Imagine_Maths_CB_Grade2_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 2

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Fo re wo rd

Mathematics is not just another subject. It is an integral part of our lives. It shapes the very foundation of our understanding, personality and interaction with the world around us. However, due to the subject’s abstract nature, the stress of achieving high academic scores and complex teaching methods, most children develop a fear of mathematics from an early age. This fear not only hinders their mathematical thinking, logical reasoning and general problem solving abilities, but also negatively impacts their performance in other academic subjects. This creates a learning gap which widens over the years. The NEP 2020 has distinctly recognised the value of mathematical thinking among young learners and the significance of fostering love for this subject by making its learning engaging and entertaining. Approaching maths with patience and relatable real-world examples can help nurture an inspiring relationship with the subject. It is in this spirit that Uolo has introduced the Imagine Mathematics product for elementary grades (1 to 8). This product’s key objective is to eliminate the fear of mathematics by making learning exciting, relatable and meaningful for children. This is achieved by making a clear connection between mathematical concepts and examples from daily life. This opens avenues for children to connect with and explore maths in pleasant, relatable, creative and fun ways. This product, as recommended by the NEP 2020 and the recent NCF draft, gives paramount importance to the development of computational and mathematical thinking, logical reasoning, problem solving and mathematical communication, with the help of carefully curated content and learning activities. Imagine Mathematics strongly positions itself on the curricular and pedagogical approach of the Gradual Release of Responsibility (GRR), which has been highly recommended by the NEP 2020, the latest NCF Draft and other international educational policies. In this approach, while learning any new mathematical concept, learners first receive sufficient modelling, and then are supported to solve problems in a guided manner before eventually taking complete control of the learning and application of the concept on their own. In addition, the book is technologically empowered and works in sync with a parallel digital world which contains immersive gamified experiences, video solutions and practice exercises among other things. Interactive exercises on the digital platform make learning experiential and help in concrete visualisation of abstract mathematical concepts. In Imagine Mathematics, we are striving to make high quality maths learning available for all children across the country. The product 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 h apt e r— a Q u i c k G lanc e

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. Th

4 Tens

8 Ones

2 Thousands 5 Hundreds

tiples

Let's Warm-up

Introductory

Concept

Write the correct place value of the coloured numbers.

page with a Find the first

introduction are multiples of .

multiples of . Check__________ by dividing if 2 and 1 32 ng holidays is always fun!quick You first decide on a place to visit, warm-up 2 548 you want__________ 1 2 esearch what you can do there, and then finally make arrangements. 3 876 __________ Do It Together

4563 s going to Ooty. The train departs every second day.

y Tuesday Wednesday

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

__________

6×1=6

6 × 2 = ____

6 × ____ = 24

6 × ____ = ____

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

Multiplication by 1-digit Number We know that the number obtained from multiplication is the product.

Add 12,344 and 1115.

A quick-thinking

21 question 22

6 × ____ = ____

Do It Together

What do you think do

TTh

even number?

Find the factors of 36 using the division method. What do we get?

Check the remainder

=31 ×

multiplicand

TTh

multiplier

36 ÷ 3

1= 2= 3= 4= 5=

3 6 9 12 15

____

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

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 = 369

123 × 3 = __ __9

123 × 3 = __69

Did You Know?

Rinne Tsujikubo of Japan broke The productthe of 123 and 3 is 369.world record for Guinness fastest mental arithmetic on Chapter 3 • Multiplication January 17, 2023 by correctly adding 15 sets of three-digit numbers in 1.62 seconds.

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The total number of fiction books = 1219 The total number of non-fiction books = 1567

Are the numbers factors of 36?

____

Let us multiply 123 and 3.

hat 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, Face Value Numbers Thinkinand Telltotal number =6-digit The of fiction books 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 ____

= 62

We can find the product of two numbers by placing them horizontally next to each other.

hat do we know?

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

Horizontal Method

Let us start finding the total number of books step by step.

n travel on the following dates - 2, 4, 6, 8, 10, 12, 14, 16 and so on. 6 92 Divide numbers by 36

to the concept

ing Multiples

n the school library, there are 121 fiction 9/11/2023 PM books and 1 4:24:58 non fiction books. How many books are there in total?

Are the multiples of an even number always an

Do It Together

Fun fact, related

Think and Tellhave in common?

Story Sums

all the circled numbers

Multiplication Rules

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

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

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2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 +2 + 2 + 2 + 2………

He has learnt 14 words already! Hurray! Sanju struggles to find how many words will he learn in whole January.

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

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

example

0 1 Friday 2 3 Thursday

9958

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. He starts adding quickly.

with a real life

__________

4 5

Understanding Multiplication Real Life Connect

The total number of books in the library

We learnt beyond about the concept of face value in the previous section. as the 2 7 It8is defined 6 6=to1219 find + 1567 numericalmore value ofofthe factors 36? digit on a particular place in a number. Solve to find the answer.

out 36 ÷ 5 7 1 ____ For example, the Pincode on Ajay’s 3 × 6 = An 18important So,Pointing the total number of books in the library is 2786. ____ 0 Yes letter was 781005. The face value of It Yourself 5A 36 ÷ 6 keep in commonly made 3 × 7 = point 21 toDo Error Alert! The city organised a two day donation drive. the Lakhs place nisthe simply 7.of the drive, 13 clothes were Remember! Remember! first day So, the factors of 36 are ___________________________________________________________________. 3 × 8 = mind 24 mistakes and When we add 1000 to a collected. n the second day of the drive, 1000 Never confuse Face Value with Place Value! For A number is a multiple of itself too. Similarly, we say that the face value of 4-digit number, only the clothes were collected. How many clothes were 3 × 9 = 1 27Colour the balloons that are multiples of 2. howinto avoid example, in 781005, the Value of the Lakhs digit Face in the thousands For example, multiples of 5 are 5, total? the digit on thecollected Ten Thousands place place changes. place is 7 and the Place Value is 7 × 100000 = 700000. Do15, It Yourself 3 × 10 = 30 10, 20, 25,5C 30 and so on! them 4

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

Example 4

a 11

To the nearest 100s

b 4589 ÷ 3 c

is 8.

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

e 5555 ÷ 5

What do we know?

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 people. About how many tables are needed?

[Round off the dividend to the nearest hundred]. Number of clothes collected duringin thethe second day ofplace the drivein = 1000 What is the face value of the number lakhs 348673? Show 18 in different arrangements. Then, list the factors of 18.

2 n also check if a number is a multiple of a number using division. If the remainder Word Problems What do we need to find? Show 20 in different arrangements. Then, list the factors of 20. We know that face value is the numerical value of the digit in a particular place. Let us hen the bigger number is a multiple of the other3number. For example: Example 6

ves no remainder

15 – 15 00

3 11

1 238 children went to a school camp. If one tent can be shared by 4 children, number of clothes collected = 1366 + 1000 Find the factors of the following numbers using multiplication. write the placeTotal value chart for 348673:

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

c 36

19 L

g 48

h 50

20 30 TTh

approximately how many tents will be needed for the camp?

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

Estimate the amount of money that each student gets.

Points to Remember HOTS: end Is 18 a factor of 126? Explain your answer. 6 The face value ofChapter the number in the Lakhs place is 3. viding 15 by 5, we get 0 remainder. On dividing 16 by 5, we get remainder 1. Is of 6 a the factorgiven of 64? Explain your answer. 7 Find the first five multiples numbers. 2 • The number being divided is called the dividend. The number by which we divide is Applicative summary called the divisor. The result of the division is called the quotient. The number left over Do It is a multiple of 5. So, 16 8is not multiple 5.10 have exactly TWO factors? Which a numbers betweenof 1 and Thousands division is called the place remainder. in 800234? a 7 b 8 c 9 dTogether e 11value of the number in the after 10 What is the face and analytical • To check if our answer after division is correct, we can use: Dividend = (Quotient × UM24CB_G4.indb 30

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

h 14

Points to Remember m

Word Problems

place value chart for 800234: j 16 15 Let us write the

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.

________

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. • • •

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________

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.

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

________

thousands place form the remainder and the remaining digits form the quotient.

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

Representing 6-digit Numbers

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.

Chapter 4 • Division

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Place value Scavenger Hunt:

to interactive

Materials Required: Newspapers, Magazines, or the Internet

For 6-digit numbers, the Lakhs place falls in the Lakhs Period.

Setting: Groups of 4

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

Divide the entire class into groups of 4.

classroom

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

Lakhs Period

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.

Lakhs

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

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

Place value and face value of each digit.

Thousands Period Ten Thousands (TTh)

Ones Period

Thousands (Th)

Hundreds (H)

Tens (T)

Ones (O)

We can therefore represent our 6-digit number 781005 as:

orrect num er re resenta on. orrectly wri en num er names.

Lakhs Period

Correctly order the numbers in ascending and descending order ound o the num ers to the nearest 10s, 100s and 1000s.

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We learnt that the Thousands period includes Ten Thousands and Thousands places. The QR Code: Access Ones period includes the Hundreds, Tens and Ones places.

Chapter 1 • Numbers up to 6-digits

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7,81,005

Thousands Period

Ones Period

iii 9

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The face value of the number in the thousands place is _________. • When a number is divided by 1000, the digits in the ones place, tens place and

ways can she arrange the eggs?

Math Lab

multidisciplinary and fun

________

Let us continue to learn about the4:26:03 “periods” convention for large numbers. 9/11/2023 PM

o TTh 25

Divisor) + Remainder.

•

  

k 17

g 13

  

f 12 questions

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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 multiples of . 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

1 3 4 3 5 Find the first multiples of . Check by dividing whether 1

Did You Know?

is a multiple of . The number 4 is the 5 only number with the same number of letters as its value in the English language.

Always remember that place value is the value of the digit in a number based on 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 player chooses multiple that Also, find the lowest and the highest 3 Find factors ofathe pairsnumbers of of numbers. 3 Find the thecommon factors of the following using multiplication. 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

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C o nt e nt s

1 2 3 4 5

Numbers up to 200 ............................ 1

Addition of 2-digit Numbers .......... 21

Subtraction of 2-digit Numbers ..... 38

• Understanding Numbers up to 200 • More Types of Numbers

• Adding 2−digit Numbers

• Subtracting 2-digit Numbers

• Understanding Multiplication

Multiplication Tables 2, 5 and 10 ............................................... 70

Numbers up to 999 .......................... 87

Addition and Subtraction of 3-digit Numbers ............................. 105

Multiplication Tables 3, 4 and 6 ... 124

• Understanding Numbers up to 999 • Comparing and Ordering Numbers

• Operations on 3-digit numbers • When to add? When to subtract?

Multiplication ................................... 56

• Multiplication Tables

2 11

• Multiplication Tables • Multiplying 2-digit Numbers

88 96

106 115

125 133

Introduction to Division ............... 144

• Understanding Division • How to Divide

145 158

Understanding Fractions .............. 166

• Understanding Fractions

167

Measurement ................................. 178

• Length • Weight • Capacity

179 188 194

Shapes and Patterns ..................... 204

• All About Lines • All About Shapes • Patterns Around Us

205 207 215

Time ................................................ 224

• Reading Time on a Clock • Reading The Calendar • Story Problems on Time

225 229 237

Money ............................................. 244

• Indian Currency • Operations on Money

245 248

Data Handling ................................ 257

• Understanding Data

258

Answers ..................................................... 274

Numbers up to 200

Let's Recall We use numbers to count. This is 1 ladyfinger.

These are 2 pears.

These are 3 cabbages.

These are 4 cauliflowers.

These are 5 tomatoes.

These are 6 apples.

These are 7 bananas.

These are 8 capsicums.

These are 9 onions.

Let's Warm-up

Match the following balls with the right number. 1

5 I scored _________ out of 5.

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Understanding Numbers up to 200 Real Life Connect

Soham’s father bought 10 boxes of sweets for a festival. There are 10 sweets in each box. He asked Soham to count all the sweets. There are 100 sweets in all the boxes.

Correct!

In the evening, some more boxes with 10 sweets in each were added. “Let’s count all the sweets now!” said the father. Soham could easily count up to 100. This was more than 100! How would he count now?

Introducing 3-digit Numbers Let us help Soham count numbers greater than 100. 1 sweet

1 ones

= 1 box with 10 sweets

1 is a 1-digit number. =

10 ones

1 tens

10 boxes with 10 sweets in each.

10 is a 2-digit number.

10 tens

1 hundred or 100 100 is a 3-digit number.

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Think and Tell There are 20 boxes with 10 sweets in each. How many tens does it have? How many hundreds?

Remember! 2-digit numbers end with 99. 3-digit numbers start from 100.

Building Numbers up to 200 This chart shows numbers greater than 100! Up to 200! The table shows numbers 101 to 200. We can count forward from number 101 to 200. We can also write numbers by counting backwards. Counting Forward: 113, 114, 115, 116, 117

Counting Backwards: 140, 139, 138, 137, 136 Let us take another example:

Counting Forward: 161, 162, 163, 164, 165

Counting Backwards: 198, 197, 196, 195, 194

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

Let’s build some of these numbers with place value blocks. 102 – one hundred two Hundred

Tens

Ones

Hundred

Tens

Ones

Chapter 1 • Numbers up to 200

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115 – one hundred fifteen

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134 – one hundred thirty-four

153 – one hundred fifty-three

Hundred

Tens

Ones

Hundred

Tens

Ones

178 – one hundred seventy-eight

Example 1

200 – two hundred

Hundred

Tens

Ones

Hundred

Tens

Ones

Count the hundreds, tens and ones shown by the blocks. Write the number and the number's name. Hundred

Tens

Ones

The number's name will be one hundred thirty-three. Do It Together

Write down the numbers and the number name. Hundred

Tens

Ones

Number Name

______

One hundred fourteen

______

_____________

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Error Alert! Proper way of writing number names: 167: one six seven

167: one hundred sixty-seven

Place Value and Expanded Form Let us learn to read the place value of the digits in a 3-digit number. Let’s take 123 as an example. 123 = Hundred

Tens

Ones

1 is at the HUNDRED’S place. The place value of 1 is 100.

3 is at the ONE’S place. The place value of 3 is 3.

2 is at the TEN’S place. The place value of 2 is 20.

Here is another way to write 123:

123 = 1 hundred + 2 tens + 3 ones = 100 + 20 + 3.

This is known as the expanded form of the number. Example 2

Write the place value of the digits in 154. Also, write its expanded form. H 1

Do It Together

T 5

O 4

100 50

Expanded form of 154: 154 = 100 + 50 + 4.

Write the place value of the digits in 196. Also, write its expanded form. H 1

Chapter 1 • Numbers up to 200

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T 9

O 6

____ ____ 100

Expanded form of 196: 196 = _____ + 90 + _____. 5

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Do It Yourself 1A 1

Complete the tables by writing the missing numbers. a

111

113

116

151

153

155

158

191

193

195

198

189

187

185

Write the numbers for the number names. a

one hundred forty-three

one hundred sixty-one

one hundred eleven

one hundred ninety-seven

one hundred eighty-six

Write down the place value of the red digits in the numbers. 132

114

123

156

155

198

The expanded form of the numbers are given. Write down the numbers. One is done for you. a

100 + 30 + 8 = 138

100 + 00 + 4

100 + 90 + 2

100 + 50 + 2

100 + 40 + 6

100 + 40 + 9

How many more tens should we add to 132 to get 152? Draw tens and ones to show. Use for 1 ten (T), and

180

Read the blocks. Write the numbers.

200

183

118 119

for 1 one (O).

How many tens and ones need to be added to 140 to make the number 165? Draw to show the tens and the ones. Use for 1 ten (T), and

for 1 one (O).

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Comparing and Ordering Numbers Suppose Soham had 8 boxes with 10 sweets in each.

8 tens = 80 His sister had 10 boxes with 10 sweets in each.

10 tens = 100 Who would have more sweets? More or less: To know this, we need to know which total is more—80 or 100. 80

100

Tens

Ones

Hundreds

Tens

Ones

3-digit numbers are always more than 2-digit numbers. So, 100 is greater than 80: 100 > 80. We can also say that 80 is less than 100: 80 < 100.

Chapter 1 • Numbers up to 200

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Remember! We use the signs < and > to show less than and more than. The alligator always opens its mouth towards the greater number.

100 > 80

80 < 100

Greater than or more than

Less than or smaller than

Let us compare more numbers. Which number is greater—183 or 167?

H 1

O 7

1. Compare the hundreds. 183 has 1 hundreds. 167 has 1 hundreds. Since the hundreds are the same, compare the tens. 2. Compare the tens. In 183, there are 8 tens. In 167, there are 6 tens. 8 tens > 6 tens or 80 > 60.

So, 183 is more than 167. We can write this as 183 > 167.

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Which number is smaller—125 or 129?

O 9

Compare the hundreds. Both numbers have 1 hundreds. Since the hundreds are the same, compare the tens. 2 Compare the tens. Both numbers have 2 tens. Since the tens are the same, compare the ones. 1

Compare the ones. In 125, there are 5 ones. In 129, there are 9 ones. 5 ones < 9 ones or 5 < 9.

So, 125 is less than 129. We can also say 129 is more than 125.

Did You Know? When two numbers are the same, we use = sign Example: 187 = 187

We can write this as: 125 < 129 or 129 > 125. Before and After: Look at the number line below:

124

125

126

127

128

129

130

131

127 comes before 128 and 129 comes after 128. Using more or less than signs, we can write these numbers as: 127 < 128 < 129 or 129 > 128 > 127. Chapter 1 • Numbers up to 200

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Increasing and Decreasing Order In increasing order, we write the numbers starting with the smaller number. We move to greater numbers.

The numbers on the number line in increasing order are: 124, 125, 126, 127, 128, 129, 130, 131. In decreasing order, we write the numbers starting with the greater number. We move to smaller numbers. The numbers on the number line in decreasing order are: 131, 130, 129, 128, 127, 126, 125, 124. Example 3

Which of these numbers come before 150 — 175, 108, 132, 124, 103, 162? Let’s check these numbers on the number chart. 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130

103, 108, 124 and 132 come before 150.

Less

101 102 103 104 105 106 107 108 109 110

131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

Example 4

Which of these numbers come after 113 — 105, 200, 124, 143, 156? Let’s check these numbers on the number chart given above. 124, 143, 156 and 200 come after 113.

Do It Together

Write these numbers in increasing and decreasing order – 123, 143, 111, 132, 109. Increasing Order

Decreasing Order

109, _______, _______, 132, _______

143, _______, _______, 111, _______

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Do It Yourself 1B 1

Circle the box with the greater number. a

122

100

166

110

101

198

189

123

143

133

193

132

136

123

143

102

129

_______199

179 _______

Which number comes before the given number? _______ 123

_______ 134

Which number comes after the given number? a

Which number is greater? Which one is smaller? Are they equal? Use <, >, or = signs to show.

112 _______

100 _______

129

Arrange these numbers in increasing and decreasing order. a

123, 114, 109, 154, 134

112, 110, 119, 117, 118

73, 100, 99, 101, 111

100, 187, 119, 111, 99

Write if True or False. a

156 is less than 165.

___________

107 and 170 are equal numbers.

___________

These numbers are in decreasing order: 132, 128, 120, 112, 110

___________

These numbers are in increasing order: 111, 108, 109, 104, 100

___________

More Types of Numbers Real Life Connect

Four friends are in a sack race on sports day. Tina is watching them.

Tina is confused. Who is winning this race? Chapter 1 • Numbers up to 200

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Ordinal Numbers Let's help Tina. We need to mark the position of each friend in the race.

first (1st) second (2nd) third (3rd) fourth (4th)

First, second, third and fourth tells us the position of each friend. These numbers are known as ordinal numbers. The ordinal numbers up to 10 are:

Example 5

first

second

third

fourth

fifth

sixth

1st

2nd

3rd

4th

5th

6th

seventh eighth 7th

8th

ninth

tenth

9th

10th

Three students are in a lunch line. Circle the first and the third student.

Did You Know? The numbers used for counting—1, 2, 3, and so on are called cardinal numbers.

first (1st)

third (3rd)

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Do It Together

Read the letters. Answer the questions. B

Which is the 1st letter?

Which is the 3rd letter?

______

Which is the 5th letter?

Is there a 10th letter here?

______

Do It Yourself 1C 1

Colour the sixth pot. The first pot is marked for you.

First 2

Circle the 4th bird from the left.

Rohan lives in the 1st (purple) house on the street. His friend Raman lives in the 5th house. Circle Raman’s house.

1st Chapter 1 • Numbers up to 200

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3rd 13

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Fill in the blanks to show the positions of the things given. rose

apple

grapes

sunflower

mango

carrot

brinjal

first

The grapes are in the ___________ position.

The ___________ is in the 5th position.

The apple is in the ___________ position.

The sunflower is in the ___________ position.

Read the text. Colour the boxes accordingly. The first box is coloured red. a

Colour the 3rd and the 10th box yellow.

Colour the 6th and 8th box green.

Colour the 7th and 9th box pink.

Meena is standing 5th in a line. Soham is the last person in the line. Tina is standing between Meena and Soham. What is Tina’s position in the line?

Odd and Even Numbers Tina's four friends took part in a sack race yesterday. Today, they are practising for the pair race. Everyone has a partner. They are even in number.

