Underline the question.

B: Box the key words.

E: Evaluate/draw

S: Solve and check.

There are 654 cherry trees and 256 plum trees on Joseph’s farm. How many trees are there in total ? Evaluate: 654 trees + 256 trees Check the answer using order property of addition.

Solve. H

H 2

1 5

Thus, the total number of trees on Joseph’s farm are 910. Do It Together

There are 480 girls and 435 boys in a school. How many students are there in the school? H T O Number of girls = 480

Number of boys = ____

Total number of students = 480 + ____

___ ___ ___

Thus, total number of students in the school are ________.

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Do It Yourself 2G 1

Raju buys seeds for farming. He buys a packet which contains 28 seeds, and the second packet has 35 seeds. How many seeds are there in total?

A toy shop sold 134 toys in the month of January and 217 toys in the month of February. How many toys were sold in these two months together?

A number exceeds 5415 by 2364. What is the number?

The cost of bicycle is ₹4231, and the cost of a music system is ₹4566. What is the total cost of both the items?

Mr Saxena went to the market and purchased a few items. Look at the table and answer the questions that follow. a b c

ow much money did Mr Saxena spend on a hair H dryer and a quilt?

Item

ow much money did Mr Saxena spend on a H bottle of perfume and a bag?

Hair dryer

hat is the total money spent by Mr Saxena if he W bought all 4 items?

Price

Quilt

₹2155

Perfume

₹900

Bag

₹3015 ₹1525

Points to Remember • W hen two numbers are added then each number is called the addend. The result obtained is called the sum. • T he order does not matter when two numbers are added to each other. • W hen 1 is added to any number, then the sum is the successor of that number. • W hen 0 is added to any number, then the sum remains the same.

• When there are more than 9 ones, then regroup 10 ones as 1 ten.

• When there are more than 9 tens, then regroup 10 tens as 1 hundred. • W hen there are more than 9 hundreds, then regroup 10 hundreds as 1 thousand.

• T o solve word problems using the CUBES strategy, circle the numbers, underline the question, box the keywords, evaluate the problem and finally solve and check the answer.

Chapter 2 • Addition of 3-digit Numbers

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Math Lab Aim: To understand addition of 3-digit numbers.

Materials Required: Three dice, paper, and pencil. Setting: In groups of 3. Method: 1

Roll all three dice at the same time.

Note down the digits that appear on the dice.

Make the largest number from the three digits and the smallest number from the three digits.

Add the numbers.

The person whose sum is biggest three times in a row is the winner.

Chapter Checkup 1

Find the missing term. a

45 + 1 = ______

14 + 0 = ______

87 + ______ = 48 + 87

5 + 3 = 3 + ______

1 + ______ = 84

______ + 18 = 18

Find the sum by expanding the numbers. a

35 + 61

19 + 70

56 + 23

21 + 48

64 + 25

35 + 42

Add without regrouping. a

457 + 121

146 + 723

814 + 111

4517 + 4021

6170 + 3128

5164 + 2231

Tick the correct option. a

15 + 16 + 17 = ______ i

iii

The ones digit in the sum of 48 and 22 is ______ i

iii

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40 + 30 + 20 + 10 = ____ i

110

146

154

iii

125

100

847 more than 254.

325 more than 481.

748 more than 369.

415 more than 871.

78 more than 361.

Fill in the boxes to find the answer. H 3

___ ___ ___ Th

___ ___ ___ ___

H 4

___ ___ ___ Th

___ ___ ___ ___

H 5

___ ___ ___ ___

Find the missing digits. a

+ c

___

84 + 8

+ d

Estimate the sum to the nearest ten. a

25 + 52

34 + 17

___

36 + 63

Find the sum of the numbers and then round off the result to the nearest 10. a

48 + 52

45 + 36

Chapter 2 • Addition of 3-digit Numbers

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100

145 more than 456.

iii

Find the value of:

146 + 154 + 125 = ____ + 125 + 146 i

23 + 49

56 + 11

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Solve. a

What is the sum of the largest 2-digit number and largest 3-digit number?

What is the sum of largest 3-digit number and smallest 3-digit number?

What is the sum of the largest 3-digit number and second largest 3-digit number?

hat is the sum of smallest 4-digit number, smallest 3-digit number and smallest W 2-digit number?

Word Problems 1

I n a library, there are 1025 Mathematics books, 987 Science books and 689 Hindi books. What is the total number of books in the library?

here are 3 blocks in a society. 87 people live in the first block, T 98 people live in the second block and 117 people live in the third block. How many people live in the society?

t a carnival, there were 1547 men, 2048 women, 1023 boys and A 1988 girls. a How many boys and girls were there at the carnival? b How many men and women were there at the carnival? c What is the total number of people who went to the carnival?

ishwa has just started collecting tazos. He has 47 tazos with him. His V friend Ishan had 18 more tazos than Vishwa 2 weeks earlier. How many tazos does Ishan have now, if he collected 37 more tazos in the last 2 weeks?

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Subtraction of 3-digit Numbers

Let’s Recall

We love to play with toys. Playing with toys with friends is even more fun! Imagine you have these 8 toys.

Now, you give your friend 2 toys.

How many toys will you have left?

When we take away objects from a group, we use subtraction to count what is left! Let us subtract by counting backwards. We had 8 toys, so let us mark on a line as shown. We gave away 2 toys, so we jump 2 places backward. We reach 6!

We could have also have written this as:

8 − 2 6

We can say, 8 toys − 2 toys = 6 toys.

Let’s Warm-up

Match the following.

1 2 3 4

6 3 8

5 I scored ___________ out of 4.

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Reviewing Subtraction Real Life Connect

In a hockey match, there are 22 players on the field. In hockey, there is a concept of “foul”. A foul happens when a player breaks the rules of the game. A player can even be sent off the field if a serious foul is committed! Amit and Anand love hockey! They organise hockey tournaments each year. This year Amit sold 38 tickets and Anand sold 64 tickets out of the 100 tickets each one had. How many tickets were left unsold with Amit and Anand, respectively?

Properties of Subtraction

Did You Know? Hockey is India’s national sport. India has won the Hockey World Cup thrice – the Men’s Cup in 1975 and the Women’s Cup in 2004 and in 2017!

The match is going on and all the players are in their positions. No player is either leaving or coming on the field. How many players are there? There were 22 players at the beginning. If no one is leaving or coming in, 0 players are added or subtracted. 22 – 0 = 22.

Remember! Number – 0 = Number. For example, 4 – 0 = 4.

So, 22 players remain on the field. Subtracting 1

When 1 is subtracted from a number, the difference is the number before. This before number is called the predecessor. For example, 9 is the predecessor 10. During the match, a player committed a serious foul and was asked to leave the field. How many players were left on the field? 1 player committed a foul and was asked to leave. So, 1 player has to be subtracted from 22. 22 – 1 = 21.

So, 21 players remain on the field. 50

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Notice that 21 is exactly 1 place before 22. So, 21 is the predecessor of 22. Subtracting 0

When 0 is subtracted from a number, the difference is the number itself. For example, 10 – 0 = 10. A predecessor refers to the number that comes immediately before a given number. Suppose we have all the players in the match, which is 22. After the match was over, all players left the field. So how many players remained on the field?

Remember! Number – Number = 0. For example, 4 – 4 = 0.

All 22 players left, so 22 players must be subtracted from number of players who were there at the beginning. 22 – 22 = 0.

So, 0 or no players remain on the field. Subtracting the Same Number

When a number is subtracted from itself, the difference is 0. For example, 10 – 10 = 0. 19 – 19 = 0.

Example 1 Do It Together

19 – 1 = 18.

Example 2

Example 3

19 – 0 = 19.

Fill in the blanks. 1 4 7

31 – 31 = 0

21 – 20 = ____ 18 – 17 = 1

2 5 8

54 − ____ = 0

36 – 35 = 1

15 – 0 = ____

3 6 9

41 – 1 = ____

80 − ____ = 80 66 – 1 = ____

Do It Yourself 3A 1

Fill in the blanks using the subtraction facts. a

____ − 72 = 0

27 – 0 = ____

____ − 1 = 78

87 – 87 = ____

19 − ____ = 19

56 – 1 = ____

Find the predecessor of the given numbers. a

Chapter 3 • Subtraction of 3-digit Numbers

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Write if True or False.

27 – 0 = 27

64 – 64 = 0

76 – 0 = 75

82 – 1 = 81

93 – 93 = 93

43 – 0 = 0

500

501

What is the predecessor of 500?

499

Plot the predecessor of 450 on the number line. –1 +1

450

Word Problems 1

Jacob bought 12 pens from a shop on Saturday. He gave 1 pen to Akshay on Sunday. How many pens does Jacob have left?

Suresh baked 26 cookies for a party. There were no cookies left after the party. How many cookies were eaten at the party?

A cake weighed 44 ounces. The guests ate 44 ounces of cake. How many ounces of cake are left?

Quick Subtraction This year Amit sold 38 tickets, while Anand sold 64 tickets for their hockey tournament. What if they want to find how many more tickets Anand sold than Amit?

Anand can use any one of the two methods given below to find how many more tickets he sold than Amit. By Counting Forward on a Number Line We can subtract 2-digit numbers by counting forward on a number line. Subtract 38 from 64 using the number line. +2

38 40

+10

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Step 1

Step 2

Start at 38.

Add 2 to get to 40. Then add 10, and 10 again to get to 60. Then add 4 to get to 64.

Start at the smaller number.

Count forward until you reach 64.

Step 3

Step 4

Add the number of jumps to find the difference.

Complete the subtraction sentence. 64 – 38 = 26.

2 + 10 + 10 + 4 = 26.

The difference between 64 and 38 is 26. Example 4

Subtract 42 from 78 using the number line. +8

+10

42 50

Step 1

Step 2

Start at 42.

Add 8 to get to 50. Then add 10, and 10 again to get to 70. Then add 8 to get to 78.

Step 3

Step 4

Add the number of jumps to find the difference.

Complete the subtraction sentence.

Start at the smaller number.

Count forward until you reach 78.

78 – 42 = 36.

8 + 10 + 10 + 8 = 36.

The difference between 78 and 42 is 36. Do It Together

Fill in the blanks to subtract 12 from 35 using the number line. +8

Chapter 3 • Subtraction of 3-digit Numbers

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+10

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Step 1

Start at the smaller number.

Step 2

Start at 12.

Count forward and add 8 until you reach 20.

Step 3

Step 4

Add the number of jumps to find the difference. 8 + 10 + ____ = ____.

Then add 10 to get to ____. Then add 5 to get to ____. Complete the subtraction sentence. 35 – 12 = ____.

The difference between 35 and 12 is ____. By Expanding the Smaller Number

We can also subtract 2-digit numbers by expanding the smaller number. Let us subtract 38 from 64 using this method. Step 1

Identify the smaller number. The smaller number is 38. Step 3

Subtract the tens in the smaller number from the larger number. 64 – 30 = 34.

Step 2

Expand the smaller number into tens and ones.

64 – 38 = ? 30

Step 4

Subtract the ones in the smaller number from the number you got in Step 3. 34 – 8 = 26.

The difference between 64 and 38 is 26. Example 5

Subtract 25 from 84. Step 1

Identify the smaller number. The smaller number is 25. Step 3

Subtract the tens in the smaller number from the larger number. 84 – 20 = 64.

Step 2

Expand the smaller number into tens and ones.

84 – 25 = ? 20

Step 4

Subtract the ones in the smaller number from the number you got in Step 3. 64 – 5 = 59.

The difference between 84 and 25 is 59. 54

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Do It Together

Subtract 16 from 45 by expanding the smaller number. 45 – 16 = ?

The difference between 45 and 16 is ____.

Do It Yourself 3B Subtract by counting forward.

76 – 59 = ____

56 – 27 = ____

21 – 13 = ____

72 – 57 = ____

33 – 15 = ____

45 – 36 = ____

Subtract by expanding the smaller number.

41 – 17 = ____

63 – 26 = ____

32 – 13 = ____

46 – 17 = ____

93 – 45 = ____

71 – 24 = ____

When 15 is subtracted from 43, how many jumps of tens will be drawn towards the right of a number line?

When 46 is subtracted from 61, how many jumps of tens will be drawn towards the right of a number line?

Dan is subtracting 46 from a number. He takes 2 jumps of 10 and one jump of 3. What is the number that Dan is subtracting 46 from?

Word Problems 1

A pumpkin patch has 85 pumpkins. Some of them are picked. There are 48 left. How many pumpkins were picked?

You sold 72 sandwiches; Alec sold 57 sandwiches and Navin sold 38 sandwiches.

How many more sandwiches did you sell than Navin?

How many fewer sandwiches did Navin sell than Alec?

Sam sold 59 tickets for a show, Anna sold 47 tickets and Sana sold 85 tickets. How many more tickets did Sana sell than Anna?

Chapter 3 • Subtraction of 3-digit Numbers

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More on Subtraction Real Life Connect

A Read-a-thon is a contest of reading books! The Orchid School arranges an annual Read-a-thon for Primary (1 to 5), Middle (6 to 8) and Secondary (9 to 12) grade students. The table below shows the number of books read by the students in each category and the total number of books they need to read in all. Reading Contest

Grade

Number of Books Read

Goal

Middle

533

950

Primary

513

Secondary

925

584

975

Students are curious to know the least number of books they need to read to reach their goal.

Subtraction Without Regrouping Primary grade students want to find the least number of books they need to read to reach their goal. They have read 513 books and their goal is to read 925 books. We can subtract to find out. So, let us subtract 513 from 925. Step 1

Write the numbers in the columns.

–

Step 3

Write 1 in the tens column.

–

We always begin subtraction from the ones place.

Step 2

5 – 3 = 2 ones.

Subtract the ones. Write 2 in the ones column.

Subtract the tens. 2 – 1 = 1 ten.

Remember!

9 5

2 1

5 2

–

Step 4

Subtract the hundreds.

9 – 5 = 4 hundreds.

9 5

5 2

–

Write 4 in the hundreds column.

5 2

So, the students in primary grade at Orchid School need to read a minimum of 412 more books to reach their goal. 56

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Example 6

Subtract 325 from 837. Step 1

Write the numbers in the columns.

–

Step 3

–

3 – 2 = 1 ten.

Subtract the tens.

7 – 5 = 2 ones.

–

Write 2 in the ones column. Step 4

8 – 3 = 5 hundreds.

8 3

–

7 2

Subtract the hundreds.

Write 1 in the tens column.

Subtract the ones.

Step 2

Write 5 in the hundreds column.

So, 837 – 325 = 512. Example 7

Subtract 120 from 682. Writing the numbers in the columns to find the answer.

–

So, 682 – 120 = 562. Do It Together

Subtract and fill in the boxes. 1

–

8 3

H 9

–

6 5

2 2

Do It Yourself 3C 1

Subtract the ones, then tens, and then hundreds. Write the answer. a

Subtract the ones

–

H 7 1

T 6 2

O 9 8

Chapter 3 • Subtraction of 3-digit Numbers

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Subtract the tens

–

H 7 1

T 6 2

O 9 8

Subtract the hundreds

–

H 7 1

T 6 2

O 9 8

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Subtract the ones

–

H 8 7

T 9 1

Subtract the tens

O 6 5

Subtract the hundreds

–

H 8 7

T 9 1

O 6 5

T 1 1

O 9 8

–

H 4 2

T 0 0

O 3 0

–

H 9 9

–

H 8 7

T 9 1

O 6 5

–

H 3 1

T 7 3

O 7 2

–

H 6 2

T 6 6

O 6 5

Subtract to find the answer.

T 6 0

O 9 9

–

H 5 1

T 8 2

O 7 4

–

H 7 1

Arrange the following numbers in columns and subtract them in your notebook.

758 − 426

689 − 566

483 – 150

529 − 218

342 − 310

786 − 684

Mala’s Tech Store had a big sale. The store had 265 computers in stock. During the sale, 142 computers were sold. How many computers were not sold?

Read the data on the number of stamps with 3 friends. Read the table and answer the questions. a How many more stamps does Rahul have Name Number of Stamps than Gyan? Gyan 245 b Who has more stamps – Ravi or Gyan? How Ravi 545 many more? Rahul 789

Word Problems 1 2 3

Vinay sold 594 tickets for the school play. Arvind sold 273 tickets. How many more tickets did Vinay sell than Arvind?

Yukti collected 469 bottles for recycling. Priya collected 227 fewer bottles than Yukti. How many bottles did Priya collect? Bhakti scored 265 points in a computer game. Gauri scored 142 points. How many more points did Bhakti score than Gauri?

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Subtraction With Regrouping Regrouping Tens The middle grade students at Orchid School want to find the least number of books they need to read to reach their goal. They have read 533 books and their goal is to read 950 books. How many more to go? So, let us subtract 533 from 950. Step 1

Write the numbers in the columns. Step 2

–

Subtract the ones.

3 ones cannot be subtracted from 0 ones.

So, regroup 5 tens and 0 ones into 4 tens and 10 ones. Write 10 over the 0 in the ones column and 4 over the 5 in the tens column. 10 – 3 = 7 ones.

Write 7 in the ones column.

–

0 7

Step 3

Step 4

Subtract the tens.

Subtract the hundreds.

4 – 3 = 1 ten.

9 – 5 = 4 hundreds.

Write 1 in the tens column.

Write 4 in the hundreds column.

H 9

–

So, the middle grade students at the Orchid School need to read 417 more books to reach their goal.

Chapter 3 • Subtraction of 3-digit Numbers

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Example 8

Subtract 238 from 894. Step 1

So, regroup 9 tens and 4 ones into 8 tens and 14 ones.

Write 14 over the 4 in the ones column and 8 over the 9 in the tens column.

Write the numbers in the columns. Step 2

–

Subtract the ones. 8 ones cannot be subtracted from 4 ones.

14 – 8 = 6 ones.

–

Write 6 in the ones column.

4 6

Step 3

Step 4

Subtract the tens.

Subtract the hundreds.

Write 5 in the tens column.

Write 6 in the hundreds column.

8 – 3 = 5 tens. H 8

–

8 – 2 = 6 hundreds.

–

So, 894 – 238 = 656. Example 9

Subtract 365 from 783.

Writing the numbers in the columns to subtract. H

–

So, 783 – 365 = 418. 60

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Do It Together

Complete the subtraction with regrouping. 1

–

5 2

O 2

–

So, 532 – 204 = ____.

–

So, 643 – 328 = ____.

So, 752 – 439 = ____.

Error Alert! Never forget to change the digits in case of a carryover!

–

10 0 7 3

–

6 4 2

Regrouping Hundreds The secondary grade students want to find the least number of books they need to read to reach their goal. They have read 584 books and their goal is to read 975 books. So, let us subtract 584 from 975. Step 1

Write the numbers in the columns. –

Step 2

5 – 4 = 1 ones.

Subtract the ones. Write 1 in the ones column.

–

Step 3

Subtract the tens.

8 tens cannot be subtracted from 7 tens.

So, regroup 9 hundreds and 7 tens into 8 hundreds and 17 tens. Chapter 3 • Subtraction of 3-digit Numbers

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1 O

17 7

–

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Write 17 over the 7 in the tens column and 8 over the 9 in the hundreds column. 17 – 8 = 9 tens.

Write 9 in the tens column. Step 4

Subtract the hundreds. 8 – 5 = 3 hundreds.

So, the students in secondary grade at Orchid School need to read a minimum of 391 more books to reach their goal.

–

17 7

Write 3 in the hundreds column.

Let us look at some more examples. Example 10

Subtract 293 from 548. Step 1

Write the numbers in the columns. –

Step 2

8 – 3 = 5 ones.

Subtract the ones. Write 5 in the ones column.

–

Step 3

Subtract the tens.

9 tens cannot be subtracted from 4 tens.

So, regroup 5 hundreds and 4 tens into 4 hundreds and 14 tens.

5 O

14 4

–

Write 14 over the 4 in the tens column and 4 over the 5 in the hundreds column. 14 – 9 = 5 tens.

Write 5 in the tens column. Step 4

Subtract the hundreds. 4 – 2 = 2 hundreds.

Write 2 in the hundreds column. So, 548 – 293 = 255.

14 4

–

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Example 11

Subtract 183 from 456. Writing the numbers in the columns to subtract. H

15 5

–

So, 456 – 183 = 273. Do It Together

Complete the subtraction with regrouping hundreds. H

–

H 3

14 4

843 – 680 = ____.

–

12 2

4 3

326 – 154 = ____.

–

427 – 142 = ____.

Regrouping Twice Now, let us subtract 457 from 742. Step 1

Write the numbers in the columns. Step 2

Subtract the ones.

–

7 ones cannot be subtracted from 2 ones.

So, regroup 4 tens and 2 ones into 3 tens and 12 ones. Write 12 over the 2 in the ones column and 3 over the 4 in the tens column. 12 – 7 = 5 ones.

Write 5 in the ones column.

Chapter 3 • Subtraction of 3-digit Numbers

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–

2 5

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Step 3

Subtract the tens.

5 tens cannot be subtracted from 3 tens.

So, regroup 7 hundreds and 3 tens into 6 hundreds and 13 tens.

–

13 – 5 = 8 tens.

Write 8 in the tens column.

Step 4 Subtract the hundreds. 6 – 4 = 2 hundreds.

Write 2 in the hundreds column. So, 742 – 457 = 285. Example 12

–

Subtract 169 from 241. Step 1

Write the numbers in the columns. Step 2

Subtract the ones.

–

9 ones cannot be subtracted from 1 ones.

So, regroup 4 tens and 1 ones into 3 tens and 11 ones. Write 11 over the 1 in the ones column and 3 over the 4 in the tens column. 11 – 9 = 2 ones.

Write 2 in the ones column.

–

1 2

Step 3

Subtract the tens.

6 tens cannot be subtracted from 3 tens.

So, regroup 2 hundreds and 3 tens into 1 hundred and 13 tens. 13 – 6 = 7 tens.

Write 7 in the tens column.

–

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Step 4

1 – 1 = 0 hundreds.

Subtract the hundreds. Write 0 in the hundreds column.

–

So, 241 – 169 = 72. Example 13

Do It Together

Subtract 193 from 400.

Write the numbers in the columns to subtract.

10 10

So, 400 – 193 = 207.

–

Complete the subtraction. H

–

6 4

640 – 386 = ____.

–

637 – 359 = ____.

954 – 867 = ____.

Do It Yourself 3D 1

Write in columns and find the difference by regrouping tens. a d

361 − 142

875 − 346 783 − 365

c f

827 − 365 805 − 362

b e

759 – 286

501 − 360

c f

Write in columns and find the difference by regrouping twice. a d

624 − 276 704 − 239

Chapter 3 • Subtraction of 3-digit Numbers

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891 − 179 275 − 149

Write in columns and find the difference by regrouping hundreds. a

573 − 256

b e

570 − 383 300 − 114

c f

624 − 154 823 − 243 600 − 257 801 − 568 65

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Complete the subtraction.

–

6 4

T 11 2 1

5 6 9

–

H 6 7 1

3 4

4 8

–

2 1

3 7

O 18 8 9

Read the data on the number of tickets for a play sold by 3 friends. Read the table and answer the questions. a Akhil sold 159 fewer tickets than Joginder Name Number of Tickets and Mohan sold together. How many tickets Joginder 282 did Akhil sell? Mohan 178 b How many more tickets would each of them Prasad 331 need to sell so that each of them sells 350

tickets?

Word Problems 1

The number of computer games sold during a sale was 257. This is 172 more than the number sold the week before the sale. How many computer games were sold the week before the sale?

Darshana sold 336 muffins at the bake sale. Bharti sold 287 muffins. How many more muffins did Darshana sell than Bharti?

Subtracting Bigger Numbers Now what if we want to subtract bigger numbers? Let us learn through an example. Let us subtract 7564 from 9687.

Remember! A 4-digit number has ones, tens, hundreds, and thousands places. For example, 3451 can be written as:

Th 3

H 4

O 1

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The steps remain the same. Let us see! Step 1: Subtract the ones. 7 – 4 = 3 ones.

–

7 3

Step 3: Subtract the hundreds. 6 – 5 = 1 hundred.

–

7 3

Step 2: Subtract the tens. 8 – 6 = 2 tens.

–

8 2

7 3

Step 4: Subtract the thousands. 9 – 7 = 2 thousands.

–

9 2

7 3

So, 9687 – 7564 = 2123. Example 14

Subtract 1102 from 4325. Step 1: Subtract the ones. 5 – 2 = 3 ones.

–

5 3

Step 3: Subtract the hundreds. 3 – 1 = 2 hundreds.

–

5 3

Step 2: Subtract the tens. 2 – 0 = 2 tens.

–

2 2

5 3

Step 4: Subtract the thousands. 4 – 1 = 3 thousands.

–

4 3

5 3

So, 4325 – 1102 = 3223.

Chapter 3 • Subtraction of 3-digit Numbers

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Do It Together

Subtract and fill in the table.

–

So, 3789 – 1569 = _______.

Do It Yourself 3E Complete the subtraction.

–

Th 6 1

H 9 3 6

T 8 6

O 6 3

–

Th 2 1

H 3 2

T 6 2

O 7 6

7 4

6 2

0 0

1 2

–

Th 9 1

H 8 7

T 7 6

O 9 0

9 1

8 7

5 1

3 3

Complete the subtraction.

–

3 1

4 2

7 6

9 1

–

Write in columns and find the difference.

5569 − 1230

3735 − 2524

3457 – 2402

7957 − 1542

3466 − 3352

6398 – 2202

A total of 2740 students attend college. How many boys are there if 1430 are girls?

What must be added to 5860 so that the sum is 6987?

Word Problems 1

A clockmaker sold 7407 clocks in 2022. In 2023, he sold 8638. How many more clocks were sold in 2023?

Liza went on a trip with her family. She spent ₹3142 out of ₹5275. How much money does she have left?

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Estimating the Difference Real Life Connect

A play has been organised in a local theatre. Veena, Manisha, and Sonia are responsible for selling the tickets for the play. About how many more tickets do each of them need to sell to reach 50 tickets? We can estimate to find about how many more.

Play Tickets Sold

Number of Tickets

Veena

Manisha Sonia

28 17 33

We can round off 28 to the nearest tens which is 30. 20

30 28

Thus, 50 – 30 = 20 tickets.

So, Veena needs to sell about 20 tickets more to reach the goal of selling 50 tickets. Similarly, we can round off 17 to the nearest tens which is 20. 10

Remember! When we don’t need an exact answer, we can estimate by rounding off numbers.

Thus, 50 – 20 = 30 tickets.

So, Manisha needs to sell about 30 tickets more to reach her goal of selling 50 tickets. Finally, we can round off 33 to the nearest tens which is 30. 30

Thus, 50 – 30 = 20 tickets.

So, Sonia needs to sell about 20 tickets more to reach her goal of selling 50 tickets. Let us look at some more examples.

Chapter 3 • Subtraction of 3-digit Numbers

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Remember! The rules of rounding off remain the same in estimation.

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Example 15

Round off 53 and 29 to the nearest tens and then estimate their difference. Step 1

Round off the bigger number.

50 53

53 is rounded off to 50. Step 2

Round off the smaller number.

30 29

29 is rounded off to 30. Step 3

Find the estimated difference. Estimated difference = 50 – 30 = 20. So, the estimated difference is 20. Example 16

Round off to tens and find the difference of 89 and 53. Step 1

Round off the bigger number.