Tina also wants to join, but she does not have a partner. She is the odd one out.

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Let us learn what odd and even numbers are. There are 6 leaves. We can put all these leaves in twos or pairs. So, 6 is an even number.

Pair 1

Pair 2

Pair 3

In even numbers, the objects will always be in twos or pairs. Now, let’s take 7 leaves. Check if we can pair them.

Pair 1

Pair 2

One leaf is left out. So, 7 is an odd number.

Not in Pair

Pair 3

In odd numbers, only one object will not be in a pair. Example 6

Think and Tell

There are 5 candies. Are they an odd or even in number?

If we add two odd numbers. Do we get an odd number or an even number?

One candy is not in a pair. So, 5 is an odd number. Example 7

There are 6 pencils. Is 6 an even or an odd number?

All the pencils are in pairs. So, 6 is an even number. Do It Together

Circle the balls for each number to make a pair. If one is left, cross it ( ). 1

Chapter 1 • Numbers up to 200

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Write the numbers where all the balls are in pairs. Write the numbers where one ball is not in a pair.

2, _____, 6, _____, _____ _____, _____, 5, _____, 9

All of these are even numbers. All of these are odd numbers.

Do It Yourself 1D 1

Circle the objects in pairs. Write if they are odd or even.

Circle the box with an even number of objects.

Write if True or False. a b c d

Odd/Even

Sonam has 6 kites. She can form 3 pairs.

Mohan has 5 apples. He can form 4 pairs.

Riya has 3 mugs. She has an odd number of mugs. Jiya has 8 pens. She has an even number of pens.

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Draw an even number of 3 pairs of circles and an odd number of 9 triangles.

Rupa has 6 mangoes. a

How many pairs can she make from them?

How many more pairs of mangoes does she need to make 10 mangoes?

Points to Remember •

10 tens make one hundred or 100.

•

A 3-digit number is always more than a 2-digit number.

• • • •

123 is a number and 1, 2, 3 are the digits.

Ordinal numbers are used to show the positions of an object in a line.

An even number of objects will always be in pairs. 2, 4, 6, 8, 10 are even numbers.

In an odd number of objects, one object is always left without a pair. 1, 3, 5, 7, 9 are odd numbers.

Math Lab Setting: In groups of 4.

What’s my position!

Materials Required: 1 set of 10 objects in each group. Method: 1 2 3 4 5

In your group, collect any 10 objects from your pencil boxes and bags. One member will arrange these objects in a line.

The same member will ask the position or the name of the object: For example, in what position is the pencil? What is in the fifth position in line? The other members will point to the object or the position of the called-out object.

Take turns in your group. The next member will rearrange the objects in a line and repeat the activity.

Chapter 1 • Numbers up to 200

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Chapter Checkup 1

Fill in the blanks with the missing numbers. a

101 ____ 103 ____ 105 ____ ____ 108

162 ____ ____ 165 166 ____ ____ 169

____ 181 ____ ____ ____ 185 ____ 187

147 ____149 ____ 151 ____ 153 ____ 155

Fill in the blanks. a

1 hundred + 5 tens + 6 ones = _____.

_____ hundred + 7 tens + 5 ones = 175.

1 hundred + _____ tens + 0 ones = 190.

1 hundred + 3 tens + 4 ones = _____.

Match the blocks with the correct numbers they make. 128

161

136

130

Complete the table. Before a

Between

123

After 125

198

b c

112

134

114 135

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Circle the greatest number. a c

154 176

143 154

If 2 tens blocks are taken away, what is the remaining number?

Write the numbers with the help of the place value. H

134 120

100

Write the expanded form of the given numbers. b f

187 167

c g

122 176

d h

199 103

Write if True or False. a

156 is written as one hundred five six.

167 is written as one hundred sixty-seven.

100 + 30 + 9 = 139

There are 2 tens in 132.

Match the children correctly with their position. One has been done for you. START

1st

5th Chapter 1 • Numbers up to 200

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195 123

What number do they make?

134 198

142 132

There are 1 hundred, 7 tens, and 9 ones blocks.

133 184

3rd

4th

1st

2nd 19

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Match the pictures correctly with even or odd. One is done for you.

Even

Odd

A building has five floors. Rohan lives on the 5th floor. Juhi lives on the floor above Riya. Riya lives on the 2nd floor. On which floor does Juhi live?

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n ers

Let's Recall We use numbers to tell how many. These are 4 apples. These are 5 bananas. Now what if we put these apples and bananas together? Let us put them together and count!

So, 4 apples and 5 bananas together are 9! This is called addition. 4+5=9 When items are together, we use addition to find the total.

Let's Warm-up

Match the following. 1

2+3

4+0

8+1

5+2

4+4

I scored _________ out of 5.

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Adding 2−digit Numbers Real Life Connect

Seema: Hi Meena, I have 15 colour pencils in my colour box.

Meena: I have 13 crayons in my colour box.

Seema: Let's find out how many we have altogether. Meena: But I do not know how to count numbers using my fingers. Do you?

Addition Without Regrouping Meena and Seema were unable to add numbers using their fingers. Let us help them! Let us show the number of colours using the place value blocks.

Remember!

1 ten =

1 one =

Seema has 15 colour pencils. 15 can be written as: +

1 ten

5 ones

Meena has 13 crayons. 13 can be written as: =

1 ten

3 ones

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Now, let us add 15 and 13 using the place value blocks. Step 1 Draw the place value blocks. Tens

Step 2 We add the ones. 15 + 13 Tens

Ones

15 colour pencils with Seema

+ 13 crayons

with Meena

8 ones Step 3 We add the tens. 15 + 13 Tens

Step 4 The tens and ones gives us the answer. Ones

15 colour pencils with Seema

2 tens + 8 ones = 28

+ 13 crayons

The sum of 15 and 13 is 28.

with Meena

Remember! 2 tens

8 ones

Chapter 2 • Addition of 2-digit Numbers

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When we add numbers, the result is always known as the sum of the numbers. Example: 12 +12 = 24 The sum of 12 and 12 is 24. 23

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Vertical Method We can add numbers by writing them one below the other. Adding 23 and 32. Step 1 Add the ones.

Step 2 Add the tens.

Tens Ones +

Example 1

2 3

Tens Ones

Add 34 and 25. 3

The sum of 34 and 25 is 59.

Step 3 Write the answer.

Do It Together

23 + 32 = 55.

Find the sum.

Remember!

42 and 23 Tens Ones +

_____ _____

_____ 5

When we add 0 to any number, there is no change in that number. Example: 12 + 0 = 12.

The answer is ____________.

Horizontal Method Let us add 2 numbers by writing them side by side. Add 24 and 35. Step 1

Step 2

Add the ones. 24 + 35

Add the tens. 24 + 35 Tens Ones 9

Tens Ones 5

So, 24 + 35 = 59 24

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Example 2

Do It Together

Add 42 and 32 by writing the numbers side by side. Tens

Ones

42 + 32 = 74

Add. 34 + 42 = 7____

Do It Yourself 2A 1

Complete the additions with the help of place value blocks.

Add 24 and 52

= ____ tens ____ ones = ____

Add 41 and 60

= ____ tens ____ ones = ____

Add 32 and 24

= ____ tens ____ ones = ____

Solve the following.

__________ + __________ = __________ 3

Find the sum. a

+ d

Tens Ones 2 0 1 3

32 + 42

Chapter 2 • Addition of 2-digit Numbers

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+ e

72 + 21

__________ + __________ = __________ Tens Ones 2 2 2 3

+ f

Tens Ones 2 8 1 1

24 + 53 25

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What needs to be added to 20 to get 39? Draw.

Circle the sums with the correct answer. C a

34 + 12 = 46

33 + 14 = 87

72 + 22 = 50

34 + 21 = 55

14 + 13 = 21

56 + 21 = 77

Addition With Regrouping Remember Seema had 15 colour pencils. + 1 Ten

Her friend Tina gave her 5 more colour pencils. =

= 5 Ones

5 Ones

15 colour pencils

5 colour pencils

How many crayons does Seema have now? Let’s add and find out. Step 1 Draw the place value blocks. Tens

Ones

Step 2 We first add the ones. Tens

Ones

Here, we get 5 + 5 = 10 ones.

10 ones make one ten.

So, we change the 10 ones to 1 ten.

10 Ones 26

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Step 3 Move the 1 ten to the tens place. Tens

Ones

Step 4 Now add the tens. Tens

Ones

We get 2 tens and 0 ones.

There are 0 ones.

2 tens = 20

So we write 0 in the ones place.

The sum of 15 and 5 is 20.

So, 15 + 5 = 20. Addition With Regrouping 10 Let us understand how to add two 2-digit numbers by regrouping. Adding 25 and 15. Step 1: Add the ones. Step 2: Write 0 in the 5 ones + 5 ones = 10 ones ones place. Move 1 10 ones = 1 ten + 0 ones ten to the tens place.

Step 3: Add the tens. 2 tens + 1 ten + 1 carry over ten = 4 tens. Write 4 in the tens place.

Tens

Ones

Tens

Ones

Tens

Ones

So, the sum of 25 and 15 is 40. Example 3

Find the sum of 29 and 41. Tens

Ones

Chapter 2 • Addition of 2-digit Numbers

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The sum of 29 and 41 is 70. 27

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Do It Together

Add 48 and 22. Tens

Ones

_____

_____ +

The sum of 48 and 22 is ___________. Regrouping to More than 10 Here, we are going to look at sums where we always get more than 10 by adding the digits in the ones place. Let’s add 15 and 26. Step 1: Add the ones. Step 2: Write 1 in the ones Step 3: Add the tens. 5 ones + 6 ones = 11 ones place. Move 1 ten to the 1 ten + 2 tens + 1 carry over ten = 4 tens. 10 ones = 1 ten + 1 ones tens place. Write 4 in the tens place. Tens Ones +

1 2

Tens Ones

5 6

1 2

5 6

Tens Ones 11 = 1 ten + 1 one

So, the sum of 15 and 26 is 41. Example 4

28 + 9.

Error Alert! Tens 1

Ones

25 + 35 510

1 25 + 35 60

In regrouping we always shift the 10 ones from the ones place to the tens place as 1 ten.

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Do It Together

Add 16 and 26. Tens

Ones

____

Think and Tell When adding 2 numbers can we ever regroup 2 tens?

Do It Yourself 2B 1

Solve the sums by regrouping 10. Tens Ones

Tens Ones +

Tens Ones

3 9

Tens Ones

Circle the correct answer. a

25 + 45 =

23 + 19 =

35 + 15 =

34 + 27 =

Add the numbers by writing them one below the other. a

21 + 9

59 + 19

35 + 15

21 + 19

58 + 17

35 + 48

Pot A has 13 flowers and Pot B has 17 flowers. How many tens do you need to add to get the answer?

Chapter 2 • Addition of 2-digit Numbers

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Tens Ones

Solve the sums by regrouping to more than 10. a

Tens Ones

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Adding More than 2 Numbers Sam used 8 colour pencils for her drawing. Rina used 4 colour pencils and Tina used 6 colour pencils. How many colour pencils did they use in altogether? To find this, we have to add the three numbers. Let us see how: Step 1 Write the numbers one below the other.

8 ones

Rina

4 ones

Tina

6 ones

Step 2 Add any two numbers first.

8 4

Sam

8 +

Step 3 Then, add the third number to the sum of the first two numbers. 8

8 + 4 = 12

12 + 6

So, 8 + 4 + 6 = 18. Let us now find the sum of 8, 4, and 6 using the number line. Step 1

Always start from the 1st number. Here it is 8.

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

Step 2

Then jump 4 steps. Because we want to add 4 to 8. We reach 12.

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

Step 3

Now jump 6 steps. Because we want to add 6 to 12. We reach 18.

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

We get the same result! 8 + 4 + 6 = 18. 30

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These were three 1 digit numbers. Let us now learn how to add three 2-digit numbers. How do we find this? Add 12, 15, and 25. Step 1

Write the numbers one below the other.

Tens

Ones

Tens Ones

+ +

Step 3

Tens

Ones

2 5 5 2

Think and Tell What comes in the ones place if we add 34 and 16?

So 12 + 15 + 25 = 52 Example 5

1 1 1 2

We get 12 in the ones place. 12 = 1 ten and 2 ones We write only 2 in the ones place. 1 ten is moved to the tens place.

Add the tens.

Add the ones.

Step 2

Add 3, 4, 6 using a number line. Step 1 Always start from the 1st number. Here it is 3. Step 3 From 7, jump 6 steps to the right. We reach 13.

Step 2 Then jump 4 steps to the right. We reach 7.

3+4

7+6

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

So, 3 + 4 + 6 = 13. Chapter 2 • Addition of 2-digit Numbers

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Example 6

Find the sum.

Remember!

Tens Ones

To check if the answer is correct, we can change the order of the numbers and find the sum again. If the sum is the same, then our answer is correct. 15 + 12 + 12 = 39 12 + 12 + 15 = 39 12 + 15 + 12 = 39 In all the cases the sum is equal to 39.

Do It Together

Add 2, 8, 5 using the number line and the vertical method. Check if the answer is same. +8 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2 + 8 + 5 = ________

8 + 5 + 2 = ________

___

5 + 8 + 2 = ________

___

Are all the answers same? Yes/No

Do It Yourself 2C 1

Add the numbers using the number line. a

3+2+4

1+3+8

2+2+4

1+2+5

5+5+1

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

Fill in the blanks. a

3 + 2 + 1 = ______

4 + 4 + ______ = 9

6 + 6 + 1 = ______

2 + 2 + ______ = 6

2 + 3 + ______ = 10

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Find the sum.

Tens Ones

31 + 45 + 24

31 + 21 + 11

Tens Ones

41 + 21 + 11

How much do we add to 5 and 2 to get 10? ________________

T There are 20 books on a shelf. How many more books do you need to add to get 50 books? ________________

Story Sums We can use the CUBES method to solve story sums. In the CUBES method, we follow the 5 given steps . C

Circle the Numbers

Underline the Question S

Evaluate/Draw

E Underline the Question

Box the Key Words

Solve and Check!

Rina and Geeta went to buy apples. Rina bought 18 apples. Geeta bought 15 apples. How many apples did they buy in total? Box the Key Words Circle the Numbers

Apples Rina bought = 18 Apples Geeta bought = 15

Evaluate/ Draw

Total number of apples = 18 + 15 Tens

1 1 1 3

Ones 8 5 3

Solve

Rina and Geeta have 33 apples in total.

Chapter 2 • Addition of 2-digit Numbers

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Example 7

Class 1 has 35 students. Class 2 has 30 students, and Class 3 has 25 students. How many students are there in total? Let us use the CUBES method to solve this problem. C

Circle the Numbers E

Underline the Question

Evaluate/Draw

Box the Key Words

Solve and Check!

Circle the numbers.

Class 1 has 35 students. Class 2 has 30 students, and Class 3 has 25 students. How many students are there in total? Box the Key Words

Evaluate

Underline the question.

Total number of students = Students in class 1 + Students in class 2 + Students in class 3 = 35 + 30 + 25 Solve Tens Ones 1

+ +

Do It Together

3 9

0 0

There are 90 students in total.

Rohan solved 15 sums on Monday, 23 sums on Tuesday, and 17 sums on Wednesday. How many sums did he solve in total? Solve using the CUBES strategy. Evaluate:

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Tens Ones + + + Rohan solved __________ sums in total.

Do It Yourself 2D 1

Riya bought 24 candies and her friend Aryan gave her 37 more candies. How many candies does Riya have now?

A balloon seller has 56 red balloons, 21 blue balloons and 12 green balloons. How many balloons are there in total?

In a garden, there are 48 red roses, 32 yellow roses and 17 white roses. How many roses are there in the garden?

Arun has 42 stickers and his friend Arjun gives him 26 more stickers. How many stickers does Arun have in total? Check your answer.

In a grocery store, there are 42 mangoes on one shelf and 39 more mangoes on another shelf. How many mangoes are there in total? Check your answer.

Esha has 7 toy cars and her friend Alim has 5 more than Esha. How many toy cars do they have in total? Check your answer.

Points to Remember •

Addition is when we put numbers together to find the total.

•

We use the “+” sign to show that we are adding numbers.

•

When we add, we start with the ones place and then move to the tens place.

•

If we add 0 to a number, it doesn’t change the number.

•

If we change the order of the numbers we are adding, the sum does not change.

Chapter 2 • Addition of 2-digit Numbers

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Math Lab Race to 100! Setting: In groups of 4

Materials Needed: • Printed copies of number grid 1−100 (1 per group) • Small tokens, coins or stones (1 per player) • Deck of number cards of 1-10 (1 deck per group) Method:

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Set up the game:

81 82 83 84 85 86 87 88 89 90

Divide into small groups.

Give each group a game board, game markers, and a deck of cards.

91 92 93 94 95 96 97 98 99 100

How to play: 1

Players take turns to draw two cards from the deck.

Add the two numbers together to find the sum.

Move your token forward by that many spaces on the game board.

If you get the sum wrong, stay in your current position.

Win the game: 1

The first player to reach 100 wins!

Chapter Checkup 1

Using a number line, add the given numbers. a

8+2

7+5+2

12 + 5

16 + 3 + 5

7+3+2

Add the numbers by drawing place value blocks. a

13 + 21

18 + 2

24 + 35

26 + 14

32 + 19

18 + 0 + 27

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Solve the given questions using the vertical method.

Tens Ones

Add the numbers horizontally.

Tens Ones

26 + 13

Tens Ones

48 + 22

57 + 38

Circle the correct answer.

23 + 42

12 + 11

32 + 25

62 + 14

Rohan had 23 marbles and his friend Soham gave him 46 more marbles. How many marbles does Rohan have now?

A fruit vendor has 28 apples, 41 oranges and 29 bananas. How many items of fruit does the vendor have in total?

Rani sold 15 bangles on Monday, 12 bangles on Tuesday and 10 bangles on Wednesday. How many bangles did she sell in total?

Seema added 3 tens and 2 ones to 4 tens and 5 ones. How much did she get?

What number will you get if you add the smallest 2-digit number to a dozen?

Word Problems 1

Mohan went to a bookstore. He bought 5 books for himself, 6 books for his sister and

There were 13 mangoes on a tree on Monday. On Tuesday there were 16 more

7 books for his brother. How many books did he buy altogether?

mangoes, and on Wednesday there were 18 more mangoes. How many mangoes were there in total?

Chapter 2 • Addition of 2-digit Numbers

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Subtraction of 2-digit Numbers

Let's Recall Let us say we have 9 candies. If we give 4 candies to a friend, how many candies do we have left? We learnt that we use subtraction when items are taken away. So here, we are giving the candies away to a friend. We will use subtraction to find how many candies we have left. We jumped forward in addition. In subtraction, we jump backwards. We had 9 candies, so we start from 9. To subtract 4, we will take 4 backward jumps from 9. We will reach 5. So we are left with 5 candies! 9 candies – 4 candies = 5 candies –

9 Candies

Take away 4

3 =

9 candies minus 4 candies is equal to 5 candies: 9 – 4 = 5

Fill in the blanks. 5 pots

= _________ pots left 6 apples

– 1 pot broken

= _________ apples left

–

2 apples

5 Candies left

We can also write this as:

Let's Warm-up

9 – 4 5

Subtract and match. 7–1

5–5

2–0

I scored ___________ out of 5.

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Subtracting 2-digit Numbers Real Life Connect

Sara loves to read books. Sara is reading a book on planets. There are 56 pages in the book. Sara has finished reading 12 pages. How many are left?

Subtracting by 2-digit Numbers Let us help Sara find out how many pages are left. Here we see the pages are decreasing in number. So, we have to subtract. Subtraction Without Regrouping Let us subtract 12 pages from 56 pages. 1 page = 1 one =

10 pages = 1 ten =

Steps Write down the numbers 56 and 12 according to their place value.

Start with the ones place. We have 6 ones in the ones place. We take away 2 ones.

Subtract the tens place. We have 5 tens in the tens place. We take away 1 ten.

Chapter 3 • Subtraction of 2-digit Numbers

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Explanation

–

Tens

Ones

Write the big number on top and small number below during subtraction.

Tens

Ones

We are left with 4 ones in the ones place.

Tens

Ones

5 4

We are left with 4 tens in the tens place.

6 4

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So, 56 – 12 = 44. 44 pages are left for Sara to read. The next day Sara read only 3 pages. How many are left now? We subtract 3 from 44 pages. Steps

Write the number according to the place value.

Subtract the ones place. We have 4 ones. We take away 3 ones.

Subtract the tens place. We have 4 tens only and 0. So, 4 tens remain in tens place.

Explanation

–

Tens

Ones

Tens

Ones

There is 1 one in the ones place.

Ones

3 is in ones place. When there is nothing in tens place. It is 0.

Tens 4

Write 44 in tens and ones place.

The number of tens remain the same.

4 1

So, 44 – 3 is 41. Now, 41 pages are left. Example 1

Subtract 10 from 30.

Let’s follow the steps and solve.

–

Tens

Ones

3 2

0 0

Subtract 5 from 17.

–

Tens

Ones

1 1

7 2

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Do It Together

Draw place value blocks to solve. Use 1

–

Tens

Ones

for 1 ten and 1

for 1 ones.