90 89

89 is rounded off to 90. Step 2

Round off the smaller number.

60 53

53 is rounded off to 50. Step 3

Find the estimated difference. Estimated difference = 90 – 50 = 40. So, the estimated difference is 40. Do It Together

Estimate the difference of 32 and 16. Step 1

Round off the bigger number.

32 is rounded off to _______.

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Step 2

Round off the smaller number.

16 is rounded off to _______. Step 3

Find the estimated difference.

Estimated difference = _______ – _______ = _______. So, the estimated difference is _______.

Do It Yourself 3F Round off the numbers to tens. Find the estimated difference.

43 − 31

57 − 21

53 − 28

30 – 14

58 − 36

96 − 15

Use rounding off to estimate the difference.

–

7 2

3 2

–

7 4

6 8

–

Anand wanted to buy a new pen worth ₹78. He had already saved ₹37. Estimate how much more money Anand needed to save to buy the new pen.

Ajay collected 42 seashells at the beach. He gave 23 seashells to Vijay. About how many seashells does Ajay now have?

Arun used the rounding off strategy to find 43 – 19. He rounded off 43 to 50 and 19 to 20 and then estimated the difference. Was Arun right? Why or why not?

Word Problems 1 2 3

There were 32 houses in a village. Now there are 67 houses. About how many houses were newly built in the village?

Ashok has 83 stickers and Madan has 56 stickers. About how many more stickers does Ashok have than Madan? There are 96 chocolates in a bowl. Navin takes 15 chocolates. Darshana takes some chocolates. There are 68 chocolates left. How many chocolates has Darshana taken?

Chapter 3 • Subtraction of 3-digit Numbers

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Word Problems Real Life Connect

Vijay was surprised to know that Jacob reads a lot of storybooks. There was a total of 728 books sitting on a bookcase in Jacob’s bedroom, until he sold 193 of them. Can you help Vijay to count the number of books left on the bookcase? Here’s a trick to solve such problems. Let us start finding the total number of books left on the bookcase.

Remember! We subtract when we need– • to find out how much is left. • to find out the difference between two numbers.

Let us rewrite the problem.

CUBES C: Circle the numbers. U: Underline the question. B: Box the key words. E: Evaluate/draw S: Solve and check.

Circle the numbers.

Vijay was surprised to know that Jacob reads a lot of storybooks. There was a total of 728 books sitting on a bookcase in Jacob’s bedroom, until he sold 193 of them. How many books are left on the bookcase?

Underline the question.

Box the key words.

Solve

Check

Work out the answer.

If 728 – 193 = 535, then 193 + 535 should equal to 728.

–

728 – 193 = 535.

So, the answer is correct.

So, 535 books are left on the bookcase. 72

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Example 17

545 people visited a book fair in the morning. 730 people visited the book fair in the evening. How many more people visited the book fair in the evening than in the morning? Let us solve this problem using the cubes method. Circle the numbers.

CUBES C: Circle the numbers. U: Underline the question. B: Box the key words. E: Evaluate/draw S: Solve and check.

545 people visited a book fair in the morning. 730 people visited the book fair in the evening.

How many more people visited the book fair in the evening than in the morning? Box the key words.

Underline the question.

Solve

Check

Work out the answer.

If 730 – 545 = 185, then 545 + 185 should equal to 730.

H 6

–

730 – 545 = 185.

1 4

So, the answer is correct.

185 more people visited the book fair in the evening.

Chapter 3 • Subtraction of 3-digit Numbers

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Example 18

Mr Smith and Mrs Smith are in the business of making apple pies. Mr Smith bought 170 apples from the market. Mrs Smith bought 120 apples from the same market. They baked several pies with 200 apples. How many apples were left? Let us solve this problem using the cubes method. CUBES C: Circle the numbers. U: Underline the question. B: Box the key words. E: Evaluate/draw S: Solve and check.

Circle the numbers.

Box the key words.

Solve

Check

Total apples = 170 + 120 H

So, 90 apples were left.

Do It Together

Apples left = 290 – 200 H

–

200 + 90 = 290 H

2 2

So, the answer is correct.

Manish has 423 seashells. He has 345 more seashells than Babita. How many seashells does Babita have? Use the CUBES method to solve.

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Do It Yourself 3G 1

Ravi has 478 stickers and his friend, Shashi, has 689. Who has more stickers and how many more?

500 people were invited to the party but 230 people could not come due to bad weather. How many people came to the party?

At a local book fair, a bookseller sold 487 books on the opening day. He sold 189 fewer books the next day. How many books were sold the next day?

In a cricket match, Team A scored 435 runs and Team B scored 146 runs less than Team A. How many runs did Team B score?

There are 5397 bags of wheat in the warehouse. If 3075 bags are taken out, how many bags will remain in the warehouse?

Nikhil bought 5788 pairs of shoes for his newly opened shop in January. On 1st February, he had 1475 pairs left. How many pairs of shoes did he sell in January?

Mrs Jones baked 50 chocolate cookies and 900 oatmeal cookies. She sold 765 cookies. How many cookies did she have left?

Soham has three cards with the numbers 6, 3 and 4. Make the greatest and the smallest 3-digit number using the cards. Also, find the difference between the two numbers.

Word Problems 1

An artist collected 915 cardboard rolls for an art exhibition. He used 268 cardboard rolls for his first exhibit and 380 cardboard rolls for his second exhibit. How many cardboard rolls did he have left? Amit collects stamps from all over the world. He has 467 stamps in his stamp collection. His father gives him another 133 stamps. How many more stamps must he collect if he wants to have 800 stamps in his collection?

Narendra has 442 packages to deliver. David has 464 packages to deliver. Narendra delivers 174 packages, and David delivers 188. Who is closer to finishing his deliveries?

Chapter 3 • Subtraction of 3-digit Numbers

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Points to Remember • W e always subtract a smaller number from a bigger number. The answer of subtraction is called the difference. • When we subtract 0 from a number, the difference is the number itself.

• W hen we subtract 1 from a number, we get the predecessor of the given number.

• W hen we subtract any number from itself, the difference we get is always zero. • T he difference between 2-digit numbers can be estimated by rounding off the numbers to the nearest tens.

Math Lab Chit Game for Subtraction! Setting: In groups of 3. Materials Required: Number chits from 0-9. Method: 1 2 3

Make chits for numbers 0 to 9 using sheets of paper. Shuffle the chits.

Player 1 picks 3 different chits and forms a 3-digit number. Everyone must pick chits randomly!

Player 2 picks 3 chits from the remaining ones and forms a 3-digit number.

Player 3 finds the difference of these numbers correctly.

Hint: Try forming the biggest possible numbers! The team with the smallest difference wins.

Chapter Checkup 1

Fill in the blanks using the subtraction facts. a

____ − 64 = 0

59 – 0 = ____

____ − 1 = 92

23 – 23 = ____

16 − ____ = 16

75 – 1 = ____

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Subtract by counting forward.

52 – 29 = ____

61 – 46 = ____

64 – 35 = ____

92 – 67 = ____

43 – 24 = ____

71 – 42 = ____

Subtract by expanding the smaller number.

52 – 27 = ____

84 – 55 = ____

76 – 29 = ____

23 – 14 = ____

68 – 49 = ____

62 – 21 = ____

Arrange the following numbers in columns and find the difference.

456 – 234

842 − 587

210 − 187

734 – 542

863 − 185

2456 – 1214

Round off to tens and then find the estimated difference.

96 − 12

82 – 29

61 − 44

Word Problems 1

I n an office, 678 pages were kept for printing in a month, out of which, 259 pages have been printed. How many pages are still left for printing?

enuka read 829 pages of her storybook. The book contains 978 pages. R How many pages are still to be read?

85 people came to watch a hockey match. 197 people left after one 9 hour and another 668 left before half-time. How many people watched the whole match?

vegetable vendor bought 925 kg potatoes from the market. 123 kg A potatoes were rotten. He could sell only 678 kg. How many potatoes does he have left?

musician wants to buy a set of speakers that costs `672. He saves `224 A each month for 2 months. How much money does he still need to save?

Chapter 3 • Subtraction of 3-digit Numbers

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Multiplication Tables

Let’s Recall

We use Addition to add items together. What if we have the items in similar groups? For example, we can see 3 groups of candies. Each group has 2 candies. Let us count the total number of candies.

2 Candies + 2 Candies + 2 Candies = 6 Candies

This process of adding the same number again and again, is called repeated addition. This repeated addition is the same as Multiplication. In this case, we add the number 2, three times. This is the same as 3 × 2 = 6. Let us take another example.

2 Basketballs + 2 Basketballs + 2 Basketballs + 2 Basketballs + 2 Basketballs = 10 Basketballs

Here, we add the number 2, five times. This is the same as 5 × 2 = 10.

Let’s Warm-up Fill in the blanks. 1

3 + 3 + 3 + 3 = 4 × ____ = ____

5 + 5 + 5 + 5 = 4 × ____ = ____

10 + 10 + 10 = 3 × ____ = ____

4 × 6 = ____

6 × 8 = ____ I scored ____________ out of 5.

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Understanding Multiplication Real Life Connect

Raghu, a farmer, wants to plant some saplings on his farm. He plants an equal number of saplings in different rows. He also has to take care of the saplings by watering them.

Multiplication Facts Raghu wonders how many saplings he has to plant in his field. He goes home and asks his brother, Vian, for the number of saplings. Let us look at how many saplings Raghu has planted in the field in total. Total number of saplings = 4 groups of 2 = 4 × 2 = 8 saplings Raghu asks Vian what if they had 2 rows with 4 saplings each? Would he still get the same number of saplings? Vian answers, “Yes! The number of saplings would still be the same.” If there are 2 rows of 4 saplings, Total number of saplings = 2 groups of 4 = 2 × 4 = 8 saplings If there are 4 rows of 2 saplings, Total number of saplings = 4 groups of 2 = 4 × 2 = 8 saplings Chapter 4 • Multiplication Tables

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Multiplication symbol Equals to 4

Multiplier Multiplicand Product

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Raghu wonders how many saplings there were in 1 row. There are 4 saplings in each row. Number of saplings in 1 row = 1 × 4 = 4 saplings

We can also see if any number is multiplied by 0 we get 0 only. = 0 × 4 = 0. Multiplication Facts

Order Property of Multiplication We can multiply two numbers in any order, and the product always remains the same. Example: 4 × 2 = 2 × 4 = 8

Multiplicative Property of One When multiplying a number by 1, the product is always the number itself. Example: 4 × 1 = 4

Multiplicative Property of Zero When multiplying a number by 0, the product is always zero. Example: 4 × 0 = 0

Error Alert! Multiplication does NOT always make a number bigger. If we multiply 4 by 2, it becomes bigger (4 × 2 = 8). But if we multiply 4 by 0, it becomes 0 and 0 < 4. If we multiply 4 by 1, it stays 4, and does not become bigger.

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Fill in the blanks. 4×0=0 6×5=5×6 1 × 15 = 15 Do It Find the missing number. Together

Example 1

6 × 9 = _____ × 6

Example 2

Find the product. 5 × 2 = 10 9×0=0 19 × 1 = 19

_____ × 1 = 14

8 × _____ = 0

18 × 1 = _____

Do It Yourself 4A 1

Fill in the blanks. a

3 + 3 + 3 + 3 + 3 = ____ × 3

8 + 8 + 8 = 3 × ____

2 + 2 + 2 + 2 = ____ × ____

____ + ____ + ____ + ____ + ____ = ____ × 13

State true or false. a

When you multiply any number by 1, you get the same number.

When you multiply a number by 0, you always get 1.

Order matters when multiplying numbers.

What is 8 added 9 times? a

8+9

9×8

9–8

Find the missing numerals. a

9 × 3 = ____ × 9

2 × ____ = 0

____ × 7 = 7

5 × 8 = 8 × ____

47 × ____ = 47 × 94

____ × 1 = 123

Raghu is planting 15 trees on his farm. How many rows are there if there are 5 trees in each row?

Word Problems 1

Sophie is helping her mom bake cookies. The recipe is for 3 batches of 4 cookies each. Sophie wants to know if the total number of cookies will be the same if she multiplies 3 by 4 or 4 by 3. Can you help Sophie determine the correct order of multiplication?

Chapter 4 • Multiplication Tables

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Building Multiplication Tables Remember, Raghu was planting saplings in his field. The saplings have been planted. Now the saplings are to be taken care of. What are the steps that he needs to take? Raghu and Vian have to regularly water the saplings! Table of 6 Rahul and Vian discuss that 6 litres of water per plant should be enough. But how much water do they need? To water 1 sapling they need 6 litres To water 2 saplings they need 6 + 6 = 2 × 6 = 12 litres To water 3 saplings they need 6 + 6 + 6 = 3 × 6 = 18 litres To water 4 saplings they need 6 + 6 + 6 + 6 = 4 × 6 = 24 litres To water 5 saplings they need 6 + 6 + 6 + 6 + 6 = 5 × 6 = 30 litres To water 6 saplings they need 6 + 6 + 6 + 6 + 6 + 6 = 6 × 6 = 36 litres To water 7 saplings they need 6 + 6 + 6 + 6 + 6 + 6 + 6 = 7 × 6 = 42 litres To water 8 saplings they need 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 8 × 6 = 48 litres To water 9 saplings they need 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 9 × 6 = 54 litres To water 10 saplings they need 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 10 × 6 = 60 litres We have just devised the table of 6! Let us write in the table format: 1×6=6 2 × 6 = 12 4 × 6 = 24 7 × 6 = 43

3 × 6 = 18

5 × 6 = 30

8 × 6 = 48

6 × 6 = 36

9 × 6 = 54

10 × 6 = 60

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We can also build the same table by skip counting in 6s! 1 9 17 25 33 41 49 57 Example 3 Do It Together

Multiply.

2 10 18 26 34 42 50 58

6 × 6 = 36

3 11 19 27 35 43 51 59

4 12 20 28 36 44 52 60

5 13 21 29 37 45 53 61

6 14 22 30 38 46 54 62

7 15 23 31 39 47 55 63

8 16 24 32 40 48 56 64

7 × 6 = 42

Complete the 6 times table. 6

Table of 7 Just like for 6, let us build the table for 7. We have flowers, and each flower has 7 petals. How many petals do we have in the flowers? 1 flower with 7 petals

2 flowers with 7 petals each 3 flowers with 7 petals each 4 flowers with 7 petals each 5 flowers with 7 petals each 6 flowers with 7 petals each 7 flowers with 7 petals each 8 flowers with 7 petals each 9 flowers with 7 petals each

10 flowers with 7 petals each Chapter 4 • Multiplication Tables

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1×7=7 2 × 7 = 14 3 × 7 = 21 4 × 7 = 28 5 × 7 = 35 6 × 7 = 42 7 × 7 = 49 8 × 7 = 56 9 × 7 = 63 10 × 7 = 70 83

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We can build the same table by skip counting in 7s! 1 10 19 28 37 46 55 64 73

Example 4

Find the product. 5 × 7 = 35

Do It Together

2 11 20 29 38 47 56 65 74 2

3 12 21 30 39 48 57 66 75

4 13 22 31 40 49 58 67 76

5 14 23 32 41 50 59 68 77

6 15 24 33 42 51 60 69 78

7 × 8 = 56

Complete the 7 times table. 7

7 16 25 34 43 52 61 70 79

8 17 26 35 44 53 62 71 80

9 18 27 36 45 54 63 72 81

7 × 11 = 77

Table of 8 Just like for 7, let us build the table for 8.

We have flowers, and each flower has 8 petals. How many petals do we have in the flowers? 1 flower with 8 petals

2 flowers with 8 petals each 3 flowers with 8 petals each 4 flowers with 8 petals each 5 flowers with 8 petals each 6 flowers with 8 petals each 7 flowers with 8 petals each 8 flowers with 8 petals each 9 flowers with 8 petals each

10 flowers with 8 petals each

1×8=8 2 × 8 = 16 3 × 8 = 24 4 × 8 = 32 5 × 8 = 40 6 × 8 = 48 7 × 8 = 56 8 × 8 = 64 9 × 8 = 72 10 × 8 = 80

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We can also build the same table by skip counting in 8s! 1 10 19 28 37 46 55 64 73

Example 5 Do It Together

Find the product.

2 11 20 29 38 47 56 65 74 1

3 12 21 30 39 48 57 66 75

4 13 22 31 40 49 58 67 76

4 × 8 = 32

5 14 23 32 41 50 59 68 77

Complete the 8 times table. 16

6 15 24 33 42 51 60 69 78 2

7 16 25 34 43 52 61 70 79

8 17 26 35 44 53 62 71 80

9 × 8 = 72

9 18 27 36 45 54 63 72 81 3

8 × 12 = 96

Table of 9 Just like for 8, let us build the table for 9.

We have flowers, and each flower has 9 petals. How many petals do we have in the flowers? 1 flower with 9 petals

2 flowers with 9 petals each 3 flowers with 9 petals each 4 flowers with 9 petals each 5 flowers with 9 petals each 6 flowers with 9 petals each 7 flowers with 9 petals each 8 flowers with 9 petals each

9 flowers with 9 petals each

1×9=9 2 × 9 = 18 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 7 × 9 = 63 8 × 9 = 72 9 × 9 = 81

10 flowers with 9 petals each 10 × 9 = 90 Chapter 4 • Multiplication Tables

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We can also build the same table by skip counting in 9s! 1 11 21 31 41 51 61 71 81 91 Example 6

3 13 23 33 43 53 63 73 83 93

4 14 24 34 44 54 64 74 84 94

5 15 25 35 45 55 65 75 85 95

6 16 26 36 46 56 66 76 86 96

7 17 27 37 47 57 67 77 87 97

8 18 28 38 48 58 68 78 88 98

9 19 29 39 49 59 69 79 89 99

10 20 30 40 50 60 70 80 90 100

Think and Tell Do you observe a pattern in the table?

Find the product. 1

Do It Together

2 12 22 32 42 52 62 72 82 92

6 × 9 = 54

9 × 9 = 81

Complete the 9 times table. 18

Tables of 10, 20, …, 90

Did You Know?

Multiplication by 10 If each sapling is given 10 litres of water, then how much water is given to the saplings? Number of saplings = 8

Samarth Bhagyesh Patel from India holds the record for solving 10 random multiplication items correctly the fastest, with a time of 1 minute 30.60 seconds.

Total water given = 8 × 10 litres = 80 litres To multiply any number by 10, write 0 at the ones place and multiply the number by 1. Examples: 5 × 10 = 50

11 × 10 = 110

154 × 10 = 1540

Multiplication by 20, 30, 40, …, 90 To multiply any number by 20, 30, 40, ...,90 write 0 at the ones place and multiply the remaining numbers. Examples: 5 × 20 = 100

3 × 70 = 210

8 × 90 = 720

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Error Alert! NEVER place zeroes in the wrong place when multiplying by 10. 15 × 10 = 105

Example 7

Remember! On multiplication by 10, 20, 30, …, 90, there is always 0 in the ones place.

15 × 10 = 150

Multiply. 1

9 × 70

dd zero at the end and multiply A 9 with 7

dd zero at the end and multiply A 14 with 1

9 × 7 = 63

14 × 1 = 14

9 × 70 = 630 3

14 × 10 = 140

7 × 70

dd zero at the end and multiply A 7 with 7 7 × 7 = 49

7 × 70 = 490 Do It Together

14 × 10

10 × 90

dd 0 at the end and multiply 10 A with 9

10 × 9 = 90

10 × 90 = 900

Fill in the missing numbers. 1 3

5 × 10 = ____ 2 60 × ____ = 420

80 × 8 = ____ 4 15 × ____ = 1350

Tables of 100, 200, ..., 900 Multiplication by 100

To multiply any number by 100, write two 0’s at the ones place, and the tens place and then multiply the number by 1. 4 × 100 = 400

44 × 100 = 4400

444 × 100 = 44400

Note: A product of 100 will always have two zeroes at the end. Multiplication by 200, 300, 400, …, 900.

Chapter 4 • Multiplication Tables

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To multiply any number by 200, 300, …, 900 write two zeroes in the ones and tens place. Multiply the remaining numbers. 3 × 200 = 600 Example 8

7 × 800 = 5600

Multiply. 1

Do It Together

9 × 500 = 4500

65 × 100

100 × 300

800 × 9

Add 2 zeroes at the end and multiply 65 by 1

Add 2 zeroes at the end and multiply 100 by 3

Add two zeroes at the end and multiply 8 with 9

65 × 1 = 65

100 × 3 = 300

8 × 9 = 72

65 × 100 = 6500

100 × 300 = 30000

800 × 9 = 7200

Fill in the blanks. 1

14 × 200 = ____

8 × 700 = ____

300 × 6 = ____

Do It Yourself 4B 1

Fill the missing blanks.

Compare using >, <, =

9 weeks = ____ days

8×8

5 days = ____ hours

9 × 10

100 × 1

1 hour = ____ minutes

4 × 99

400

____ weeks = 70 days

6×7

Find the product. a

8×9

80 × 3

700 × 10

90 × 4

4 × 40

10 × 10

____ × 4 = 400

6×8

Complete the multiplication facts. a

8 × 8 = ____

7 × ____ = 560

Raj gives 6 candies to each of his 9 friends. How many candies did he distribute altogether?

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Word Problems 1

player has hit 5 centuries in one day internationals. How many runs A did he hit by centuries? (1 century = 100 runs)

cricketer hits 5 sixes, and another cricketer hits 8 fours. How many A runs do they both make altogether?

Points to Remember • The order does not matter when two numbers are multiplied to by each other.

• When a number is multiplied by 1, the product is always the number itself. • When a number is multiplied by 0, the product is always 0.

• To multiply a number by 10, put a zero to the right of the number.

• To multiply a number by 100, put 2 zeroes to the right of the number.

Chapter 4 • Multiplication Tables

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Math Lab Dice Game Setting: In groups of 3.

Materials Required: Two dice Method: 1 2 3 4

Roll the dice together.

Multiply your two numbers.

Colour the product on the grid.

The first person to colour four in a row wins. 18 36 4 10 36 10 18 1

12 30 24 12 12 25 20 30

24 12 4 25 12 1 9 4

8 9 8 15 30 9 10 20

10 2 6 20 5 5 16 2

24 5 8 6 12 6 15 3

6 4 15 16 5 10 4 6

15 18 3 8 30 20 3 15

Chapter Checkup 1

State true or false. a

45 × 8 = 8 × 45

4 × 6 = 24

89745 × 0 = 89745

5 × 8 = 40

9 × 8 = 72

6 × 600 = 3600

45 × 100 = 450

Find the different ways to make the number in the centre. a

3 × ×

× 15

24 ×

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Look at the pattern and complete it. a

8, 16, 24, ______, ______, ______, ______, ______

13, 26, 39, ______, ______, ______, ______, ______

30, 40, 50, ______, ______, ______, ______, ______

18, 27, 36, ______, ______, ______, ______, ______

14, 28, 42, ______, ______, ______, ______, ______

200, 400, 600, ______, ______, ______, ______, ______

ultiply the number from the row with the number from the column to get the M product, and write it in the corresponding box. ×

24 16

28 25

9 18

100

Compare using >, <, or =. a

5 × 70

350

8×9

44 × 100

4444

5 × 60

60 × 5

48975 × 1

8 × 700

6200

Chapter 4 • Multiplication Tables

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Use multiplication to fill in the spaces. a

8 7 6

10 × 5

12 2

2 4

6× 8

ajesh has 10 cookie boxes with him. There are 7 cookies in each box. How many R cookies does he have in total?

ivan bought 9 chocolates, each worth ₹6. He paid the shopkeeper ₹100. How much V money did he get in return?

haan has 900 boxes to pack. Each box will have 9 towels. Write the multiplication S fact and find the product.

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Multiplication by 2-digit Numbers

Let’s Recall Let us say we have 3 balloons. We can call them 1 group of 3 balloons. Now suppose we have 6 groups of 5 balloons.

How many balloons do we have in total? 5 + 5 + 5 + 5 + 5 + 5 = 6 × 5 = 30 We have 30 balloons. We learnt in the previous chapter that this is called a multiplication fact.

Let’s Warm-up Write the multiplication fact for the pictures. 1

______________________ 2

______________________ 3

______________________ 4

______________________

I scored ____________ out of 4.

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Multiplying Numbers Real Life Connect

Rahul: Hi, Aisha! Do you have recipes for baking cakes? Aisha: Hi, Rahul! Yes, I have a recipe that makes 1 cake. Rahul: But we have an order for 24 cakes. How can we bake 24 cakes?

Remember! On multiplying a number by 1, the product is always the number itself.

Aisha: Don’t worry, Rahul! We can multiply all the amounts of the ingredients by 24! Rahul: Ok! if the original recipe needs 1 cup of sugar, we will use

1 × 24 = 24 cups

Aisha: Exactly! That means we need 24 cups of sugar. Now, let us do the same for all the other ingredients.

Multiplying by Expanding the Bigger Number We saw how Rahul and Aisha planned for 24 cups of sugar.

What if each cake required 2 cups of flour? What would they have done then? How would they find the total number of cups of flour required? They would use multiplication again! In this case it would be, 2 cups × 24

But how can we calculate that? Let us learn. 94

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We can multiply bigger numbers by 1-digit numbers by expanding the bigger number. Step 1 Expand the bigger number. 24 = 20 + 4

Step 2 Place the numbers.

Step 3 Multiply the smaller number.

Step 4 Add all the products. 40 + 8 = 48

2×

20 2 × 20 = 40

2×

4 2×4=8

So, they need 48 cups of flour for the cakes! Now, what if Rahul and Aisha wanted to make 240 cakes? How would they find the amount of flour needed? Let us use the same method. Each cake requires 2 cups of flour. In this case it would be: 2 cups × 240

Remember!

Step 1 Expand the bigger number. 240 = 200 + 40 + 0 Step 2 Place the numbers. 2×

200

Step 3 Multiply the smaller number. 200 2 × 2 × 200 = 400

40 2 × 40 = 80

The product of any number with zero is always 0.

0 2×0=0

Step 4 Add all the products. 400 + 80 + 0 = 480 So, they need 480 cups of flour. Chapter 5 • Multiplication by 2-digit Numbers

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Let us see more examples of multiplication by expanding the bigger number. Example 1

Find the product of 221 and 4 by expanding the bigger number. Step 1 Expand the bigger number. 221 = 200 + 20 + 1 Step 2 Place the numbers. 4×

200

Step 3 Multiply with the smaller number. 200 4 × 4 × 200 = 800

20 4 × 20 = 80

1 4×1=4

Step 4 Add all the numbers. 800 + 80 + 4 = 884 So, 221 × 4 = 884. Do It Together

Find the product of 122 and 3 by expanding the bigger number. Step 1 Expand the bigger number. 122 = 100 + 20 + 2 Step 2 Place the numbers. 3×

100

Step 3 Multiply with the smaller number. 100 3 × 3 × 100 = _________

20 3 × 20 = 60

2 3 × 2 = ____

Step 4 Add all the numbers. ___ + 60 + ___ = ___ So, 122 × 3 = ______. 96

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Do It Yourself 5A 1

Multiply the following by expanding the bigger number. a

32 by 3

20 by 4

21 by 4

42 by 2

31 by 2

10 by 5

Expand the bigger number and multiply. a

13 by 3

24 by 2

23 by 3

Find the product of the following by expanding the bigger number. a

124 and 2

111 and 4

223 and 3

311 and 3

310 and 3

201 and 5

Multiply 120 and 4 by expanding the numbers.

Sam multiplied 321 by 2 as given below. Mark the error that he made. Solve correctly.

321 × 2 300 20 1 2 × 3 × 100 = _________ 2 × 20 = 40 3 × 1 = ____

Word Problem 1

nna wants to multiply 123 by 3 by expanding the bigger number. A How many tens will you multiply by 3?

Multiplying by 1-digit Number We have learnt to multiply by expanding the bigger number. Let us now learn to multiply by the vertical multiplication method.

Did You Know?

Have you ever heard of ‘Vedic Math’? It’s a super cool system of mathematics from India! Imagine doing maths like a real maths magician! With Vedic Math, you can learn fun and quick ways to add, subtract and multiply numbers in your head, just like magic tricks!

Aisha and Rohit have baked all the cakes, now they start packing them. One carton of cakes can have 122 cakes, so how many cakes can they put in 3 such cartons? Chapter 5 • Multiplication by 2-digit Numbers

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One carton can hold 122 cakes. So, 3 such cartons will be able to hold 122 × 3 cakes. Let us do it by the vertical multiplication method. Vertical Multiplication Example 2 Step 1 Step 2 Multiply by the digit Multiply by the digits in the ones place. in the tens place. ×

H 1

T 2

O 2 3 6

H 1

3 × 2 ones = 6 ones

T 2

Step 3 Multiply by the digits in the hundreds place.

O 2 3 6

3 × 2 tens = 6 tens

We get 122 × 3 = 366.

H 1

T 2

O 2 3 6

3 × 1 hundreds = 3 hundreds

So, we can have 366 cakes in 3 cartons. Example 3

Multiply 232 by 2.

Step 1 Multiply by the digit in the ones place. ×

H 2

T 3

O 2 2 4

2 × 2 ones = 4 ones

Step 3 Multiply by the digits in hundreds place.

Step 2 Multiply by the digits in the tens place. H 2

T 3

O 2

2 4

H 2

T 3

O 2 2 4

2 × 2 hundreds = 4 hundreds

2 × 3 tens = 6 tens

Answer = 464 Do It Together

Multiply 121 by 4. Step 1 Step 2 Step 3 Multiply by the digit Multiply by the digits Multiply by the digits in in the ones place. in the tens place. hundreds place. ×

H 1

T 2

O 1 4 4

4 × 1 ones = 4 ones

H 1

T 2 ____

O 1 4 4

H 1

T 2

____

O 1 4 4

4 × 2 tens = _____ tens 4 × 1 hundreds = _____ hundreds

Answer = _____ 98

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With Regrouping Now let us see how to multiply numbers with regrouping. Multiply 16 by 4. Step 1 Multiply the number by the digits in the ones place. We get 6 × 4 = 24 24 is 2 tens and 4 ones. So, we write the 4 in the ones place and regroup the 2 tens in the tens place, as shown.

1 ×

Step 2 We multiply the number by the tens digit, which is 1 × 4 = 4. We add the regrouped tens to 4. So, we get 4 + 2 = 6. We get 64.

1 × 6

6 4 4

Now let us try multiplying a 3-digit number with a 1-digit number. Let us find the product of 116 and 4!

Step 1 Multiply the number by the digit in the ones place. 4 × 6 ones = 24 ones 24 is 2 tens and 4 ones. So, we write the 4 in the ones place and regroup the 2 tens in the tens place, as shown. Step 2 Multiply the number by the digits in the tens place, and add the regrouped tens, if any. 4 × 1 ten = 4 tens 4 tens + 2 tens (regrouped) = 6 tens Step 3 Multiply the number by the digits in the hundreds place, and add the regrouped tens, if any. 4 × 1 hundreds = 4 hundreds We get 464.

6 4 4

4 4

Error Alert! When multiplying 2 numbers with regrouping, do not add the carried over tens or hundreds before multiplying.

Chapter 5 • Multiplication by 2-digit Numbers

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Example 4

Find the product of 175 and 5. Step 1 Multiply the number by the digit in the ones place. 5 × 5 ones = 25 ones Regroup 25 ones into 2 tens and 5 ones

Step 2 Multiply the number by the digits in the tens place, and add the regrouped tens, if any. 5 × 7 tens = 35 tens 35 tens + 2 tens = 37 tens Regroup 37 tens as 3 hundreds and 7 tens

Do It Together

5 5 5

Step 3 Multiply the number by the digits in the hundreds place, and add the regrouped hundreds, if any. 5 × 1 = 5 hundreds 5 hundreds + 3 hundreds (regrouped) = 8 hundreds We get 875.

5 5 5

Find the product of 237 and 6. Step 1 Multiply the digit in the ones place. 2

Step 2 Multiply the digits in the tens place.

6 ___

Step 3 Multiply the digits in the hundreds place.

7 6 2

___

H 1

T 2

7 6 2

Do It Yourself 5B 1

Find the product of the numbers. a

H 2

T 1

O 1 3

H 2

T 3

O 2 2

100

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H 3

× 2

O 3

H 2

T 1

O 2

H 1

T 1

O 0

Multiply the numbers with regrouping. a

× 3

T 3

Multiply by writing in columns.

6 8

101 × 9

313 × 2

111 × 8

234 × 2

212 × 4

321 × 3

315 × 6

408 × 5

315 × 3

227 × 3

223 × 4

218 × 4

184 × 7

258 × 8

365 × 6

208 × 5

128 × 9

256 × 7

346 × 8

259 × 5

A bakery sold 230 boxes of cupcakes, and each box contained 5 cupcakes. How many cupcakes did the bakery sell in total? 1 7

Daniel solved a multiplication problem as given here. Circle the error and solve correctly.

9 3 2

Word Problem 1

here are 8 shelves in a library, and each shelf can hold 120 books. T How many books can the library hold in total?

Multiplying by 2-digit Numbers Rahul: We need 12 choco-chips for 1 cake. How many choco-chips will we require for 24 cakes? Aisha: We will multiply them to find the right number of choco-chips, 12 × 24. Rahul: Okay! But how? Aisha: Let me show you. Chapter 5 • Multiplication by 2-digit Numbers

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Without Regrouping We need to multiply 24 and 12 to help Rahul and Aisha.

T 2

O 4

Step 3 Add the products.

Step 2 Multiply by the tens.

Step 1 Multiply by the ones.

10 + 2

(24 × 2)

T 2

O 4

10 + 2

(24 × 10)

× +

2 2

T 2

O 4

1 4 8

2 0 8

Error Alert! NEVER place the numbers in incorrect place value columns for multiplication.

T 1

O 2

2 2 7

Example 5

4 2

2 2

T 1

O 2

2 4 8

4 0 8

Find the product 23 × 21. Step 1 Multiply by the ones. ×

T 2

O 3

Step 2 Multiply by the tens. × 4

T 2

O 3

2 6

Step 3 Add the products.

1 0

× +

4 4

T 2

O 3

2 6 8

1 0 3

102

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Do It Together

Multiply 13 × 12. Step 1 Multiply by the ones. 13 × 2 = ______

Step 2 Multiply by the tens. 13 × 10 = ______

T 1

O 3

T 1

O 3

____

Step 3 Add the products. ______ + ________ = ______

____

____ ____

T 1

O 3

____ ____

With Regrouping We learnt how to multiply a 2-digit number with another 2-digit number. But what if the numbers are bigger? Let us learn! Multiply 28 × 14. Step 1 Multiply by the ones. 28 × 4 = 112

Step 2 Multiply by the tens. 28 × 10 = 280

Step 3 Add the products. 112 + 280 = 392

1 2

1 8

1 2 3

1 8 9

4 0 2

The Product of 28 and 14 is 392. Example 6

Find the product of 34 and 25. 2

1 6 8

2 8 5

20 + 5

0 0

34 × 5 34 × 20

The Product of 34 and 25 is 850.

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Do It Together

Multiply 45 and 31. 4

5 1

30 + 1 45 × 1

45 × 30 Add both the products

Do It Yourself 5C 1

Find the products. a

Write in the given columns and find the product. a

39 × 26

17 × 12

60 × 94

27 × 15

29 × 25

60 × 78

104

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Multiply by writing in columns. a

34 × 23

43 × 21

39 × 45

15 × 86

12 × 56

24 × 21

28 × 32

23 × 78

32 × 73

18 × 95

48 × 26

24 × 90

39 × 26

32 × 32

58 × 34

60 × 15

24 × 27

78 × 27

45 × 46

45 × 67

What is the product of the greatest 2-digit number and the smallest 2-digit number?

There are 15 candies in each packet. There are 39 packets. How many candies are there in total?

Word Problem 1

In a garden there were 23 rows of trees. Parul planted 5 trees in each row. How many trees were there in the garden?

Estimating the Product Real Life Connect

Rina’s birthday is coming in a week. She and her father are planning the party! Father: Dear, we need to plan your upcoming birthday party. Let’s estimate the number of gift packets we will need. Rina: Sure, Daddy! I am excited. We will have 46 guests and we will give each guest 5 gift packets. How many packets will we need?

Father: We will need around 250 packets.

Rina: Great, Dad! How did you find that so fast?

Estimation Rina’s father had to find 46 × 5. He estimated the number of packets by rounding off to the nearest 10. Let’s learn more about it. Chapter 5 • Multiplication by 2-digit Numbers

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Step 1 Round off the bigger number to the nearest 10. 46 is rounded up to 50. Step 2 Multiply the numbers. 50 × 5 = 250 Estimated product of 46 and 5 is 250. Example 7

Round off 1

Round down If the ones digit is less than 5, round down to the same tens.

Round up If the ones digit is 5 or more than 5, round up to the next tens.

Estimate by rounding off the bigger number to the nearest 10. a

63 × 5

Step 1 Round off the bigger number to the nearest 10. 63 is rounded down to 60. Do It Together

Step 2 Multiply the numbers. 60 × 5 = 300 The estimated product of 63 and 5 is 300.

Estimate the product by rounding off to the nearest tens. a 88 × 8 Round off the bigger number to the nearest 10. ____ is rounded to _______. Multiply the numbers. 90 × 8 = _______. The estimated product of 88 and 8 is _______. b 92 × 5 The estimated product of 92 and 5 is _______.

Do It Yourself 5D 1

Round off the following to the nearest tens. a

Estimate the product by rounding off the bigger number to the nearest tens. a

44 × 5

32 × 6

98 × 9

43 × 7

26 × 4

81 × 2

106

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Find the estimated product. Compare the answer with the actual product. a

66 × 22

18 × 12

99 × 1

67 × 3

45 × 2

33 × 23

Find the estimated product of 37 and 13 by rounding off both numbers to the nearest tens.

First estimate the product by rounding off the bigger number to the nearest 10. Then find the actual product and compare them by subtraction. Actual Product

Estimated Product

Comparison

46 × 9 32 × 3 53 × 5 68 × 9 26 × 6 63 × 8

Word Problem 1

Rhea is packing bangles in boxes. She packs 45 boxes with each box having 24 bangles. What is the estimated number of bangles that she packed?

Word Problems Real Life Connect

Shirley is helping her mother in their toy shop. Shirley’s mother has asked her to count all the balls. There are 14 bags containing the same number of balls.

Shirley: I have counted the balls in the first bag. There are 34 balls in one bag. Mother: Great! Are you going to count all the bags one by one? Shirley: No, no I have learnt the magic of multiplication. I will count them with the help of multiplication.

Step 1 What do we know? Balls in 1 bag = 34 Bags = 14

Chapter 5 • Multiplication by 2-digit Numbers

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Step 2 What do we need to find?

Total no. of balls = 34 × 14

There are 476 balls in total.

× +

1 3 4

1 4 7

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Example 8

A charity program is going to be organised at Sachin's school for Christmas.

Sachin wants to knit 128 scarfs for the needy people. Each scarf requires 4 balls of yarn. Can you help Sachin find how many balls of yarn he needs for all the scarfs? Step 1 What do we know?

No. of balls of yarn required for 1 scarf = 4 No. of scarfs to be made = 128 Step 2 What do we need to find?

Total no. of balls of yarn required = 128 × 4 Total no. balls of yarn are needed = 512. Do It Together

8 4 2

Sona used 23 beads to make a necklace. How many beads does she need to make 22 necklaces? Step 1 What do we know?

Step 2 What do we need to find?

No. of beads in a necklace = _____. Total no. of beads required = _____ × _____. No. of necklaces to be made = _____.

Total beads required for 22 necklaces are _____.

Do It Yourself 5E 1

A box contains 13 erasers. How many erasers would there be 12 such boxes?

There are 45 balloons in a packet. How many balloons will there be in 54 such packets?

The cost of a table is `100. How much will 12 such tables cost?

In an orchard, there are 64 apple trees. Vishal planted 7 trees more. How many trees are there in the orchard?

A car that can seat 6 people makes 14 trips a day. If the car is completely full on all its trips, how many people travelled by the car?

108

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Word Problem 1

Sally went to Mr. Jacob’s store to buy Christmas decoration items. Read the price list and answer the questions. a b c

What would be the price of 45 candles? ow much would Sally pay for the H stars if she bought 25 stars?

ally bought a packet with 45 bells. S How much did she pay for the bells?

Item

Price

Bells

`45

Stars

`50

Candy

`35

Candles

`12

Points to Remember • On multiplying a number by 1, the product is always the number itself.

• On multiplying a number by 0 the product is always 0. • We use estimation to quickly get a rough idea of the result without performing actual multiplication. • To round off to the nearest 10, look at the digit in the ones place – if it is 5 or greater, we round up to the next higher 10, and if it’s 4 or smaller, keep the same number of tens.

Math Lab Maths Dice Game: Multiplication Edition Setting: In groups of 2

Material Required: Dice, pencils Method:

Each player will roll the dice three times to form a 3-digit number, and then roll the dice two more times to form a 2-digit number. Multiply the two numbers correctly. The player with the most correct answer will be declared the winner.

You can also increase the difficulty level by setting a time limit.

For example, complete the task in 1 minute, 50 seconds, 30 seconds and so on.

Chapter 5 • Multiplication by 2-digit Numbers

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Chapter Checkup 1

Find the product by expanding the bigger number. a

23 × 9

89 × 4

205 × 3 135 × 6

28 × 6

78 × 8

205 × 7

45 × 5

29 × 3

12 × 4

210 × 3

231 × 2

121 × 8

218 × 4

127 × 3

168 × 5

278 × 2

142 × 7

83 × 46

Solve. ×

Multiply. Regroup twice.

Multiply. Regroup once.

a 5

Multiply without regrouping. a 221 × 4 b 243 × 2 a

34 × 5

Find the product. a 14 × 84

987 × 5

378 × 6 20 × 63

91 × 11

83 × 50 27 × 10

Write if True or False. a

62 × 2 = 124

45 × 1 = 0

25 × 25 = 625

89 × 12 = 1289

57 × 0 = 0

Find the estimated product by rounding off the bigger number to the nearest 10. a e i

54 × 6 38 × 2

663 × 4

b f j

49 × 7 91 × 3

234 × 5

c g

34 × 3

304 × 4

d h

120 × 6 441 × 2

110

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A bus that can seat 76 people makes 16 trips in a day. If the bus is completely full on all 16 trips, how many people travelled in the bus?

A crate holds 45 apples. How many apples are there in 12 such crates?

Word Problems 1

A sheet of stickers consists of 56 stickers. How many stickers are there in

A maths book contains 340 pages. How many pages are there in 6 such

56 such sheets? books?

9 buses were arranged to carry children for a picnic. If 25 children 3 could sit in a bus, how many children went for the picnic? t the zoo, 36 children paid ₹30 each at the entrance. How much money A was paid at the entrance? box contains 6 chocolates, and there are 15 boxes. If each box costs ₹9, A how much money will Raj need to buy all the chocolates? I n a multiplex theatre, there are 4 auditoriums. 425 people can sit in each auditorium. How many people can watch movies in the multiplex theatre at one time? At two times? Rahul and his friends are going on a trip. Given below is the list of items,

they are taking on the trip. Calculate the number of items he will be taking in total. Items

No. of items required

Hats

T-shirts

Shorts

Socks

8 pairs

_______ pairs

Shoes

2 pairs

_______ pairs

Chapter 5 • Multiplication by 2-digit Numbers

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25 persons

45 persons

Total

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Division

Let’s Recall

Imagine there are 4 cookies. Let us share these cookies between these 2 children. Sharing doubles the joy of eating! How can we share the cookies between these two children, so that each child gets the same number of cookies? Let us give 1 cookie to each.

Now, the children have 1 cookie each, but we still have 2 cookies left.

Let us give 1 more cookie to each child.

Now, the children have 2 cookies each and no cookies are left.

We distributed 4 cookies between 2 children. Each child got 2 cookies.

This breaking up of a number into equal parts is called division. In the above case, 4 was divided into 2 groups. The result — the number of cookies with each child was 2. This can also be written as 4 – 2 = 2.

Let’s Warm-up Write if True or False. 1 2 3 4

The marbles can be distributed equally among 6 friends. ________________ The marbles can be distributed equally among 2 friends. ________________ The marbles can be distributed equally among 4 friends. ________________ The marbles can be distributed equally among 3 friends. ________________ I scored ____________ out of 4.

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What Division Means Real Life Connect

Sera, Mona and Amir have come to Soham’s house to play. Soham’s mother baked cookies for the kids. Soham, here are 12 cookies. Place equal number of cookies in 4 plates.

Sure, Mom!

Soham placed the cookies equally in 4 plates. All the kids enjoyed the cookies.

Understanding Division Soham’s mother asked him to share 12 cookies equally in four plates. Equal sharing is also known as division. In other words, division helps us share or separate things into equal parts. It is represented by the “÷” sign. Let us see how Soham shared the cookies in four plates! Equal sharing Soham started by putting 1 cookie in each plate. 4 cookies are placed in 4 plates.

He put 1 more cookie in each plate. 8 cookies are placed in 4 plates.

Finally, he put 1 more cookie in each plate. Now there are 12 cookies in 4 plates.

Chapter 6 • Division

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So, when he distributed the 12 cookies onto 4 plates, they got 3 cookies each. This can be written as: 12 (number of cookies) ÷ 4 (number of kids) = 3 (number of cookies each got). Example 1

Swapna has 24 candies. She gives 8 candies to each of her friends. How many friends does Swapna have? Number of candies Swapna has = 24. Number of candies she gives to each friend = 8. To find the number of friends, we will make groups of 8 candies. 8

Group 1

Group 2

Group 3

As there are 3 groups of 8 candies, therefore Swapna divides the candies among 3 friends. It can also be given as: 24 (number of candies) ÷ 8 (number of candies each friend gets) = 3 (number of friends). Do It Together

Riya has 30 stickers. She can use only 5 stickers on each gift box. On how many gift boxes can the stickers be put? Let us share 30 stickers in groups with 5 stickers in each group. 5 ____

1 Group ____

____

3 Group ____

10 ____ 20 ____ ____ ____

Group ____ Group ____ Group ____ Group ____

As there are _____ groups of 5 stickers, therefore Riya can put stickers on. _____ gift boxes. 30 ÷ _____ = _____. 114

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Division as Repeated Subtraction Komal has 20 coins, and she wants to put 5 coins in each pouch. Let us help her to divide 20 by 5 using repeated subtraction. Step 1 Subtract 5 from 20 until we get 0.

Total number of coins = 20.

–

Let’s take away 5.

Number of remaining coins = 15.

–

Let’s take away 5 again.

Number of remaining coins = 10.

–

Let’s take away 5 again.

Number of remaining coins = 5.

–

Let’s take away 5 again.

Number of remaining coins = 0.

0 5

5 0 5 0

Step 2 Count the number of times 5 has been subtracted. We subtracted 5, four times.

So, there are four 5s in 20. Hence, Komal requires 4 pouches to keep the coins. Example 2

How many 7s are there in 21?

Step 1 Subtract 7 from 21 until we get 0. 2 –

1 – –

1 7

4 7 7 0

Chapter 6 • Division

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Step 2 Count how many times 7 has been subtracted. We subtracted seven 3 times. So, there are three 7s in 21.

Error Alert! 3

Always count how many times the number has been subtracted, not the number itself.

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Do It Together

Find the number of 6s in 24. Step 1 Subtract 6 from 24 until we get 0.

Step 2 Count how many times 6 has been subtracted.

–

___

–

___ ___

We subtracted 6 ______ times.

–

So, there are ______ 6s in ______.

–

___ ___ 0

Do It Yourself 6A 1

Circle the objects to share them among the number of people shown.

a b

2 people

7 people

4 people

9 people

4 people 5 people

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Divide using repeated subtraction method. a

How many 5s are there in 15?

How many 8s are there in 32?

How many 1s are there in 9?

How many 3s are there in 9?

How many 11s are there in 22?

How many 6s are there in 36?

How many 9s are there in 27?

How many 7s are there in 28?

Colour an equal number of balloons in red, blue, and green.

Look at the picture. Draw apples to show an equal number of apples in each basket. Fill in the blanks.

Total number of apples = ______.

Number of apples in each basket = ______. Number of baskets = ______. 5

Match the following. 24 has

8 groups of 4

56 has

4 groups of 6

32 has

9 groups of 9

81 has

8 groups of 7

Word Problems 1 2 3

Karthik made 15 rotis. If there are 5 members in the house and each gets an equal number of rotis, how many rotis will each member get? Vijay and Sunita wants to share 16 pencils between themselves. How many will each get? Naina has 36 matchsticks. If she uses 3 matchsticks every day, how many days will it take for her to finish all the matchsticks?

Chapter 6 • Division

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Division and Multiplication Real Life Connect

Sudha and Vishal go to the market to sell oranges. Vishal asks, “How many oranges do you have Sudha?” I have 6 baskets with 4 oranges in each basket. How many oranges do you have?

I have 24 oranges in 6 baskets.

After reaching the market they find that they have an equal number of oranges in each of their baskets.

Division and Multiplication Facts Sudha has 6 baskets with 4 oranges in each basket.

4 + 4 + 4 + 4 + 4 + 4 = 6 × 4 = 24 Vishal has 24 oranges in 6 baskets. So, 24 divided among 6 groups will have 4 each.

Remember! Division is all about sharing or dividing things into equal groups. On the other hand, multiplication is like adding groups of things together.

This can be written as: 24 (number of oranges)

6 ÷ = (number of baskets)

4 (number of oranges in each basket)

This is called ‘Dividend’.

This is called ‘Divisor’.

This is called ‘Quotient’.

The above division can be given as:

Dividend ÷ Divisor = Quotient, where:

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Dividend = The number which is being divided. Divisor = The number which divides a given number. Quotient = The number we obtain when we divide one number by another. In the above example, we saw that 6 × 4 = 24 and 24 ÷ 6 = 4. This tells us that division and multiplication are closely related. Using dividend, divisor and quotient, the division and multiplication fact can be given as: Division fact = Dividend ÷ Divisor or Dividend ÷ Quotient = Divisor. Multiplication fact = Quotient × Divisor = Dividend. Multiplication fact 6 × 4 = 24

Division fact 24 ÷ 6 = 4 24 ÷ 4 = 6

Error Alert!

Remember! For most of the multiplication facts, there are two division facts.

Multiplication fact is given as: Quotient × Divisor = Dividend. 2 × 10 = 5

5 × 2 = 10

Let us look at one more example of how multiplication and division are related. Look at the picture. This shows 3 bottles with 10 marbles in each bottle. Number of groups = 3 Number of marbles in each group = 10

Total number of marbles = 3 × 10 = 30

Multiplication Fact = 3 × 10 = 30 Now let us write Division facts for the 30 marbles.

Chapter 6 • Division

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There are 30 marbles. Distribute 30 marbles equally in different ways.

Total marbles = 30

30 ÷ 3 = 10

30 ÷ 10 = 3

Bottles = 3

Bottles = 10

10 marbles in 1 bottle 30 ÷ 3 = 10

3 marbles in 1 bottle Division Facts

Multiplication Fact 3 × 10 = 30

Example 3

30 ÷ 10 = 3

Division Fact 30 ÷ 3 = 10 30 ÷ 10 = 3

Write the multiplication fact for 32 ÷ 8 = 4. Dividend = 32. Divisor = 8.

Quotient = 4.

Multiplication fact = Quotient × Divisor = Dividend.

Therefore, the multiplication fact for 32 ÷ 8 = 4 = 4 × 8 = 32. Example 4

Write the division facts for 12 × 3 = 36.

Here the dividend is 36. Both 12 and 3 can be the divisor. So, the division facts are 36 ÷ 3 = 12 and 36 ÷ 12 = 3. 120

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Do It Together

Find the division and multiplication facts. Division Fact 45 ÷ 5 = 9 45 ÷ 9 = 5

22 ÷ 2 = 11 22 ÷ 11 = 2

____ ÷ ____ = 6 ____ ÷ ____ = 7 36 ÷ 6 = 6

____ ÷ ____ = _____ ____ ÷ ____ = _____

Multiplication Fact 9 × 5 = 45 11 × ____ = 22 7 × 6 = 42 ____ × ____ = ____ 4 × 8 = 32

Using Multiplication Tables We can use the multiplication tables to help us with division. Suppose we want to divide 12 bananas equally among 3 children. As we need to divide 12 items among 3 children, we will use the multiplication table of 3 and see how many times 3 is 12. 3×1= 3 3×2= 6 3×3= 9 3 × 4 = 12 We can see that, 3 times 4 equals 12. Therefore, each child will get 4 bananas. 6× 1 = 6 Example 5 Find 54 ÷ 6 using the multiplication table. 6 × 2 = 12 6 × 3 = 18 We look for the multiplication fact that gives us 54 when 6 × 4 = 24 multiplied by 6. 6 × 5 = 30 Say the table of 6 until you get 54. 6 × 6 = 36 6 × 7 = 42 In the multiplication table for 6, we find that 6 × 9 = 54. 6 × 8 = 48 Therefore, 54 ÷ 6 = 9. 6 × 9 = 54 6 × 10 = 60 Chapter 6 • Division

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Do It Together

Solve the following using multiplication tables. 7 × 6 = 42

42 ÷ 7

Therefore, 42 ÷ 7 = 6 9 × 8 = 72

72 ÷ 9

Therefore, 72 ÷ 9 = ______ ______ × ______ = 48

48 ÷ 6

Therefore, 48 ÷ 6 = ______ 8 × ______ = ______

56 ÷ 8

Therefore, ______ ÷ 8 = ______ ______ × ______ = ______

63 ÷ 9 72 ÷ 8

Therefore, ______ ÷ 9 = ______ ______ × ______ = ______ Therefore, ______ ÷ ______ = ______

Properties of Division 10 ÷ 1 = 10 There are four properties of division. 1

hen we divide any number by 1, we get the same W number.

For example, 2 ÷ 1 = 2.

– –

rom the given repeated subtraction, we can say that F there are two 1s in 2. 2

hen we divide any number by itself, the answer is W always 1.

For example, 8 ÷ 8 = 1.

rom the repeated subtraction, we can F say that there is one 8 in 8. 3

–

2 1

1 0

8 8

When we divide 0 by any number, the answer is always 0. For example, 0 ÷ 6 = 0.