Subtraction with Regrouping The next day, she completed 13 pages. How many pages are left now? We have to subtract 13 from 41. Steps

Write the number according to the place value.

Subtract the ones place. We cannot take away 3 from 1. We shift 1 ten from the tens place to the ones place.

Take away 3 ones from 11 ones.

Take away 1 ten from 3 tens.

Explanation Tens

Ones

–

Tens

Ones

–

1 11

Tens

Ones

–

8 Ones

–

We get 8 ones in ones place.

1 11

Tens 43

1 ten = 10 ones We get 11 ones in the ones place.

We get 2 tens in the tens place.

1 11 8

41 – 13 = 28. So, 28 pages are left. Chapter 3 • Subtraction of 2-digit Numbers

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Example 2

Subtract 8 from 20. Steps

Explanation Tens

Write the number according to the place value.

Subtract the ones. We cannot take away 8 ones from 0. We shift 1 ten from the tens place to the ones place.

–

Tens –

Tens Take away 8 ones from 10 ones.

–

0 8

Ones

We get 10 ones in the ones place.

0 10 8

We are left with 2 ones in ones place.

Ones 0 10 8 2

Tens Subtract the tens.

Ones

21 1

Ones 0 10

We are left with 1 ten in the tens place.

20 – 8 = 12. Example 3

Solve 71 – 28. Use the steps to solve the problem.

–

Tens

Ones

76 4

1 11 3

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Do It Together

Solve 82 – 28. Draw place value blocks to solve. Use 1 one.

–

Tens

Ones

for 1 ten and

for

Finding the Missing Number Sara was solving a puzzle in her book. She had to find the missing number. We can find missing numbers in subtraction by using addition.

Addition and Subtraction Facts

Let us understand how addition and subtraction are related. There are 8 apples and 5 mangoes. = 8 apples = 5 mangoes 8

–8

–5

So, using 3 different numbers 8, 5 and 13 we can write the addition and subtraction facts as given below: 8 + 5 = 13

5 + 8 = 13

13 – 8 = 5

13 – 5 = 8

Let us now learn how to find the missing numbers in a subtraction problem.

–

_____

Smaller number

10 is the answer.

Chapter 3 • Subtraction of 2-digit Numbers

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Bigger number

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Steps

Check the ones place.

Check tens place.

Example 4

Explanation

–

We add the digit of the smaller number and the answer in the ones place to find the missing digit of the bigger number.

4+0=4

Tens

Ones

_____

We subtract the digit of the answer in the tens place from the digit of the bigger number in tens place.

2–1=1

Tens

Ones

Write down the subtraction and addition facts of 9, 8, and 17. There are 9 fishes and 8 turtles:

–8

–9

The addition and subtraction facts are: 9 + 8 = 17 Do It Together

8 + 9 = 17

17 – 8 = 9

17 – 9 = 8

Write down the addition and subtraction facts for 6, 7, and 13. There are 6 tomatoes and 7 potatoes.

___

+ ___

–6

– ___

___

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

Example 5

7 + ____ = 13

Find the missing number.

–

Tens

Ones

_____

_____ 2

13 – 6 = ____

Error Alert! Solve the subtraction carefully!

–

13 20 13

–

Steps

Check the ones place.

Check tens place.

Do It Together

13 – ____ = 6

20 13 7

Explanation

–

We subtract the digit of the answer in the ones place from the digit of the bigger number in the ones place.

6–4=2

Tens

Ones

Tens

Ones

_____

4 2

We add the digit of the small number in the tens place and the digit of the answer in the tens place.

2+2=4

Find the missing number.

–

Tens

Ones

_____ 1

_____

Chapter 3 • Subtraction of 2-digit Numbers

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Do It Yourself 3A 1

Look at the blocks. Cross out the blocks to show the subtraction. Write the answer. a

–

Ones

Tens

–

Tens

Ones 3

Tens

Ones

Write down the addition and subtraction facts for the following numbers. a

9, 6, and 15

There are 9 shells and 6 stones.

The addition and subtraction facts of 9, 6, and 15 are:

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Write down the addition and subtraction facts for 3, 8, and 11.

Draw the place value blocks and subtract with regrouping. a

Tens 3

–

Tens

–

Ones 5

–

Tens

Ones

Find the missing numbers. a

–

Ones

___

2 4

___

– ___

–

___

4 4

___

– ___

There were 56 bags in a shop. Meena bought 4 bags. Neha bought some more bags. There were 42 bags left in the shop. How many bags did Neha buy?

Word Problem 1

There are 45 children in Bus A and 78 children in Bus B. How many more children are there in Bus B than in Bus A?

Story Sums One day Sara went to a shop. She bought 5 pencils. Her friend Nisha bought 9 pencils.

How many more pencils does Nisha have than Sara?

Chapter 3 • Subtraction of 2-digit Numbers

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Using Subtraction to Compare We saw Nisha has more pencils than Sara. How many more? Let us match Nisha’s pencils with Sara’s. Nisha

Sara

We can use subtraction to find out how many more. We subtract 5 from 9. Nisha’s pencils

Sara’s pencils

–5

How many more?

Nisha has 4 more pencils than Sara. The next day, Sara bought 10 balloons, and her friend Rita bought 8 balloons. How many less balloons does Rita have? Sara

Rita

We use subtraction to find out how many less? Balloons with Sara

Balloons with Rita

–8

How many less?

Rita has 2 less balloons than Sara. 48

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Example 6

Sia has 35 marbles and Ria has 15 marbles. How many fewer marbles does Ria have than Sia? Number of marbles with Sia = 35 Number of marbles with Ria = 15 How many fewer marbles are with Ria? = 35 – 15

3 –

5 5

Ria has 20 marbles fewer than Sia. Do It Together

There are 2 roses in a garden and 3 sunflowers. How many more sunflowers are there than roses? Number of sunflowers = _____ Number of roses = 25 How many more sunflowers? = _____ – 25 There are _____ more sunflowers than roses. Checking Subtraction Using Addition Satish has 18 storybooks He gives 10 storybooks to Manish. How many books does Satish have left? What is given?

Number of storybooks Satish has = 18

Number of storybooks Satish gives to Manish = 10 What do we need to find?

Number of storybooks Satish has left. How do we find? Storybooks Satish has – Storybooks Satish gives to Manish = 18 – 10 Solve and check your answer.

–

Tens

Ones

0 8

Chapter 3 • Subtraction of 2-digit Numbers

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Remember! When we add the small number and the answer, we get the big number. Then our answer is correct.

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Satish has 8 storybooks left. Checking the answer using addition.

–

Big number

Small number

Answer

8 +

When we add the answer of subtraction and the small number. We get the big number as the answer. So, our answer is correct.

Example 7

Jenny had 19 pencils. She gave 8 pencils to her friend. How many does she have now? Check your answer. What is given? Number of pencils Jenny had = 19 Number of pencils Jenny gave away = 8

Tens

Ones

–

What do we need to find? Number of pencils Jenny has left. How do we find?

Number of pencils Jenny has - Number of pencils Jenny gave away = 19 – 8 Solve and check your answer. Jenny has 11 pencils left. Checking the answer: 1 – 1

Big number

Small number

Answer

1 +

1 8

The answer is correct.

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Do It Together

There were 33 toy cars. 13 were sold. How many are left? Check your answer. Number of toy cars = 33

Tens

Ones

Tens

Ones

Number of toy cars sold = ____ Number of toy cars left = 33 – ____ Checking the answer:

Tens

Ones

–

Do It Yourself 3B 1

Jiya had 51 flowers. Raju had 31 flowers. How many more flowers does Jiya have?

Mohan has 45 items of fruit with him. Minal has 21 items of fruit with her. How many fewer items of fruit does Minal have?

Gini has 27 pens. She gives 15 pens to Jimmy. How many pens does Gini have left? Check your answers.

There were 28 birds in a tree. 11 birds flew away. How many birds are left in the tree? Check your answer.

Sheetal has 23 cupcakes in her box. Monal has 34 cupcakes in her box. Who has greater number of cupcakes? And how many more?

Points to Remember •

When we subtract, the number of things becomes less.

•

We can add the answer and the small number to see whether the subtraction is correct.

•

We can find the missing number in subtraction by adding or subtracting.

•

Any three numbers will have 4 addition and subtraction facts.

•

Subtraction helps to find how many more and how many fewer.

Chapter 3 • Subtraction of 2-digit Numbers

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Math Lab Setting: In pairs

Count and Check!

Things Required: Number of objects like chalk, pencils and a pouch. What to do? • Each pair will get some objects in a pouch.

• Count the number of objects in the pouch.

• One of the children will take away some object from the pouch.

• Count and find out how many are left and how many have been taken away. • Repeat this for 6 rounds.

Chapter Checkup 1

Solve and match with the correct answers. 30 45 – 23 23 87 – 68 22 78 – 48 19 28 – 12 16 79 – 56

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Crack the code.

Plants need me! Who am I?

83 – 73 = S 91 – 56 = L 78 – 65 = N

72 – 51 = H

36 – 19 = I

74 – 42 = U

92 – 38 = T

87 – 55 = G

Fill in the letters according to the code.

10 3

3 9 – 2 2

4 6 – 3 6

Solve the subtraction and check the answer. a

Tens Ones –

Chapter 3 • Subtraction of 2-digit Numbers

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Solve the subtraction.

9 9 – 6 7

Tens Ones

Tens Ones –

Tens Ones

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Tens Ones –

Tens Ones

Write down the addition and subtraction fact for the following numbers. a

Tens Ones

9, 8 and 17

4, 3 and 7

5, 9 and 14

Circle the correct subtraction for the answers. 45 – 34

35 – 12

67 – 18

13 – 12

78 – 67

39 – 27

66 – 33

82 – 62

26 – 17

77 – 18

42 – 18

44 – 42

98 – 82

78 – 49

88 – 33

45 – 35

Find the missing numbers. Tens Ones –

2 3

Tens Ones –

Sunita has 46 mangoes. She sold 35 mangoes. How many mangoes does Sunita have left?

There are 67 ice creams in an ice cream store. 12 ice creams were sold. How many ice creams are left?

Misty has 35 balls with her. Leena has 45 balls. How many more balls does Leena have than Misty?

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Word Problems 1

Twisha has 56 crayons in her box. Aarav has 42 crayons in his box. How many fewer crayons does Aarav have?

Nisha has 78 balloons in her shop. She sold 67 balloons. How many balloons does she have left? Check the answer.

Lily has 54 fruit. Robin takes away 13 fruit and John takes away 10 fruit. How many items of fruit does Lily have left?

Chapter 3 • Subtraction of 2-digit Numbers

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Multiplication

Let's Recall A vegetable market is a fun place. We buy vegetables from the market. We know how to count our vegetables.

These are 3 cabbages.

These are 4 cauliflowers.

We also know how to add the number of vegetables. Addition will help us find the total number of vegetables. So, the total number of vegetables = Number of cabbages + Number of cauliflowers +

3+4=7

Let's Warm-up

Match the following. Vegetables bought 1

3 Tomatoes and 4 Brinjals 2

1 Tomato and 4 Cauliflowers 3

4 Brinjals and 2 Cabbages 4

4 Tomatoes and 5 Cabbages 5

4 Brinjals and 4 Cauliflowers

Total vegetables

8 vegetables 7 vegetables 5 vegetables 6 vegetables 9 vegetables I scored _________ out of 5.

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Understanding Multiplication Real Life Connect

Raghu bought 5 bunches of balloons. Each bunch has 3 balloons in it. How many balloons are there altogether?

Bunch 1

3 balloons

Bunch 2

3 balloons

Bunch 3

3 balloons

Bunch 4

3 balloons

Bunch 5

3 balloons

Think and Tell

Grouping

Will it be easy to find the total if there are unequal groups of things?

There are 5 bunches of balloons. Let’s call 5 bunches 5 groups of balloons. Each group has 3 balloons. Let us find the total.

Group 1

Group 2

3 balloons

Group 3

3 balloons

Group 4

3 balloons

3 5 15 balloons _______ groups of _______ balloons = _______ Example 1

Group 5

3 balloons

There are 3 groups of mangoes. Each group has 2 mangoes.

Group 2 2 mangoes

Group 3 2 mangoes

⎧ ⎨ ⎩

Group 1 2 mangoes

2 3 6 _______ groups of _______ mangoes = _______ mangoes Chapter 4 • Multiplication

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Example 2

There are 5 flowers. Each flower has 5 petals.

Group 1

Group 2

Group 3

Group 4

Group 5

Here, each flower is a group of petals. Each group has 5 petals. 5 5 25 petals _______ groups of _______ petals = _______

Do It Together

There are ___________ plates. Each plate has 4 guavas.

___________ groups of ___________ guavas = ___________ guavas

Do It Yourself 4A 1

Circle the following in groups of 3. Write the total.

___________ groups of 3 stars = ___________ stars 2

Circle the following in groups of 4. Write the answer.

___________ groups of 4 balls = ___________ balls 58

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Look at the pictures. Fill in the blanks. a

There are ____ bicycles. Each bicycle has ____ wheels.

There are ____ baskets. Each basket has ____ items of fruit.

Look at the pictures. Fill in the blanks. There are ____ groups here. Each group has ____ grapes.

How many groups of crayons are there? What is the total number of crayons?

There are _______ groups of crayons. There are _______ crayons in total.

Word Problem 1

Gyan has 2 boxes of colour pencils. Each box has 6 colour pencils. How many colour pencils does Gyan have in total?

Repeated Addition

Remember Raghu had 5 bunches of balloons. How did we find out how many balloons Raghu had in all? We added 3 balloons 5 times. Chapter 4 • Multiplication

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When we add the same number over and over again, it is called repeated addition. + Group 1

+ Group 2

+ Group 3

5 groups of 3 balloons

+ Group 4

Group 5

3 balloons + 3 balloons + 3 balloons + 3 balloons + 3 balloons = 15 balloons Raghu bought 15 balloons in total. Example 3

There are 3 plates with 2 biscuits on each. How many biscuits are there in total? 3 groups of 2 biscuits 2

There are 6 biscuits in all. Example 4

There are 5 buttons with 4 holes in each. How many holes are there in all the buttons? 5 groups with 4 holes 4 + 4 + 4 + There are 20 holes altogether.

Do It Together

There are 3 bunches of flowers with _____ flowers in each. How many flowers are there in all the bunches together? 3 groups of _____ flowers 5

There are _______ flowers altogether.

_______

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Do It Yourself 4B Look at the pictures and answer the questions. 1

How many leaves are there altogether?

_______

There are _______ leaves altogether. 2

How many cookies are there in all the jars?

_______

There are _______ cookies in all. 3

How many flowers are there altogether?

_______

There are _______ flowers altogether. 4

There are 6 boxes. Each box has 5 Eclairs in it. How many Eclairs are there in total?

_______ + _______

+ _______ + _______ +

_______

+ _______

_______

There are _______ Eclairs in total. Chapter 4 • Multiplication

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Rina got 3 cherries every day for 3 days. How many cherries did she get altogether?

Day 1

_______

Day 2

_______

Day 3

There are _______ cherries altogether.

_______

Word Problem Sara put 4 flowers in each of the 3 vases. How many flowers did Sara put in vases altogether?

What is Multiplication? Hi, Riya. I got 5 bunches of three balloons yesterday. Wow! You got 15 balloons? Yes. How did you calculate so fast? I used multiplication.

RAGHU

RIYA

Multiplication is a fast way of adding repeatedly. We use the ‘×’ sign for multiplication. Here are the 5 bunches of balloons which Raghu bought. +

Group 1 Group 2 3 3 + +

5 groups of 3 balloons

Group 3 Group 4 3 3 + +

Group 5 3

5 groups of balloons × 3 balloons in each group = 15 balloons

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This can also be written as:

Number of groups

3 Number of things in each group

15 Number of things in total

This can be read as any one of the following:

5 groups of 3 are 15

5 threes are 15

5 times 3 is 15

Example 5

There are 3 ladybugs. Each ladybug has 4 spots on it. How many spots are there in total?

Remember!

3 groups of 4

For multiplication, each group must have the same number of things in it.

4 + 4 + 4 = 12. 3 × 4 = 12.

There are 12 spots in total. Example 6

There are 5 fish bowls with 2 fish in each bowl. How many fish are there?

5 groups of 2

2 + 2 + 2 + 2 + 2 = 10 5 × 2 = 10

There are 10 fish altogether. Chapter 4 • Multiplication

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Think and Tell If there are 3 groups and each group has 5 stars. How many stars are there in total?

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Do It Together

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

_______ groups of 5

5 + 5 + 5 = 15. ___ × 5 = 15.

Error Alert! Never put a different number of things in groups during multiplication.

There are _____ crayons in all.

Do It Yourself 4C 1

There are 7 vases. Each vase has 3 roses. How many roses are there in total?

_______ groups of _______ = _______ times _______ _______ + _______ + _______ + _______ + _______ + _______ + _______ = _______ _______ × _______ = _______ There are _______ roses in total. 2

There are 4 cakes. Each cake has 4 candles on it. How many candles are there in total?

_______ groups of _______ = _______ times _______ _______ + _______ + _______ + _______ = _______ _______ × _______ = _______ There are _______ candles in total. 64

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There are 5 bunches of keys. Each bunch has 2 keys. How many keys are there in altogether?

_______ groups of _______ = _______ times _______ _______ + _______ + _______ + _______ + _______ = _______ _______ × _______ = _______ There are _______ keys in all. 4

Match the following. a

2 times 4

5 times 2

4 times 2

3 times 3

4 times 5

Match the following with the correct multiplication form. a

4×2

3×6

Chapter 4 • Multiplication

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2×3

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Word Problem There are 4 rooms. Hira puts 2 pillows in each room. How many pillows did he have?

Points to Remember •

Adding the same number, again and again, is called repeated addition.

•

Multiplication is a fast way to do repeated addition.

•

In multiplication the number of things in each group remains the same.

•

For multiplication, we use the × sign.

•

For multiplication, do the following: Number of groups × Number of things in each group = Total number of things

Math Lab Setting: In pairs Materials Required: 20 things like crayons, chalks or rajma beans. To do: 1

Make 5 groups with 2 things in each.

Make 2 groups with 8 things in each.

Make 2 groups with 10 things in each.

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Chapter Checkup 1

Identify the number of groups and things in each group in the pictures. a

_______ groups of _______ chalks in each group.

_______ groups of _______ marbles in each group.

Find the number of things in total. a

____ + ____ + ____ + ____ = ____ There are ____ mangoes in all. b

____ + ____ = ____ There are ____ books in all.

Count the groups. Count the number of things in each group. Circle the correct option.

Chapter 4 • Multiplication

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6 groups of 3

2 groups of 3

3 groups of 6

3 groups of 8

2 groups of 4

3 groups of 2

5 groups of 3

4 groups of 2

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Write the correct multiplication form for each picture. a

__________ × __________ b

__________ × __________ c

__________ × __________ 5

There are 2 jars. There are 9 sweets in each jar. How many sweets are there in total? _______ groups of _______ There are _______ sweets.

Circle the picture which shows 4 × 3.

Circle the things to make 5 groups of 2.

Circle the things to show 3 × 3.

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Pooja bought 3 boxes. Each box has four sweets in it. How many sweets are there in total? Number of boxes: _______

Number of sweets in each box: _______ Total number of sweet: _______ groups of _______ = _______ Pooja bought _______ sweets in total. 10

Rohan has 5 bags. Each bag has 3 gift boxes. How many boxes are there in total? Number of bags: _______

Number of boxes in each bag: _______ Total number of boxes: _______ + _______ + _______ + _______ + _______ = _______ _______ × _______ = _______ There are _______ boxes in total.

Word Problems 1

Some children were playing a game. They made 6 groups to play the game. There were 4 children in each group. How many children were playing the game? Number of groups: _______

Number of children in each group: _______ Total number of children:_______ × _______ There were _______ children in total. 2

Tina has two boxes filled with toys. Each box has 10 toys. How many toys are there altogether? Number of boxes: _______

Number of toys in each box: _______ Total number of toys: _______ × _______ There are _______ toys altogether.

Chapter 4 • Multiplication

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Multiplication Tables 2, 5 and 10

Let's Recall An apple a day keeps the doctor away! Is each plate a group?

Yes! Because each plate has the same number of apples. These are 5 groups having 2 apples each. Let us count the total number of apples. 2 + 2 + 2 + 2 + 2 = 10 This is repeated addition, which is the same as multiplication. We can also write this as 5 × 2 = 10. So, 2 + 2 + 2 + 2 + 2 = 5 × 2 = 10

Let's Warm-up

Fill in the blanks. 1

____ pears + ____ pears = ____ pears

These are 2 groups of ____ pears each.

We can say, 2 × ____ pears = ____ pears

I scored __________ out of 3.