There is no end to this division. Hence, it is always 0. 122

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You can’t divide any number by 0. There’s no answer. This can be seen using repeated subtraction as given:

e will keep on subtracting 0 from the number but will not W get 0 as answer. Find 26 ÷ 1.

Example 6

When you divide any number by 1, you get the same number. Therefore, 26 ÷ 1 = 26.

– – – –

5 0 5 0 5 0 5 0 ...

Find 54 ÷ 54.

Example 7

When you divide any number by itself, the answer is always 1. Therefore, 54 ÷ 54 = 1. Do It Together

Solve the division problems. 81 ÷ 0

No answer

56 ÷ 1

___________________

58 ÷ 0

___________________

0 ÷ 99

96 ÷ 96 0 ÷ 46

0 ÷ 99 = 0

___________________

Think and Tell! What is 8735 ÷ 8735?

___________________

Do It Yourself 6B 1

Match the division facts with their multiplication fact. 56 ÷ 4 = 14

9 × 8 = 72

92 ÷ 2 = 46

8 × 6 = 48

84 ÷ 7 = 12 72 ÷ 9 = 8

65 ÷ 5 = 13 48 ÷ 6 = 8 2

13 × 5 = 65 7 × 12 = 84 46 × 2 = 92

Write the division facts for the multiplication facts. a

7 × 4 = 28

5 × 9 = 45

3 × 6 = 18

8 × 2 = 16

10 × 3 = 30

6 × 7 = 42

Chapter 6 • Division

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14 × 4 = 56

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Fill in the blanks using multiplication tables. a

60 ÷ 6 = _______

36 ÷ 4 = _______

56 ÷ 7 = _______

28 ÷ 2 = _______

27 ÷ 3 = _______

32 ÷ 4 = _______

Answer the following using the properties of division. a

25 ÷ 1

12 ÷ 0

0÷5

9÷9

7÷1

100 ÷ 100

0÷3

15 ÷ 0

Find the divisor. Dividend 20

42 63 24 32

÷ ÷ ÷ ÷

Divisor _______

_______

_______ _______ _______ _______

= = = =

Quotient 10 7 5 7 6 8

Word Problems There are 18 cupcakes at a party, if each child gets 1 cupcake, how many children are there at the party? 2 Maya has 45 apples. She divided the apples among her 9 friends so that they get 5 each. Write the multiplication fact. 3 Ravi has 36 marbles, and he wants to put them equally into 4 bags. Find out how many he will put in each bag. (Use multiplication tables) 1

Points to Remember • Division means sharing equally. It is represented by “÷”. • Dividend ÷ Divisor = Quotient.

• Division can also be done using repeated subtraction.

• Division and Multiplication are closely related and are opposite operations. • We can solve division using multiplication tables.

• When you divide any number by 1, you get the same number.

• When you divide any number by itself, the answer is always 1. • When you divide 0 by any number, the answer is always 0. • You can’t divide any number by 0. There’s no answer. 124

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Math Lab Setting: 5 Groups.

Material required: 30 paper sticks for each group, pen and paper, timer. Method: 1 2 3 4

Distribute the sticks among the groups.

The teams need to use the sticks and make as many equal groups of sticks as possible.

The teams will note down the multiplication and division fact for the groups formed in their notebook. The team who makes the most correct groups, wins!

Chapter Checkup 1

Circle the objects to share them among the number of people shown. a

8 people

3 people

6 people

2 people

Divide using the repeated subtraction method. a

24 ÷ 3

36 ÷ 6

45 ÷ 9

72 ÷ 8

56 ÷ 7

63 ÷ 9

54 ÷ 9

80 ÷ 8

Write the multiplication fact for the given numbers. a

36 ÷ 3 = 12

88 ÷ 4 = 22

96 ÷ 8 = 12

40 ÷ 5 = 8

25 ÷ 5 = 5

60 ÷ 6 = 10

48 ÷ 6 = 8

72 ÷ 9 = 8

Chapter 6 • Division

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Write two division facts for each multiplication fact.

9 × 5 = 45

4 × 8 = 32

5 × 3 = 15

7 × 2 = 14

4 × 6 = 24

9 × 8 = 72

2 × 10 = 20

3 × 7 = 21

Answer the problems using multiplication tables.

57 ÷ 9

45 ÷ 5

63 ÷ 7

35 ÷ 5

42 ÷ 6

54 ÷ 9

27 ÷ 3

80 ÷ 8

Write two examples for each property of division.

When you divide any number by 1, you get the same number.

When you divide any number by itself, the answer is always 1.

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

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

uma baked 32 cupcakes. If she wants to share them with 4 of her friends, how many R cupcakes will each friend get?

rushi has 24 marbles, and she wants to divide them equally among her 6 cousins. A How many marbles will each cousin get?

teacher has 30 pencils and wants to distribute them among 10 students. How many A pencils will each student get?

fruit vendor has 36 apples and wants to divide them equally into 6 baskets. How A many apples will each basket have?

Word Problem 1

here are 20 toy cars to be divided among 20 children. How many toy T cars will each child receive?

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Division by 1-digit Numbers

Let’s Recall

In the previous chapters, we learnt that multiplication and division are closely related.

We use multiplication to find the total number of objects when we know the number of groups and items in each group. For example there are 4 groups containing 3 smileys each. How many smileys are there? There are 4 × 3 = 12 smileys.

We use division when we want to group a set of items into equal groups, so that each group contains the same number of items.

For example, let us say we want to form 4 equal groups of these 12 smileys: Now, the groups will be formed as before: This time, we say that 12 ÷ 4 = 3 We formed 4 groups containing 3 smileys each. So, 4 × 3 = 12 and 12 ÷ 4 = 3.

Multiplication Equal groups of items

Total number of items Division

Let’s Warm-up

Match the following. 1

16 ÷ 4

4 × 9

3 × 5

8 × 8

21 ÷ 3

63 ÷ 7

36 I scored ___________ out of 6.

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Dividing Numbers Real Life Connect

Arjun has a big box of 62 marbles. He wants to share them equally among his 2 friends, Karan and Rohan. I will put 1-1 marble in each of two bags until I finish all the 62 marbles.

ow the only kn to 20! e w t u B p f two u table o

But that will take a lot of time. We can use multiplication table of 2.

Long Division Sometimes the numbers are large, and we may not be able to divide them using the multiplication table. That is the time when we use long division. In long division, we write the division terms as shown: A number that divides another number. Value left after the division.

Divisor

Quotient

Dividend

Remainder

The number we get when we divide one number by another. The number that is to be divided.

Long Division Without Remainder Let us help Arjun to divide the marbles between his friends. The first thing we do is write the dividend and divisor in the division house.

2 62

Step 1 Divide.

Take the first digit of the dividend (62) which is 6. Divide it by 2 and write the answer above 6. Step 2 Multiply. Multiply 3 and 2 and put the answer right below 6.

2 62 6÷2=3 3

2 62 2×3=6 6

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Step 3 Subtract.

2 62 –6 0

Subtract 6 from 6. That is 6 – 6 = 0 Step 4 Bring Down.

2 62 –6 02

Bring down the next digit 2 of the dividend and write it next to 0. Now we repeat the same steps for the next digit:

Step 1 ÷ Step 4 Bring Down

Step 2 × Step 3 –

Divide: Divide 2 by 2 and write the answer above 2.

Multiply: Multiply 2 and 1 and put the answer right below 2.

Subtract: Subtract 2 from 2. That is 2 – 2 = 0.

3 1

2 62 –6 02 3 1

2 62 –6 02 2

2÷2=1

2×1=2

3 1

2 62 –6 02 –2 0

Bring down: There is nothing to bring down. The quotient of 62 ÷ 2 = 31. Therefore, each friend will get 31 marbles. All 3 friends are fond of stamps. They have 489 stamps with them. They divide the stamps equally using the same method. On dividing 489 by 3, each friend gets 163 stamps.

Chapter 7 • Division by 1-digit Numbers

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1 63

3 489 –3 18 –18 09 –9 0 129

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Example 1

Divide. 78 ÷ 6

400 ÷ 4

1 3

1 00

6 78 –6 18 –18 0

616

4 400 –4 0 –0 0 –0 0

78 ÷ 6 = 13 Do It Together

1232 ÷ 2 2 1232 –12 32 –2 12 –12 0

400 ÷ 4 = 100

1232 ÷ 2 = 616

Divide. 65 ÷ 5 1 3

5 65 –5 15 –15 0

147 ÷ 3 ______

3 147 – ___ –

600 ÷ 3 – 00

3 600 –

1468 ÷ 2 ______

2 1468 –

–

Division With Remainder Is it always possible to share something equally? Rohan has 5 crayons, and he wants to share them equally with Arjun and Karan.

Left over.

When we divide, it's not always possible for things to be shared equally. This can result in having something left over, which will give us a remainder other than zero. Kavya has a pack of 35 biscuits. She wants to divide the biscuits so that each of them gets 3 biscuits. Let us see how many classmates will get 3 biscuits. 130

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Divisor

Remainder (Number of biscuits Kavya has left.)

Quotient (Number of classmates who will get 3 biscuits.)

11 3 35 –3 05 –3 2

Dividend

Think and Tell

Is there a way to check whether our division is correct?

Can remainder be greater than divisor?

Yes, we can check division by using the formula: (Quotient × Divisor) + Remainder = Dividend

Let us check the above division using the formula:

Here, Quotient = 11, Divisor = 3, Remainder = 2, Dividend = 35 (11 × 3) + 2 = 35 33 + 2 = 35

Error Alert!

35 = 35

Hence, our division is correct.

Do not forget to add the remainder to the product of quotient and divisor.

The division 67 ÷ 5 = 13, R = 2 can be checked as: (13 × 5) = 67

Example 2

(13 × 5) + 2 = 67

Divide the numbers. Check your answer. 468 ÷ 5 93 5 468 –45 18 – 15 3

Quotient

Remainder

Checking Division:

(Quotient × Divisor) + Remainder = Dividend (93 × 5) + 3 = 468 465 + 3 = 468 468 = 468 Hence, our division is correct. Chapter 7 • Division by 1-digit Numbers

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1523 ÷ 7 217 7 1523 –14 12 –7 53 –49 4

Quotient

Remainder

Checking Division:

(Quotient × Divisor) + Remainder = Dividend (217 × 7) + 4 = 1523 1519 + 4 = 1523 1523 = 1523 Hence, our division is correct. 131

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Do It Together

Solve and check the given divisions. Divide 44 ÷ 3

Divide 83 ÷ 5

14 3 44 –3 14 –12 2

6 5 83 –

Checking division:

(Quotient × Divisor) + Remainder = Dividend

–

Divide 458 ÷ 4

Divide 4801 ÷ 6

4 458 – 5 –

6 4801

– Checking division:

Checking division:

(14 × 3) + 2 = 44 42 + 2 = 44 44 = 44

Word Problems Let’s explore some word problems on division. A shopkeeper has 2896 pencils. He puts the pencils in packs of 8. How many packs of pencils does the shopkeeper have? What do we know? Total number of pencils = 2896 Number of pencils in each pack = 8 What do we need to find?

Did You Know? Yuvraj Panwar from India holds the world record of solving 28 division sums of 4 Digits × 1 Digit in 1 minute.

Number of packs of pencils that the shopkeeper has. How to find? Divide to find the answer. 2896 ÷ 8 132

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Solve to find the answer. We can find the number of packs by dividing the total number of pencils by the number of pencils in each pack. Therefore, the shopkeeper has 362 packs of pencils.

Example 3

362 8 2896 –24 49 – 48 16 –16 0

A library has 486 books. If each shelf holds 6 books, what is the total number of shelves in the library? Step 1 What do we know? Total number of books = 486 Number of books each shelf holds = 6 Step 2

Step 3

What do we need to find?

How to find?

Number of shelves.

Divide to find the answer. 486 ÷ 6

Step 4 Solve to find the answer.

We can find the number of shelves by dividing the total number of books with the number of books each shelf holds.

81 6 486 –48 6 –6 0

Therefore, there are 81 shelves in the library. Example 4

Alex has 152 stickers. He divides the stickers equally among 7 of his friends. How many stickers will he have left? Step 1

Step 2

What do we know?

What do we need to find?

Total number of stickers = 152

Number of stickers Alex has left.

Number of friends = 7 Chapter 7 • Division by 1-digit Numbers

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Step 3 How to find? We can find the number of stickers Alex has left by dividing the total number of stickers by the number of friends.

Remember! If the question is about whatʼs left after dividing, we find the remainder, not the quotient.

152 ÷ 7 Step 4 Solve to find the answer. Number of stickers each friend gets.

21 7 152 –14 12 –7 5 Do It Together

Stickers Alex has left.

Solve using the given method. What do we know? What do we need to find? How to find? Solve to find the answer. 1

jug can hold 7 cups of juice. How many jugs are required to hold 819 A cups of juice? mily has 46 apples. She shares them equally among 5 friends. How E many apples does each friend get?

Do It Yourself 7A 1

Find the quotient using the long division method. a

68 ÷ 4

72 ÷ 6

88 ÷ 5

436 ÷ 9

528 ÷ 4

2156 ÷ 5

8000 ÷ 8

5532 ÷ 6

700 ÷ 7

412 ÷ 5

Find the quotient and remainder. a

55 ÷ 3

79 ÷ 7

97 ÷ 9

235 ÷ 4

758 ÷ 3

1532 ÷ 7

2145 ÷ 8

6785 ÷ 2

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Solve and check the division. a f

541 ÷ 6

68 ÷ 5

b c d e f g

2562 ÷ 9

Match the following. a

41 ÷ 2

89 ÷ 7

4121 ÷ 8

(7 × 5) + 3

(9 × 6) + 5

(12 × 4) + 1

d i

132 ÷ 3

5124 ÷ 6

324 ÷ 5

(5 × 8) + 4

(20 × 2) + 1

(15 × 3) + 2

(11 × 7) + 2

A store puts some shirts of different brands on sale. Answer the questions. Brand A Cost of 3 shirts = 360 a b

Brand B Cost of 5 shirts = 475

Brand C Cost of 2 shirts = 128

What is the price of 1 shirt of Brand A?

Which brand shirt is cheaper – Brand B or Brand C?

Word Problems 1 2 3 4

toy store has 945 types of toys. If the shopkeeper wants to arrange A the toys in boxes of 5, how many boxes does he need? here are 7385 people at a theatre. If each row in the theatre holds T 7 people, how many rows are filled completely? here are 57 puppies at a shelter. If each doghouse can hold 9 T puppies, how many puppies will be left without a doghouse? Solve the problems using the method given.

hat do we know? What do we need to find? How to find? Solve to W find the answer. a b c

ou have 3548 flower seeds. How many seeds will you have left Y after planting them in rows of 6? t a picnic, there are 74 cups of lemonade. If each tray holds 8 A cups, how many trays are needed? school has 513 storybooks. If each classroom gets A 9 storybooks, how many classrooms will receive them?

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Points to Remember • Long division helps us to divide large numbers.

• I n long division, we write dividend, divisor, quotient and remainder in the following way:

Quotient Divisor Dividend

• A remainder is a left-over number that we get when we divide numbers.

Remainder

Math Lab Whole class Setup: Whole class

Material required: 6 transparent glasses, 40 pebbles or beads. Method: 1 2 3 4 5 6

Show students a bunch of beads/pebbles.

xplain that you will divide the 40 beads/pebbles equally into 6 glasses E and show them.

Ask how many items there are in each glass and how many are left over. Do the long division method for 40 ÷ 6 on the board.

Connect the long division method and the beads/pebbles activity.

how them the dividend, divisor, quotient and remainder in both the S procedures.

Chapter Checkup 1

Solve. a e

36 ÷ 2

384 ÷ 6

52 ÷ 4

596 ÷ 9

84 ÷ 6

1491 ÷ 7

d h

165 ÷ 5

2496 ÷ 8

Find the quotient. a

6 90

4 52

7 84

8 728

5 945

9 891

4 5284

6 6726

5 8255

3 9348

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Find the remainder.

a e i

59 ÷ 4 =

725 ÷ 8 =

9461 ÷ 7 =

b f

74 ÷ 9 =

3652 ÷ 3 =

a e i

57 ÷ 2

552 ÷ 5

9854 ÷ 7

b f

91 ÷ 4

645 ÷ 8

623 ÷ 5 =

8127 ÷ 9 =

6000 ÷ 6 =

125 ÷ 6

188 ÷ 7

Solve and check the divisions.

486 ÷ 6 =

1842 ÷ 6

7856 ÷ 8

Match the following.

(13 × 4) + 2

153

(3041 × 2) + 1

981

(21 × 7) + 6

389

(297 × 4) + 1

6083

(128 × 3) + 5

(122 × 8) + 5

Fill in the blanks with the help of long division.

a c e g

(10 × 4) + _____ = 43 (_____ × 6) + 2 = 50

(_____ × 3) + 1 = 352 (_____ × 8) + 6 = 94

b d f h

1189

(_____ × 2) + 1 = 49 (7 × 9) + _____ = 64

(42 × 5) + _____ = 214 (21 × 7) + _____ = 151

There are 800 beads for crafting. If each necklace requires 8 beads, how many necklaces can be made in total?

There are 126 marbles. If you want to divide them into bags of 9, how many marbles will be there in each bag?

At a zoo, there are 5245 tickets to be sold. If each booklet contains 5 tickets, how many booklets need to be prepared?

What number needs to be added to 156 so that it can be divided by 7 without a remainder?

Word Problems 1

A bakery has 84 cookies. If they want to pack them in boxes of 4, how

There are 720 pencils in a box. If each student receives 3 pencils, how

At a party, there are 156 cups. If each tray can hold 10 cups, how many

many boxes will be required?

many students will receive pencils? cups will remain outside the trays?

Chapter 7 • Division by 1-digit Numbers

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38 Shapes and Patterns Let’s Recall

Drawing shapes is so much fun! Let us draw some shapes that we have already learnt about. Lines Standing Line

STRAIGHT LINES Sleeping Line

Slanting Line

CURVED LINES

Flat Shapes These are shapes that can be drawn on paper. Square

Oval

Triangle

Rectangle

This water bottle is the shape of cylinder.

This party cap is the shape of a cone.

This football is the shape of a sphere.

Circle

Solid Shapes These are shapes that are like objects around us in the real world. Let us see some examples

This duster is This die is the the shape of a shape of a cube. cuboid.

Let’s Warm-up Which two objects have similar shapes? Circle them. Name the shape. 1

I scored ____________ out of 4.

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2-D Shapes Real Life Connect

Mohit’s class is playing a ‘shape hunt’ game in the classroom. The teacher asks the students to search for objects that have the same shape and raise their hands to answer. Mohit: I can see rectangles on the noticeboard and in my notebook. Teacher: Very good, Mohit! Sujata looks out of the window and says: I see circles in the sun and the wall clock. Teacher: Excellent, Sujata! The students kept on discussing objects of similar shapes.

Features of 2-D Shapes There are four basic shapes that we can see in objects around us – square, circle, triangle, and rectangle.

Circle

Triangle

Rectangle

Basic shapes are also called 2-dimensional or 2-D shapes. They are flat and have no height. So, a 2-D shape has only length and width or breadth.

corner

width

length

Square

Sides: The line segments that form the shape are called sides. Corners: The point at which the two sides meet is a corner. Let’s check the number of sides and corners in the 4 basic 2-D shapes.

Chapter 8 • Shapes and Patterns

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side

There are 2 more features of 2-D shapes – sides and corners.

side

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Rectangle: The shape is a rectangle. It has: • 4 straight sides • 4 corners The opposite sides of a rectangle are equal. It has straight sides.

Side 4

Corner 2 Side 3

Here, side 1 = side 3, and side 2 = side 4.

Corner 1 Side 1

Rectangle

Corner 3

Corner 4

Side 2

Square: The shape is a square. It has: • 4 sides

Corner 2

• 4 corners All the sides of a square are equal. It has straight sides.

Side 3

Side 4

Corner 1

Side 1

Square

It means, side 1 = side 2 = side 3 = side 4. Corner 3

Triangle: The shape is a triangle. It has: • 3 sides

Side 2

Corner 4

Corner 1

• 3 corners The sides of the triangle may or may not be equal. A triangle has straight sides.

Side 2

Side 1

Triangle Corner 2

Side 3

Corner 3

Look at the triangles. Each of the triangles has 3 sides but not all sides are equal.

Circle: This shape is a circle. It is round. It has: • no sides • no corners

Circle

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Oval: This shape is an oval. It is made of one curve. It has: • no sides

Oval

• no corners

Think and Tell How many sides and corners does this shape have? Are the sides in the shape straight?

Example 1

Example 2

Look at the picture. Count the shapes and fill in the table. Circle

Triangle

Square

Rectangle

Look at the shapes of the objects. Complete the table.

Shape = Rectangle Sides = 4

Corners = 4 Do It Together

Shape = Circle Shape = Triangle Sides = 0 Corners = 0

Sides = 3

Corners = 3

Shape = Square Shape = Oval Sides = 4

Corners = 4

Sides = 0

Corners = 0

There are the coloured dots on the dot paper. Join the corners to draw the sides of the shape. One is done for you. Write the number of triangles, circles, squares and rectangles. Yellow dots: Corners of a rectangle Green dots: Corners of a square Red dots: Corners of a triangle Blue dots: A circle Triangle: _______

Chapter 8 • Shapes and Patterns

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Circle: _______

Square: _______

Rectangle: _______

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Do It Yourself 8A 1

What is the shape of these objects? a

Match the shapes with the number of sides they have. Shapes

Sides 0

Count and write the number of shapes in the figure. Square = ________

Rectangle = ________

Triangle = ________

Circle = ________

Write if true or false. a

A triangle has 3 curved sides.

The opposite sides of a rectangle are equal in length.

An oval has 0 sides and 0 corners.

The 4 sides of a square are straight sides.

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Colour the squares in red, circles in orange, rectangles in pink and triangles in brown in the given picture.

Symmetry in 2-D Shapes Mohit and Sujata enjoyed learning about 2-D shapes in their Maths classroom. Now, it is time for their art class. The art teacher gives them square sheets of paper. Teacher: Fold the paper in half. Then, open it and draw dotted lines on the fold. Sujata: Mohit, look! I got two similar rectangles when I drew a line on the fold. Mohit: But I got two equal triangles! How does this happen? Let’s help Sujata and Mohit understand this! The two same rectangles or triangles are because of symmetry in a square! A shape is symmetrical if it can be divided in such a way that the two halves are exact copies of each other.

Chapter 8 • Shapes and Patterns

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Many figures and shapes around us show symmetry. See these examples:

A line that divides the shape in equal halves is called the line of symmetry. It can be a standing or a sleeping line along the sides. Let’s see this in some 2-D shapes. Line of symmetry Standing Lines of Symmetry: Sleeping Lines of Symmetry: Some shapes also have slanting lines of symmetry:

Some shapes can have more than one line of symmetry. Take a square for example. It can be divided into equal halves by a standing, a sleeping, or two slanting lines. It has 4 lines of symmetry.

Similarly, a rectangle has 2 lines of symmetry. It has a standing and a sleeping line of symmetry.

Did You Know?

In a circle, the number of lines of symmetry cannot be counted. It can have infinite lines of symmetry.

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Example 3

Which of these shapes do not show symmetry along the dotted line?

A leaf

A jug

A smiley face

A butterfly

The jug does not show symmetry along the dotted line. The leaf, smiley face, and the butterfly show symmetry. Do It Together

Draw any one line of symmetry on these shapes. Colour the two halves with different colours. One is done for you. 1

Do It Yourself 8B 1

Which of these shapes show symmetry along the dotted line? a

Which of these rectangles do NOT show the correct line of symmetry?

Draw a standing line of symmetry on these shapes.

Draw a line of symmetry on these figures. a

Chapter 8 • Shapes and Patterns

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Draw a slanting line of symmetry on these shapes. a

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Word Problem 1

Ratna folds a rectangular sheet of paper into a perfect half and then again in half. When she opens it, she finds 4 lines marked on it. Are these lines of symmetry? Draw a standing line and a sleeping line on it to show symmetry.

3-D Shapes Real Life Connect

In the evening, Mohit went to the park with his father and sister Tina. They saw an ice-cream cart and asked their father to buy them an ice cream each. Mohit: I want this triangular one, with three circles on the top. Tina: I don’t want an ice cream. I want a can of juice. Mohit saw the shape of his sister’s can. He wondered what he should call this shape. Let us help Mohit and learn more about shapes! Look at the shapes of different objects in the table. These objects of our day-to-day life have the following shapes – cube, cuboid, cylinder, cone, and sphere. These shapes are called solid shapes OR 3-D shapes. Solid Shapes

Cube

Cuboid

Cylinder

Cone

Sphere

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Features of 3-D Shapes Solid shapes are also called 3-dimensional or 3-D shapes. We can measure the length, width, and height of a 3-D shape. Each 3-D shape has faces, edges, and corners. • The surface of a 3-D shape is its face. The face can be plane or curved. • Two faces meet at an edge. The edge can also be straight or curved. • Two or more edges meet at a corner.

corner face

edge

Let’s check the number of sides, corners, and edges in each solid shape. A cube has:

• 6 plane faces • 12 straight edges • 8 corners A cuboid has: • 6 plane faces • 12 straight edges • 8 corners A cylinder has:

• 2 plane faces and 1 curved face • 2 curved edges • no corners A cone has: • 1 plane face and 1 curved face • 1 curved edge • 1 corner or vertex A sphere has:

• 1 curved face • no edges • no corners Chapter 8 • Shapes and Patterns

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straight edge

cube

straight edge

plane face

cuboid plane face curved edge curved face

plane faces

curved edge curved edge

plane face

curved face

vertex

curved face

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Example 4

Name the 3-D shape of the given objects. 1

Speaker

Example 5

Cap

Box

Object

Speaker

Cap

Box

Shape

Cylinder

Cone

Cube

How many corners does the box have? The object is a cuboid. A cuboid has 8 corners.

Do It Together

Complete the table for each 3-D shape. 3-D Shapes Cube Cylinder Cuboid Sphere Cone

Faces Plane

Edges

Curved Straight Curved

Corners

_____

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Do It Yourself 8C 1

Colour the solid shapes as instructed.

• cube in blue • cone in red • cuboid in pink • sphere in brown

Name the solid shapes of the objects. a

• cylinder in green

Match the shapes with the number of corners they have. Shapes

Corners 1

8 0 4

Match the description with the name of the solid shapes. 6 plane rectangular faces Only 1 curved face 1 plane and 1 curved face 6 plane square faces 2 plane faces and 1 curved face

Fill in the blanks. a

A cuboid has ________ straight edges.

A sphere has ________ edge.

A cone has ________ curved edge.

A cylinder has ________ curved edges.

A cube has ________ straight edges.