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Multiplication Tables Real Life Connect

Meena and Tina go to an apple farm. The farmer puts apples in the baskets. The farmer tells them that all baskets have an equal number of apples. Let us help them to count all the apples. Multiplication by 2 We learnt that repeated addition is called Multiplication. When items are put in groups and each group has the same number of items, multiplication helps us to find the total number of items. For example, if the farmer has 2 baskets, with 1 apple each, we get:

Number of groups

sign of multiplication

Total no. of items

Number of items in each group

When a number is multiplied by 1, the answer is the number itself. Each basket is a group, and the number of apples is the number of items in each group. What if each group had 2 apples? We would get 2 × 2 = 4

This way of multiplying by 2 is called the “Multiplication Table of 2”.

Chapter 5 • Multiplication Tables 2, 5 and 10

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Let’s read the multiplication table of 2 together: 2×1=2

2 ones are 2

2×2=4

2 twos are 4

2×3=6

2 threes are 6

2×4=8

2 fours are 8

2 × 5 = 10

2 fives are 10

2 × 6 = 12

2 sixes are 12

2 × 7 = 14

2 sevens are 14

2 × 8 = 16

2 eights are 16

2 × 9 = 18

2 nines are 18

2 × 10 = 20

2 tens are 20

We can also understand multiplication by counting. Imagine you are playing a game on steps that are numbered. The rule is that you jump two steps. +2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 You start at 0. Each jump that you make is of 2 steps. So, you reach 2 on the first jump, then on second jump you reach 4, on the third you reach 6 and so on. 2

This is counting in 2s, which is also Multiplication by 2. What is the double of 5? 5 + 5 = 10

2 × 5 = 10

Remember! Double means adding the number itself or multiplying by 2

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Example 1

How many groups of 2 cars are there? There are 3 groups of 2 cars. Group 1

Group 2

Group 3 Do It Together

Complete this table. 2

1×2=2

___ + ___ + ___

3×2=6

2+2

2×2=4

2+2+2+2

4 × 2 = ___

___ + ___ + ___ + ___ + ___

5 × 2 = ___

Do It Yourself 5A 1

Fill in the blanks.

Chapter 5 • Multiplication Tables 2, 5 and 10

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Repeated addition fact

Multiplication fact

___ + ___ + ___ + ___ = ___

___ × ___ = ___

___ + ___ = ___

___ × ___ = ___

___ + ___ + ___ = ___

___ × ___ = ___

___ + ___+ ___ +___+ ___ =___

___ × ___ = ___

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Write the multiplication fact for the given pictures. __________ × __________ = __________

__________ × __________ = __________

Fill in the blanks. a

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

_______ × _______ = _______

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

_______ × _______ = _______

Write the doubles of the following numbers. a

Draw a picture representing 2 groups with 5 apples in each group. What is the total number of apples in the picture?

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Multiplication by zero Meena and Tina went to the farm in the evening. They saw two empty baskets which had no apples in them.

= 0

There are 2 groups of 0 apples 2×0=0 When you multiply 0 by any number, the answer is always 0. Do It Together

Rohit’s father gave him 3 empty vases. How many flowers are there in the vases?

________

3 × 0 = _________ Multiplication by 5 The next day, Tina went to the garden alone. She collected 5 apples. Can you help her to count the apples? Here we have 1 group of 5 apples 1 × 5 = 5 apples What if Tina had 2 such baskets? She would have 2 × 5 = 10 apples. This is called Multiplication by 5. Let us see how to read the multiplication table of 5. Chapter 5 • Multiplication Tables 2, 5 and 10

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Remember! 5 groups of 4 are same as 4 groups of 5. Both will give the same answer.

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5×1=5

5 ones are 5

5 × 2 = 10

5 twos are 10

5 × 3 = 15

5 threes are 15

5 × 4 = 20

5 fours are 20

5 × 5 = 25

5 fives are 25

5 × 6 = 30

5 sixes are 30

5 × 7 = 35

5 sevens are 35

5 × 8 = 40

5 eights are 40

5 × 9 = 45

5 nines are 45

5 × 10 = 50

5 tens are 50

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Let us play the game of steps again. Now the rule is that you jump five steps. +5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 You start at 0. Each jump that you make is of 5 steps. So, you reach 5 on the first jump, then on the second jump you reach 10, on the third you reach 15 and so on. Example 2

Tom wants to reach the hole. How many times will he jump to reach the hole?

1 0

2 5

3 10

4 15

5 20

6 25

Tom reaches the hole in 6 jumps. Do It Together

5 ______ groups of ______ flowers equals ______ 5 × ______ = ______ ______

Chapter 5 • Multiplication Tables 2, 5 and 10

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Do It Yourself 5B 1

Count the fingers of your hand and fill the boxes. If the number of hands is

The number of fingers

Write the multiplication fact. _________ × _________ = _________

_________ × _________ = _________ _________ × _________ = _________ _________ × _________ = _________ 3

Show jumps in 5 steps. 0

Tom wants to reach the chapati. He jumps 5 numbers each time.

How many times does Tom jump? _____ 9 jumps of 5 steps each _____ × _____ = _____ 5

Draw a picture to show 5 groups with 6 grapes in each group. Write down the total number of grapes in the picture.

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Multiplication by 10 Tina saw that the farmer had 10 small baskets. There was 1 apple in each basket.

Here we have 10 baskets of 1 apple. 10 × 1 = 10 apples. What if the farmer had 10 baskets with 2 apples each?

Remember! A number, when multiplied by 10 always has a “0” at the end.

He would have 10 × 2 = 20 apples.

This is called multiplication by 10. Let us see the multiplication table of 10.

Chapter 5 • Multiplication Tables 2, 5 and 10

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10 × 1 = 10

10 ones are 10

10 × 2 = 20

10 twos are 20

10 × 3 = 30

10 threes are 30

10 × 4 = 40

10 fours are 40

10 × 5 = 50

10 fives are 50

10 × 6 = 60

10 sixes are 60

10 × 7 = 70

10 sevens are 70

10 × 8 = 80

10 eights are 80

10 × 9 = 90

10 nines are 90

10 × 10 = 100

10 tens are 100

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Let us play the game of steps once again. Now the rule is that you jump ten steps. +10

+10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 You start at 0. Each jump that you make is of 10 steps. So, you reach 10 on the first jump, then on the second jump you reach 20, on the third you reach 30, and so on.

Example 3

How many groups of pencils are there? Also give the total number of pencils.

10 3 30 ______ groups of ______ pencils equals ______ 3 × ______ 10 = ______ 30 ______ Do It Together

Mitthu wants to reach the red chilli. He jumps 10 steps each time.

5 jumps of 10 steps each.

100

5 × 10 = ______

How many times does Mitthu jump? Write the multiplication fact. _________ × _________ = _________. 80

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Do It Yourself 5C 1

Write the multiplication fact. ________ × ________ = ________

________ × ________ = ________

________ × ________ = ________ 2

Fill in the blanks. 0

100

_______ jumps of 10 each _______ × _______ = _______ 0

100

_______ jumps of 10 each _______ × _______ = _______

_______ jump of 10 _______ × _______ = _______ 3

What will be 4 jumps of 10 steps each?

Draw lines to match the multiplication fact to its answer. 10 × 3 80 10 × 7 30 10 × 4 60 10 × 8 70 10 × 6 40

Count by 10s up to 100. 10

_____

Chapter 5 • Multiplication Tables 2, 5 and 10

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_____

100 81

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Story Sums Tina sees a big basket that can hold 8 apples. The farmer tells Tina that he has 10 such baskets. How many apples can 10 baskets hold? What do we know? The number of baskets the farmer has = 10. The number of apples each basket can hold = 8. What do we want to know? How many apples can 10 baskets hold? How do we find the answer? The total number of apples that 10 baskets can hold = The number of baskets × The number of apples that each basket holds Solve to find the answer. = 10 × 8 = 80 apples So, 10 baskets can hold 80 apples. Example 4

A box contains 10 packets of candies, and each packet has 7 candies in it. How many candies are there in total? What do we know? The number of packets of candies = 10. The number of candies in each packet = 7. What do we want to know? The total number of candies How do we find the answer? The total number of candies = The number of packets × The number of candies in each packet Solve to find the answer. = 10 × 7 = 70 candies So, there are 70 candies in total.

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Do It Together

There are vases in the garden. ach vase has flowers are there in total?

flowers in it. How many

What do we know? The number of vases in the garden = 5 The number of flowers in each vase = _____

What do we want to know? The total number of flowers in all the vases The total number of flowers = the total number of vases × the flowers in each vase Solve to find the answer. = 5 × ____ = ____ flowers So, there are ____ flowers in total.

Do It Yourself 5D 1

A bookstore has 10 shelves, and each shelf can hold 6 books. How many books can the bookstore hold?

There are 9 boxes of cookies, and each box contains 10 cookies. How many cookies are there in all the boxes?

There are 6 oranges in a fruit basket. If there are 10 such fruit baskets, how many oranges are there in total?

Tom made 4 batches of cupcakes, and each batch had 10 cupcakes. How many cupcakes did Tom make altogether?

Lisa collected 2 jars of marbles, and each jar contained 10 marbles. How many marbles did Lisa collect in total?

Points to Remember • The multiplication of any number by 1 is always the same number. • The product of any number by zero is always zero. • Double means adding the number itself or multiplying by 2. • When we multiply any number by 10, we multiply it by 1 and add a 0 to the right of the answer. Chapter 5 • Multiplication Tables 2, 5 and 10

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Math Lab Multiplication Bingo Materials Required: Bingo cards, Caller list, pencils. Setting: Group activity A caller reads a multiplication problem aloud from the caller list.

Other students solve the problem and cut the answer from the Bingo cards. Students who solve the problem and cut the whole line of Bingo card either horizontally, or vertically, or diagonally are the winners. Bingo cards – Create Bingo cards using a 5 × 5 grid. Write ‘BINGO’ across the top and write the answers to the caller problems in the remaining squares with some filler answers. Sample of a Bingo card B

100

Caller list – List of multiplication problems. For example : • 2×5 =

• 2 × 12 =

• 2×9 =

• 34 × 0 =

• 7 × 10

• 10 × 10 =

• 78 × 1 =

Chapter Checkup 1

Write if true or false. 2 × 6 = 12 5×1=0 7×0=1 10 × 5 = 50

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Show multiplication on a number line. 2×5

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

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

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

Fill in the blanks with the correct number. Each blank has the same number. a b

= 10

Fill in the boxes. a

2 times 8

5 times 8

10 times 1

0 times 8

1 times 8

2 times 5

Chapter 5 • Multiplication Tables 2, 5 and 10

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Write multiplication facts for the given problems. a

There are 5 sticks in a bundle. How many sticks are there in 10 such bundles?

__________ × __________ = __________

One box contains 9 balls. How many balls do 10 boxes contain?

__________ × __________ = __________

There are 10 students in a class. Each student has 1 pencil. How many pencils are there altogether?

__________ × __________ = __________

A pack contains 6 crayons. If there are 10 packs, how many crayons are there in total?

Shreya bought 10 packs of candy, and each pack contains 10 pieces. How many pieces of candy does Shreya have in total?

There are 5 sticks in a bundle. How many sticks are there in 10 such bundles?

One box contains 7 balls. How many balls do 10 boxes contain?

Rahul and his friends are going on a trip. Below is the list of items he has decided to take on the trip. Calculate the number of items he will be taking in total. Items

No. of things required

5 persons

Total

Hats

_________

T-shirts

_________

Shoes

2 pairs

_________

_________ pairs

Word Problems 1

A car can carry 5 people. How many people can be carried in 10 such cars?

Sarah has 3 baskets, and each basket contains 5 apples. How many apples does Sarah have in total?

There are 10 students in a class. Each student has 1 pencil. How many pencils are there in total?

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6 Numbers up to 999 Let's Recall Toys are so much fun!

Do you know that toy at the store has a price tag on it. The price of a toy can be a 2-digit or a 3-digit number. We already know about 2-digit and 3-digit numbers.

Let us say that the price of the teddy bear is `65. We write 65 as: 6 tens and 5 ones.

Tens

The place value of the tens place is 60.

The place value of the ones place is 5.

Ones 5

Let us say that the price of the basketball is `195. We write 195 as: 1 hundred, 9 tens and 5 ones. The place value of the hundreds place is 100. The place value of the tens place is 90. The place value of the ones place is 5.

Hundreds 1

Tens 9

Ones 5

Let's Warm-up

Match each number with its expanded form. 1 93 1 hundred, 2 tens, 1 one 2

121

1 hundred, 4 tens, 8 ones

148

9 tens, 3 ones

163

1 hundred, 9 tens, 9 ones

199

1 hundred, 6 tens, 3 ones

I scored _________ out of 5.

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Understanding Numbers up to 999 Real Life Connect

Pooja and Rohit went to a sweet shop with their father. Father: Which sweets do you both want?

Rohit: Wow! There are so many! Which one should we buy, Pooja?

Pooja: Father, let us buy laddoos.

Father: Okay, one box with 200 laddoos and one box with 25 laddoos. Pooja: Wow! 225 laddoos!

Rohit: How did you count that? Please teach me to count more than 200.

Forming Numbers up to 999 Let us help Rohit count numbers more than 200. We know how to count and write numbers from 0 to 200. We can write numbers more than 200 the same way as we write numbers from 1 to 100. Let us write numbers by counting forward from 201. Numbers 201 to 300 201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

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We know that a 3-digit number has hundreds, tens and ones. We can show a 3-digit number using place value blocks. We also know that 10 ones = 1 ten, 10 tens = 1 hundred.

Hundreds Tens Ones

= 10 ones

= 1 ten

10 tens

1 hundred

Let us now see how the 225 sweets are shown using place value blocks. =

1 sweet = 1 one

10 sweets = 1 ten

100 sweets

1 hundred

So, 225 sweets are shown as 2 hundreds' blocks, 2 tens' blocks and 5 ones' blocks. +

2 Hundreds + 2 Tens + 5 Ones

200 + 20 + 5 = 225 sweets

225 is read as two hundred twenty-five. Let us understand this concept better. Number H 1

one hundred

two hundred

Chapter 6 • Numbers up to 999

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Number name

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H 3

three hundred

H 4

four hundred

H 5

five hundred

H 6

six hundred

H 7

seven hundred

H 8

eight hundred

nine hundred

Let us show some more 3-digit numbers using place value blocks and in the place value chart. Example 1

Think and Tell Which is the smallest 4-digit number?

3 hundreds + 1 ten + 2 ones = 300

Remember!

345 is a number. 3, 4 and 5 are digits of the number.

We will read it as three hundred twelve. 90

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Example 2

2 hundreds + 2 tens + 3 ones = 200

We will read it as two hundred twenty-three.

Do It Together

Think and Tell How will you write 11 tens as a number?

Fill in the boxes with the correct number

hundreds

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tens

ones

tens

ones

O 1

__________________________ H

Chapter 6 • Numbers up to 999

ones

Six hundred thirty-three H

tens

hundreds

ones

hundreds

tens

Three hundred twenty-four 91

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Do It Yourself 6A 1

Write the missing numbers.

STOP

Did You Know? The numbers that we use today, 0 to 9, originated in ancient India! 405

402

300

302

305

720

722

725

c e

309

813

4 hundreds, 6 tens and 5 ones 6 hundreds and 3 ones

9 hundreds and 6 tens

310

728 816

Which number has? a

START

Complete the following.

811 3

401

b d f

818

7 hundreds, 7 tens and 7ones 5 hundreds and 5 ones

6 hundreds, 2 tens and 3 ones

Show the given numbers using place value blocks. Write their number names. a

345

459

567

678

999

108

Hundred =

Ten =

One =

Write the numbers for the given number names. five hundred sixty-one

three hundred six

two hundred twenty-seven

seven hundred ten

nine hundred thirty-five

four hundred nineteen

one hundred twenty-seven

six hundred fifty-eight

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Place Value and Expanded Form

We saw that Rohit and Pooja's father bought 225 sweets for them. Then, we learnt how to express 225 using place value blocks.

2 hundreds + 2 tens + 5 ones

Now, let us see how to write a 3-digit number using place value, expanded form and as a number name. Place Value Place value is the value of a digit based on its position in a number. Each digit has a place value, such as ones, tens, hundreds and so on.

Remember! The place value of 0 is always 0 irrespective of its position in the number.

For example, in 225, there are 2 hundreds, 2 tens and 5 ones. We can write 225 as: H 2

O 5

Place value is 5 ones or 5. Place value is 2 tens or 20. Place value is 2 hundreds or 200.

So, the place value of the hundreds place is 200. The place value of the tens place is 20. The place value of the ones place is 5. Example 3

Place value of 407. H 4

O 7

Place value is 7 ones or 7. Place value is 0 tens or 0. Place value is 4 hundreds or 400. Chapter 6 • Numbers up to 999

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Do It Together

Write the place value of the coloured digits. 234

4 ones

953

________

806

________

662

Expanded Form Let us understand the expanded form of numbers up to 999. Expanded form refers to writing a number as the sum of its place value. Expanded form of 983. H

O 3

Standard form – 983

3 80 900 Example 4

Expanded Form – 900 + 80 + 3 Number Name – nine hundred eighty-three

Expanded form of 129. H

O 9

Standard form – 129

9 20 100 Do It Together

Expanded Form – 100 + 20 + 9 Number Name – one hundred twenty-nine

Write the expanded form. 453

400

102

340

980

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Do It Yourself 6B 1

Write the place value of all the digits in the given numbers. Then, write the numbers in their expanded form. a

398

170

654

6 70 500

2 0 700

Tick the numbers in which the place value of: 7 is 700 6 is 60

3 is 300 2 is 2

9 is 900 4

237

Write the number.

4 80 900 3

701

693

345

290

900

679

567

639

324

459

896

130

132

199

Complete the table. Before 322 221

Between

After

431

432

324 223

326

327

889 5

Solve the riddle.

• I am a 3-digit number. • My ones digit is less than 1. • My tens digit is the greatest single digit number. • My hundreds digit is 5.

Who am I? 6

How many numbers can you make using the digits 2, 4, 7 without repeating them? H

Chapter 6 • Numbers up to 999

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Comparing and Ordering Numbers Real Life Connect

Pankaj and Ria like to play with marbles. On Monday, Pankaj had 120 marbles and Ria had 69 marbles. Pankaj: I have more marbles than you. Ria: No, I think I have more.

Comparing Numbers Who has more marbles? Pankaj has 120 marbles.

Ria has 69 marbles. H

It is a 2-digit number.

O 0

It is a 3-digit number.

So, Pankaj has more marbles than Ria as 69 < 120 (69 is less than 120).

Remember! A number that has more digits is always greater!

A 2-digit number is always less than a 3-digit number. Now, what if the number of digits in the two numbers are the same? For example, how should we compare 547 and 328? Both are 3-digit numbers. In this case, we first compare the digits in the hundreds place of both the numbers. H 5

O 8

5 is greater than 3 So, 547 > 328 (547 is greater than 328). 96

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Now, what if the number of digits is the same and the digits in the hundreds place are also the same? For example, how shall we compare 437 and 453? We will check the digits in the tens place. H

Same digit in the hundreds place.

4 is equal to 4, 4 = 4 Since the digits in the hundreds place is the same, we compare the digits in the tens place. 3 is less than 5. So, 437 < 453. Now, what if the number of digits is the same and the digits in the hundreds and tens places are also the same? For example, how shall we compare 847 and 849? We will check the digits in the ones place. H 8

O 7

Same digits in the hundreds and tens place.

H 8

O 9

Here, hundreds place as well as tens place digits are equal. We will compare the digits in ones place. 7 is less than 9. So, 847 < 849. When both the numbers are equal, we use the equal to sign (=). 344 = 344 Chapter 6 • Numbers up to 999

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Error Alert! Compare the digits in the tens and ones place ONLY IF the digits in the hundreds place of the 2 numbers are the same! 97

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Example 5

Example 6

Compare 58 and 971. 58 is a 2-digit number and 971 is a 3-digit number. A 2-digit number is always less than a 3-digit number. So, 58 < 971. Compare 689 and 681. H 6

O 1

Same digits in the hundreds place. 6=6 Same digits in the tens place. 8=8 Different digits in the ones place. 9>1 Do It Together

So, 689 > 681

Compare 491 and 466. Both 491 and 466 are 3-digit numbers. H 4

O 6

Same digits in the hundreds place. _______ = _______ ____________ digit in the tens place. __________________________

So, we can say that 491 _______ 466.

Ordering Numbers We learnt how to compare two numbers. Let us now compare more than 2 numbers. Let us compare 34, 871 and 679. We know that 2-digit numbers are always smaller than 3-digit numbers. So, 34 is less than both 871 and 679. 98

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Now, let us compare 871 and 679. H 8

O 9

8 is greater than 6 So, 871 is greater than 679, or we can also say 679 is less than 871. Therefore, 34 < 679 < 871. We have arranged the numbers from the smallest to the largest number. This is called increasing order. The three numbers in this order would be: 34, 679, 871. We could also have said that 871 > 679 > 34. The numbers are arranged from largest to smallest. This is called decreasing order. The three numbers in this order would be: 871, 679, 34. Example 7

Arrange the numbers 682, 972 and 123 in increasing and decreasing order. We can see that 682 < 972. We also see that 123 < 682. So, 123 < 682 < 972. This way, the numbers are arranged from the smallest to the largest. So, the numbers arranged in increasing order are 123, 682, 972. We can also say that, 972 > 682 > 123. This way, the numbers are arranged from the largest to the smallest. So, the numbers arranged in decreasing order are 972, 682, 123.