Chapter 8 • Shapes and Patterns

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Cube Cone Cylinder Cuboid Sphere

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View of Objects Every night, after dinner, Mohit sits down with his sister Tina to draw. Today, they are drawing a cup-and-plate set. Tina’s drawing looks like this:

Mohit’s drawing looks like this:

Why do these drawings of the same thing look different? Tina looked at the cup-and-plate set from the top. Mohit looked at the cupand-plate set from the side. This is why their drawings look different. 3-D objects look different when we view them from the top, sides or front. Let’s see some more examples: An open umbrella looks different when viewed from the top and the side. Top View

Side View

A scooter looks different when viewed from the front and the sides. Front View

Side View

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Example 6

Look at the pictures. Label the top view, side view, and front view. View 1

View 1 is the front view of the shoe. View 2 is its side view. View 3 is its top view. Example 7

Ritik is riding a bicycle. Which pictures show him from the sides? Picture A, C, and E show Ritik from the sides. Picture B shows him from the front. Picture D shows the back view.

Do It Together

Look at the objects. Draw the front, side, and top views of these objects. Objects

Front

Side

Top

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Do It Yourself 8D 1

Which view shows this sweet from the side?

View A

View B

Which view shows this box from the top?

View A

View B

View C

Look at the pictures. Draw the top view of these objects.

Draw the front and side views of these objects.

Draw your Maths textbook from the top and any one side. What shapes do you get in each drawing?

Patterns Around Us Real Life Connect

Sujata’s mother got a new saree. Sujata: Maa, your saree is beautiful! Mother: Thanks, Sujata! I really liked its colour and border. Sujata: Oh, the border has red and yellow rectangles one after another. Mother: Yes, Sujata! It is a pattern! Sujata: A pattern? On a saree border?

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Understanding Patterns See the border of Sujata’s mother’s saree. It has red and yellow rectangles one after another. The shapes that repeat one after other make patterns. Patterns can be seen everywhere around us. Let’s see a few examples of patterns in our day-to-day lives.

Patterns in buildings

Patterns on a bedsheet

Patterns of a flower

Patterns follow a rule. Let us see a few patterns to understand some rules. Repeating Pattern Patterns repeat a unit. A repeating unit could be one or many lines, shapes, colours, numbers, letters, or objects. Here, the shapes that are being repeated are squares and triangles. So, we see 1 square, 1 triangle, 1 square, and again, 1 triangle.

Here, the colour of the balls are repeated as yellow, red, green; yellow, red, green.

repeating unit.

Rotating Pattern The unit changes direction with each next step in a rotating pattern. In this pattern, the arrow changes direction clockwise as up, right, down, left, up. In this pattern, the rectangle is rotated with each step as up, right, up, right.

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Growing Pattern One or many lines, shapes, colours, numbers, letters, or objects are added to every next unit to grow the pattern. Thus, the pattern increases in number or size. In this pattern, 1 triangle and 1 star are added in the next unit.

In this pattern, the figure increases in size. 1 triangle is added to the next unit. Number Patterns These patterns are made of numbers. They also follow the same rule of repeating a unit. Here, the number 5 is added each time to the next unit (number) in the pattern. In both these patterns, the number 2 is added every time to the next unit. In this pattern, the number 7 is added to the next unit. The next numbers of the pattern will be: 55 + 7 = 62 and then, 62 + 7 = 69

4, 6, 8, 10, 12, 14… 3, 5, 7, 9, 11, 13…. 27, 34, 41, 48, 55…

Combination of Patterns Sometimes, the unit of the pattern has a pattern within itself. The pattern is made of a combination of patterns.

Error Alert! Do not add random parts to the pattern. It can disrupt the overall flow of the pattern.

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Secret Message A secret message is a fun way of writing a message using patterns. Let us try to read a secret message: 5H5O5W 5A5R5E 5Y5O5U5? Here, the number 5 is repeated after each letter of the alphabet. Highlight the alphabets letters and see the message: 5H5O5W 5A5R5E 5Y5O5U5? The message is: HOW ARE YOU? Tiling Patterns Have you ever noticed how the tiles are arranged on a footpath? The tiles also form a pattern. Let us explore more of such patterns around us. We may see many patterns on the floors and walls of the houses. These patterns are made with tiles. The way of covering a surface completely with tiles of the same shape and size is called tiling. It follows a pattern too! Let’s have a look at these tiling patterns:

Did You Know? Hawa Mahal of Jaipur has a huge number of patterns in it. The jharokhas (windows) of the palace display a honeycomb-like pattern.

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Example 8

What would be the next two units in the pattern?

Let us find the repeating unit for the pattern. The number of dots increases with each dice. So, the repeating unit is:

As the first unit of the repeating unit is already there, the next units will be:

Example 9

Which of these shapes can be used in tiling patterns?

Both the shapes can be used in tiling patterns as shown here:

Do It Together

Complete the tiling pattern by colouring the white shapes. A part of each pattern is coloured for you. 1

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Do It Yourself 8E 1

Underline the repeating units in the pattern. a

Colour the units to complete the pattern. a

Find the pattern and add the next unit. a

b c

28, 32, 36, 40, ______, ______

35, 45, 55, 65, ______, ______

45, 47, 49, 51, ______, ______, ______

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Which of the following is NOT a tiling pattern? a

Decode the secret message. a

JTJHJE

JCJAJR

ATBHCE

JIJS

DSEKFY

2L3I4K5E

JRJEJD

GIHS

IBJLKULE

6D7O8S9A

Points to Remember • Flat shapes which have only length and width are called basic shapes or 2-dimensional (2-D) shapes.

• Square, rectangle, triangle, and circle are some examples of 2-D shapes. • Solid shapes have length, width, and height. They are also called 3-dimensional (3-D) shapes. • Cube, cuboid, cone, cylinder, and sphere are some examples of 3-D shapes.

• A shape is in symmetry if it can be folded or divided into two equal halves. The dividing line is called the line of symmetry.

• A pattern is a series or sequence of repeating units. It can be formed with a set of lines, shapes, colours, numbers, letters, or objects. • The pattern made for covering a surface with tiles of the same shape and size is called tiling.

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Math Lab Create a Figure with Shapes! Setting: In pairs

Materials Required: 1 tangram set of shape cutouts.

Prepare Material: You may do it at home or in class. Take a white square sheet of paper. Draw the shapes on it as shown in the picture here. You may colour each shape as shown. Then cut out along the lines to get 1 set of shapes. What to Do? • With your partner, point to any one figure made with tangram shape cutouts.

• Both partners will arrange the shape to make the figure. You may help each other to arrange the shapes in the right way. • Try to create as many figures as possible. You may create any other figure of your choice as well.

Chapter Checkup 1

a b

Write the number of shapes in the given figure.

Colour the squares in pink, circles in red, triangles in green, and rectangles in blue.

Square = ________

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Rectangle = ________

Triangle = ________

Circle = ________

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Draw the lines of symmetry on the figures as instructed. a

Standing line of symmetry:

Sleeping line of symmetry:

Match the objects with their 3-D shapes.

Draw the top, side, and front view of the lunch box.

Top

Side

Front

Colour the unit to complete the patterns. a

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Complete the patterns. a

Complete the number patterns. a

12, 16, 24, 28, _______, _______, _______

48, 56, 64, 72, _______, _______, _______

32, 37, 42, 47, _______, _______, _______

29, 32, 35, 38, _______, _______, _______

80, 82, 84, 86, _______, _______, _______

56, 61, 66, 71, _______, _______, _______ Colour to complete the tiling patterns. e

Draw and write the shape of a table when seen from the side and the top.

Make a tiling pattern of your own choice by colouring the shapes.

Draw another tiling pattern using triangles, rectangles, and squares. Colour it.

Side

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Top

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Length, Weight and Capacity

Let’s Recall

We know that we use length to tell us how long something is. For example, our foot is longer than our finger. We can use our body parts to measure length!

Foot

Finger

Let us use our forearm to measure the length of the table. As shown, this table is about 2 forearms long! Weight is the measure of how heavy an object is.

When we go to a vegetable market, the vendor uses a seesaw-like object to compare weights. This machine is called a weighing balance. It helps us to compare weights of objects. Let us say the vendor puts 5 apples on one side and 1 apple on the other side.

The side with 5 apples is heavier. So, that side will go down as shown.

The capacity of an object tells us how much liquid an object can hold. Look at the jug for example. It holds juice!

Now we pour the juice into glasses. Let us say it fills 5 glasses. We can say that the capacity of the jug is 5 glasses.

Let’s Warm-up

Write if true or false. 1

The book

The watermelon

The capacity of each of the glass that of the jug

is 7 erasers

long.

__________

is heavier than the pen .

is less than

__________

I scored ___________ out of 3.

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Length Real Life Connect

John wanted to buy a light string to decorate his house. He went to a light shop for it. Sure! Here are some strings.

I want a light string, please.

The shopkeeper showed him different lengths of light strings. John picked the suitable length of string and went home.

Measuring Length We saw that the shopkeeper showed different lengths of light strings. Length refers to how long or tall an object is from one end to another. It is also the distance between two places. The length of objects or the distance between the places are measured using standard units. Units of Length We can use different units based on the type of length to be measured. Type of length

Unit

Short form

Short length

Centimetres

Nail, safety pin

Long length

Metres

Cloth, wire

Short distance Metres

Distance from bedroom to kitchen

Long distance

Kilometres

Distance from home to hospital

Height

Centimetres, Metres

cm, m

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Examples

Height of a tower

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To identify the correct unit when measuring length, first identify the type of length and then choose the unit to be used. Example 1

Which unit would you use to measure the length of your bedroom?

Did You Know? Burj Khalifa is the tallest building in the world. Its height is 828 m.

As the length of the room is long, we will use the unit ‘metre’ to measure its length. Do It Together

Circle the correct unit for measuring the following things. 1 2 3 4 5 6 7 8 9 10

Length of the school grounds

Length of a desk

Length of the bus

Distance between a park and the house Length of a shoe

Height of a street light pole Length of a bat

Length of a saree

Height of a flagpole

Distance between a shop and the school

cm cm cm cm cm

m m

km km

Measuring Length Using a Ruler A ruler is a tool used to measure the length of small objects. A ruler with short and long lines on it is shown below. The longer lines that have a number written on them are centimetre lines. The distance between two centimetre lines is 1 centimetre.

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To measure an object using a ruler, place the ruler against the object. Make sure that one end of the object is at 0 cm.

Remember! Another name for a ruler is a ‘scale’.

Let’s measure the length of a crayon!

This crayon is 6 cm long. How long is the ribbon?

Example 2

The ribbon is 8 cm long. Do It Together

Ravi is using a ruler to find the length of different things at his house. 1

Ravi has two plants. The distance between the plants is __________ cm.

The length of the photo is __________ cm.

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Ravi marked the length of a book on the ruler. The length is __________cm.

Ravi measured a pan. Draw an arrow to help Ravi to mark the ruler at 18 cm.

Converting Units of Length We have learnt that metre and centimetre are the two units of length. Do you know that there is a relationship between centimetres and metres? 1 metre = 100 centimetres

Remember! The unit ‘metre’ is longer than the unit ‘centimetre’.

Remember John who went to buy a light string? John asked for a 2 m long string but the shopkeeper is used to measuring the string in cm. Let us help the shopkeeper to convert m into cm. We know that 1 m = 100 cm 2 m = 2 × 100 = 200 cm Therefore, the shopkeeper will give John a string of 200 cm. What if John wanted a 2 m 50 cm string? We have already found that 2 m = 200 cm 2 m 50 cm = 200 cm + 50 cm = 250 cm On the other hand, we can also convert cm to m. Let us convert 300 cm into m. 300 cm = 100 cm + 100 cm + 100 cm = 1 m + 1 m + 1 m (as 1 m = 100 cm) =3m Therefore, 300 cm = 3 m.

Error Alert! Do not forget to add the length given in cm after converting m to cm. 3 m 45 cm = 3 × 100 cm = 300 cm 3 m 45 cm = 3 × 100 + 45 cm = 300 cm + 45 cm = 345 cm

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Example 3

Kiran has 8 metres of wire. How many cm of wire does she have? We know that 1 m = 100 cm; 8 m = 8 × 100 cm = 800 cm Kiran has 800 cm of wire.

Example 4

Indu has a 400 cm long cloth. How many metres of cloth does she have? We know that 100 cm = 1 m Then, 400 cm = 100 cm + 100 cm + 100 cm + 100 cm =1m+1m+1m+1m =4m Therefore, 400 cm = 4 m. Length in m

Do It Together

Length in cm

___ + ___ + ___ + ___ + ___ = ___ 500 cm 4m

___ × ___ = ___ cm

9 m 45 cm

___ = 9 × 100 + ___ cm = ___ cm + 45 cm = ___ cm

7 m 25 cm

6 m 30 cm

7m 25 cm = 7 × 100 + 25 cm = ___ cm + 25 cm = ___ cm

___ = ___ × ___ + ___ = 600 cm + 30 cm = ___ cm

Do It Yourself 9A 1

Choose the suitable unit to measure the following objects. a

A seesaw

A toy car

The distance between two cities

A pipe

A phone

The height of a person

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Measure and write the length of the following objects. a

________ cm b

________ cm c

________ cm d

________ cm e

________ cm f

________ cm 3

Convert the following into cm. a

2 m 52 cm

4 m 15 cm

9 m 9 cm

7 m 26 cm

5 m 55 cm

Convert the following into m. a

700 cm

600 cm

400 cm

800 cm

500 cm

900 cm

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

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Word Problems 1

Bobby wants to measure the length of a hammer. Which unit should he use for measuring it?

Giri has a woollen thread of 6 m 50 cm length. How long is the thread in cm?

Deepu has a pipe of 700 cm long. How many metres long is the pipe?

Word Problems on Length Real Life Connect

Let’s explore some real-life situations related to length!

The next day, John went to buy two ropes. He wanted one rope of length 38 cm and another of 52 cm. Let us find the total length of rope that John bought. Step 1: What do we know?

Step 2: What do we need to find?

Length of first rope = 38 cm

As we need to find the total length, we will add the lengths given.

Length of second rope = 52 cm

38 cm + 52 cm = 90 cm

Therefore, the total length of the two ropes is 90 cm. Example 5

Chintu’s height is 125 cm, and Neelu’s height is 132 cm. How much taller is Neelu than Chintu? Step 1: What do we know? Chintu’s height = 125 cm Neelu’s height = 132 cm

Step 2: What do we need to find?

To find how much taller Neelu is than Chintu, subtract Chintu’s height from Neelu’s height. 132 cm – 125 cm = 7 cm

Therefore, Neelu is 7 cm taller than Chintu.

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Example 6

A red pipe is 43 m long and a green pipe is 35 m long. What is the total length of the two pipes? Step 1: What do we know?

Step 2: What do we need to find?

Length of red pipe = 43 m

As we need to find the total length, we will add the lengths.

Length of green pipe = 35 m

43 m + 35 m = 78 m

The total length of the two pipes is 78 m. Do It Together

On Monday, Soumya travelled a distance of 6 km, and on Tuesday, she covered 12 km. What is the total distance she covered over the two days? Step 1: What do we know? Distance travelled on Monday = 6 km Distance covered on Tuesday = _______ Step 2: What do we need to find? As we need to find the total distance covered, we will _______ the distances. 6 km _______ = _______ km The total distance travelled by Soumya is _______ km.

Do It Yourself 9B 1

A blue ribbon is 50 cm long, and a red ribbon is 30 cm long. What is the total length of the two ribbons?

A wire is 5 m long, and a rope is 2 m long. How much longer is the wire than the rope?

A green cloth is 14 m long, and a yellow cloth is 22 m long. What is the total length of the two pieces of cloth?

Rima travelled a distance of 4 km to reach Saira’s house. She travelled a further 9 km to reach the school. How much distance did she travel?

A pencil is 15 cm long, and a crayon is 11 cm long. What is the difference between the pencil and the crayon’s length?

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Word Problems 1

An auto driver travels 25 km in three hours and 18 km in the next two hours, what is the total distance travelled by the driver in 5 hours?

A copper wire is 1 m 50 cm long, and a silver wire is 2 m long. What is the total length of the two wires in cm?

An orange thread is 4 m long, and a blue thread is 350 cm long. Which thread is longer, and by how much? Write the answer in cm.

Weight Real Life Connect

Naveen wasn’t feeling well, so his parents took him to the hospital to see a doctor.

Dr. Smith greeted him and asked him to step on a machine called a weighing scale. Curious, Naveen stepped on the scale, and the numbers started moving. Dr. Smith wrote down the measurement.

Why do you need to know my weight, Dr Smith? Weight helps me keep track of how well you are growing!

Measuring Weight Weight is the measurement of the heaviness of an object.

We saw that Dr Smith used a weighing scale to measure Naveen’s weight. Can a fruit vendor use the same weighing scale to weigh fruit?

No! The weighing scale for measuring human weight is different from the weighing machine used for fruit and vegetables. We use different machines to find the weight of different things. Different types of weighing machines are shown below.

Platform Traditional Tabletop Scale Scale Scale Chapter 9 • Length, Weight and Capacity

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Hanging Weighing Scale machine to measure body weight

Did You Know? The weight of an elephant is around 3500 kg.

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Units of Weight We have learnt that we measure the weight of an object in grams or kilograms. Grams

to measure smaller weights

Kilograms

to measure larger weights

Some of the common weights used with weighing scales are:

5 kg Example 7

2 kg

1 kg

500 g

200 g

100 g 50 g

Which unit should be used to measure the weight of a bag of wheat? As the weight of the bag would be heavy, we should use kg to measure its weight.

Do It Together

Below are some objects at the bakery shop. Tick () the suitable weight measurement unit for the following objects. Item

Unit (g)

Unit (kg)

Cupcake

Tall Cake

kg 

Pack of biscuits

Slices of Bread

Oven

Cabinet

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Converting Units of Weight There are some items which can be measured both in grams and kilograms. Like a packet of sugar! The relationship between grams and kilograms can be given as: 1 kilogram = 1000 grams

Error Alert!

Let’s find out how many grams there are in 2 kg

Multiply the kg by 1000 to convert it into g.

We know that 1 kg = 1000 g

5 kg = 5 × 100 g = 500 g

Therefore, 2 kg = 2 × 1000 g = 2000 g Example 8

500 g

2 kg

5 kg = 5 × 1000 g = 5000 g

Uma has luggage weighing 7 kilograms and 300 grams. How many grams of weight does she have? Weight of Uma’s luggage = 7 kg and 300 g We know that 1 kg = 1000 g 7 kg = 7 × 1000 g = 7000 g 7 kg 300 gm = 7000 g + 300 g = 7300 g Therefore, the total weight of Uma’s luggage is 7300 g.

Do It Together

Read the sentences that show things Rama noticed on a day at the market. Fill in the blanks. 1

he shopkeeper has 5 kg of apples. T He has 5000 g of apples.

iya bought 2 kg and 500 g of carrots. R She bought ______ g of carrots.

bag of potatoes weighs 8 kg. The bag A weighs ______ g.

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

eena purchased 3 kg and 450 g of bananas. She purchased ______ g M of bananas.

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Do It Yourself 9C Write the correct unit of measurement for the given objects.

Unit of measurement

Object

Unit of measurement

Object

Feather

Pan

Car

Television

Pillow

Bar of soap

Chair

T-shirt

Mia goes to the grocery store and picks up a big watermelon. How will the shopkeeper measure its weight, in kg or g?

Lilly has a pencil. Is the pencil measured in kg or g?

Convert kg into g. a

8 kg

1 kg 500 g

9 kg

4 kg 200 g

7 kg 750 g

3 kg 300 g

6 kg 460 g

2 kg 250 g

Ram buys a bag of rice that weighs 5 kg. What is the weight of the bag in grams?

Word Problems 1

Sarah’s pet weighs 3 kg and 300 g. How much does the pet weigh in grams?

Mohit’s computer weighs 8 kg and 750 g. How much does the computer weigh in grams?

Vinay has a basket of fruit that weighs 9 kg and 250 g. What is the weight of the basket in grams?

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Word Problems on Weight To solve the word problems, we will use the two-step strategy which we learnt previously. Remember Naveen who went to the doctor? The doctor found his weight to be 25 kg. The doctor saw that Naveen’s weight was 23 kg at the last visit. Let us find the increase in Naveen’s weight. Step 1: What do we know? Naveen’s current weight = 25 kg Naveen’s previous weight = 23 kg Step 2: What do we need to find? Increase in weight = current weight – previous weight = 25 kg – 23 kg = 2 kg Therefore, Naveen’s weight has increased by 2 kg. Example 9

Arya’s bag weighs 1300 g, while Ved’s bag weighs 1500 g. What is the total weight of the two bags? Step 1: What do we know? Weight of Arya’s bag = 1300 g Weight of Ved’s bag = 1500 g Step 2: What do we need to find? Total weight = Ved’s bag weight + Arya’s bag weight = 1500 g + 1300 g = 2800 g Therefore, the total weight of the two bags is 2800 g.

Do It Together

Bhanu’s suitcase weighs 15 kg, while Vidya’s suitcase weighs 19 kg. How much heavier is Vidya’s suitcase compared to Bhanu’s suitcase? Step 1: What do we know? Weight of Bhanu’s suitcase = _____ kg Weight of Vidya’s suitcase = 19 kg Step 2: What do we need to find? Difference in weight = _____ – _____ = _____ kg Therefore, Vidya’s suitcase is _____ kg heavier than Bhanu’s suitcase. Chapter 9 • Length, Weight and Capacity

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Do It Yourself 9D 1

A box of chocolates weighs 500 g, and a box of candies weighs 750 g. What is the total weight of both boxes?

Shalu went to the market and bought 4 kg of vegetables and 5 kg of fruit. How much more fruit did she buy than vegetables?

Tina’s backpack weighs 10 kg. She adds a few items that weigh 3 kg to the backpack. What is the weight of the backpack now?

The weight of a watermelon is 5 kg. Seema cuts it into two pieces. The weight of one of the pieces is 2 kg. What is the weight of the other piece?

Aman baked a cake weighing 1200 g, while Shreya baked a cake weighing 1900 g. What is the difference in the weight of the baked cakes?

Word Problems 1

John sold 4 kg and 200 g of newspapers and 700 g of magazines. Find the total weight of articles sold.

A fruit basket weighs 2 kg. After taking out a banana weighing 100 g and an apple weighing 150 g, what is the weight of the fruit basket?

Capacity Real Life Connect

Asha’s family and friends are going on a picnic. Asha is helping her mom to make orange juice. Asha: How much juice should we take with us, Mumma? Mom: We will be 8 members at the picnic. 2 bottles of juice will be sufficient. Asha pours the juice into the bottles and puts them inside the basket.

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Measuring Capacity We have learnt how to measure the length and weight of objects. In the case of liquids like water, milk and juice we need to find the capacity. Capacity is defined as the maximum quantity a container can hold when full. Given below are some containers with different capacities!

Units of Capacity As different containers have different capacities, we use standard units to measure the capacity. Millilitre (mL) and litre (L) are the units used for measuring capacity. Millilitre

Litre

to measure small capacities to measure large capacities

500 mL

Example 10

Measuring cups, injections and measuring spoons are measured in mL.

mL 15 10 mL 5m L

Water bottles, cans and jars are usually measured in litres.

250 mL 100 mL

200 mL 100 mL

How will you measure the capacity of a swimming pool? A swimming pool is quite big. It needs a lot of water. Therefore, we will use the unit litre to measure its capacity.

Do It Together

Circle the suitable measurement unit for the following objects.

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Converting Units of Capacity We have learnt the conversions of m to cm and kg to g. Let’s now understand how the units of capacity are related to each other. 1 Litre = 1000 mL Asha’s mom made 2 L of juice for the picnic. Let us find out the capacity of juice in mL. We know that, 1 L = 1000 mL. Then, 2 L = 2 × 1000 mL = 2000 mL What if they need 4 L 250 mL of Juice?

Think and Tell Is 2 L of juice sufficient for a group of 30 people?

Then, 4 L = 4 × 1000 mL = 4000 mL 4 L 250 mL = 4000 mL + 250 mL = 4250 mL Example 11

Bhavya filled her car with 9 L and 500 mL of petrol. How much petrol did she fill in mL? Petrol filled = 9 L and 500 mL 1 L = 1000 mL 9 L = 9 × 1000 mL = 9000 mL 9 L 500 mL = 9000 mL + 500 mL = 9500 mL

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The total amount of petrolCapacity filled is 9500 mL. Capacity in L in mL Do It Together

6 L = 6 × 1000 = 6000 mL

3 L and 250 mL

3 L = 3 × 1000 = 3000 mL 3 L 250 mL = 3000 mL + 250 mL = ________ mL

5 L and 500 mL

5 L = 5 × 1000 = _____ mL

5 L 500 mL = _____ + 500 mL = ________ mL

8 L and 750 mL

________ = 8 × 1000 = ________ mL

8 L 750 mL = ________ + ________ = ________ mL

9 L and 900 mL

9 L = ________ = ________ mL

9 L 900 mL = ________ + ________ = ________ mL

Do It Yourself 9E 1

Circle the items that are measured in mL. a

Items

Cough Syrup

Bucket of water

COUGH SYRUP

Syringe

Hand sanitizer

Tub of water

Barrel of water

Glass of milk

Spoon of oil

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Convert the following into mL.

4 L 500 mL

9 L 200 mL

5 L 850 mL

8 L 725 mL

7 L 355 mL

Rohan wants to make lemonade for his friends. He needs 3 litres of water for the recipe. How many millilitres of water does he need?

Priya used 1 L and 500 mL of oil to fry chips. How many millilitres of oil did she use?

Neha is filling her fish tank with water. The tank can hold 8 litres 650 mL of water. How many millilitres of water does Neha need to fill the entire tank?

Word Problem 1

Nihal poured 6 L and 250 mL of water onto his plants. How many millilitres of water did he use?

Word Problems on Capacity Asha had 2 L of orange juice. Her mother made 5 L of mango juice. Let us find out the total amount of juice that Asha was taking to the picnic. Step 1: What do we know?

Step 2: What do we need to find?

Amount of orange juice = 2 L

Total amount of juice = 2 L + 5 L = 7 L

Amount of mango juice = 5 L Therefore, the total amount of juice is 7 L. Example 12

Rima opened a 900 mL bottle of milk. She filled a 250 mL glass with it. How much milk is left in the bottle? Step 1: What do we know?

Step 2: What do we need to find?

Total amount of milk in the bottle = 900 mL

Amount of milk left in the bottle = 900 mL – 250 mL = 650 mL

Amount of milk poured into the glass = 250 mL

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Do It Together

Sam filled a mini truck with 44 L of petrol, a car with 30 L of petrol and a bike with 5 L of petrol. With how much petrol did he fill the three vehicles? Step 1: What do we know? Amount of petrol to fill the truck = 44 L Amount of petrol to fill the car = _____ Amount of petrol to fill the bike = _____

Step 2: What do we need to find?

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

Do It Yourself 9F 1

A shopkeeper sold 23 L of cooking oil in one week and 31 L of cooking oil in another week. How much cooking oil did the shopkeeper sell in total?

A tub has 5 L 600 mL of water, how many mL of water is there in the tub?

Mohan filled a 500 mL water bottle three times to water his plants. How much water did he use in total?

Aditya sold 8 L 750 mL of milk. How many mL of milk did he sell?

Raju poured 4 L of water into a jug and then transferred 750 mL of the water into a glass. How much water is left in the jug?

Word Problem 1

A water tank initially had 5 L and 550 mL of water in it, and later, it was filled with 3 L and 300 mL of water. How much water is there in the tank in total, in mL?