Do It Together

Arrange the numbers 421, 81 and 612 in increasing and decreasing order. 81 is a 2-digit number while 421 and 612 are 3-digit numbers. So, 81 is _____________ both 421 and 612. We can also see that 421 < 612 because the digit in the hundreds place is smaller in 421. So, the increasing order (smallest to largest) is _______, _______, _______. And the decreasing order (largest to smallest) is _______, _______, _______. Chapter 6 • Numbers up to 999

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Do It Yourself 6C 1

Circle the bigger number. a

167

879

799

901

204

178

480

982

984

278

940

Write the greater number under the big teddy and smaller number under the smaller teddy. 459, 234

340, 348

______ 3

______

Colour the box with the greatest number red in each of the following groups. a

239

709

551

446

783

269

175

865

159

537

538

Colour the box with the smallest number yellow in each of the following groups. a

892

834

847

596

443

436

213

913

951

293

693

337

Arrange the numbers in an increasing order.

789, 345, 100, 1000

100

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Points to Remember •

While writing the number name of a 3-digit number, we write the hundreds place first, then the tens and the ones place together.

•

Place value is the value of a digit based on its position in a number. The place value of a digit is not fixed.

•

Expanded form refers to writing a number as the sum of its place values.

•

In increasing order, we arrange the numbers from smallest to greatest. In decreasing order, we arrange the numbers from greatest to smallest.

Math Lab Fun game–Roll the dice

Things required: 1 Dice, 1 Pencil Setting: Sit with your partner, roll a dice thrice and write the digits shown in the given table as follows: Roll 1 : for ones Roll 2 : for tens Roll 3 : for hundreds Read the number and write the number name in the blank place. Player 1 H

Player 2 O

_______________________________

Chapter 6 • Numbers up to 999

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_______________________________

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Chapter Checkup 1

Tommy loves to play with toy cars. He has a collection of 200 toy cars. He wants to make number cards for every toy car. He has already made 100 number cards. Will you help him to make next number cards? 201

300 2

Write the place value of each digit in the given numbers. Write the numbers in their expanded form. 567

202

986

Write the number. before

between

after

245

247

456

967

254

256

698

180 555 340

433 219 995

435 221 997

515 357 951

102

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Write the ones, tens, and hundreds in the given numbers. Compare the numbers using the symbols <, >, or =. ones tens

hundreds 5

349

______________

ones

______________

hundreds

______________

tens

456

______________

ones

______________

hundreds

______________

tens

______________

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

345

232

1000

678

344

123

856

945

Solve the following number puzzles. a

What number comes after 375?

What number comes before 888?

What number is 10 more than 50?

What number is fifty less than 750?

What number comes after 999?

Write the numbers in decreasing order. a

234, 567, 986

559, 678, 345

109, 289, 678

345, 696, 873

Write the numbers in increasing order. 1000, 170, 590

540, 330, 257

678, 447, 567

600, 120, 499

How many 3-digit numbers are there between 101 and 999?

Chapter 6 • Numbers up to 999

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847

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Choose the numbers from the balloons and fill in the boxes.

459

289

769

229

985

123

890

590

Less than 500 More than 500 11

Colour the boxes by following these instructions.

Colour the square green if the digits in the ones are greater than 5. Colour the square yellow if the digits in the tens are greater than 5. Colour the square pink if the digits in the hundreds are greater than 5. H 4

Word Problems 1

Diya’s grandfather collects coins. He has 450 coins. His friend has 299 coins. Who has more coins?

Toni, a labourer, built a wall using 790 bricks. His neighbour, Ramu, also built a wall but he used 689 bricks. Who used more bricks?

104

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n an

ra ers

Let's Recall Imagine we have 25 marbles. We find 13 more marbles. How many marbles do we have? Here, we have got 13 more marbles. So, we will add 13 to 25 to find the total number of marbles. Let us add 25 + 13. 25 = 2 tens + 5 ones

13 = 1 ten + 3 ones

2 tens + 1 ten = 3 tens

T O 2 5 1 3 3 8

5 ones + 3 ones = 8 ones

So, there are 38 marbles in all.

Now, what if we lost 15 marbles, how many marbles will we have? We had 38 marbles, out of which we lost 15. So, we will subtract 15 from 38 to find the marbles left. Let us subtract 15 from 38.

–

38 = 3 tens + 8 ones 3 tens – 1 ten = 2 tens

15 = 1 ten + 5 ones

T O 3 8 1 5 2 3

8 ones – 5 ones = 3 ones

We have 23 marbles left.

Let's Warm-up 1

___ ___

–

___ ___

___

O 5

___ ___ 3

I scored _________ out of 4.

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Operations on 3-digit numbers Real Life Connect

Rakesh is a fruit seller. He bought 115 mangoes on Monday. He bought 123 apples on Tuesday. Let us find out the total number of fruits with Rakesh on Tuesday. To find the total number of fruits, we need to add the number of fruits bought on Monday and Tuesday.

Addition of 3-digit Number Addition Without Regrouping How many fruits are there with Rakesh? There are 115 mangoes and 123 apples.

115 = 1 hundred (H)+ 1 ten (T) + 5 ones (O)

123 = 1 hundred (H) + 2 tens (T) + 3 ones (O) = 1 hundred (H), = 1 ten (T) and

We know that

= 1 one (O).

We will now show the numbers 115 and 123 using the place value blocks. 115 =

123 =

To find out how many fruits are there, we add 115 and 123. We can add the numbers by writing them vertically and using the place value blocks. Step 1 Write the numbers vertically.

H 1 1

T 1 2

O 5 3

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Step 2 Add the digits in the ones place. 5 + 3 = 8 ones

3 8

We get 8 ones. Step 3 Add the digits in the tens place. 1 + 2 = 3 tens

We get 3 tens. Step 4 Add the digits in the hundreds place. 1 + 1 = 2 hundreds

We get 2 hundreds. We get 2 hundreds, 3 tens and 8 ones. 115 + 123 = 238 fruits

Chapter 7 • Addition and Subtraction of 3-digit Numbers

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Addition with Regrouping First, Rakesh bought 115 mangoes. Then, he bought 123 apples. So, the total number of fruits with Rakesh are 238. Now, Rakesh bought 177 bananas.

Remember!

Let us see how many fruits are there now.

When we add, the number of things become more.

Add 238 and 177. Let us add the 2 numbers using place value blocks.

10 ones = 1 ten 238

+ 177

10 tens = 1 hundred

So, 238 + 177 = 415. Now let us see if we get the same answer by adding vertically. Step 1 Add the ones. 8 ones + 7 ones = 15 ones 10 ones = 1 ten Write 5 and move 1 ten to the tens place.

7 5

108

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Step 2 Add the tens. 3 tens + 7 tens + 1 ten = 11 tens 10 tens = 1 hundred Write 1 and move 1 to the hundreds place.

Example 1

Add 289 and 32. Step 1 Write the numbers vertically according to their place value.

Step 3 Add the hundreds. 2 hundreds + 1 hundred + 1 hundred = 4 hundreds Write 4 in the hundreds place. So, we see that we get the same answer on adding 238 + 177 using place value blocks and vertical addition.

Error Alert! Write the numbers according to their place value. Add 256 and 34.

H 2 3 5

T 5 4 9

O 6

Step 2 Add the ones. 9 ones + 2 ones = 11 ones. 10 ones = 1 ten. Write 1 and move 1 ten to the tens place.

H 2 2

T 5 3 9

O 6 4 0

Step 3 3 2 Add the tens. 8 tens + 3 tens + 1 ten = 12 tens. 10 tens = 1 hundred. Write 2 and move 1 ten to the hundreds place.

Step 4 Add the hundreds. 2 hundreds + 1 hundred = 3 hundreds. Write 3 in the hundreds place.

Chapter 7 • Addition and Subtraction of 3-digit Numbers

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Do It Together

Add 239 and 562 using the place value blocks and writing numbers vertically. for 1 hundred (H),

Use

for 1 ten (T) and

for 1 ones (O).

Place Value Blocks

Do It Yourself 7A 1

Add the 3-digit numbers with the 1-digit number. H

3 6

347 + 6

6 9

457 + 8

679 + 5

Add the given 3-digit numbers with the 2-digit numbers. H

457 + 63

664 + 45

783 + 54

346 + 91

487 + 34

568 + 58

Add the numbers using place value blocks. Use a

for 1 hundred (H),

123 + 543

for 1 ten (T) and

801 + 111

for 1 ones (O).

453 + 212

720 + 158

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Add the given 3-digit numbers. a

707 + 128

209 + 340

656 + 322

349 + 521

527 + 412

549 + 144

763 + 126

239 + 256

239 + 432

What number will you add to 245 to get 356?

Word Problems 1

Dan bought a bunch of roses for `345 and a sheet of wrapping paper for `35. How much did Dan spend on the two items?

A dance academy has 2 centres. Centre A has 125 students and Centre B has 543 students. What is the total number of students at the dance academy?

Subtraction of 3-digit Numbers Raghu had 475 fruits on Wednesday. He sold 322 fruits. How many are left with him now? To find the number of fruits left, we need to subtract 322 from 475. 475 – 322

Remember! Subtraction means taking away. We take away the smaller number from the bigger number. The number of things become less in subtraction.

Subtraction Using Place Value Blocks Let us see how can we subtract 2 numbers using place value blocks. Step 1 Show the bigger number using place value blocks. 475

Chapter 7 • Addition and Subtraction of 3-digit Numbers

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Step 2 Cross out or take away as many blocks as in the smaller number. 475 – 322

Step 3 Count the number of hundreds, tens and ones left. That gives us the answer. 475 – 322 = 153

Vertical Subtraction Let us see how can we subtract 2 numbers by writing them vertically. Step 1 Write the numbers vertically as per their place values. The smaller number is written under the bigger number. H –

Step 3 Subtract the tens. 7 tens – 2 tens = 5 tens Write 5 in the tens place. H –

Step 2 Subtract the ones. 5 ones – 2 ones = 3 ones Write 3 in the ones place. H –

Step 4 Subtract the hundreds. 4 hundreds – 3 hundreds = 1 hundred Write 1 in the hundreds place. H –

So, we see that we get the same answer on subtracting 322 from 475 using place value blocks and vertical subtraction. There are 153 fruits left with Raghu. 112

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Error Alert! We subtract smaller number from the bigger number. Write the smaller number under the bigger number. H –

Example 2

3 1

H –

Remember! When we subtract two same numbers, we get 0. 9–9=0

4 1

Subtract 23 from 138 by writing the numbers vertically and using the place value blocks and vertical subtraction. Use

for 1 hundred (H), for 1 ten (T) and

for 1 ones (O). H –

So, 138 – 23 = 115 Do It Together

Solve 567 – 123 using the place value blocks and vertical subtraction. Use

for 1 hundred (H), for 1 ten (T) and

for 1 ones (O).

–

Chapter 7 • Addition and Subtraction of 3-digit Numbers

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_____

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Do It Yourself 7B 1

Subtract using place value block. Use

for 1 hundred (H),

457 – 14

458 – 327

854 – 301

923 – 112

H –

668 – 118

O 5

–

8 3

768 – 45

–

894 – 42

O 5 3

Subtract the given 3-digit numbers. H –

457 – 55

for 1 ones (O).

Subtract. a

for 1 ten (T) and

–

8 2

–

9 1

780 – 600

589 – 589

879 – 209

989 – 209

987 – 367

357 – 123

Write the numbers vertically and subtract them. a

948 – 25

136 – 6

667 – 63

563 – 243

869 – 35

875 – 521

310 – 200

664 – 302

484 – 4

How much do you take away from 567 to get 400?

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Word Problems 1

Sarah picked 364 apples from the orchard. She sold 251 apples. How many apples were left with her?

Diya had 357 colourful beads. She used 145 beads to make bracelets. How many beads are left with her?

When to add? When to subtract? Shreya and her friends went to a library. Teacher: Could you please help me arrange the books? Shreya: Yes, ma’am. There were 135 books on the table. Teacher gave 125 more books. Shreya and her friends arranged 100 books. Shreya: Do you know how many books are there now?

Identifying the Right Operation Let us help Shreya with counting and arranging the books! First, there were 135 books. Then, 125 more books were added. So, Shreya needs to add 135 and 125 to find the total number of books.

Remember! When we have to find the total number, or how many in all, we add.

There are 260 books in all. Shreya and her friends arranged 100 books. So how many are remaining?

Chapter 7 • Addition and Subtraction of 3-digit Numbers

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We have to subtract 100 from 260.

–

Remember! When we have to find how many are left or remaining, we subtract.

160 books are left for arranging. Situation

Example 3

There were 235 apples in a basket. 125 apples were sold. How many apples are left?

Situation

Example 4

Add or Subtract? Addition Subtraction

 

We have to find how many are left. So, we subtract.

–

Add or Subtract?

There were 110 books. 100 Addition  more books were added. How many books are there Subtraction in all? We have to find out how many are there in all. So, we add.

Do It Together

Solve H

Solve H +

0 0

Read the situation. Underline the keywords that tell you whether to add or subtract. Then, solve. Situation

Addition

Subtraction

Solve

There were 234 students in the hall. 150 more students joined them. How many students are there in the hall now?

Rahul had 262 crayons, he lost 130 crayons. How many crayons are left?

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Do It Yourself 7C 1

Identify the correct operation and solve. Situation

Addition

Subtraction

Solve

There are 456 books on a table. The teacher keeps 198 more books on the table. How many books are there on the table?

There were 568 toys in a toy store. 232 were sold. How many toys are left now?

Read the table that shows the number of animals in a farm. Find the correct operation and solve the problems.

Animal

What is the total number of sheet and goat on the farm?

Sheep

How many more dogs are there than sheep?

What is the total number of animals on the farm?

If 100 more cats were brought to the farm, what would be the total number of animals?

Number of Animals

Goat Dog

134

227 189

Word Problems 1

Anna had 235 toy cars. Her mother donated 100 toy cars. How many toy cars are left with Anna?

Shanti collected 567 seashells on Monday. She collected 123 more on Tuesday. How many seashells does she have now?

Chapter 7 • Addition and Subtraction of 3-digit Numbers

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Word problems on Addition and Subtraction There were 350 parents and 573 students at the annual school function. What is the total number of people who attended the annual function? Let us follow a step-by-step method to find the number of people who attended the function. What do we know? Parents who attended the function = 350

Students who attended the function = 573 What do we find? Total number of people who attended the function. How do we find? The keyword ‘total’ tells us that we need to add. Parents + students = 350 + 573 Solve to find the answer. H

So, 923 people attended the annual function. Example 5

Rudransh has 237 stamps. He gave 132 stamps to his brother. How many stamps are left with him? What do we know?

There were 237 stamps.

132 stamps were given away. What do we find?

Number of stamps left. How do we find?

The keyword ‘left’ tells us that we need to subtract.

Stamps left = Number of stamps – Number of stamps given away 118

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Solve the problem to find the answer. H 2

–

So, 105 stamps are left with Rudransh. Do It Together

Manya has 124 candies. She gave 120 candies to her friends. How many candies are left? Use the method given below to solve. What do we know?

What do we find?

How do we find (keyword)?

Solve the problem to find the answer.

Do It Yourself 7D 1

A shopkeeper had 583 packets of biscuits. He sold 272 packets. How many packets are left with the shopkeeper?

There were 764 mangoes in one basket and 220 in another basket. How many mangoes are there in total?

A bookshop had 234 books. 120 books were sold. How many books are left now?

Animesh had 398 cricket balls. He gave 171 to his friend. How many balls are left with him?

Suresh bought 456 red and 134 blue balloons for the school function. He used 378 balloons for decoration. How many balloons were left with him?

Word Problems 1

Priyansh’s grandfather planted 129 apple trees and 134 guava trees. How many trees did he plant altogether?

David has 234 beads. Simran has 448 beads. How many beads are there in all? If they used 140 beads to make bracelets, how many beads are left with them?

Chapter 7 • Addition and Subtraction of 3-digit Numbers

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Points to Remember • • • • • •

We write numbers according to their place value while adding and subtracting them.

To add or subtract numbers, we start from the ones place and move higher on the place value chart. In subtraction, the smaller number is always subtracted from the bigger number.

In vertical addition or subtraction, a blank space means that the number in that place is zero.

In word problems, words like join, add, added, put together, total and in all tell us that we need to add the numbers. In word problems, words like take away, subtract, less than, fewer, left and remaining tell us that we need to subtract the numbers.

Math Lab Setting: In group of 4 Materials Required: Number chits, pencil, operation chits Method: 1

Make chits for number 0 to 9. Make 2 operation chits by writing the addition (+) and subtraction (–) symbol on them.

Player 1 will pick 3 chits and form a 3-digit number.

Player 2 will again pick 3 chits and form a 3-digit number.

Player 3 will choose the operation chit: addition or subtraction. (Hint: Always remember to write smaller number below the bigger number in subtraction.)

Player 4 will solve it.

Repeat the cycle until everyone gets their turn to solve.

120

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Chapter Checkup 1

Add. H

+ d

+ 2

– d

–

+ e

– e

–

Find the answers.

+ f

6 3

–

Subtract 400 from 850.

Sum of 345 and 100.

567 + 235

Subtract the smallest 3-digit number from 289.

379 – 170

Solve. a

301 + 245

789 – 234

301 + 301

478 – 235

500 – 500

123 + 234

Fill in the blanks. a

456 + 456

9 hundreds + _____ tens + 2 ones

763 + 234

_____ hundreds + 9 tens + 7 ones

435 + 546

9 hundreds + 8 tens + _____ one

165 + 678

_____ hundreds + 4 tens + 3 ones

598 + 254

8 hundreds + _____ tens + 2 ones

Chapter 7 • Addition and Subtraction of 3-digit Numbers

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Subtract. a

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Identify the correct operation and solve. Situation

Addition

Subtraction

Solve

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

Mona had 123 marbles. Her friend Tina had 167 marbles. How many marbles are there in all?

Misty has a book with 167 pages. She read 123 pages. How many pages are left to be read?

A milkman delivers milk to different houses. Solve the riddles in Column 2 and match them to the correct house numbers in Column 1. Add or subtract to find the answers. Column 1

Column 2

Mr Parikh house no. is 599.

My number is 100 more than 816.

Mr Ahmad house no. is 300.

My number is the number after 600.

Ms Shah house no. is 916.

My number is the number before 600.

Mrs Paul house no. is 242.

My number is 10 less than 310.

Mrs Sharma house no. is 601.

My number is the number before 800.

Mr Parikh house no. is 799.

My number is 25 less than 267.

There are 568 English books and 345 Hindi books in a school library. Which books are fewer and by how much?

Sanchi has 456 marbles. Out of which, she lost 124 marbles. Find out how many marbles are left with her.

There are 145 mango trees and 206 apple trees in the garden. How many trees are there in all?

122

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Given below are place value blocks to show a number. [Hundred =

, Tens = , Ones =

]

What is the number shown by the place value blocks?

What will the new number be, if Anaisha adds 145 to this number?

Word Problems 1

345 people visited the Book fair on Monday. On Tuesday, 257 people visited the Book

Rohit baked a batch of 340 biscuits for an event. He baked 105 more biscuits for the

fair. How many people visited the Book fair on Monday and Tuesday?

same event. He sold 130 biscuits at the event. How many biscuits does he have now?

Chapter 7 • Addition and Subtraction of 3-digit Numbers

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38 Multiplication Tables 3, 4 and 6 Let's Recall Repeated addition is adding the same number again and again. For example, here are 5 groups of 4 flowers.

= 20

To find the total number of flowers we add 4 five times. This is known as repeated addition.

Let's Warm-up

Match the following. 4+4+4 6+6+6+6 2+2+2+2+2+2 6+6+6 8+8+8+8+8

I scored _________ out of 5.

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Multiplication Tables Real Life Connect

Aditya is helping her mother to set the table. Some guests are coming for lunch. Place 3 plates on the table. Bring 2 bowls for each plate. How many bowls should I bring?

Multiplying by 3 Multiplying by 3 means counting all the groups of 3 together.

= 6

3 groups of 2 = 6 or 3 twos are 6. 3 × 2 = 6 bowls. Let’s count the bowls to build the multiplication table of 3.

Chapter 8 • Multiplication Tables 3, 4 and 6

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Remember! Multiplication is repeated addition.

3 ones are 3

3×1=3

3 twos are 6

3×2=6

3 threes are 9

3×3=9

3 fours are 12

3 × 4 = 12

3 fives are 15

3 × 5 = 15

3 sixes are 18

3 × 6 = 18

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Example 1

3 sevens are 21

3 × 7 = 21

3 eights are 24

3 × 8 = 24

3 nines are 27

3 × 9 = 27

3 tens are 30

3 × 10 = 30

Count the number of groups. Count the number of ducks in each group. Write the multiplied answer.

There are 3 groups.

There are 5 ducks in each group.

The multiplied answer is: 3 × 5 = 15. Example 2

Use the table of 3 to find 3 × 7. 3 × 7 = 21.

Do It Together

Draw stars to show the table of 3. 3×5 3×8 3×2 3×9 3×6

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Do It Yourself 8A 1

Write the multiplication fact. a b c d

Use the table of 3 and answer. a

3×9

3×5

Fill in the blanks.

3×8

3 × 10

3 × _____ = 18

3 × _____ = 30

3 × _____ = 6

3 × _____ = 27

3 × _____ = 24

3 × _____ = 3

3×4

Write the multiplication statement for the following from the table of 3. a

3×6

Fill in the missing numbers using the table of 3. a

3, 6, 9, ___

18, 21, ___, 27

12, ___, ___, ___, 21

___, 24, ___, 30

9, ___, ___, ___

15, ___, ___, ___

Word Problems 1

Akhil has 3 keychains with 6 keys in each keychain. How many keys are there together?

Macy wrote a poem of 3 lines. Each line has 8 words. How many words are there in all?

Kunal, Manvi and Ruchi have 7 books with them. How many books are there in total?

Chapter 8 • Multiplication Tables 3, 4 and 6

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Multiplying by 4 Aditya is sitting at the table with his parents. Aditya’s sister Mohi walks in. Aditya, place 1 more plate for Mohi. Place 3 cookies on each plate. Sure Mom!

There were 3 plates. Aditya placed one more plate. There are 4 plates now. He placed 3 cookies on each plate.

4 groups of 3 = 12

4 × 3 = 12 cookies

Let’s count the number of cookies to build the table of 4. 4 ones are 4

4×1=4

4 twos are 8

4×2=8

4 threes are 12

4 × 3 = 12

4 fours are 16

4 × 4 = 16

4 fives are 20

4 × 5 = 20

4 sixes are 24

4 × 6 = 24

4 sevens are 28 4 × 7 = 28 4 eights are 32

4 × 8 = 32

4 nines are 36

4 × 9 = 36

4 tens are 40

4 × 10 = 40

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Example 3

Count the number of groups. Count the number of marbles in each group. Write the multiplication fact.

There are 4 groups of 6 marbles.

Think and Tell

Multiplication fact: 4 × 6 = 24 Example 4

What is 4 × 11?

Use the table of 4 to find 4 × 9. 4 × 9 = 36.

Do It Together

Fill in the missing numbers. 1

11 21

25 34

Do It Yourself 8B 1

Write the multiplication fact. a

4 groups of 3

4 groups of 8

4 groups of 2

4 groups of 6

4 groups of 9

4 groups of 1

4 × 10

Use the table of 4and answer. a

4×5

4×3

Fill in the blanks.

4×7

4 ______ are 20

4 ______ are 40

4 ______ are 36

4 ______ are 16

4 ______ are 8

4 ______ are 24

Chapter 8 • Multiplication Tables 3, 4 and 6

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4×1

4×8

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Write the multiplication statement using the table of 4. a

There are 4 boxes with equal number of books. How many books are there in total, if there are: a

6 books in each box

8 books in each box

3 books in each box

7 books in each box

5 books in each box

4 books in each box

Word Problems 1

Niha has 5 flowers in one basket. If she has 4 such baskets, how many flowers does she have in total?

A puzzle has 4 pieces in it. How many puzzles will have 36 pieces?

Order in Multiplication

Think and Tell

In multiplication, the order in which we put the numbers does not change the answer.

7 + 7 + 7 + 7 + 7 + 7 = ___ × ___ = ___

= 12

3 groups of 4 is the same as 4 groups of 3. 3 × 4 = 12 and 4 × 3 = 12 Therefore, no matter how you arrange two numbers in multiplication, the result remains the same.

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Multiplying by 6 After lunch, everyone played a game with balloons. Mohi, we are 6 members. We need 4 balloons for each member! How many balloons do we need in total?

Multiplying by 6 means counting all the groups of 6 together. So, 6 members with 4 balloons will have,

6 × 4 = 24 balloons or 6 fours are 24.

Let’s count the number of balloons to build the table of 6. 6 ones are 6

6×1=6

6 twos are 12

6 × 2 = 12

6 threes are 18 6 × 3 = 18 6 fours are 24

6 × 4 = 24

6 fives are 30

6 × 5 = 30

6 sixes are 36

6 × 6 = 36

6 sevens are 42 6 × 7 = 42 6 eights are 48 6 × 8 = 48

Chapter 8 • Multiplication Tables 3, 4 and 6

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6 nines are 54

6 × 9 = 54

6 tens are 60

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Example 5

Count the number of groups. Count the number of pens in each group. Write the multiplication fact.

There are 6 groups of 7 pens. Multiplication fact: 6 × 7 = 42, or 7 x 6 = 42 Example 6

Use table of 6 to find 6 × 8. 6 × 8 = 48.

Do It Together

Circle the numbers that come in the multiplication table of 6 as the answer 2

Do It Yourself 8C 1

Write the multiplication statement for the pictures. a b c

Use the table of 6 and answer. a

6 times 7

6 times 4

6 times 8

6 times 10

6 times 3

6 times 9

Fill in the blanks. a

6 × ____ = 30

6 × ____ = 42

6 × ____ = 54

6 × ____ = 12

6 × ____ = 48

6 × ____ = 18

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Use the table of 6 and answer. a

6×8

6×1

6×7

6×4

6×9

6×6

Fill in the missing numbers using table of 6. a

30, ______, 42

12, ______, 24

24, ______, 36

48, ______, 60

Did You Know? When a number is multiplied by 0, the answer is always a 0 (7 × 0 = 0). When a number is multiplied by 1, the answer is always itself (5 × 1 = 5).

Word Problems 1

Preetham has 6 baskets and each basket contains 5 apples. How many apples does Preetham have in all the baskets?

Sarah wants to buy 6 packs of stickers and each pack has 9 stickers. How many stickers will Sarah have in total?

A packet has 6 cookies in it. How many packets will have 48 cookies?

Multiplying 2-digit Numbers Real Life Connect

Meghna went to a shop to buy some eggs. In the shop, she saw eggs in trays. There were 4 trays, and each tray had 12 eggs inside it. She wondered how many eggs would there be in total. But I don’t know how to find 12 × 4.

Chapter 8 • Multiplication Tables 3, 4 and 6

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Multiplication Without Regrouping To multiply a 2-digit number with a 1-digit number, we can use the column method. The shopkeeper has 4 trays with 12 eggs in each tray. We need to multiply 12 and 4. Let us multiply 12 by 4 using the multiplication table of the smaller number 4. Step 1

Step 2

Step 3

Write the 2-digit number according to its place value in the table. Write the smaller number below it.

Multiply the smaller number with the ones of the 2-digit number. 4×2=8 Write 8 in the ones place.

Multiply the smaller number with the tens of the 2-digit number. 4×1=4 Write 4 in the tens place.

So, 12 × 4 = 48. Example 7

Multiply 23 × 3. Step 1

Step 2

Step 3

3×3=9

3×2=6

So, 23 × 3 = 69.

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Do It Together

Solve the multiplication. T 2 ×

O 1 4 4

T 3 × 9

O 2 3

T 3 ×

O 4 2

T 4 ×

O 0 2

Do It Yourself 8D 1

Find the missing number. a

____ 2

____

Find the answer. a

Multiply. a

20 × 4

34 × 2

44 × 2

31 × 3

42 × 2

21 x 4

Multiply 13 with 3.

Sohel has 2 boxes. He has 43 books in each box. How many books are there in total?

Word Problem 1

Sam packed 21 boxes of cupcakes. He puts 3 cupcakes in one box. How many cupcakes are there in total?

Chapter 8 • Multiplication Tables 3, 4 and 6

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Multiplication with Regrouping Let's learn how to group ones and tens to make multiplication of larger numbers easier! Regrouping Ones A bag has 13 items of fruit. There are 5 such bags. How many items of fruit are there in total? We need to multiply 13 × 5. Look at the steps: Step 1

Step 2

Step 3

Write the 2-digit number according to its place value in the table. Write the smaller number below it.

Multiply the smaller number with the ones of the 2-digit number. 5 × 3 = 15 15 has 1 ten and 5 ones. Write 5 in the ones place and 1 on top of the tens place.

Multiply the smaller number with the tens of the 2-digit number. 5×1=5 Add 1 from tens. 5+1=6 Write 6 in the tens place. So, 13 × 5 = 65.

T 1 ×

Example 8

O 3 5

T +1 1 ×

O 3 5 5

T +1 1 × 6

O 3 5 5

Multiply 28 × 3. Step 1

T 2 ×

O 8 3

Step 2

Step 3

3 × 8 = 24

3×2=6 6+2=8

T +2 2 ×

O 8 3 4

T +2 2 × 8

O 8 3 4

So, 28 × 3 = 84. 136

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Do It Together

Multiply. T +1 4 ×

O 6 2 2

T 2 ×

O 9 3 7

T 1 ×

O 9 4

T 1 ×

O 2 6

Regrouping Tens Ruchi put 42 cashewnuts in one packet. She gave 3 such packets to her friends. To find the total, we need to multiply 42 × 3. Look at the steps: Step 2

Step 1 Write the 2-digit number according to its place value in the table. Write the smaller number below it. H

T 4 ×

Multiply the smaller number with the ones of the 2-digit number. 3×2=6 Write 6 in the ones place.

O 2 3

T 4 ×

O 2 3 6

Step 3 Multiply the smaller number with the tens of the 2-digit number. 3 × 4 = 12 Write 1 in the hundreds place and 2 in the tens place. H

T 4 × 2

O 2 3 6

So, 42 × 3 = 126. Example 9

Multiply 51 × 4. Step 1 H

T 5 ×

O 1 4

Step 2

Step 3

4×1=4

4 × 5 = 20

T 5 ×

O 1 4 4

T 5 × 0

O 1 4 4

So, 51 × 4 = 204. Chapter 8 • Multiplication Tables 3, 4 and 6

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Do It Together

Multiply. 1

T 6 ×

O 2 3 6

T 7 ×

O 1 4

T 8 ×

O 4 2

T 9 ×

O 1 6

Regrouping Ones and Tens Abdul has 93 marbles in each packet. He has 4 such packets. To see how many marbles Abdul has in total, we need to multiply 93 by 4. Look at the given steps: Step 1 Write the 2-digit number according to its place value in the table. Write the smaller number below it. Step 2 Multiply the smaller number with the ones of the 2-digit number.

T 9 ×

T O +1 9 3 × 4 2

4 × 3 = 12

12 has 1 ten and 2 ones.

O 3 4

Write 2 in ones place and 1 on top near tens place. Step 3 Multiply the smaller number H T with the tens of the 2-digit +1 9 number. × 9 × 4 = 36 3 7 Add 1 from tens. 36 + 1 = 37 Write 3 in the hundreds place and 7 in tens place. So, 93 × 4 = 372.

Error Alert! O 3 4 2

H 2

T O +2 3 4 × 7 1 8

T O +2 3 4 × 7 3 8

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Multiply 63 × 8.

Example 10

Step 1

Step 2

Step 3

8 × 6 = 48 48 + 2 = 50

8 × 3 = 24 T 6 ×

O 3 8

T +2 6 ×

O 3 8 4

T +2 6 × 0

O 3 8 4

So, 63 × 8 = 504 Do It Together

Multiply. H

T O +2 5 6 × 4 4

T 3 × 7

O 5 5

Do It Yourself 8E 1

Multiply. a

Solve.

18 × 4

45 × 2

6 × 61

3 × 92

5 × 59

28 × 6

Martin has 13 jars, and each jar has 6 marbles in it. How many marbles does he have in total?

A farmer planted 6 rows of corn, and each row had 41 corn plants. How many corn plants were planted?

Chapter 8 • Multiplication Tables 3, 4 and 6

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At the market, 2 sisters and 3 brothers bought 92 sugar canes each. How many sugar canes did they buy altogether?

Word Problem 1

In a store, there are 59 boxes of crayons, and each box contains 5 crayons. How many crayons are there altogether?

Story Problems on Multiplication Let us explore some story problems in multiplication. Megha went to another shop and saw 6 trays with 30 eggs in each tray. How many eggs were there in total? Step 1 What do we know? Total trays = 6 Eggs in each tray = 30

Step 2

Step 3

What do we need to find? Solve to find the answer. H T O We need to find the total number of eggs by 3 0 multiplying 30 × 6. × 6 1

There are 180 eggs in total. Example 11

n a garden, there are rows of flowers, and each row has 2 flowers. How many flowers are there in the garden? Step 3 What do we know? What do we need to find? Solve to find the answer. Number of rows = 5 The total number of H T O Number of flowers in flowers by multiplying +1 6 2 each row = 62 62 × 5. × 5 3 1 0 There are 310 flowers in the garden. Step 1

Step 2

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Do It Together

A hall has desks, and can sit in the hall? H

people can sit at each desk. How many people

So, _______ people can sit in the hall.

Do It Yourself 8F 1

There are 98 packets, and 5 candies in each packet. How many candies are there in total?

A bus has 46 seats, and there are 4 such buses. How many seats are there in total?

A big box contains 85 pencils, and each pencil costs ₹6. What is the total cost of all the pencils?

There are 6 pins in each pouch. If there are 52 such pouches, how many pins are there in total?

Deepak, Sandy, Kavya and Ali collected 38 stamps each. How many stamps do they have in total.

Word Problem 1

A pond has 68 fish. If a lake has fish three times that of the pond, how many fish are there in the lake?

Points to Remember •

We can use the multiplication tables to multiply numbers by 3, 4 and 6.

•

The order of multiplication doesn't change the answer.

•

To multiply 2-digit numbers with 1-digit, we can use the column method.

•

Always multiply with the digit in ones and then multiply with the digit in tens.

•

Regroup ones and tens wherever needed.

Chapter 8 • Multiplication Tables 3, 4 and 6

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Math Lab What Is My Position!

Setting: Whole class

Materials Required: 150 ice cream sticks, 6 transparent glasses To do: 1

Take 4 glasses and 36 ice cream sticks.

Make bundles of tens with the ice cream sticks. Keep the single sticks on side. Put all of these in the glasses.

Make 4 such groups of ice cream sticks in 4 glasses.

This shows 4 groups of 36 or 4 × 36.

Put all the ice cream sticks together and find the total.

Multiply 36 by 4 using the column method.

Match your answer with the total number of ice cream sticks. Discuss the answer in class.

Try solving more multiplication problems using both methods.

Chapter Checkup 1

Complete the table of 6. 6×1=

6×2=

6×6= 2

6×7=

6×7

6×4=

6×8=

Solve the given multiplication. a

6×3=

4×9

6×6

Fill in the missing numbers.

6×5=

6×9= d

6 × 10 =

3×5

4×8

3×9

4 × 8 = ____ × 4 = ____

7 × 6 = 6 × 7 = ____

6 × ____ = 10 × ____ = 60

5 × 3 = ____ × 5 = ____

4 × 5 = 5 × 4 = ____

6 × ____ = 5 × ____ = 30

Multiply the given numbers. a

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Multiply.

25 × 4

38 × 5

47 × 6

56 × 3

82 × 5

69 × 2

73 × 6

61 × 5

In a cricket match, Rahul hit the ball for 6 rounds, and each round earned his team 7 runs. How many runs did his team score?

Ramesh bought 4 boxes of mangoes from the market, and each box contained 28 mangoes. How many mangoes did he buy?

There are 6 plates of dosa, and each plate costs `85. How much do all the dosas cost in total?

A teacher bought 5 packets of star stickers, and each packet had 38 stickers. How many stickers did she buy?

Ananya practised her dance for 6 days in a dance class, and each day she spent ₹76 on travelling. How much money did she spend in total?

Word Problem 1

A vegetable vendor sells 5 baskets of tomatoes, and each basket contains 42 tomatoes. How many tomatoes does he sell?

Chapter 8 • Multiplication Tables 3, 4 and 6

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Introduction to Division

Let's Recall 3 groups with 2 birds in each. 3×2=6

4 groups with 5 balloons in each. 4 × 5 = 20

Let's Warm-up

Match the pictures with the correct statement. 1

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

I scored ___________ out of 4.

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Understanding Division Real Life Connect

Sam has 6 chocolates.

Sam wants to share the chocolates with his friend, Ravi. Both of them should have the same number of chocolates. How many chocolates will Sam share with Ravi?

Division as Equal Sharing Let us divide the 6 chocolates equally between Sam and Ravi. First, each one takes 1 chocolate.

Sam

Ravi

We strike out 2.

4 chocolates are left with Sam. Then, again they take 1 more chocolate each.

Sam

Ravi

We strike out 2 more chocolates. Chapter 9 • Introduction to Division

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Now, 2 chocolates are left with Sam. Then, they take 1 more chocolate each.

Sam

Ravi

We strike out 2 chocolates.

No more chocolates are left with Sam.

Sam

Ravi

We get 2 groups of 3 chocolates.

Sam and Ravi have 3 chocolates each. Then, one more friend Priya joins and they have only 6 chocolates. How will they share now? They again put their chocolates together.

First, they will take 1 chocolate each.

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Sam

Priya

Ravi

We strike out 3 chocolates.

3 chocolates are left with Sam. They will again take 1 chocolate each.

Sam

Priya

Ravi

We strike out 3 more chocolates.

No chocolates are left with Sam.

Sam

Ravi

We get 3 groups of 2 chocolates.

Priya

Sam, Ravi and Priya have 2 chocolates each. Chapter 9 • Introduction to Division

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Example 1

Share 4 laddoos between Meena and Tina.

First, we strike out 2 laddoos and give Meena and Tina one each. 2 laddoos are remaining. Meena and Tina each have 1 laddoo each. 2 laddoos are remaining.

Then, we strike out the 2 laddoos and give Meena and Tina one each. Meena and Tina each have 2 laddoos now. No more laddoos are remaining. Meena and Tina gets 2 laddoos each. We get 2 groups of 2 laddoos. Example 2

There are 10 apples. Circle to show 2 apples in each basket.

There are 2 apples in each basket. There are 5 groups of 2 apples.

Remember! In division, equal number of objects are kept in each group.

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Do It Together

Share 16 strawberries among 4 friends.

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

Do It Yourself 9A 1

Circle the picture that show equal sharing. a

Chapter 9 • Introduction to Division

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Circle the objects to make equal number of groups. a

Share 8 bananas among 4 children.

There are _________ groups of 2. b

Share 12 cupcakes among 4 children.

There are _________ groups of 3. c

Share 10 biscuits among 2 children.

There are _________ groups of 5. 3

Draw and share the objects equally. a

Share 9 carrots among 3 rabbits.

Each rabbit will get _________ carrots. b

Share 8 apples between 2 friends.

Each friend will get _________ apples.

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There are 20 mangoes.

Divide the mangoes among 2 children.

Each child will get __________ mangoes. b

Divide the mangoes among 5 children.

Each child will get __________ mangoes. 5

There are 18 laddoos. Divide the laddoos in the given plates, so that each plate have the same number of laddoos. Draw and show.

There are __________ laddoos in each plate.

Division as Repeated Subtraction Next day, 8 chocolates were divided between Sam and Ravi. They got 4 chocolates each. Chapter 9 • Introduction to Division

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Let us understand this using subtraction. There were 8 chocolates.

Sam

Ravi

One chocolate was taken by each. 8–2=6

6 chocolates are left. One more chocolate was taken by each. 6–2=4

4 chocolates are left One more chocolate was taken by each. 4–2=2

2 chocolates are left. Again, one more chocolate was taken by each. 2–2=0

No chocolates are left.

We see that 2 is subtracted from 8 four times. So, division is also known as repeated subtraction. Let us see using a number strip.

2–2=0

4–2=2

6–2=4

8–2=6

The answer is 4 because we are subtracting 2 four times until we get 0. 152

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Division Fact Dividing 8 in equal groups of 2 can be written as 8 ÷ 2 = 4. This is the division fact.

Remember! We keep subtracting from the total until the answer is 0.

÷ is the symbol used to show division. 8÷2=4

8 divided into groups of 2 will give 4 groups. Number of things in each group.

Total number of things. Example 3

Number of groups.

Divide 12 pencils among a group of students such that each student gets 3 pencils. Use repeated subtraction to find the number of students. 12 – 3 = 9 9–3=6 6–3=3 3–3=0

3 is subtracted from 12 four times. 12 ÷ 3 = 4 is the division fact , so 4 students get 3 pencils each. Example 4

Show the division fact 12 ÷ 4 using number strip. We start going back from 12 by 4 steps. 4–4=0

12 – 4 = 8

8–4=4 3

2 3

1 7

The answer is 3 because we are subtracting 4 three times until we get 0. Chapter 9 • Introduction to Division

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Do It Together

Divide 15 apples in group of 5. Show using repeated subtraction and using a number strip. Write down the division fact. 15 – 5 = _______ 10 – _______ = 5 _______ – _______ = 0

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

Do It Yourself 9B 1

Use repeated subtraction to show the answer. How many children will get these items if: a

18 chocolates are shared equally in groups of 6?

9 books are shared equally in groups of 3?

14 pens are shared equally in groups of 2?

8 apples are shared equally in groups of 4?

Circle the correct division fact. a

12 books shared in groups of 3.

15 pencils shared in groups of 5.

3 ÷ 12 15 ÷ 5

12 ÷ 3 5 ÷ 15

12 ÷ 12 15 ÷ 15

20 candies shared in groups of 5. 5 ÷ 20

20 ÷ 20

20 ÷ 5

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Show the repeated subtraction using the number strip. 15 ÷ 3

10 ÷ 5

0 4

Complete the given problems.