Points to Remember Measurement Length

Capacity

Measured in cm, m and km

Measured in g and kg

Measured in mL and L

1 m = 100 cm

1 kg = 1000 g

1 L = 1000 mL

Chapter 9 • Length, Weight and Capacity

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Weight

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Math Lab Setting: Groups of 5.

Materials Required: Measuring tape, Rulers and a 2-metre length of ribbon cut into 5 pieces of different lengths. Method: 1 2 3 4 5 6

The teams measure the ribbon with a ruler and write down the length in centimetres (cm).

Write down the answers given by the groups on the board and add them up. Join all five ribbons and measure it using a measuring tape. Write down the length in metres (m).

Compare the total length in cm and the length in metres.

Convert metres into centimetres and check if the answers match.

Chapter Checkup 1

Circle the object which is measured in metres (m). Objects a

The length of a spoon

The height of a house

The height of a tree

The length of a room

The width of a book

The length of a wallet

The length of a swimming pool

The length of a needle

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Find the length in cm.

Convert the lengths into centimetres (cm). 5m

6 m 890 cm

8 m 50 cm

7 m 250 cm

500 cm

200 cm

300 cm 600 cm

4 m 900 cm

800 cm

Convert the lengths into metres (m). a

8 m 300 cm

g 4

400 cm

Circle the object which is measured in kilograms (kg). Objects

An empty box

Candy

A banana

Two watermelons

A bag of rice

A bag of flour

A cylinder

Two apples

Convert the weight into grams (g). a

8 kg

9 kg

7 kg 450 g

2 kg 999 g

3 kg 760 g

4 kg 640 g

5 kg 500 g

1 kg 278 g

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Circle the object which is measured in litres (L).

Objects a

Tank of water

Bottle of shampoo

Cup of tea

3 jugs of lemonade

Barrel of water

Petrol Tank

Spoonful of oil

Glass of juice

Change litre (L) into millilitres (mL).

5 L 800 mL

6 L 550 mL

8 L 900 mL

7 L 450 mL

9 L 100 mL

red string is 30 centimetres long, and a purple string is 86 centimetres long. What A is the total length of the two strings? 10 A bag of sand weighs 4 kg and 500 g. How much does the bag weigh in grams? 9

Word Problems 1 2 3 4 5 6

aria has a piece of wire of 5 m and 66 cm in length. What is the length of F the wire in cm? Manvi has a tub that can hold 7 L 500 mL of water. What is the capacity of the tub in mL? Kusha has 850 mL of orange juice in a big jug. He pours 500 mL of juice into a vessel. How much orange juice has remained in the jug? atika has a box that weighs 6 kg 450 g. She adds 2 kg 250 g of things L to the box. What is the total weight in grams?

ameer has a tub with 5 L 500 mL of water. He uses 3 L 200 mL of water S from the tub. How much water is left in the tub in mL? tailor has 600 cm of cloth. He cuts 3 m of cloth to make a skirt. How A many cm of cloth does he have left?

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10 Time Let’s Recall An early bird catches the worm! So we should always be punctual! The clock helps us to read time. Take a look at this clock. Notice that it has numbers from 1 to 12 written on it. It has two “hands”. One is big and one small. They point at the numbers at all times and help us to see the time. The big hand that moves faster is called the minute hand. The smaller hand moves slower and is called the hour hand. Let us say that the hour hand is at 8 and the minute hand is at 12 as shown. What is the time? The time is 8 o’clock. Now let us say, the hour hand is at 8 and the minute hand is at 6. We say it is 8:30 or eight-thirty. We can also say it is half past 8.

Let’s Warm-up Draw the hour hand and the minute hand for the time given below. 1

Half past 4

5:00

6:30

12:00

I scored ____________ out of 4.

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Understanding Time Real Life Connect

Sonu and Tina are playing during lunchtime. The teacher said, ˮKids, lunchtime will be over at 1 o’clock. After that, we will go to the art class. So, hurry up!ˮ Tina: I want to play some more! But I do not want to miss the art class either.

Sonu: Let me check the time. It is quarter to 1 now. We have 15 minutes more to play. Tina: Thanks, Sonu! I wish I could read the clock too!

Sonu: You can! Come, I will teach you. Look at the clock. What do you see?

Tina: I see numbers from 1 to 12 and some arrows. How do we tell time with these?

Remember! The minute hand is always longer than the hour hand.

Reading Time To read time, we look at the minute hand and the hour hand. The longer hand is the minute hand and the short hand is the hour hand. We see numbers 1 to 12 on the clock. The face of a clock is called the dial.

hour hand minute hand

Did You Know? Both the hour and the minute hands always move towards increasing numbers. The direction in which they move is called the clockwise direction.

Read Time on a Clock Hour time: The hour hand on the number shows the hour time. When the time is to the hour, the minute hand is on 12. The hour hand tells us the time. It is read as o’clock. 186

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For example, if the hour hand is on 1 and the minute hand is on 12, the time is 1 o’clock.

1 o’clock

2 o’clock

3 o’clock

4 o’clock

5 o’clock

6 o’clock

7 o’clock

8 o’clock

9 o’clock

10 o’clock

11 o’clock

12 o’clock

Remember! It is 0 minute when the minute hand is on 12. So, the minute hand is always on 12 when it is a full hour.

Minute time: When the minute hand moves from 0 to 1, 5 minutes have passed. We keep adding 5 more minutes as the minute hand keeps moving to the next number. Look at the clocks given. To tell minutes by numbers, we divide the clock in two halves.

5:15 or five fifteen

8:55 or eight fifty-five

For the first half of the clock (12 to 6), we read minutes added in the current O'CLOCK hour, using the word ‘past’. For the second half of the clock (6 to 12), we read minutes left to the next hour, using the word ‘to’. 15 minutes past the hour and 15 minutes to the next hour is read as ‘quarter’. 30 minutes past the hour is read as half. Chapter 10 • Time

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QUARTER TO

QUARTER PAST

HALF PAST

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Let’s read time by the minutes on the clock.

Example 1

8:00 8 o’clock

8:05 5 minutes past 8

8:10 10 minutes past 8

8:15 15 minutes past 8 OR quarter past 8

8:20 20 minutes past 8

8:25 25 minutes past 8

8:30 30 minutes past 8 OR half past 8

8:35 25 minutes to 9

8:40 20 minutes to 9

8:45 15 minutes to 9 OR quarter to 9

8:50 10 minutes to 9

8:55 5 minutes to 9

Look at the clock. What time is it? b

6:00 6 o’clock Do It Together

6:10 10 minutes past 6

6:45 Quarter to 7

7:00 7 o’clock

Draw the hour and minute hands on the clock to tell the time. Write the time in one more way. a

4 o’clock

20 minutes past 5

5 minutes to 3

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Time as A.M. and P.M. One day has 24 hours. On the clock, we have numbers only from 1 to 12. When the hour hand of the clock goes around once, it completes 12 hours. In a day, the hour hand goes round the clock twice to complete 24 hours.

Think and Tell How many times does the hour hand meet a number in one day?

A new day begins at 12 o’clock midnight. From 12 o’clock midnight until 12 o’clock noon is a.m.

The next 12 hours, from 12 o’clock noon until 12 o’clock midnight are p.m.

MIDNIGHT

a.m. Example 2

MIDNIGHT

NOON

p.m.

Every morning, Tara gets on her school bus at 8 o’clock. What time is it — 8:00 a.m. OR 8:00 p.m.? It is a.m. from midnight 12 o’clock to noon 12 o’clock. 8 o’clock in the morning is before noon. So, Tara gets on the bus at 8:00 a.m.

Do It Together

Look at Tom’s chart of a day. Tell the time of his activities in a.m. and p.m. Morning

8:30 Brush teeth

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10:00 Have breakfast

Noon and Evening

4:00 Play outdoors

6:30 Study

Night

8:30 Go to bed

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Do It Yourself 10A 1

What do A and B show on the clock.

Match the clock with the correct time.

A B

Half past 4 Quarter to 3 25 minutes to 8 25 minutes past 11 3

Look at the minutes and the hour hands. What time is it? a

Read the time of Sam’s daily activities. Fill in the blanks with a.m. OR p.m. a

Sam wakes up at 7 _______ in the morning.

He reaches school by 9 _______ in the morning.

Sam comes back from school at 1 _______ at noon.

He goes to play with his friends at 6 _______ in the evening.

Sam eats dinner and goes to bed by 9 _______ at night.

Draw the hour hand and the minute hand to show the time on the given clocks.

5 minutes past 2

20 minutes to 4

Half past 10

Quarter past 1

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Word Problems 1

iru wakes up when the alarm clock rings. Look at the alarm. N At what time did she wake up today?

eera needs to be at her dance class at 2 o’clock. When she M gets there, the clock is showing this time. What time does Meera reach her dance class?

n a Sunday, Ruhi watches a show that starts at half past eleven and O ends at 12:30 around noon. Write the time the show starts and ends in a.m. and p.m.

Units of Time on a Clock Real Life Connect

Tina: Thanks, Sonu! Now I can tell time too!

Sonu: You are welcome, Tina!

Just then the bell rings and their teacher comes over.

Teacher: Remember, the art class is sixty minutes long. Be back on time. Tina: Sonu, why did teacher say sixty minutes? I thought the art class was for 1 hour.

Sonu: Tina, one hour is the same as 60 minutes. Let us see how. We know that the hour and minute hand move round the clock. When the hour hand moves from one number to the next, it completes 1 hour. For example, the time now on the clock is 1 o’clock. When the hour hand reaches 2, the time will be 2 o’clock, thus 1 hour will have passed. In the same way, from 2 o’clock to 3 o’clock, another 1 hour will have passed. 2 hours 1 hour 1 o'clock

1 hour 2 o'clock

3 o'clock

Think and Tell Remember! Minutes and hours are the units of time. Chapter 10 • Time

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Converting Time We know that the hour and minute hands move around the clock. When the hour hand moves from one number to the next, it completes 1 hour. When the hour hand moves from one number to another, the minute hand moves around the clock. So, 1 hour = 60 minutes. Example 3

The hour hand has moved from 12 to 1. How many hours have passed? 1 hour is complete when the hour hand moves from one number to the next. So, 1 hour has passed.

Do It Together

12:00

1:00

Jenny is doing her art project this evening. The time was 6 o’clock when she started. It is 8 o’clock when she finishes. 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.

How many minutes has Jenny spent doing the project? We know that 1 hour = 60 minutes. So, _________ hour = 60 minutes + _________ minutes = _________ minutes.

Estimating Time Lunchtime at Sonu and Tina’s school is for 30 minutes. They play for 15 minutes. Their art class is for 1 hour. Have you noticed that they spend different times doing different activities? Some activities take less than a minute, such as sneezing, snapping fingers or clapping hands.

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Some activities take some minutes to complete. For example:

Brushing teeth

Combing hair

Some activities even take hours to complete. For example, we spend many hours at school. We may play for more than an hour. A movie may be longer than an hour too.

Packing the School bag

Think and Tell Name any two activities that may take days to complete.

So, different activities take different times to complete. Guessing which activity will take how much time to complete is called estimating time. By this, we can plan our activities and day better. Example 4

Look at some of Mia’s activities. Which activities will take her minutes to complete? Which ones will take more than an hour?

Waking up

Getting dressed

Breakfast

Time in school

Dance class

Sleeping at night

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Waking up, getting dressed and having breakfast will take Mia minutes to complete. Time at school, dance class and sleeping will be for more than an hour. Do It Together

Look at the activities. Write ‘M’ if it takes minutes and write ‘H’ if it takes hours to complete.

Putting on a T-shirt

Playing a football match

Putting on shoes

Drinking a glass of water

Celebrating a birthday

Do It Yourself 10B 1

Fill in the blanks. a

The minutes hand of a clock completes one round in _______ minutes.

The hour hand of a clock completes one round in _______ hours.

There are _______ minutes in 1 hour.

How many hours have passed when the hour hand has moved from a

4:00 to 7:00

10:00 to 12:00

12:00 to 4:00

How many hours have passed between the times given? a

3:00 to 4:00 1:20 to 2:20

3:30 to 5:30

7:15 to 11:15

Write whether the activity will take minutes or hours to complete. a

Filling a glass of milk

Boiling water

Eating a banana

Watering a plant

Washing, ironing, and folding some clothes.

There are 60 minutes in 1 hour. There are 24 hours in a day. How many minutes are there in a day?

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Word Problems 1

I t was 3 o’clock when Anuj entered his swimming class. He came out of the class at 5 o’clock. How many hours did Anuj spend in the class?

ibhu’s test was from 9 o’clock to 10 o’clock. How many minutes did V the test take?

ast night, Anju went to bed at 10 o’clock. She woke up this morning L at 6:10. How many hours and minutes did she sleep?

Calendar Real Life Connect

Mia’s school has a new rule. Children can wear dresses of their choice every second Friday of the month. Mia is getting ready for school this morning. Mia: Mummy! I don’t want to wear my uniform today! Can I wear my new dress? I know it is 4 August. Is it the second Friday of the month? Is the new dress rule starting today? A calendar can help Mia with what she wants to know.

Units of Time on a Calendar A calendar tells us which day of the week, month and year it is today. For example, 4 August 2023 is a Friday. It is the first Friday of the month. Days of the week, months, and a year are the units of time on a calendar.

Month

Days of the week

AUGUST

2023

Year Date

Days of the Week: A day is the smallest unit of time on a calendar. Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday are 7 days of the week. Together they make 1 week. Chapter 10 • Time

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Months and Year: A month is longer than a week. There are 12 months and together they make one year.

2024

Some months have 30 days, while others have 31. February is special which has either 28 or 29 days. A year has 365 days. If February has 29 days, the year is called a leap year. A leap year has one extra day, making it 366 days.

Did You Know? Remember! A leap year comes after every 4 years.

Example 5

The year 2024 is a leap year. It has 29 days in February. In total, there are 366 days in 2024.

How many months are there in a year? Name them. There are 12 months in a year – January, February, March, April, May, June, July, August, September, October, November, and December.

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Do It Together

Look at the 2024 calendar given above. Count and write the number of days in each month. January :

days February :

days March :

days

April :

days May :

days June :

July :

days August :

days September :

days

October :

days November :

days December :

days

Do It Yourself 10C 1

Match the units of time on a calendar. 2024

Day of the week

26th

Year

January Friday 2

Month

Date of the month

Fill in the blanks using days OR weeks. a

There are 7 _______ in a week.

A year is divided into 12 _______.

A year has 365 _______, if it is not a leap year.

Write if True or False. a

Sunday is a month.

December is a month.

May is the first day of the week.

A leap year has 29 days in February.

Write the name of the days of the week.

1 month = 30 days. How many days will be there in 2 months?

Chapter 10 • Time

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Word Problems 1

nand has been practising for a dance performance for two weeks A now. How many days has he practised?

I n a year, 7 months have 31 days, 4 months have 30 days and February has 29 days. How many days are there in total in this year?

Reading a Calendar Remember the new dress rule in Mia’s school is starting from the second Friday of August. Mia was not sure if she could wear her new dress on 4 August. Let’s read a calendar to help her! The second Friday will be on 11 August. Mia can wear her dress then but not today!

AUGUST 1

2023 2

1st Friday 2nd Friday

Reading and Interpreting the Calendar Reading a calendar is fun! It helps us know the day and dates for special events and count the number of days left before the event. Let us look at an example: We know that India celebrates its Independence Day on 15 August every year. It is circled on the calendar above. Read the calendar for more details: • We can tell that in year 2023, 15 August is on a Tuesday. • If today is 4 August, by counting the next days we can tell that 11 days are left until 15 August. We also find dates on a calendar which can be written in different ways. We usually write date as: date/month/year. For example, in 11/09/2024, 11 is the date, 09 is the month and 2024 is the year. We can also write the date as Date Month Year, which is 11 September 2024.

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Example 6

Rehan’s birthday is on 10 July and Muskaan’s birthday is on 15 July. 1

On what days are their birthdays?

Let’s check their birthday date on the calendar. Rehan’s birthday is on Wednesday. It is circled in blue, Muskaan’s birthday is on Monday. It is circled in orange. 2

JULY 1

2024 2

ow many days will be left to celebrate H Muskaan’s birthday after Rehan’s birthday?

Let’s count the number of days from Wednesday to Monday. It is 5 days to Muskaan’s birthday from Rehan’s birthday. Example 7

Read the calendar and fill in the blanks. 1

How many days are there in June 2024? 30

What is the date on the first Tuesday? 4

How many Saturdays are there in June 2024? 5

Do It Together

On what day will June 12 fall? Wednesday

JUNE

2024

Read the calendar for March 2024. Fill in the blanks. 1

The day of the week on 2 March: Saturday

The day of the week on 16 March: ___________

The day of the week on 25 March: ___________

The day of the week on 31 March: ___________

The date on the first Monday: _________ March

MARCH 31

The date on the last Monday: _________ March

The number of Sundays in the month: 5

The number of Saturdays in the month: ______________

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Making a Timeline A timeline helps us to show the journey over the year, in a year or in a month. We mark special years, months, days and dates on a timeline. We can show special years of our life events on a timeline. Look at the timeline of special school events in Mia’s life.

2017 1 Year old Mia

2019 Nursery

Remember! On a timeline, we mark the years, months or days of the events in an order on a line.

2020 KG Class

2022 Grade 1

2024 Grade 3

We can also show months and dates of the special events and festivals on a year timeline. Look at this timeline showing some celebrations and festivals in a year.

26 January 24 March Republic Day Holi

13 April Baisakhi

15 August 1 November 25 December Independence Day Diwali Christmas

In the same way, a timeline can show special days and dates in a month. Look at this timeline showing test and result schedule of a class: Month: March 1 March EVS test

3 March English test

5 March Maths test

7 March Hindi test

10 March Arts and PT

25 March Result

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Example 8

Birthdays of 4 friends born in the same year are given in the table. Show them on a timeline. Step 1 Draw a timeline. Anu

21 August

Danny

10 November

Samira Raj

Remember! On a timeline, we always mark events in the order in which they come first. So, we will mark birthdays in the order of months as they come in a year.

12 April 7 May

12 April Samira's birthday Do It Together

Step 2 Mark events on it.

7 May Raj’s birthday

The table shows some of the days that Mia wants to celebrate. Show them on the timeline.

21 August Anu’s birthday

10 November Danny’s birthday

Mia’s birthday

14 June

Dad’s birthday

10 January

Mom’s birthday Parents’ Day

Grandparent’s Day Friendship Day

2 April

23 July

10 September 8 August

Reading a Birth Certificate A birth certificate gives details of where and when you were born along with the details of your parents which is made after you are born. It also shows if the baby born is a boy or a girl, the place of birth, parents’ names, and registration number. You write dates every day in your notebook. Dates can be seen on many other papers. Let’s see this birth certificate: Chapter 10 • Time

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Mia was born on 14 July in the year 2016. These dates can help us to know how much time has passed since she was born. Example 9

Look at Mia’s birth certificate. Answer the questions. 1

What is Mia’s place of birth? Mia’s place of birth is New Delhi.

ow old Mia would have been on H 14 July 2020? Count forward from 2016 to 2020: 2016, 2017, 2018, 2019, 2020. There are four years up to 2020. So, Mia would have been 4 years old on 14 July 2020.

BIRTH THIS DOCUMENT ACKNOWLEDGE THAT

Mia

born on

It’s a girl

Surbhi Jain

MOTHER’S NAME Place of Birth WEIGHT

July 14, 2016 Aakash Jain

New Delhi

LBS

FATHER’S NAME

LENGTH

14 INCH

WNDLS-2016

Registration Number

Signature

In what year will Mia be 15 years old? Add 15 to the year 2016: 2016 + 15 = 2031. So, Mia will be 15 years old in the year 2031.

Do It Together

Look at Mayank’s birth certificate. Fill in the blanks. 1 2

Mayank’s date of birth is: ___________. e was only ____________ year old in H 2022. e will be _____________ years old in H 2025. I n the year 2030, Mayank will be _____________ years old.

BIRTH THIS DOCUMENT ACKNOWLEDGE THAT

Maynak

born on

It’s a girl

Diana Das

MOTHER’S NAME

Abhi Das

FATHER’S NAME

St. Mary’s Hospital, Goa

Place of Birth WEIGHT

8 October 2020

LBS

LENGTH

13 INCH

W-GOA-2020

Registration Number

Signature

Think and Tell How many years old were you last year? In which year would you have been born?

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Do It Yourself 10D 1

Look the calendar. Answer the questions. a

Which year does this calendar show?

How many days are there in this month?

Read the calendar. Fill in the blanks. a b

There are __________ (5/4) Sundays in this month. he month starts from a __________ T (Monday/Tuesday).

2034 2

On 25 May, the day is __________ (Tuesday/Thursday).

The next day after 18 May is a __________ (Friday/Monday).

2 May is a Tuesday. The next Tuesday will be on __________ May.

30 May is the last __________ (Tuesday/Thursday) of the month.

The month ends on 31 May. It is on __________ (Wednesday/Saturday).

In this month, Saturdays are on dates 6, _______, _______, and ________.

In this year, the month of June is starting from ________ (Sunday/Thursday).

There are 5 festivals in the month of October and November. Draw them on a timeline. Ram Navami 29 October

MAY

Diwali

Dusshera

20 November 31 October

Bhai Dooj

Guru Nanak Jayanti

25 November

27 November

The table shows the month in which the school is planning sports events in the year 2024. Draw this sport schedule on a timeline. Cricket match

Football match

Kho-Kho match

Tug-of-war match

Basketball match

February

November

December

October

August

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Read the timeline. Answer the questions. Rina was Rina went Rina's baby Born to school sister was Born 2010

2014

2017

Rina won a dance competition

Rina went to college

Rina got a Job

2025

2028

2034

In which year was Rina born?

How old was Rina when her sister was born?

How old was she when she won the dance competition?

How old will Rina be in 2034?

Word Problems 1

eema was born on 17 April 2018. How old was she in the S year 2022?

aru was born on 05 July 2010. How old will she be on 05 A July 2025?

inu was born on 31 July 2015. His friend Mitu was born on 31 July T 2021. Who is older of them? By how many years?

Points to Remember • We read time using clocks. They helps us plan our day. • The 2 hands on the clock show minutes and hours.

• W hen the hour hand moves from one number to another, 1 hour has passed.

• W hen the minute hand moves from one number to another, 5 minutes have passed. • 1 Hour = 60 Minutes

• T he time from midnight to 12 o’clock noon is a.m. The time from 12 o’clock noon to 12 o’clock midnight is p.m. • There are 7 days in a week. A year has 12 months. 204

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• I n total, 365 days make a year if it is not a leap year. A leap year always has 366 days.

• A calendar tells us which day, month and year it is. Using a calendar, we can tell which day it is on what date. • The date can be written in different ways: 12/07/2024 OR 12 July 2024.

• O n a timeline, the events are always written in the order in which they come first. • If we know the birth date, we can tell the age in the coming year.

Math Lab My Birth Certificate Setting: In pairs

Preparation At Home: Ask the help of your parents to fill in your birth certificate.

In Math Lab: Share your birth certificate with your partner. Check when he/she was born. Find out how old your partner is or will be this year.

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 Motner: Date of Registration: Registration Number: Date:

Signature of issuing authority

Chapter Checkup 1

Look at the minutes and the hour hands. What time is it? a

Chapter 10 • Time

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Draw a clock to show the times given. a 4 o’clock b 9 o’clock d

20 minutes past 9

Quarter to 7

9 o’clock to 3 o’clock

5:20 to 7:20

9:15 to 11:15

7:30 in the morning

3 o’clock in the afternoon

6:15 in the evening

9 o’clock at night

5 minutes to 12 midnight

5 minutes after 12 midnight

Making tea

Washing a shirt

Blinking your eyes 5 times

A picnic day

Baking two cakes and some cookies

Write the time using a.m. OR p.m.

10 minutes past 12

2:10 to 4:10

Write if the following activities would take less than a minute, some minutes or hours to complete.

Match the following. Day before Monday

2024

Month before March

Sunday

February

Month after March

2021

Year before 2022

April

Year after 2023

Tuesday

Fill in the blanks. a If it is not a leap year, there are _________ days in the year. b c d e f g

Half past 1

How many hours have passed between the times given? a 2 o’clock to 5 o’clock b 7 o’clock to 10 o’clock

Day after Monday

The date on the last day of the year is always _________ December. The date on the first day of the year is always _________ January. If today is 30 April 2023, the date tomorrow will be _________. If today is 12 June 2023, yesterday’s date was _________.

If today is Monday, 1 June 2023, the date after a week will be _________.

ia’s birthday is on Friday, 20 May. The date, a week before Sia’s birthday would be S _______________ May.

Draw a timeline with the following events in a year.

Gandhi Jayanti Independence Day Republic Day Children’s Day Earth Day 2 October

15 August

26 January

14 November

22 April

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This is 2024. a Which year will be the next?

b c 10

What year was it 2 years ago?

Which year will it be after 5 years?

Draw a calendar for the month of July. The month starts on a Sunday. Then, answer the questions. a How many Sundays are there in the month? b c d

What is the date on the 2nd Saturday? Write the dates of all Mondays.

What is the day on these dates? 11 July

19 July

iii

25 July

30 July

Word Problems 1

Rama woke up at 7 o’clock in the morning and was in bed by 9 o’clock that

The hour hand moves from number 8 to 10. How many hours have

Atul was born on 02 March 2015. When will he turn 10 years old?

Aditi turned 7 years old on 28 August 2007. In which year will she

Diya was born on 12 August 2003. How old will she be on her birthday

Chapter 10 • Time

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night. Write the time she woke up and went to bed using a.m. and p.m. passed?

become 14 years old? in 2020?

oday is Monday, 17 April 2023. Arun’s uncle is coming to stay with T them in 5 days time. On what day and date will Arun’s uncle come?

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Money

Let’s Recall Money is important to get things we need in our daily lives.

When we go to the market to buy food, we take money with us. The shopkeeper gives us what we need in exchange for money. These are the commonly used coins and banknotes in India:

₹1 Coin

₹2 Coin

₹5 Coin

₹10 Coin

₹10 Banknote

₹20 Banknote

₹50 Banknote

₹100 Banknote

Now let us say we want to buy a chocolate for ₹50. In how many different ways can we pay for it? We can pay with:

Two ₹20 notes One ₹20 note and Five ₹10 notes. and one ₹10 note. three ₹10 notes.

One ₹50 note.

Let’s Warm-up Fill in the blanks. 1

We can get ______ ₹10 notes or coins for ₹20.

We can get ______₹5 coins for ₹30.

_______ ₹2 coins and ______ ₹1 coins make ₹15.

_______ ₹2 coins make ₹20.

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I scored ____________ out of 5.

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Understanding Money Real Life Connect

Mom: Mohit, could you please go and bring a packet of salt from the market? Mohit: Sure, mom! Mom gave Mohit some notes and a few coins. Mohit went to the store. The shopkeeper gave the packet of salt and charged him ₹21.50. Mohit made the payment and went home.

Writing Rupees and Paise We have already learnt about the types of coins, that is rupee coins and paise coins. Let us learn to write the rupees and paise together.

Did You Know? Each bank note has its value written in the script of 17 languages.

Rupee and Paise Amounts Mohit paid ₹21.50 for the packet of salt.

₹21.50 The number on the left of the dot shows rupees.