Leena needs to divide 12 chocolates equally among 4 friends. Show using a number line. 0

The division fact is ______________. 4 is subtracted ______________ times until she gets 0. 5

Write if true or false. a

If 15 objects are divided in 3 equal groups, there are 5 objects in each group. ______________

If 12 objects are divided in 4 equal groups, there are 2 objects in each group. ______________

20 in 4 equal groups can be written as 4 ÷ 20. ______________

Word Problems 1

Ravi has 24 flowers that he wants to put in 8 vases. How many flowers can he put in each vase? Show using equal sharing.

There are 30 candles that are to be packed in 6 boxes. How many candles will be packed in each box. Show using repeated subtraction.

Division and Multiplication are Related Let us see how multiplication and division are related. Case 1: 8 chocolates are divided between Sam and Ravi. They have 4 chocolates each. Chapter 9 • Introduction to Division

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We have 2 groups of 4.

Division fact: 8 ÷ 2 = 4 How do we get this using multiplication? Say the table of 2 until we get 8. We know: 2 × 4 = 8. (Multiplication fact) So, 8 ÷ 2 = 4. Case 2: 8 chocolates are divided among 4 children. They get 2 chocolates each. We have 4 groups of 2.

Division fact: 8 ÷ 4 = 2 How do we get this using multiplication? Say the table of 4 until we get 8.

Error Alert! Divide 12 in 3 equal group is written as:

We know:

12 ÷ 3 = 4

4 × 2 = 8. (Multiplication fact)

3 ÷ 12 = 4

So, 8 ÷ 4 =2.

For 1 multiplication fact, there can be 2 division facts: Or

4×2=8 8÷2=4

8÷4=2

2×4=8 8÷2=4

8÷4=2

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Example 5

Write the division fact and the multiplication fact for the following. There are 4 groups of 3 balloons.

We have 4 groups of 3.

Multiplication fact: 4 × 3 = 12

Think and Tell!

Division facts: 12 ÷ 4 = 3 and 12 ÷ 3 = 4 Example 6

Can you divide 13 mangoes among 4 friends?

Find the answer for 14 ÷2.

How many will each friend get?

We say the table of 2 until we get 14. 2 × 7 = 14

So, 14 ÷ 2 = 7 Do It Together

Write down division fact from the given multiplication fact. 3 × 5 = 15 _____ ÷ 3 = 5

15 ÷ _____ = 3

Do It Yourself 9C 1

Fill in the blanks to write down the division and the multiplication facts. 5 × 4 = _______

_______ ÷ 4 = 5

6 × 2 = 12

12 ÷ _______ = 2

4 × 7 = _______

28 ÷ _______= 7

5 × 7 = 35

35 ÷ _______ = 7

10 × 5 = _______

_______ ÷ 5 = 10

Chapter 9 • Introduction to Division

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Write the multiplication fact. Then write one division fact for the multiplication fact. 3 groups with 5 in each

Multiplication Fact

Division Fact

4 groups with 2 in each 6 groups with 3 in each 5 groups with 5 in each 3

Write 2 division facts for the given multiplication facts. a

4×2=8

3 × 4 = 12

5 × 6 = 30

Look at the picture and write down the multiplication facts and the division fact.

20 apples are divided in 4 groups. Write down the multiplication fact and the division fact.

Word Problem 1

Anna wants to equally share 24 juice bottles among 12 of her friends. How many will each friend get? Write the division fact to show the answer. Write the multiplication fact.

How to Divide Real Life Connect

Shweta has 18 roses with her. She needs to make 6 garlands with equal number of flowers in each garland. How many roses will each garland have?

We know 18 ÷ 6 = 3 (We say the table of 6 until we get 18, 6 × 3 = 18) Each garland will have 3 flowers in it.

Let us understand other ways of writing and solving division. 158

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Long Division We will use the division house to divide two numbers. 18 ÷ 6 = 3 can be written as: 3. Say the table of 6 until we get 18. 6 × 3 = 18. So, 3 is the answer.

1. Write the bigger number inside the division house. 3 6

2. Write the smaller number outside the division house. Example 7

Solve 15 ÷ 5. 3 5

Do It Together

We say the table of 5 until we get 15.

5 × 3 = 15

So, 3 is the answer.

Solve 16 ÷ 4.

Write the answer here.

Do It Yourself 9D 1

Solve the given sums using the long division method. a

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Which sum shows the correct way to write long division method. Circle it.

12 ÷ 3 = 4

5 4

12 4

18 ÷ 2 = 9

5 9

Circle the sum that is solved correctly. 6 2 b

9 3

7 5

27 5

Write down the sums and solve using the long division method. a

20 ÷ 4 = 5

18 ÷ 2

20 ÷ 5

16 ÷ 2

28 ÷ 4

42 ÷ 6

Show long division method to show 21 chocolates in 7 groups of 3.

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Word Problems on Division We can use the CUBES method to solve story sums. In the CUBES method, we follow the 5 given steps. Circle the numbers.

C: Circle the numbers. U: Underline the question.

18 flowers are kept equally in 3 baskets. How many flowers are there in each basket ? Underline the question.

Box the key words.

B: Box the key words. E: Evaluate/draw. S: Solve and check!

Total number of flowers = 18 Number of baskets = 3

Evaluate

Flowers in each basket = 18 ÷ 3 There are 6 flowers in each basket. Check: 3 × 6 = 18. So, the answer is correct. Example 8

Solve and Check! 3

20 balls are kept equally in 5 boxes. How many balls are there in each box ? 4 5

There are 4 balls in each box. Do It Together

Mother bought 30 sweets for a festival. She has to give equal number of sweets to 6 members of the family. How many sweets will each family member get? Total number of sweets = ______________ Number of family members = ______________ Number of sweets each family member will get = 30 _____6 Each family member will get ______________ sweets. Chapter 9 • Introduction to Division

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Do It Yourself 9E 1

There are 12 pencils. The pencils are kept equally in 4 pencil boxes. How many pencils are there in each box?

There are 20 cherries. The cherries are placed equally on top of 5 cakes. How many cherries are there on each cake?

Rita has 10 apples. She needs to give equal number of apples to 5 friends. How many apples will each friend get?

Nidhi has 18 books with her. She needs to arrange the books equally on 6 shelves. How many books will there be on each shelf?

What if Sherry wants to distribute 35 candies among 7 children. What will she do multiply or divide? Help her find out.

Points to Remember • Division means a set of things shared equally among groups. • Division is repeated subtraction. • The same number is subtracted unless 0 is left. • The symbol ÷ is used to show division. • Division and multiplication are related.

Math Lab Let’s Share Setting: 5 people in a group. Materials required: 20 objects like crayons, rajma beans, sticks, pebbles. What to do? 1

Start by sharing 20 things equally among 2 children. How many will each get?

Share 20 things equally among 4 children. How many will each get?

Share 20 things equally among 5 children. How many will each get? Write down the division fact in each case.

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Chapter Checkup 1

Circle to make equal groups. a

Make groups of 4.

There are _____ groups of 4. b

Make groups of 2.

There are _____ groups of 2. c

Make groups of 3.

There are _____ groups of 3. 2

Divide the objects equally among the children. Draw and show. a

15 apples among 5 children.

12 mangoes among 4 children.

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Divide the objects using repeated subtraction. a

12 balls in 4 boxes.

18 pencils in 3 boxes.

20 marbles in 5 boxes.

16 books on 2 shelves.

Use the number strip to show repeated subtraction. a

9÷3 0

14 ÷ 2 0

12 ÷ 6 0

Write down the division facts for the given multiplication fact. a

2×3=6

3 × 8 = 24

3×3=9

Solve. a

3 7

Solve using long division. a

25 ÷ 5

40 ÷ 4

30 ÷ 3

20 ÷ 2

Fill in the blanks. a

25 ÷ 5 is ________.

18 ÷ 3 is ________.

28 ÷ 4 is ________.

Julia has 18 flowers. She needs to keep equal number of flowers in 6 vases. How many flowers will there be in each vase?

Jack has 20 crayons. He needs to give equal number of crayons to 5 students. How many crayons will each student get?

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Word Problems 1

There are 24 toys in a room. Raj has to pack the toys equally in 4 boxes. How many toys will each box have?

Maya has 16 chocolates. She has to pack them equally in 4 boxes. How many chocolates will there be in each box?

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Understanding Fractions

Let's Recall We all love pizza, and it comes in pieces that are equal in size! It is split into 4, 6 or 8 pieces. But when we cut them ourselves, we might cut them into pieces that are not equal.

This pizza is divided into 2 equal parts.

This pizza is cut into 2 parts that are not equal.

A complete pizza is called one whole. When some thing is divided into equal parts, we get 2 or more parts that are exactly equal in size. Equal Parts

Parts that are not equal

Let's Warm-up

Tick the pictures showing equal parts. 1

I scored ___________ out of 4.

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Understanding Fractions Real Life Connect

Sonu and Neha were having dinner. Only one chapati was left. Both of them wanted to eat it. What can they do?

Equal Parts Mother gave them an idea to cut the chapati in equal parts.

Equal parts Here, both the parts are of the same size. They are equal parts.

Unequal parts Here, both the parts are not of the same size. They are unequal parts.

When something is divided into parts that are not equal, the parts are called unequal parts. Parts of Whole Neha got a whole chocolate. Let us help her to divide it in equal parts.

Remember! Whole of something means a complete thing.

2 equal parts

3 equal parts

4 equal parts

Think and Tell Can we divide all things in equal parts? Can we divide a sugar crystal into equal parts? Chapter 10 • Understanding Fractions

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Example 1

Tick the equal parts.



Here, the 3 parts are Here, the 2 parts are Here, the 2 parts are not equal parts. equal parts. equal parts. Example 2

 Here, the 3 parts are equal parts.

Divide the whole into equal parts.

Do It Together

2 parts

3 parts

2 parts

4 parts

Tick the box in which the image is divided into equal parts.



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Draw a line such that it cuts the shape into 2 equal parts.

Halves, Thirds and Fourths Let us learn more about fractions. We have a whole circle. Let us divide the circle in equal parts. 1

A whole is divided into two equal parts. Each part is called one-half.

A whole is divided into three equal parts. Each part is called one-third.

A whole is divided into four equal parts. Each part is called a quarter or one-fourth.

A whole is divided into four equal parts. Three out of four equal parts is called three-fourths.

A whole is divided into three equal parts. Two equal parts out of three parts is called two-thirds.

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Example 3

Colour one-half of the rectangle green.

Error Alert!

One-half means one out of two equal parts or halves.

Shape divided into unequal parts

One half

Colour two-thirds of the circle red.

Example 4

Shape divided into equal parts

Two-thirds means two parts out of the three equal parts.

Do It Together

One half

Shade the shapes to show the given fractions. 1

Three-fourths

Two-thirds

Writing Fractions Let us understand how we can write the fractions using numbers. Top part shows the number of parts shaded.

One-half

1 2 One out of two equal parts is shaded.

Remember! Bottom part shows the number of equal parts.

The parts shaded in a whole make the fraction.

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One-third

1 3

One-fourth

1 4

Three-fourths

3 4

Two-thirds

2 3

1 part out of 3 equal 1 part out of 4 equal 3 parts out of 4 2 parts out of 3 parts, shaded. parts, shaded. equal parts, shaded. equal parts, shaded.

Example 5

Write the fraction of the coloured parts in each of these shapes.

1 2

1 4

1 3

2 3

1 part out of 2 equal 1 part out of 4 equal 1 part out of 3 equal 2 parts out of 3 equal parts. parts. parts. parts.

Do It Together

Shade the parts or write the correct fraction.

3 4

1 4

Think and Tell If we divide a cake in 5 equal parts and take 4 parts away from it, then how do we write the fraction for it?

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Do It Yourself 10A 1

Circle the image which is divided into equal parts.

Tick () the fruit showing halves.

Colour two-thirds of the shape yellow.

Colour two-fourths of the shape brown.

Write the fraction in numbers. One-third

One-half

Three-fourths

Two-thirds

Write the fraction for the pizza eaten. a

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Word Problems Rachel cut the squares into 2 equal parts and shaded one part. Which of these DO NOT show the squares that Rachel might have cut out?

Priyanka cut the apple pie into 4 equal parts. She ate one part. Shade the circle to show the part that she ate.

Points to Remember •

When we divide a shape or thing into equal parts, then each part is a fraction of the whole.

•

Fractions of a whole is always equal in size.

•

When an object is cut into parts and the parts are not of the same size, they are called unequal parts.

•

When a whole is divided into 2 parts, each part is called one-half, written as

•

When a whole is divided into 4 equal parts, each part is called one-fourth or

•

1. It means one part out of two equal parts. 2

a quarter. It is written as 1 , it means one part out of four equal parts.

When a whole is divided into 3 equal parts, each part is called one-third, written as 1 . It means one part out of three equal parts.

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Math Lab Fun with Paper

Material required: A4 size white paper, colours, pencils. Setting: Groups of 4. What to do? 1

Take a A4 paper.

Fold it by bringing the opposite edges together.

Unfold the paper.

Then draw a line to show the strip split into two equal halves.

Try to divide the sheet in three and four equal parts and show the fractions you have learnt so far.

Chapter Checkup 1

Choose the image which is divided into equal parts.

Tick the image that is divided into 2 equal parts.

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Colour the shapes on each petal of the flower representing the given fraction on each flower. Colour the flowers with your own choice of colours. One has been done for you.

Onehalf

threefourths

Onefourth

Circle the correct fraction that the shaded part of the shape shows.

1 3

1 2

1 4

2 3

1 3

1 2

1 4

2 3

1 3

1 2

1 4

2 3

1 3

1 2

1 4

2 3

Match the following.

One-half Two-thirds Three-fourths One-third Chapter 10 • Understanding Fractions

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Write the fraction of one part for the given pizzas. One has been done for you. one-half

Write the fraction of the coloured part, in words. a

Fill in the blanks. a

1 means ______ part out of ______ equal parts. 2 1 means ______ part out of ______ equal parts. 4 1 means ______ part out of ______ equal parts. 3

3 means ______ parts out of ______ equal parts. 4 2 means ______ parts out of ______ equal parts. 3

Colour the given fraction for each shape.

1 2

3 4

1 3

1 4

2 3

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Write if true or false. a b c d

One-half is written in words as 1. 2 Two-third can also be written as 2. 3 When one out of 4 parts is shaded, the fraction is 1. 4 3 can be shown by shading 1 out of 4 parts. 4

Draw any shape of your choice and show the given fractions. a 1 2

_____________ _____________ _____________ _____________ b

3 4

Word Problem 1

Circle the correct fraction. a Neha, Shreya and Garima want to eat pizza. They ordered one pizza and cut it into 3 equal parts.

Pulkit divides a biscuit in 2 equal parts.

Varnit, Pariniti, Kamakshi and Rani divide a slice of watermelon into 4 equal parts.

Roopal divides a rectangle into 4 equal parts.

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Measurement

Let's Recall We use a school bag every day! What items do we have in our school bag? We have our books. We have our pencil box, which has our pencils and also erasers in it! We also have our water bottle.

The pencil is long. The crayon is short. The pencil is longer than the crayon. Is the book heavier or lighter than the pencil ? The book is heavier than the pencil! Try holding them both in your hands. Look at your water bottle. It holds water. So, does the bottle hold more water than the cup? The bottle can hold more water than the cup. So the bottle has more capacity than the cup.

Let's Warm-up Which is the tallest?

Which is the heaviest?

Which has the most capacity?

I scored _________ out of 3.

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Length Real Life Connect

Sunny and Priya have two ropes. Sunny says, “I have a long rope.”

I have a long rope.

I have a short rope.

Priya says, “I have a short rope.” “How short and how long are these ropes?” they wonder. Let’s help them find out.

Length Using Things Around Us Math Connect

We measure lengths to see how long or short something is. Sunny and Priya can use their hands and arms to find the length of the ropes. But their hands and arms are of different lengths. Is there a better way to measure the ropes? They can use a pencil to measure the length of each rope. Sunny’s rope is 5 pencils long. Priya’s rope is 2 pencils long. Let’s use something else. How about a stick? This rope is 2 sticks long. This rope is 1 stick long. We can use other things too. We may use a book, a crayon, a spoon or blocks to measure length.

Remember! The thing should be shorter than the thing we are measuring. But, it should not be too tiny like a grain.

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Think and Tell Can we measure a tall door with a small crayon? How about with a roll of newspaper?

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Example 1

Measure the length of a bottle with crayons. Step 1 Place crayons against the bottle. Step 2 Check how many crayons fit the length of the bottle.

The bottle is 3 crayons long. Example 2

Rahul has a book. He wants to measure the width of a table with it. Let’s see how!

The book is used 3 times to cover the width of the table. So, the width of the table is 3 books. Do It Together

Viraj wants to know how tall his toys are. He is using some blocks.

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The teddy is _________ blocks tall.

The toy giraffe is about _________ blocks tall. 7

The paper fan is _________ blocks tall.

The _________ and _________ are each about 2 blocks tall.

The teddy is 2 blocks taller than the toy car. The toy giraffe is _________ taller than the fan (2 blocks/1 block).

Do It Yourself 11A 1

Look at the picture. Tick () the answer. a

To measure the length of a tree ( ), we can use: A rope

To measure how tall a door is ( ), we can use: A sharpener

A ball A stick

Look at the picture. Fill in the blank. a

The door is about _______ bats tall. (10/5/3) b

The sofa is about _______ pencils long. (10/5/15) c

The mat is about _______ crayons long. (8/3/2)

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Which of these will you use to measure the length of these things? Choose the correct option from the box. crayon a

Book

rope length of the park

bottles c

length of a curtain

About how many blocks long are these things? Which is the longest?

Rani measured the height of her doll using crayons. About how tall is her doll?

The height of Rani’s doll is about __________ crayons.

Word Problem 1

A water can is 1 block taller than a bucket. The bucket is 6 blocks tall. How tall is the water can?

Length by Standard Units Ridhi wants to know how tall her bottle is. She measures it with her pencil. The bottle is 2 pencils tall. The next day, she wants to show it to her mother. The bottle is 3 pencils tall this time. How is this possible? “You must have sharpened your pencil. It has become shorter now,” Ridhi's mother tells her. Things we use to measure length can be of different lengths. We need a fixed or standard way to measure things. This helps us to get the correct measurement each time. 182

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Centimetre We can use a ruler to measure things in fixed units. It measures in centimetres. The short form of centimetre is cm. This is 1 centimetre or 1 cm on a ruler. These marks on a ruler tell us how many centimetres long a thing is.

This is a 15 centimetre or 15 cm long ruler. We mostly use centimetres to measure short lengths. An eraser, scissor, a pencil and many other things can be measured with a ruler. Let’s see some examples:

Error Alert! When using a ruler, always start from 0 cm. Never measure from the middle or the end of the ruler.

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Example 3

Look at the picture. What is the length of this pen?

We can see that the length of the pen is 9 cm. Example 4

Peter wants to know which of these things is about 5 cm long. a

Tube light

Paint brush

crayon

Peter can use a ruler. With a ruler, we can measure that a crayon’s length is about 5 cm. Do It Together

Write the length in cm.

10 cm

a c e

Toothbrush – __________ cm Key

Bottle cap

– __________ cm

b d

Pencil

– 10 cm

Iron screw – 6 cm

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Metre Metre is another standard unit of length. The short form for Metre is m. We use a metre rod or a measuring tape to measure length in metres. We use metres to measure long lengths, like a room or a piece of cloth. A tailor measures clothes with a measuring tape.

A carpenter measures doors and windows with a measuring tape or rod.

Example 5

Which of these will we measure in meters 1

We will measure a pencil in centimetres. Trees are longer than pencils. So, they need to be measured in metres. 2

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can be measured in A spoon centimetres. A bed is longer than a spoon. So, it needs to be measured in metres. 185

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Look at the picture. Circle the things that can be measured in metres.

Example 6

Bed

Photo frame Lamp Carpet

Do It Together

Window Book

Teddy

Bookshelf

Fill in the blank with the correct unit of length. 1

A door

is measured in ___________. (m, cm) m

A lamp post

A Mirror

is measured in ___________. (m, cm)

A Phone

is measured in ___________. (m, cm)

Do It Yourself 11B 1

Which one is more than a metre long. a

Fill in the blank with the correct unit. a

A truck is 8 _______ long. (cm/m)

A cooking pan is 25 _______ long. (m/cm)

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Look at the picture. How long is the fork?

___________ cm.

A car is 2 m long. An auto is 1 m long.

The car is __________ m longer than the auto.

2m 5

A photo frame is 20 cm shorter than a TV. How long is the TV? 25cm

Word Problems 1

Divya wants to find out how long her room is. Should she use a ruler or a measuring tape? Why?

Sarah has a pencil that is 12 cm long. Her friend Heena has a pencil that is 18 cm long. How much longer is Heena’s pencil?

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Weight Real Life Connect

Heena and Amir want to check whose bag is heavier. They go to a park and put their bags on each side of a seesaw.