The dot separates the rupees and paise.

The number on the right of the dot shows paise.

The amount ₹21.50 can be read as “twenty-one rupees fifty paise”. On the way home, Mohit bought a pack of pencils. The shopkeeper said that the pack costs ₹19.05.

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Let us see how to read this amount.

rupees

₹19.05

Remember! paise

If paise less than 10 a 0 after the dot.

Write

The amount ₹19.05 can be read as nineteen rupees five paise. Example 1

Write ₹52.50 in words.

rupees

₹52.50

paise

₹52.50 = fifty-two rupees fifty paise. Example 2

Write thirty-eight rupees seven paise in figures. Thirty-eight rupees = ₹38. Seven paise = 07. Thirty-eight rupees seven paise = ₹38.07.

Do It Together

Write the amounts in figures and words. ₹23.25 = twenty-three __________ __________ paise. ₹__________ = thirty-six rupees sixty paise. ₹42.______ = __________ rupees eighty paise. ₹______.03 = sixty-one rupees __________ paise. Counting Money Remember Mohit who went to buy the packet of salt? When the shopkeeper asked him to pay ₹21.50, Mohit started counting and took out the notes and coins shown below.

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Is the number of notes and coins taken out by Mohit, correct? Let us find out.

Step 1 Add the rupee notes and coins. Two ₹10 notes = ₹10 + ₹10 = ₹20. ₹10

₹10

Think and Tell Is there any other way to pay ₹21.50?

= ₹20

₹20 and one ₹1 coin = ₹20 + ₹1 = ₹21.

₹10

+ ₹1

= ₹21

Step 2 Write the paise amount separated by a dot with the total rupee amount. ₹21 and one 50 paise coin = ₹21.50.

₹10

+ ₹1

+ 50 paise = ₹21.50

As two ₹10 notes, one ₹1 coin and one 50 paise coin = ₹21.50. The amount taken out by Mohit is correct. Example 3

Count the money given below.

Chapter 11 • Money

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Step 1 Add the rupee notes and coins. One ₹200 note + one ₹20 note = ₹220. ₹220 + one ₹5 coin = ₹225. Example 4

Step 2 Write the paise amount separated by a dot with the total rupee amount. ₹225 and one 50 paise coin = ₹225.50.

Count and write the amount in figures and words.

The amount has one ₹50 note, one ₹10 note and one 25 paise coin. Step 1 Add the rupee notes and coins. ₹50 + ₹10 = ₹60. Step 2 Write the paise amount separated by a dot with the total rupee amount. ₹60 and 25 paise = ₹60.25. In figures = ₹60.25. In words = sixty rupees twenty-five paise. Do It Together

Count and write the amount in figures.

Step 1 Add the rupee notes and coins. ₹500 + ₹__________ = ₹600. ₹600 + ₹20 = ₹__________. ₹__________ + ₹2 = ₹622.

Step 2 Write the paise amount separated by a dot with the total rupee amount. ₹622 and __________ paise = ₹__________. In figures = ₹__________.

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Do It Yourself 11A 1

Write the amount in words. a

₹28.50

________________________________________________________________________.

₹36.25

________________________________________________________________________.

₹49.70

________________________________________________________________________.

₹57.35

________________________________________________________________________.

₹65.37

________________________________________________________________________.

₹71.75

________________________________________________________________________.

₹88.62

________________________________________________________________________.

₹92.48

________________________________________________________________________.

Write the amount in numerals. a

fifty-six rupees seventy paise

____________.

twenty-nine rupees eighty-eight paise

____________.

thirty-five rupees fifty-seven paise

____________.

sixty-eight rupees fifty paise

____________.

seventy-three rupees twenty-two paise

____________.

fifteen rupees sixty-six paise

____________.

eighty-eight rupees seventy-eight paise

____________.

Count the money and write the amount in figures. Amount

In figures

____________ ____________ ____________ ____________ ____________ Chapter 11 • Money

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Count the money and write the amount in numerals. a

____________.

Write fifty-six rupees eight paise in figures.

Conversion of Rupees and Paise There are situations where money has to be converted from rupees to paise and vice versa. Let us learn about the conversions! Converting rupees into paise We can convert rupees into paise using some simple steps. Let us convert ₹23.25 into paise. Step 1 Remove the dot and ₹ sign. ₹23.25 = 2325.

Step 2 Write paise with the number. Therefore, ₹23.25 = 2325 paise.

Error Alert! Remove the ₹ sign before writing paise with the number. ₹15.36 = ₹1536 paise

₹15.36 = 1536 paise

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Example 5

Example 6

Convert ₹49.00 into paise. Step 1 Remove the dot and ₹ sign.

Step 2 Write paise with the number.

₹49.00 = 4900.

Therefore, ₹49.00 = 4900 paise.

How will you convert ₹93 into paise. Here, we see only money in rupees. Step 1 Remove the ₹ sign and add 2 zeroes after the number. ₹93 = 9300.

Do It Together

Step 2 Write paise with the number. Therefore, ₹93 = 9300 paise.

Convert into paise. ₹125.36

₹56

Step 1: Remove the dot and ₹ sign.

Step 1: _____________________________.

₹125.36 = __________________________.

₹56 = _______________________________.

Step 2: Write paise with the number. Step 2: _____________________________. Therefore, ₹125.36 = _________ paise. Therefore, ₹56 = _____________ paise.

Converting paise into rupees We can also convert paise into rupees using some simple steps. Let us convert 5212 paise into rupees. Step 1 Remove the word ‘paise’ and put a dot after counting 2 numbers from the right of the given number. 5212 paise = ₹52.12. 2 places from the right

Step 2 Put the sign of ₹ before the number. Therefore, 5212 paise = ₹52.12. Chapter 11 • Money

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Error Alert! Do not put paise after the dot. 2356 = ₹23.56

2356 = ₹23.56 paise

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Example 7

Convert 8400 paise to rupees. Step 1 Remove the word ‘paise’ and put a dot after counting 2 numbers from the right of the given number.

Step 2 Put the sign of ₹ before the number. Therefore, 8400 paise = ₹84.00. ₹84.00 can also be written as ₹84.

8400 paise = 84.00. Do It Together

Convert into paise. 12365 paise

8700 paise

Step 1: Remove the word ‘paise’ and Step 1: ______________________________. put a dot after counting 2 numbers 8700 paise = ________________________. from the right of the given number. Step 2: ______________________________. 12365 paise = _______________________. Therefore, 8700 paise = ₹ ___________. Step 2: Put the sign of ₹ before the number. Therefore, 12365 paise = ₹ _________.

Do It Yourself 11B 1

Convert into paise. a e

₹229.25

b f

Convert into rupees. a d g

₹25.00

5600 paise 6241 paise

12356 paise

b e h

₹32.00

₹358.37

₹474.35

4200 paise

3652 paise

7523 paise

56214 paise

c e

₹25.36 = ________ paise

2125 paise = ₹ ________

36125 paise = ₹ ________

d h

₹112.56 ₹586.20

8562 paise

802 paise = ₹________

Fill in the blanks. a

₹41.00

d f

₹125.36 = ________ paise ₹358.80 = ________ paise

What is ₹76 in paise?

If Sia wants to buy an eraser of ₹5. How much money she will pay in paise?

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Word Problems on Money The next day, Mohit and his mother went to the market. They bought a packet of tea for ₹52.50 and a packet of biscuits for ₹40.00. Let us find out how much money they spent in total. Step 1 Write the information given in the question. Cost of tea = ₹52.50. Cost of biscuits = ₹40.00.

Remember! 0 after the dot means 0 paise. Therefore, ₹40.00 = ₹40 only.

Step 2 Choose the correct operation. We need to find the total money spent; hence we will add the costs. Step 3 Add or subtract the paise amount. Then, add or subtract the rupee amount. Both amounts have to be added or subtracted separately. Therefore, Mohit and his mother spent ₹92.50 in total. Example 8

52.50 + 40.00 92.50

Neeraj had ₹175.50 with him. He spent ₹53.00 on buying colour pencils. How much money does Neeraj have left? Step 1 Write the information given in the question. Money Neeraj had = ₹175.50. Money spent on colour pencils = ₹53.00. Step 2 Choose the correct operation. We need to find the amount Neeraj has left. Hence we will subtract the money. Step 3 Subtract rupees and paise vertically separated by the dot. Money left with Neeraj = ₹122.50. Chapter 11 • Money

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Do It Together

Anushka had ₹135.00 with her. Mom gave her ₹42.50, and Dad gave her ₹37.00. How much money does Anushka have in total? Step 1 Write the information given in the question. Money with Anushka = ₹135.00. Money given by Mom = __________. Money given by Dad = __________. Step 2 Choose the correct operation. We need to find the total money Anushka has; hence we will __________ the money. Step 3 Add rupees and paise vertically separated by dot.

135.00 42.50 +37.00 4.

Do It Yourself 11C 1

Mother gave ₹50.50 pocket money to Vaibhav and ₹75.00 to Neeraj. How much money did she give them altogether?

The price of a lunch box is ₹85.50 but Priya only has ₹72. How much more money does she need to buy the lunch box?

The prices of some books are given. The price of the English book is ₹130.00, the Hindi book is ₹129.50, and the Maths book is ₹142.00. Find the total cost of the books.

The price of a cricket bat is ₹235.50 and a ball costs ₹45.00. What is the total cost of the bat and the ball?

Suhani had ₹238.50. If she gave ₹153.00 to her mother, how much money did she have left?

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Divya spent ₹238 on Sunday and ₹125.50 on Monday. How much did she spend in total?

John and Maria have ₹284.50 and ₹156.00, respectively. Richa has an amount equal to the difference between the amounts of John and Maria. What amount does Richa have?

Anand bought a pencil box. He gave ₹100 to the shopkeeper and got ₹28.50 back. What was the cost of the pencil box?

Making Bills Real Life Connect

John went to the nearby stationery shop to buy some items. He saw that one pencil costs ₹5.00, one eraser costs ₹6.50, one notebook costs ₹15.00 and one sharpener costs ₹12.00. John: Please give me 3 pencils, 1 eraser, 2 notebooks and 1 sharpener. Shopkeeper: Sure! Here is your bill. John: I think there is some mistake in the bill. You have charged me for 4 pencils instead of 3. Shopkeeper: Sorry! Here is the correct bill. John paid the correct amount and went home. You must have seen that when we buy something or pay for something we get a list from the shopkeeper. This list is called a bill. A bill shows the details of how much we are paying for each item bought from the shop. It also tells us the total amount we have to pay for the items bought. Let us learn how the shopkeeper makes a bill.

Chapter 11 • Money

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Step 1 Make a table as shown below. Name of the items bought

Item

Number of items bought

Name of the shop Amount = Quantity × Rate

The Stationery Loft

Quantity

Rate per item

Amount Cost of each item

Total

Total Bill Amount

Step 2 Write the item names, the quantity of each item and the price of each item. Item

The Stationery Loft

Quantity

Rate per item

Pencil

₹5.00

Notebook

₹15.00

Eraser

Sharpener

1 1

Amount

Remember!

₹6.50

Quantity = Number of items bought.

₹12.00

Total

Step 3 Find the amount of each item Amount = Quantity × Rate per item. Item

The Stationery Loft

Quantity

Rate per item

Amount

Pencil

₹5.00

₹15.00

3 × 5.00 = 15.00

Notebook

₹15.00

₹30.00

2 × 15.00 = 30.00

Eraser

Sharpener

1 1

₹6.50

₹12.00

Total

₹6.50

₹12.00

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Step 4 Find the total by adding the money in the amount column. Item

The Stationery Loft

Quantity Rate per Amount item

Pencil

₹5.00

₹15.00

Notebook

₹15.00

₹30.00

Total

₹48.50

Eraser

Sharpener

Example 9

₹6.50

₹12.00

Think and Tell 15.00 6.50 15.00 +12.00 48.50

What amount would John have paid if he had not checked the bill?

Suhani bought 20 balloons for ₹2.00 each, one candle for ₹20.50, five banners for ₹15.00 each and nine party hats for ₹9.00 each from Jolly’s shop. Prepare a bill for Suhani and find the amount she needs to pay. Using steps 1 and 2: Make a table. Write the item names, quantity, and price of each item. Item

Jolly’s Shop

Quantity

Rate per item

Balloon

₹2.00

Banner

Candle

Party hat

₹20.50

₹9.00

Amount

₹15.00 Total

Using steps 3 and 4: Find the amount of each item and the total. Item

Jolly’s Shop

Quantity

Rate per item

Amount

Balloon

₹2.00

₹40.00

Banner

₹15.00

₹75.00

Candle

Party hat

₹20.50

₹9.00

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Total

₹20.50 ₹81.00

₹216.50

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Do It Together

Vishal purchased the following items from Adarsh Departmental Store. Two loaves of bread for ₹25.00 each. One packet of milk for ₹19.50. One packet of butter for ₹60.00. Three chocolates for ₹14.00 each. Complete the bill and find the amount paid by Vishal.

Item

Adarsh Departmental Store

________ Milk

Butter

Quantity

Rate per item

Amount

₹25.00

______

________

₹19.50

₹14.00

______

________

₹60.00

Total

______

The amount paid by Vishal = _____________________.

Do It Yourself 11D 1

Vipin went to a nearby store to buy the following items. How much amount does he need to pay? Item

Quantity

Rate per item

Amount

Carrot

₹10.00

₹30.00

Bitter Gourd

₹15.50

Potato Onion

Fruits and Veggies Store

7 2

₹5.00 ₹8.00

Total

₹35.00 ₹16.00 ______

Manya went to buy some items from the nearby store. The shopkeeper gave her the following bill. Is the bill correct? If not, prepare the correct bill for her.

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Item

Quantity

Rate per item

Amount

Toy car

₹85.50

Box of crayons

₹30.00

Storybook Notebook

New Era Store

₹35.00

₹12.00

Total

₹70.00 ₹60.00

₹245.50

Sam purchased the following items from the nearby supermarket. Two ice creams for ₹20.00 each.

Three packets of cookies for ₹15.00 each. One packet of chips for ₹24.50. Two bottles of juice for ₹26.00 each. Prepare a bill and find the amount paid by Sam. 4

Kavya and her friend ordered the following items at the ‘Self Service Store’. Two sandwiches for ₹90.00 each.

One glass of milkshake for ₹78.50. One cup of coffee for ₹50.00. Three packets of cookies for ₹45.00 each. Prepare a bill and find the total amount. 5

Ravi, Joe and Tanya went shopping. Look at the items with their prices.

₹5.00

₹75.50

Ravi buys

₹2.00 Joe buys

₹4.00

₹45.00 Tanya buys

2 bananas for ₹_______

1 banana for ₹_______

5 bananas for ₹_______

5 toffees for ₹_______

2 toffees for ₹_______

4 toffees for ₹_______

1 teddy for ₹_______

2 pencils for ₹_______ 1 ball for ₹_______

Amount paid = ₹_______

Chapter 11 • Money

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1 teddy for ₹_______

3 pencils for ₹_______ 1 ball for ₹_______

Amount paid = ₹_______

1 teddy for ₹_______

4 pencils for ₹_______ 2 balls for ₹_______

Amount paid = ₹_______

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Sahil had a ₹200 note with him. He went to buy some fruit from the nearby fruit store. He added 4 apples costing ₹20.00 each, 3 oranges costing ₹8.00 each, one papaya costing ₹35.50 and four guavas costing ₹12.00 each to his shopping cart. Will he be able to purchase all the fruit he added to his cart?

Points to Remember • W hen we write rupees and paise together, they are separated by a dot with rupees on the left and paise on the right. • To convert rupees into paise, remove the dot and ₹ sign and write paise.

• T o convert paise into rupees, put a dot after counting 2 numbers from the right and put the ₹ sign with the given number. • Amount = Quantity × Rate per item.

Math Lab Shopping Spree Setting: In groups of 5. Materials Required:

Price tags with various items and their cost in rupees and paise. Play money in the form of rupee and paise notes and coins. Pen and paper. Method:

Display the items along with their price tags.

The teams select the items they want to purchase and write the quantity on the paper. The teams find the total amount they need to pay.

The teams use the play money for their purchases.

The team with the correct amount and money in hand wins!

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Chapter Checkup 1

Write the amount in words. a

₹65.14

₹71.05

twenty-nine rupees fifty-five paise

Write the amount in words, as numerals. a c

₹52.36

thirty-eight rupees sixty-five paise fifty-nine rupees nine paise

Count the money. Write the amount in figures and words. a b c d e

Match the amount in rupees and paise. In rupees

In paise

₹2.35

12568 paise

₹23.56

235 paise

₹3.48

3480 paise

₹34.80

2356 paise

₹125.68

34850 paise

₹348.50 5

Convert the amount given in rupees to paise. a

348 paise

₹25.15

₹52.25

₹235.48

52364 paise

Write the amount in rupees. a

3256 paise

Chapter 11 • Money

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15236 paise

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Look at the bills and correct them if you find a mistake.

Item

All in one mart

Quantity Rate per item

Pen

₹12.00

Ruler

₹11.50

Marker

Pencil box

All in one mart

Amount

Item

₹70.00

Sugar

₹39.50

₹11.50

Oil

₹72.00

₹55.00

₹110.00

₹65.00

₹130.00

Total

₹376.50

Marker Curd

Quantity Rate per Amount item 3 2

₹40.00

₹45.00

₹125.00

₹35.00

₹70.00

₹72.00

Total ₹307.00

Divya purchased the items from the nearby store. Prepare a bill and find the amount

paid by Divya.

Three packets of rice for ₹45.00 each. Two packets of chips for ₹18.00 each. One packet of milk for ₹17.50. 9

Sam made out a bill for 5 packets of biscuits each costing ₹12.00 and 2 cans of juice

Sam spent ₹152.00 on a doll and ₹58.50 on a toy. How much money did he spend

each costing ₹35.00. The customer gave him a ₹200 note. How much change will Sam return to the customer? in all?

Word Problems 1

Kavya bought a pen for ₹23.00. She gave ₹50 to the shopkeeper. How

Reena has to pay school fees of ₹535.50 but she has only ₹425.00 with

John has ₹125.50 with him. Tanya has ₹52.00 more than John. How

Seema had ₹136.50 with her. She spent ₹55 on a notebook and the rest

much change will she get?

her. How much more money does she need? much money does Tanya have?

on crayons. How much did she spend on the crayons?

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12 Fractions Let’s Recall

Sharing food and eating together is so much fun! The friends in the picture are sharing the cake and eating together! How can they cut the the cake so that everybody gets an equal piece? The cake is whole. We divide the whole cake into as many pieces as the number of children so that each of them gets an equal “fraction” of the cake. Thus, a fraction is a part of a whole and can be used to split a whole object into equal parts.

Let’s Warm-up

Look at the pictures. Can the pictures in Column 1 and 2 be the two equal parts of a whole? Say Yes or No. Column 1

Column 2

Whole Object

1 2

I scored ___________ out of 5.

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Understanding Fractions Real Life Connect

Ravi and Manya are feeling hungry. Mother bakes a pizza for them. Ravi: Wow! The pizza looks yummy. I can’t wait to eat it.

Manya: Yes, Ravi! Let me cut the pizza into equal parts first. Manya cuts the pizza into equal parts and they both enjoy their meal.

Parts of a Whole Whole: A full or complete object or collection of objects is a whole. Whole means 1.

1 whole collection of mangoes

A whole slice of bread

A whole pizza

Fraction: Fractions are equal parts of a whole.

Let us learn how to divide a whole object into equal parts! Half When a whole is divided into two equal parts, then each part is called half of the whole. 1 It is written as , half, or one-half. 2

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half or

1 2

one-half or

Remember! Check if the whole is divided into equal parts and the number of equal parts, before writing the fraction of each part.

1 2

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One-third When a whole is divided into three equal parts, then each part is called one1 third of the whole. It is written as . 3 One-third or

1 One-third or 3

A whole

One-third or

1 3

One-fourth When a whole is divided into four equal parts, then each part is called one1 fourth of the whole. It is written as . 4 One-fourth or

1 One-fourth or 4

1 4

1 1 One-fourth or 4 4 Two-thirds: When a whole is divided into three equal parts, and 2 out of 2 3 parts are shaded, it is called two-thirds or . 3 A whole

A whole

One-fourth or

Two-thirds or

2 3

One-third or

1 3

Three-fourths

3 Three out of four equal parts is called three-fourths. It is written as . 4

Think and Tell One-fourth or A whole Chapter 12 • Fractions

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Three-fourth or

3 4

1 4

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Example 1

What fraction of the shape is shaded? Total number of equal parts = 4 Number of parts shaded = 1 1 out of 4 equal parts is shaded, hence

Example 2

Which shape is not divided into equal parts?

Divided into 2 equal parts Do It Together

1 fraction is shaded. 4

Divided into 4 equal parts

Not divided into equal parts

Divided into 3 equal parts

What fraction of the given shape is 1

shaded

not shaded

Total number of equal parts = 4 Number of parts shaded = ______ ______ out of 4 parts are shaded, hence ______ fraction is shaded. Number of parts not shaded = 1 1 out of ______ parts are not shaded, hence ______ fraction is not shaded.

Do It Yourself 12A 1

Write the fraction for the shaded portion in each figure. a

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Shade half or a

1 of each shape. 2 b

Shade one-fourth or

1 of each shape. 4

Colour each shape to represent the given fraction. 3 1 a half or b Three-fourth or 4 2

one-fourth or

1 4

two-thirds or

2 3

one-third or

1 3

Three-fourth or

3 4

Match the shaded figures to the fractions they represent. Half

One-fourth

Three-fourths

Shade one-third or a

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1 of each shape. 3 b

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Word Problem 1

Hari cut an apple pie into fourths for his friends. How many friends did he serve?

Fractions of a Collection We already know that fractions are equal parts of a whole. We also know that: 1 means 1 part out of 2 equal parts. 2 1 means 1 part out of 3 equal parts. 3 1 means 1 part out of 4 equal parts. 4 The above fact can be used to shade or find the fractional part of a collection or group of objects. Half of a collection of objects: 1 Let us find and shade of a collection of 12 bananas. 2

1 2 Divide the number of bananas in two equal groups as shown below: Collection we want to shade =

1 of the collection of 12 bananas = 12 ÷ 2 = 6 bananas in each group. 2 1 Shading of the collection of bananas can be shown as: 2 Clearly

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One-third of a collection of objects: 1 Let us now find and shade of a collection of 12 bananas. 3 1 Collection we want to shade = 3 Divide the number of bananas in 3 equal groups as shown below:

1 of the collection of 12 bananas = 12 ÷ 3 = 4 bananas in each group. 3 1 Shading of the collection of bananas can be shown as: 3 Clearly

One-fourth of a collection of objects: 1 Let us now find and shade of a collection of 12 bananas. 4 1 Collection we want to shade = 4 Divide the number of bananas in 4 equal groups as shown below:

1 of the collection of 12 bananas = 12 ÷ 4 = 3 bananas in each group. 4 1 Shading of the collection of bananas can be shown as: 4 Clearly

From the above discussion; we can say that: 1 • To find of a collection, we divide the number of objects by 2. 2 1 • To find of a collection, we divide the number of objects by 3. 3 1 • To find of a collection, we divide the number of objects by 4. 4

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Example 3

Colour one-third of the collection of crayons. Total number of crayons = 15

1 Collection of crayons we want to colour = 3 1 To find of a collection of 15, 3 – divide the objects equally into the same number of parts as the denominator – shade the number of objects in one group. 5 crayons can be coloured as:

Example 4

Solve. 1 of 20 apples 1 2 – Divide 20 apples into 2 equal parts

– Count the number of apples in 1 part.

1 of 24 trees 3 – Divide 24 trees into 3 equal parts

– Count the number of trees in 1 part. Do It Together

Colour one-fourth of the collection of balls.

1 of 20 = 10 2

1 of 24 = 8 3

Total number of balls = 8

Collection of balls we want to colour = ______ ______ balls can be coloured as:

Do It Yourself 12B 1

Colour a

1 of the collection. 2 b

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Colour

1 of the collection. 3

Colour

1 of the collection. 4

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Write if true or false. 1 a of 16 apples is 4 apples. 4 1 c of 6 mangoes is 6 mangoes. 3 Find.

1 of 6 2

1 of 12 3

1 of 9 3

1 of 16 4

c g

1 of 10 pears is 2 pears. 2

1 of 8 4

1 of 21 3

1 of 18 2

1 of 12 4

Word Problem 1

1 of the plants in her living room. How 3 many plants did she put in her living room? Ramya had 12 plants. She put

Writing a Fraction Remember, we divided the pizza into two, three and four equal parts. We also learnt that: 1 1 1 half = ; one-third = and one-fourth = 2 3 4 1 1 1 Have you noticed that the fractions , , and have two parts? One number 2 3 4 is written at the top and the other is written below it. In a fraction,

• the number written at the top is called the numerator. • the number written below is called the denominator.

Numerator: It tells us the number of equal parts chosen. In the fractions 1 1 1 , , and the numerators are 1, 1 and 1. 2 3 4

Denominator: It tells us the number of equal parts made. In the fractions 1 1 1 , , and the denominators are 2, 3 and 4. 2 3 4

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Let us now learn how to write other fractions.

Find the fraction of the blue parts in the given figure.

We learnt that fraction =

Numerator Number of parts chosen = Denominator Total number of parts

Here, number of parts chosen = Number of parts coloured blue = 5 Total number of parts = 8

The fraction of blue parts =

5 8

Error Alert! Always write the total number of parts in the denominator. For instance, the fraction of 2 slices of cake out of 7 slices will be given as:

Example 5

7 2

2 7

What fraction of the given figure is coloured pink? Number of parts coloured pink = 7 Total number of parts = 12 The fraction of pink parts =

Example 6

Number of parts coloured pink 7 = Total number of parts 12

What fraction of the balls are a

red

green

Number of red balls = 8

Total number of balls = 11 Number of red balls 8 Fraction of red balls = = Total number of balls 11 Number of green balls = 3 Total number of balls = 11 Fraction of green balls =

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Number of green balls 3 = Total number of balls 11

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Do It Together

What fraction of the balloons are: a

Yellow

Green

Number of yellow balloons = ____________ Total number of balloons = 7

Number of ____________ balloons = ____________ Total number of balloons Number of green balloons = ____________ Fraction of yellow balloons =

Total number of balloons = 7 Number of ____________ balloons Fraction of green balloons = = ____________ Total number of balloons

Do It Yourself 12C 1

What fraction of the given figures are shaded? a

Shade the figures to show the given fraction. a

1 4

3 4 e

8 14

7 8 f

5 8

4 10

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Write the fractions for the coloured and uncoloured part for the collections.

Colour the collections to show the fractions.

4 7

5 9

6 10

9 13

4 of a certain number of buses is 16. What is the total number of buses? 5

Word Problem 1

There are 24 marbles in a set. How many marbles are there in one-third of the set?

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Word Problems Let us learn how to solve word problems on fractions.

Do you remember Ravi and Manya who were ready to eat the pizza made by their mother? Manya cut the pizza into 8 equal parts. She ate 3 slices and Ravi ate the remaining 5. What fraction of pizza was eaten by Manya? Number of parts chosen Number of objects chosen We know that Fraction = or Total number of parts Total number of objects To solve a word problem on fractions: Step 1: Find the total number of parts / objects chosen.

In the above case, number of parts chosen = number of slices eaten by Manya = 3 Step 2: Find the total number of parts / objects. Here, total number of slices of pizza = 8

Step 3: Write the given information in the form of fractions. The fraction of pizza eaten by Manya = Number of slices eat by Manya = 3 Total number of slices 8 3 Manya ate of the pizza. 8 Ravi was still hungry, so mother baked one more pizza and cut it into 6 slices. Ravi ate one-third of the pizza. How many slices of the second pizza did Ravi eat? 1 whole

6 slices

1 of 6 slices = 2 3

1 of a collection is 3 equal parts. 3 Total number of slices = 6

Each equal part has 2 slices. Slices eaten Ravi = 1 of 6 = 2 slices. 3 Ravi ate 2 slices from the second pizza.

Did You Know? 1 of the earth’s 3 surface is covered with land. About

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Example 7

There are 7 ribbons in a packet. Of these, 4 ribbons are blue. What fraction of ribbons are blue? Step 1: Number of blue ribbons = 4

Step 2: Total number of ribbons = 7 Step 3: Fraction of blue ribbons = Number of blue ribbons = 4 Total number of ribbons 7 Example 8

Ranu bought a packet of bread which had 12 slices. She gave 1 of the 2 packet to a street dog. How many slices of bread did she give to the dog? Total number of slices of bread = 12

Fraction of bread given to the dog = 1 of 12 2 12 slices split into 2 equal parts gives 6 slices in each part. So, the number of slices given to the dog = 6 slices. Do It Together

Mohit bought 15 roses to decorate his house. He put 1 of the roses in a 3 vase. How many roses did he put in the vase? Total roses = __________

Fraction of roses in the vase = __________ Total number of vases = __________

Do It Yourself 12D 1

Kavya places 17 roses in a beautiful vase. It holds 8 red roses and 9 pink roses. What fraction of roses are red?

There are 24 marbles in a bag. of them are green. What fraction 3 of marbles are green?

The students of Class 3 collected 24 bottles thrown away as waste. One-half of the bottles were plastic. How many bottles were plastic?

Sunil had 15 crayons. He kept 7 crayons with him and gave the remaining 8 crayons to his sister. What fraction of crayons did Sunil give to his sister? 1 Vishal has 12 shirts. of his shirts are blue. How many shirts are 4 blue?

Chapter 12 • Fractions

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There are 25 building blocks in a bag. Ravi uses 16 blocks to build a house. What fraction of building blocks remain unused? 1 Rani has 27 books. She donates of the books. How many books does Rani have left? 3

6 7

Word Problem 1

Suhani is reading a book. The book has 24 pages. Suhani read 11 pages. What fraction of pages did Suhani read?

Points to Remember • A full or complete object is a whole. Whole means 1. • Fractions are equal parts of a whole or a collection.

• Two halves or three one-thirds, or four one-fourths make a whole. 1 • To find of a collection, we divide the number of objects equally into 2 parts. 2 1 • To find of a collection, we divide the number of objects equally into 3 parts. 3 1 • To find of a collection, we divide the number of objects equally into 4 parts. 4 • I n a fraction, the numerator indicates the number of parts chosen and the denominator indicates the total number of parts.

Math Lab Let’s Find the Fraction! Setting: In groups of 2.

Materials Required: A small bag, 30 marbles of two colours, paper and pen.

Method: Put the marbles into the bag and give it a good shake. Each student in the group takes a handful of marbles. They sort and record the fraction of each colour on the paper. The student who finishes first is the winner!

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Chapter Checkup 1

What fraction of the figures are coloured?

____________ 2

3 5

2 7

Colour the collections as per the fractions given.

1 of the brinjals 3

1 of the kites 2

1 of the cups 4

1 of the balls 3

Chapter 12 • Fractions

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____________

Colour the figures as per the fractions given.

4 9 3

____________

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Write the fractions. a

Half = _________

One-third = _________

Three-fourths = _________

One-fourth = _________

Numerator: 5; Denominator: 8 = _________

Numerator: 7; Denominator: 12 = _________

Write the fraction of the given collections. Collection of objects

Fraction Green capsicums = _______ Yellow capsicums = _______ Pink stars = _______ Blue stars = _______ Blue crayons = _______ Yellow crayons = _______

Solve. 1 a of 12 2

1 of 15 3

1 of 4 4

1 of 8 2

im has a cake, and he wants to share it equally with his 4 friends. If the cake is T divided into 5 equal parts, what fraction of the cake does each friend get?

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1 eena bought 9 flowers from the market, of which were tulips. How many of the M 3 flowers were tulips?

unita has 25 pencils. 12 of them are red and the rest are brown. What fraction of S pencils are red?

1 here are 24 apples in a basket. If of the apples are rotten, how many apples are T 4 still good?

Word Problems 1

anya planted 6 plants in her garden, of which 2 were rose plants. M What fraction of rose plants were planted in the garden by Manya?

Raj sent out invitations to 18 friends for his birthday party, but 3 of them were unable to attend. What fraction of his friends attended the party?

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313 Data Handling Let’s Recall

Going to the market with our parents is so much fun! What did we buy today? Let us see our shopping bags!

Items

Quantities

Apples

So many things! Is there a better way to show what we bought?

We can put all this data together in a table. We can also write the quantities of items that we bought. This gives all the information together in a single view!

Cabbages

3 pieces

Shampoo

250 mL

Flour

1 Kg

Vegetable Oil

Colour Pencils

1 packet

Hair Oil

200 mL

Data put together in an organised way is called information.

We have presented the data related to our shopping in the table above.

Let’s Warm-up Read the table that shows the number of balloons a man sold in a week. Answer the questions. 1

n which day did he sell the most O balloons? __________ n which day did he sell the least O balloons? ____________

Days

Number of balloons

Monday Tuesday Wednesday Thursday Friday

On which days did he sell the same number of balloons? ____________

On which day did he sell no balloons? ____________ I scored ____________ out of 4.

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Understanding Data Real Life Connect

A cricket tournament was organised at Yash’s school. He helped with scorekeeping in each match. He noted down the number of wickets that each player took. Amir took 8 wickets, Vihan took 7, Avyaan took 8, Deepak took 9, Prabhakar took 6, and Shreshth took 7 wickets.

Data Tables Can Yash put this data together in a better form? Are there details that he can draw from this data? Let us see!

Remember!

To better understand the data, let us try to put it in a table form.

Arranging data into meaningful chunks that can be easily understood is called data handling.

Data is a collection of numbers or values, that we can sort and use to understand things.

Step 1 Make a table with 2 columns and label them.

Step 2 Write the names of the players.

Players

Wickets Taken

Vihan

Amir

Avyaan

Deepak

Prabhakar Shreshth

8 8 9 6

Step 3 Write the wickets taken by each player.

Remember! A list helps organise information about things.

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Data given in a table looks a lot more organised and easier to understand than in a sentence form.

What if Yash wanted to identify the player who took the highest number of wickets? We can clearly see in the above table that Deepak took the highest wickets, which is 9.

Now what if Yash wanted to compare the performances of different players? Bowlers that take more wickets perform better! We can then re-order the data table in a descending order – so that bowlers with higher wickets appear at the top. Players

Wickets Taken

Deepak

Amir

Avyaan

Shreshth

Vihan

Prabhakar

So, now we know that Deepak, Amir, and Avyaan were the top 3 bowlers in the tournament. Example 1

A car seller collects the following data of sales of cars from his shop. Colour of Cars

Number of Cars Sold

Black

Red

Silver

White

Others Do It Together

e can see in the table that the W highest number of sold cars are black in colour.

15 17 12 6

Which colour car is sold the most?

What is the total number of cars sold? otal number of cars sold T = 15 + 20 + 17 + 12 + 6 = 70

Shruti organised a survey to note the favourite sports of the students in her class. The following data was gathered: Football, Cricket, Tennis, Badminton, Football, Football, Cricket, Tennis, Football, Badminton, Badminton, Cricket, Cricket, Cricket, Tennis, Tennis, Cricket, Football, Football, Football, Cricket, Badminton, Football, Cricket, Cricket, Football, Tennis, Badminton, Badminton, Cricket, Badminton, Cricket

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Favourite Sports Football

Number of Students 9

Tennis Complete the data table of the favourite sport of the students.

Do It Yourself 13A 1

Which of the following is true about the organised data? Tick the correct option. a

Easy to understand the order of data.

Better and neat presentation of data.

Both the statements are true.

None of the statements is true.

Write if true or false. a b

Raw data is an organised form of data. riting the numbers in ascending or descending order makes it easier to find the W greatest or smallest from the data.

Collecting data makes it easy to understand.

The data collected from surveys is called raw data.

Organise the raw data of marks obtains in Maths out of 100, from highest to lowest. 65, 70, 78, 58, 80, 98, 45, 77, 99, 83, 89.

The choices of fruit of 42 students in a class are as follows: A, O, B, M, A, G, B, G, A, G, B, M, A, G, M, A, B, G, M, B, A, O, M, O, G, B, O, M, G, A, A, B, M, O, M, G, B, A, M, O, M, O where A, B, G, M, and O, stand for Apple, Banana, Grapes, Mango and Orange, respectively. Draw a table to show the above data. Which two types of fruit are liked by equal number of students?

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Given below is the data showing the grain that some people eat. Read the data and fill in the blanks. Grains

Number of People

Wheat

Rice

Maize

Barley

Ragi

umber of people who eat Barley are N ______________. umber of people who eat Ragi are N ______________ (more/less) than those who eat rice. ost of the people eat ______________ as M their main food.

Word Problems 1

There are 8 sections of Class IV in a school. The table below shows the number of students in each section. How many more students are there in the section with the most strength than the one with the least strength? Section

Number of Students

The table shows the marks (out of 100) scored by 5 students in Maths and Science. Answer the questions. a b

Which roll number secured the highest marks in each subject?

re there any students who scored equal marks in the two subjects A combined? Roll no.

Math

Science

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Pictograph Remember Yash listed the wickets taken by the players in a data table. The table helped us to compare the wickets taken by each player. Players

Amir 8

Wickets Taken

Vihan 7

Avyaan 8

Deepak 9

Prabhakar 6

Shreshth 7

But what if Yash wanted to represent the data in an interesting way using pictures? Drawing a Pictograph Pictographs are a more interesting and attractive way of presenting data. Let us learn about them. When we use pictures or symbols to show data, it is called a pictorial representation or pictograph. The same data of the players can be represented in a pictograph. Players

Wickets Taken

Amir Vihan Avyaan Deepak Prabhakar Shreshth Key:

= 1 wicket

The key tells the meaning and the value of the picture or symbol.

But in the above chart, so many symbols have to be entered! This can get very tiresome. Is there a quicker way to represent the data? What if each

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was 2 wickets instead of 1?

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The chart would then become: Players

Wickets Taken

Amir Vihan Avyaan Deepak Prabhakar Shreshth Key:

= 2 wickets

Half a symbol can be used to show that it has half of the value of the whole symbol. In this key, so

Think and Tell

stands for 2 wickets,

Why is it important to select a key in a pictograph?

stands for 1 wicket.

Error Alert! The symbols that are drawn in a pictograph should be of same size.

Example 2

The number of students of a class using different brands of shampoos is shown. Represent the data in the form of a pictograph. Brand A 6

Brand B 3

Brand C 8

Brand D 4

Brand E 7

Let  = 1 shampoo

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Number of students using different shampoos.  Brand A  Brand B  Brand C  Brand D  Brand E  = 1 shampoo. Example 3

Draw a pictograph for the data shown in the table. Take the key as balls bowled. Bowlers

Balls Bowled

Jasprit

Bhuvneshwar Shami

Mukesh

45 40

 = 5 balls bowled

Balls Bowled

Bhuvneshwar

50 = 5 × 10

Mukesh

20 = 5 × 4

Shami

Jaidev

Bowlers Jasprit

Jaidev

45 = 5 × 9 40 = 5 × 8 20 = 5 × 4

Bowlers with the number of balls bowled. Bowlers

Balls Bowled 

Bhuvneshwar



Jasprit Shami

Mukesh Jaidev Do It Together

   = 5 balls bowled

A trip was organised for the students of class 3. The data shows how many students from 5 sections went on the trip. Represent the data using a pictograph. Section A

B C

Number of Students 7 8 6 9

One  represents 1 student. Chapter 13 • Data Handling

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Section

Number of Students





_________________________

D  = 1 student

_________________________

Reading a Pictograph Let us look at a weather data pictograph! The pictograph shows the rainfall received by a city in different months. Months June

Rainfall

July

August

September Key:

= 5 cm

What if we wanted to know the rainfall in the month of July? There are 5 5 cm of rain.

symbols in July. As per the key, each

symbol equals

So, let us find the rainfall in July: 5

Total rainfall in the month of July = 25 cm What if we wanted to find the month with the least rainfall? We can see that September has the least number of symbols. There are 2 symbols. So, each symbol = 5 cm. Therefore, 2 × 5 = 10 cm of rain was received in September.

Think and Tell Will it be easier or difficult to make the same pictograph if the key is = 1 cm?

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Example 4

Read the pictograph shown below and answer the questions that follow. Days

Number of Students Absent

Monday Tuesday Wednesday Thursday Friday Saturday

Key: 1

= 4 students

How many students were absent on Thursday?

Number of symbols for Thursday = 1 Key:

= 4 students

So, the number of students absent on Thursday = 4 2

n which day was the greatest number of students absent and O how many were absent?

The greatest number of symbols can be seen on Saturday.

So, the greatest number of students were absent on Saturday. Number of symbols for Saturday = 5

4 8 12 16 20 Thus, the number of students absent on Saturday = 20. Chapter 13 • Data Handling

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Do It Together

7 friends went shopping to buy chocolates. The pictograph shows the number of chocolates purchased by each of them. Read the pictograph and answer the questions. Names

Number of Chocolates

Shubh

Mangal Aahan

Jennifer Param

Shruthi

Devyani Key: 1

= 2 chocolates

How many chocolates did Ahaan purchase? Number of symbols of chocolates for Ahaan = 2 and ________. Key: 2

= 2 chocolates 4 ________

Thus, Ahaan purchased ________ chocolates. 2

Who purchased the most chocolates? How many?

Do It Yourself 13B 1

Write if true or false. a

A pictograph represents data using pictures and objects.

In a pictograph, more pictures mean a bigger number.

Pictographs help to understand and interpret the data.

Read the given information. One symbol represents 10 animals. How many animals are there in total for 5 such symbols? = 10 animals

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If 2 represents 10 snowflakes, then how many symbols will represent 20 snowflakes?

Draw a pictograph for the given data. Flavours

Number of Ice Creams

Strawberry

Vanilla

Chocolate

Mango Key: 5

= 1 ice cream

Complete the pictograph for the data. Favourite Swings

Number of Children

Favourite Swings

Number of Children

10 8

 = 2 children 6

Read the pictograph and answer the questions. Fruit

Number of Fruit

Apple Mango Orange Banana Key: 1 fruit = 1 unit a

How many apples are there?

Which fruit is the most in number?

Which fruit is the least in number?

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Read the pictograph showing the number of books sold for different subjects. Answer the questions. Subjects

Number of Books

Maths Hindi English Computer Social Studies Science

Key: Each

= 10 books

How many Maths books were sold?

How many Hindi books were sold?

c d

ame the subject for which the most books were sold. Name the subject for N which the least books were sold. How many Computer books were sold?

Word Problems 1

The students of a class were asked about their favourite subjects. The data is represented using a pictograph. Answer the questions that follow. Favourite Subjects

Number of Students

Mathematics Science English Art = 1 student a b c

How many students’ favourite subject is Science? How many students’ favourite subject is English?

Which subject is liked by the most number of students?

The pictograph shows the number of students who borrowed a book from the library on different days of the week. Read the pictograph and answer the questions.

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Days

Books Borrowed

Monday Tuesday Wednesday Thursday Friday Saturday = 2 students a b c d e f

How many books were borrowed on Wednesday? How many books were borrowed on Monday?

n which day was the highest number of books borrowed and how O many? n which day was the lowest number of books borrowed and how O many?

hat is the difference between the number of books borrowed on W Tuesday and Thursday? How many books in total were borrowed in the week?

Bar Graph We learnt about representing data pictorially. Are there other ways to represent data? Let us look at Yash’s data table again. The table shows wickets taken by the players in the tournament. Players Wickets Taken

Amir

Vihan

Avyaan

Deepak

Prabhakar

Shreshth

Drawing a Bar Graph A bar graph is a chart that uses bars to show comparison between categories of data. It has a horizontal axis (x–axis) and a vertical axis (y–axis). The horizontal axis shows what is being measured and the vertical axis shows the number for the categories being measured.

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Let us learn how to draw a Bar Graph. We will use Yash’s data above. Step 1 Draw the x-axis and y-axis and label them. y - axis

Step 3 Write the scale.

Step 2 Write the title of the graph.

Scale: 1 division = 1 wicket

Wickets Taken by the Players

10 9

Step 5 Draw the rectangular bars for the number of wickets taken by each player.

8 Wickets taken

7 6 5 4 3 2 1 0

i Am

a Vih

a ya

Step 4 Write the names of the players on the x-axis and the wickets taken on the y-axis.

a ep

Players

ab Pr

k ha

esh

x - axis

The title tells us what the bar graph is about (Example: Wickets Taken by the Players). Each bar has a label (Example: Wickets Taken and Players). The height of the bar graph shows how many wickets are taken by each player. Scale is the number that shows the units used (Example: 1 division = 1 mark). Example 5

Draw a bar graph for the following data. Fruit

No. of Students

Banana 8

Orange 3

Apple 5

Guava 4

Step 1 Draw a horizontal and vertical line. 260

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Step 2 On the horizontal line, we will draw bars representing fruit and on the vertical line, write all numbers representing the number of students. Step 3 Here, we take 1 unit length to represent 1 student only. The bar graph from the table can be drawn as: y - axis

Scale: 1 division = 1 student

10 9

Number of students

8 7 6 5 4 3 2 1 0

Do It Together

Banana

Orange

Fruit

Apple

Guava

x - axis

The table shows the number of pencils had by different students. Name

Number of Pencils

Ashutosh 7

Akram 6

Vinay 4

Robin 8

Atif 9

Complete the bar graph for the data given in the table above. y - axis

Scale: 1 division = 1 pencil

10 9

Number of Pencils

8 7 6 5 4 3 2 1 0

Ashutosh

Akram

Vinay

Robin

Atif

x - axis

Student Chapter 13 • Data Handling

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Interpreting Bar Graph Now that we have learnt to draw bar graphs, can we look at them and gather more details? Let us look at the following graph. y - axis

Scale: 1 division = 1 mark

Marks Scored by the Students

10 9 8

Marks

7 6 5 4 3 2 1 0

ex Al

h ais

a ep

Piy

c an

x - axis

Students

The graph shows how many marks each student scored. We also understand that data is available for 6 students. We know who among these 6 got the highest and lowest marks. Let us now answer some questions based on the graph. 1

Which students scored 8 marks? Marks scored by Alex = 8 Marks scored by Anaisha = 8 Thus, both Alex and Anaisha scored 8 marks.

Who got more marks – Ann or Piya? How many more? Marks scored by Ann = 7 Marks scored by Piya = 6 Thus, Ann scored more marks. She got 1 mark more than Piya.

Example 6

Observe the bar graph. It shows the number of saplings planted by the students in 5 days. On which day, was the most saplings planted?

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y - axis

Scale: 1 division = 1 hour

10 9

Number of saplings

8 7 6 5 4 3 2 1 0 n

y da

d We

y da

s ur Th Days

x - axis

y ida

The tallest bar shows 8 divisions = 8 saplings Day on which the height of the rectangular bar is 8 divisions = Thursday Thus, the greatest number of saplings were planted on Thursday. Example 7

The bar graph shows the number of buckets of water filled by the members of the family in a week. Who filled the most buckets and how many? y - axis

Buckets filled in a week

Scale: 1 division = 1 bucket

9 Number of buckets

8 7 6 5 4 3 2 1 0

Mother

Father Brother Members

Sister

x - axis

Tallest bar is for the father = 8 divisions

Height of the rectangular bar for the father = 8 divisions 1 division = 1 bucket

Thus, the father filled the most buckets, which is 8. Chapter 13 • Data Handling

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Do It Together

The bar graph shows the time spent on homework in different subjects in a month. Read the graph and answer the questions. y - axis

Scale: 1 division = 1 hour

10 9

Number of hours

8 7 6 5 4 3 2 1 0

Maths

Science

English

x - axis

Hindi

Subjects

hat is the difference between the hours spent on the maths homework W and the English homework? Arrange the subjects in ascending order of the time spent on them. _______________

_______________

Do It Yourself 13C 1

The data shows the number of people opting for different modes of transport. Draw a bar graph to show the data. Mode of Transport

Bus

Train

Bicycle

Bike

Auto

Number of People

The data shows the favourite colours of the students. Draw a bar graph for the data given in the table. Colour

Red

Green

Black

Yellow

Number of Students

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Read the bar graph showing the favourite TV channels of children in a class. Answer the questions. y - axis

Scale: 1 division = 1 child

Favourite TV Channel

10 9

Number of Children

8 7 6 5 4 3 2 1 0

a b c d e

Comedy

How many children like sports?

Sports Cartoon Channels

x - axis

Adventure

How many children like adventure?

Which channel is the favourite and how many children like it?

hat is the difference between the number of children who like sports and the W number of children who like adventure? On how many children was the survey conducted?

The bar graph shows the number of hours slept by 5 friends. Read the bar graph and answer the questions. y - axis

Total Number of Hours Slept

Scale: 1 division = 1 hour

Number of hours

8 7 6 5 4 3 2 1 0 a b c d

Rajat

Eric Nimisha Shoaib Friends

x - axis

Who slept the most number of hours?

Who slept the fewest number of hours?

How many more hours did Nimisha sleep than Rajat?

How many fewer hours did Raghav sleep than Shoaib?

Chapter 13 • Data Handling

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Raghav

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Word Problem 1

Students of class 3 were asked about their favourite subject. Their responses are listed below:

English, Hindi, Maths, GK, Maths, Hindi, English, Hindi, Maths, Maths, GK, GK, GK, Maths, Hindi, English, Maths, Hindi, Maths, English, GK, Hindi, Hindi, GK, GK, Maths, English, English, English, English, Maths, GK, Hindi, GK, Hindi Prepare a bar graph for the data and answer the questions. a b c d e

Which is the favourite subject among the students?

Which is the favourite subject among the least students? How many students like English? How many students like Math?

I s there any subject which is liked by an equal number of students? the students?

Points to Remember • Data is a collection of numbers gathered to give some information.

• Organisation of data means to collect the proper information from the data and arrange it in the proper format to make it more meaningful. • Pictographs represent the data in the form of pictures or objects. We can draw pictographs with the help of symbols or pictures.

• A bar graph is a graph or a chart with rectangular bars of different heights that represent the number value of each item. • Every bar graph must have: 1 2 3 4 5

A scale.

A title explaining the information in the graph. Horizontal and vertical axes. Labels explaining the axes.

Bars to show the data for each category.

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Math Lab Objective: To record and represent the data in a bar graph. Material required: Sheet of paper and pencil. Method: 1 2

Ask all the students of the class the means of transport they use to come to school. Note down the information in a table. Modes of Transportation Auto

Number of Students

Walk

Bicycle Bus

Car/Bike 3 4 5

Now take a grid and draw horizontal and vertical lines on it.

Mark all the modes of transportation on the horizontal axis and number of students on the vertical axis.

Cut strips from the origami sheets of appropriate heights and paste on the grid to represent the number of students taking the different modes of transportation.

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Chapter Checkup 1

he data given below shows the favourite fruit of the students in a class. Organise T the data in a table.

Orange, Apple, Litchi, Banana, Pomegranate, Pomegranate, Pomegranate, Orange, Orange, Apple, Litchi, Banana, Banana, Apple, Apple, Apple, Litchi, Litchi, Apple, Apple, Orange, Pomegranate, Pomegranate, Orange, Orange, Apple, Litchi, Litchi, Litchi, Pomegranate, Apple, Banana, Banana, Apple, Litchi, Orange, Orange, Apple, Pomegranate, Pomegranate, Banana, Banana, Apple, Banana, Litchi, Pomegranate 2

he table shows the number of different types of vehicles parked in a parking lot. T Look at the table and answer the questions. Vehicle

Number of Vehicles

Jeeps

Cars

Motorbikes

112

Buses

Scooters

How many jeeps are parked in the parking lot?

How many buses are parked in the parking lot?

Which type of vehicle is parked the most in the parking lot?

How many more motorbikes than scooters are parked in the parking lot?

avourite hobbies of 40 students of a class were noted. Create a pictograph for the F given data. Use = 1 student.



Singing, Dancing, Sports, Watching TV, Reading, Dancing, Singing, Singing, Sports, Sports, Watching TV, Watching TV, Watching TV, Dancing, Sports, Sports, Sports, Watching TV, Dancing, Dancing, Singing, Reading, Reading, Singing, Watching TV, Sports, Dancing, Dancing, Watching TV, Watching TV, Sports, Dancing, Singing, Reading, Reading, Watching TV, Singing, Dancing, Sports, Sports 4

ome children were asked about their favourite drink – tea, coffee, or milk. The S information is shown using a pictograph. Study the pictograph and answer the questions that follow.

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Drink

Number of Children

Tea Coffee Milk Key: a b c d

= 2 students

How many children like coffee?

Which drink is least liked?

How many children like tea?

How many more children like coffee than milk?

he table shows the marks scored by 7 students out of 10 marks in a test. Draw a bar T graph for the given information. Name

Raj

Marks Scored 6

Ronit 7

Zayn

Rhea

Venkatesh 8

Riddhi 6

Preeti 9

The bar graph shows the runs in the first 10 overs of a match. Study the bar graph and answer the questions that follow. 12 10

Runs

8 6 4 2 0 1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

Overs a b c d

How many runs were scored in the 5th over? How many runs were scored in the 7th over? In which over were the most runs scored?

How many runs were scored in all the overs?

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Word Problems 1

n inter-school cricket tournament was organised. The highest wicketA taking players were noted. The bar graph shows 4 players with the number of wickets they took. Answer the questions. 10 9

Number of wickets

8 7 6 5 4 3 2 1 0 a b c

Rohit

Sanjeev

Wasim Names

George

Which player took the most wickets?

How many more wickets did Rohit take than George?

id any two bowlers take the same number of wickets? If yes, then D how many?

hich bowler took the least number of wickets out of these 4 W bowlers and how many? Three farmers harvest tomatoes in their fields. The pictograph shows the number of tomatoes harvested. Read the pictograph and answer the questions. d

Name

Ramesh

Number of Tomatoes

Suresh Tarachand Key: a b c d

= 2 tomatoes

How many tomatoes did Ramesh harvest? How many tomatoes did Suresh harvest?

Who harvested the least number of tomatoes and how many?

How many more tomatoes did Suresh harvest than Tarachand?

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Imagine Mathematics

About This Book

MATHEMATICS

Singapore

IM_G03_MA_MB_Cover.indd All Pages

Gurugram

Bengaluru

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NEP 2020 based

NCF compliant

CBSE aligned

26/09/23 7:15 PM