Heena Whose bag is heavier? How do we know? If both are same, the seasaw stays straight.

Amir

Did You Know? On a seesaw, when one side is heavier, it goes down, and the lighter side goes up!

Can we find out how heavy Amir’s bag is? Let’s see!

Weight Using Things Around Us Math Connect

We measure weight to see how heavy or light something is! This is a weight balance. It is the same as a seesaw! We can use this to measure and compare the weight of things. Let’s put a pumpkin on one side and a corn cob on the other side of the balance. 1 pumpkin is heavier than 1 corn cob. Let’s add more corn cobs then. The balance needle is in the middle. We can say, it is balanced. So, the weight of 5 corn cobs is the same as 1 pumpkin.

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Shall we add more corn cobs? Now, 8 corn cobs are heavier than a pumpkin!

Example 7

We can also use blocks to check the weight of things. There are 3 blocks and 6 carrots. The weight is balanced. 3 So, __________

Do It Together

6 blocks = __________

Circle the heavier fruit. b

How heavy are these? Fill in the blank. a

____________

= ____________ 8

1 ____________

= ____________

Do It Yourself 11C 1

Tick () the heavier item.

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Tick () the lighter item.

3 2

Look at the weight balances. Fill in the blanks. a

____________

= ____________

____________

= ____________

____________

= ____________

If the weight of 1 book is the same as the weight of 1 pencil box, what will be the weight of 5 books?

Fill in the blank. If

Then,

= __________

Word Problems 1

Nani has 2 watermelons in a bag and Jaya has 2 bananas in a bag. Whose bag will be heavier?

5 blocks are equal to one brick. How many blocks would be equal to two bricks?

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Weight by Standard Units Math Connect

A vegetable seller is using a balance to measure the weight of some vegetables. He puts a weight bar on one side of the balance. It helps to measure the right amount of vegetables! These are called weights. Shopkeepers and vegetable sellers use weights like these on one side of the balance. On the other side, they put the thing that they want to weigh. Weight bars come in grams and kilograms. Gram A gram is a standard unit to measure weight. The short form of gram is g. These are gram weights. We use grams of weight to measure light things like fruit, candy, and small vegetables.

Example 8

Ramu is buying some fruit. The seller puts the fruit on the balance. How many grams of fruit has Ramu bought? 3 weight bars of 100 grams = 100 g + 100 g + 100 g = 300 g So, Ramu bought 300 g of fruit.

Do It Together

Read the weight of the weight bars. Write the weight of these things in grams. Bag of rice

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A candle

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Kilogram A kilogram is another standard unit to measure weight. The short form of kilogram is kg. These are kilogram weights

We use kilograms of weight for measuring heavier things. We measure sacks of rice and grains, watermelons, and our body weight in kilograms. Example 9

What’s the weight of these 4 pineapples?

Did You Know? 1kg

500 g + 500 g = 1 kg

2kg

500g

1kg

We can see 1 kg + 2 kg weights. The total weight is 3 kg. So, the weight of these pineapples is 3 kg. Do It Together

A vegetable seller has many of these weights – 1 kg and 2 kg. 1

How many weights of 2 kg should he put on the balance to weigh 4 kg of potatoes? 2kg

2kg

_______ kg + 2 kg = _______ kg So, the seller needs to put _______ weights of 2 kg to weigh 4 kg of potatoes. 192

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2 How many weights of 1 kg and 2 kg should he put to weigh 5 kg of

potatoes?

_______ kg + 2 kg + 1 kg = 5 kg

Think and Tell Can you tell another way to measure 5 kg of potatoes with 1 kg and 2 kg weights?

Do It Yourself 11D 1

Match the items with the correct units in which they should be measured. Items

Units of Weight

A basket of tomatoes

kilograms

A spoon of salt

A bag of wheat

grams

Candy floss 2

Circle the correct weight for the given items. a b

Tube of Toothpaste Suitcase

200 kg 15 kg

Write the total weight. a

100g

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200 g 15 g

500g

2kg

5kg

1kg

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Which is heavier?

500g 5

500g

3kg

Rakesh wants to weigh 3 kg of onions. How many weights of 1 kg and 2 kg should he put to weigh the onions?

Word Problem 1

Tom has three weights of 5 kg, 2 kg and 1 kg. How much can he weigh by putting them together on a balance?

Capacity Real Life Connect

Ritu has a bucket and a mug. She pours 5 mugs of water into the bucket, but it is not even half filled! What else should I use to fill this bucket faster? Should I use a glass or a jug?

A glass or a jug - Which of them will hold more water? Which of them can fill the bucket faster?

Think and Tell What holds more water – a tank or a river?

Capacity Using Things Around Us Math Connect

Capacity is how much liquid a bucket, a mug, jug or any other thing can hold. The capacity of a bucket is more than a mug. Similarly, a cup has less capacity than a bucket!

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We can use different containers, like cups and bowls, to measure liquids like water and juice. We can use smaller containers to fill a bigger container. This helps to measure capacity. glasses of juice fill a jug.

Example 10

hat’s the capacity of the jug?

= It takes 6 glasses to fill a jug. We can say that the capacity of the jug is 6 glasses of juice. ______________ Example 11

About how many spoons of soup can this bowl hold – 40 spoons or 5 spoons? The soup in the spoon is much less than the bowl. 5 spoons would not fill the bowl. A bowl can hold about 40 spoons of soup.

Do It Together

Look at the picture. Which pot has less capacity?

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

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Do It Yourself 11E 1

Which one holds more water?

Look at the pictures. Fill in the capacity. a

= ______ jugs

= ______ bowls

= 3

Tick () the pot that has more capacity.

What is the capacity of the jug in cups? =

Word Problems 1

Jyothi poured 12 buckets of water into a tank. Ali then poured 15 buckets of water to fill the tank. What is the capacity of the tank?

A pot is half filled with 6 glasses of water. What is the capacity of the pot?

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Capacity by Standard Units Tsp 3/4 1/2 Tsp 1/ 4 Ts p

So far, we have measured capacity using glasses, mugs, or jugs. We should have a standard way to measure capacity.

1T sp

Math Connect

There are measuring jars, cups, and even spoons with markings to measure capacity.

____ 100mL ____ 50mL

____ 50mL ____ 25mL

____ 20mL ____ 10mL

Millilitre Millilitre is a standard unit to measure capacity. The short form of millilitre is mL. We measure small amounts of liquids in millilitre, like a cup of tea or a spoon of cough syrup. Usually the capacity of a spoon, a cup, or a glass is measured in mL.

5 mL Example 12

Example 13

50 mL

200 mL

Which of these are measured in mL? Tick () the correct option.

About how much is the capacity of these containers.

Ladle 1 2 3

Kettle

The capacity of a ladle is about 5 mL.

The capacity of a cup is about 200 mL.

The capacity of a kettle is about 500 mL.

Chapter 11 • Measurement

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tea cup

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Do It Together

About how much is the capacity of these containers? Choose from the options below. 700mL 1

10mL

250mL

500mL

30mL

Litre The litre is another standard unit for measuring capacity. The short form of litre is L. Usually buckets, water cans, bottles and barrels measure in litres. Larger amounts of liquids such as a gallon of milk or a tank of water are measured in litres. Example 14

20 L

50 L

Which of these measure water in litres – a glass or a water bottle?

A water bottle holds more water. It is measured in litres. A water dispenser bottle holds 20 L of water. In a day, 12 L of water is used from the bottle. How much water is left in the bottle for the next day?

20 L

Example 15

Total water in the can = 20 L Water used = 12 L

Remaining water: 20 – 12 = 8 L

20 L

So, 8 L of water is left in the bottle.

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Do It Together

Look at the containers. About how much is the capacity of these containers? Choose from the option given below. 1L

20 L

100 L 2

300 L 3

Do It Yourself 11F 1

Circle the things that hold liquid in mL.

Circle the ones which measure in L.

How much water can a mug hold – 150 mL or 150 L?

Tick () the bottle that has more capacity.

Lila uses milk to make a pudding. How much milk must she have used - 1 L or 1 mL?

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Word Problems 1

Raman used a full bucket to water plants. How much water must he have used - 10 mL or 10 L?

Leela used 20 L of water for bathing. Riya used 20 L of water for washing. How many litres of water did they use in total?

Points to Remember LENGTH

WEIGHT

CAPACITY

We measure length to see how long or short something is.

We measure weight to see how heavy or light something is.

We measure capacity to see how much liquid something can hold.

We use a ruler or a measuring tape to measure length in a standard way.

We use a weight balance to measure weight in a standard way.

We use a measuring cup or jug to measure capacity in a standard way.

Centimetre (cm) and Gram (g) and kilogram metre (m) are the (kg) are the standard standard units of length. units of weight.

Millilitre (mL) and litre (L) are the standard units of capacity.

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Math Lab Setting: Whole class

Measure the Water

Materials Required: A glass, a litre bottle, a bucket, water. Method: 1

Line up the glass, bucket and bottle on a table.

Fill the glass with water to the brim. Pour the water from the glass into the bottle.

Count the number of glasses it took to fill the bottle. Write on the board.

Now, pour the water from the bottle into the bucket.

Count the number of bottles it took to fill the bucket. Write on the board.

Conclude on the board: One bottle = ______ glasses.

One bucket = ______ bottles.

Chapter Checkup 1

Circle the thing that we can use to measure the length of a lunch box.

Measure the length of the red and green strips using blocks. Which strip is longer?

Red strip = ___________ blocks. Green strip = ___________ blocks. The ____________ strip is longer. Chapter 11 • Measurement

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How many cm long is the straw?

Look at the picture. Fill in the blanks.

________ 5

Tick () the heavy thing.

What is the weight of these objects?

2kg 2kg 2kg2kg

= ________

Which is lighter? or

Look at the picture. Which pot has less capacity?

Pot A

Pot B

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Fill in the blank.

The capacity of the jug is around _________. (1L/ 2L) 10

How many g is 1 kg?

Word Problem 1

Vani put blocks in a line of 9 cm long. Her friend Tina added more blocks of 8 cm in that line. How long is the line of blocks now?

Chapter 11 • Measurement

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Shapes and Patterns

Let's Recall Have a look around your surroundings.

Think about how some things look different to others.

Some things are big and some are small. Compare the size of a toy with the size of your house. The toy is very tiny and the house is really big.

You know how you play with those colourful building blocks? Each block can be put together in different ways. Each block has a different shape and a different size. Look at this picture of two building blocks. Do A and B look the same?

No. We can see that A is bigger than B. Let us look at another picture. Is A bigger than C?

We can see in the picture that A is smaller than C. So, we can say that: A is bigger than B.

A is smaller than C.

B is the smallest.

Let's Warm-up 1

Tick ()) the bigger object. a

C is the biggest.

Tick () the smallest. a

I scored ___________ out of 4.

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All About Lines Real Life Connect

Mother and sister are making a rangoli. Sarita also wants to join them. Mother: Sarita, draw a straight line and then a curved line on the top. Sarita: I do not know how to draw these lines. Let us help Sarita understand these types of lines. These are 3 kinds of straight lines:

Standing Line

Sleeping Line

Slanting line

You can use a ruler to draw these lines. They do not bend. These are curved lines:

Curved lines bend. You cannot draw them with a ruler. Example 1

Read the word: CORAL. Which letters of the word have straight lines? Which ones have curved lines? Fill in the table. Straight Lines Standing

Sleeping

Slanting

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Do It Together

Trace the lines to help the monkeys reach the bananas. One is done for you. Name the line. Sleeping Line

Do It Yourself 12A 1

Trace the shape using straight and curved lines. a

How many straight lines make the shapes? Trace the lines.

How many of each type of lines do you see in the picture?

Sleeping lines

Standing lines

Slanting lines

Curved lines

Look how the butterflies fly to the flowers. Trace and write the kind of lines they make on their way. a

__________________ lines. __________________ lines.

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Read the word: LATIN. Choose and write the letters. a Letter with only a standing line. b Letter with sleeping and standing lines. c Letter with slanting and standing lines.

Word Problem 1

3 friends were playing. Look at the lines they ran on, to reach the ball.

Montu

Foxy

Who ran on a curved line?

Who ran on slanting lines?

Who ran straight?

Bruno

All About Shapes Real Life Connect

Sarita went inside and saw that her dad had bought some photo frames. Sarita: These photos look so good! Dad: Different shapes of the photo frames make these look even better. “Different shapes of photo frame? How so?” Sarita wondered. Let’s help Sarita understand flat shapes.

Flat Shapes These frames show different flat shapes. Square, rectangle, circle, triangle, and oval are examples of flat shapes. Chapter 12 • Shapes and Patterns

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Features of Flat Shapes

4 sides, 4 corners

0 sides, 0 corners

Square

Rectangle

Circle

Oval

Now, look at this shape: It is a triangle.

Remember!

Think and Tell

Flat shapes are:

Are there more flat shapes? What about a star and a heart shape? Are they flat shapes too? Square

Example 2

3 sides, 3 corners

Circle

Triangle Rectangle

Oval

Look at the picture. Count the number of each flat shape. The picture has: 1 triangle, 2 rectangles, 3 circles, and 4 squares.

Do It Together

Colour the shapes as instructed. One is done for you. Rectangle: Yellow Triangle: Red

Square: Blue

Circle: Orange

Drawing Flat Shapes Let’s learn to make flat shapes. We are using some ice cream sticks. To make a triangle, we join 1 sleeping and 2 slanting sticks together. Triangle 208

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To make a square, we join 2 standing and 2 sleeping sticks together. All four sticks needs to be of the same length.

Square

To make a rectangle, we join 2 standing and 2 sleeping sticks together. The opposite sticks need to be of the same length.

Rectangle

Circles and ovals have curved lines. We can use a thread to make them. Circle

Think and Tell Can we make a circle or an oval with ice cream sticks?

Oval

Did You Know? A square is also a rectangle! Its opposite sides are of equal length.

We can also draw flat shapes on dot paper. Let us see how shapes can be drawn on dot paper.

Triangle Example 3

Square

Rectangle

Join the dots to draw some flat shapes. Here, we have drawn 1 square, 1 rectangle and 2 triangles of different sizes. We can use a ruler to join the dots.

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Do It Together

Trace the dots to draw the shape. Then, colour it. One is done for you. You may use a ruler, if needed.

Do It Yourself 12B 1

Match the shape with its name. a

Rectangle

Oval

Triangle

Circle

Write if true or false. a

A square has 3 sides and 3 corners.

A rectangle has 4 equal sides.

Both a circle and an oval have 0 sides and 0 corners.

Complete the shapes by joining the dots. Name the shapes. a

Look at the pictures. Count the number of squares, rectangles, triangles, circles, and ovals. a

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Draw a square, a rectangle, and a triangle on the dot paper. You may use a ruler to join the dots.

How many triangles are there in this rectangle? Draw and fill each of them in different colours.

Word Problem 1

Look what Amina drew. Which flat shapes can you see in her drawing? Name them.

Solid Shapes Real Life Connect

Harsh goes to the room to play with his brother. These are the toys they are playing with—

Mom: Harsh, do you know the shapes of these toys? What shape do you see in these toys? Harsh: Hmm! They look like square, rectangle, and triangle. Are they flat shapes too? But these are not in drawings. Features of Solid Shapes The toys are solids. We can hold them in our hands. They are not made or drawn on flat surfaces. The shapes of these toys are Corner called solid shapes. Let us learn more about solid shapes and their features. Chapter 12 • Shapes and Patterns

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Edge Face

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Cube

This block is in cube shape.

A cube has 6 faces, 8 corners, and 12 edges. Cuboid

This block is in cuboid shape.

A cuboid has 6 faces, 8 corners, and 12 edges. Cylinder

The drum is in cylinder shape.

A cylinder has 3 faces, 0 corner, and 2 edges. Cone

The stack is in cone shape.

A cone has 2 faces, 1 corner, and 1 edge. Sphere

The ball is in sphere shape.

A sphere has 1 face, 0 corner, 0 edge.

Example 4

Name the solid shapes of these objects. Coffee mug Birthday cap

Think and Tell! Two cylinders are put on top of each other. What solid shape will they make?

This coffee mug is a cylinder. The cap is a cone. Do It Together

Match the objects of the same solid shapes. One is done for you.

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Flat Shapes in Solid Shapes Draw or trace around a solid shape on a sheet of paper. We get a flat shape. Check the tracing of some solid shapes below. See what flat shape we get.

Cuboid

Cube

Square

On tracing a cube or a standing cuboid, we get a square.

Cuboid

Rectangle

On tracing a sleeping cuboid, we get a rectangle.

On tracing a standing cylinder or cone, we get a circle. Cylinder

Cone

Circle

We also get a circle on tracing a sphere from the top.

Sphere Example 5

Which object should we trace to get a square?

Cap

Ball

Dice

The cap is a cone, and the ball is a sphere. We will get a circle on tracing them. The dice is a cube. We can get a square by tracing one of its sides. Do It Together

Match the shape with the shadow it makes. One is done for you.

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Do It Yourself 12C 1

Tick () the odd one out.

Look at the shape of the objects. Match them with their shadows.

3 5

Anya needs to draw a square. Which of these from her school bag can she use?

Crayon box 4

Pencil

Glue stick

Vinay needs to draw a circle. Which of these blocks from his block set can he use? c

Pencil box

10 such bangles are put one over the other. What shape will it make?

Word Problems 1

Jon made a tower with his blocks. Count and write down the number of solid shapes he used in this tower. a

Cube

Cuboid

Cylinder

Anya puts 3 such cubes on top of each other. What solid shape will she get?

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Patterns Around Us Real Life Connect

Joy’s father is spreading a new bedsheet. Joy: Wow! So many squares.

Father: Yes, Joy. These are making a lovely pattern! Joy: What is a pattern?

Repeating Patterns The design on this bedsheet is made of 2 colours. They are repeated one after another in every line.

Blue

Orange

Blue

Orange

Blue

Orange

A shape, number, or design that repeats itself in a fixed order makes a pattern. Let’s see more patterns. This pattern repeats a green triangle and a yellow rectangle, one after the other.

Now let us see a letter pattern. Here, the letters A and B are repeated.

We can also make patterns with turning shapes. This pattern repeats a blue and a green triangle. The blue triangles are up but the green ones are upside down.

Once we find what repeats in a pattern, we can add to the pattern. Look at this pattern for example—

Chapter 12 • Shapes and Patterns

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This pattern repeats 1 moon and 1 sun. So, to add to this pattern, we need to add 1 moon and 1 sun again. We can repeat this as many times as we want! Example 6

Look at this pattern. What is repeated in this pattern? In this pattern, 2 crosses .

Example 7

are repeated after every 2 right arrows

Look at the pattern. What should we draw next in this pattern?

This pattern repeats a leaf and a flower. So, we should draw 1 leaf and then 1 flower next. Do It Together

Colour the next shapes to complete the pattern. 1

Do It Yourself 12D 1

Which of these options show a pattern? a b c d e f

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Draw the next two lines to complete the pattern. a b c

Choose the picture that will be the next in the pattern. Draw it in the blank and colour it. a

Draw and colour the next 2 shapes to complete the pattern. b

Draw and colour the missing shapes to complete the pattern. b

Word Problem 1

Joy and Riya have some happy and sad face stickers. They pasted them in different ways. Who has created a pattern with the stickers? Riya’s stickers: Joy’s stickers:

Growing Patterns Joy now knows what patterns are. He can make patterns too! One day, he was making a pattern with his happy and sad stickers: Chapter 12 • Shapes and Patterns

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His sister Riya saw that. “Let’s have more happy faces in the pattern than sad,” she says. “How? Will it still be a pattern?” Joy is not sure. “Yes, it will be. Let me show you.” says Riya. Joy’s pattern is made of happy and sad stickers. But this is a different pattern. 1 happy

1 sad

2 happy

1 sad

3 happy

This is called growing a pattern. Let’s look at another growing pattern. Here, we are adding 1 triangle to each next part of the pattern. Example 8

Is this a growing pattern. How? This is a growing pattern. Here, the number of pink squares are increasing by 1 each time. The pattern shows 1 pink square, then 2 pink squares, then 3 pink squares, and finally 4 pink squares.

Do It Together

Draw the next part of the growing pattern.

Do It Yourself 12E 1

Which of these options show a growing pattern? a

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Draw the next shape in the patterns.

Draw the next 2 figures in the given growing patterns.

Look at the growing pattern. Fill in the blank.

In this pattern, we are adding ___________ square each time. b

In this pattern, we are adding 1 ___________ (square/circle) at the ___________ (top/side) each time. 5

In this pattern, we are adding 1 square and ___________ triangle at the ___________ (top/bottom) each time.

Look at the growing pattern. Colour the blank balls. a b c

Word Problem 1

Jay made a pattern. It starts with 1 circle and 1 square and grows by 2 circles with each step. Draw the next 5 shapes in the pattern that Jay drew.

Chapter 12 • Shapes and Patterns

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Number Patterns Joy went to the bookstore with his sister Riya. He saw a diary where designs were made using numbers. Joy: Look at this diary. Is this also a pattern? Riya: Yes, Joy. You can use numbers as well to make patterns. Let me show you!

These are some patterns using numbers:

1 2 1 2 1 2

3 3 3 3

Here, 1 and 2 are repeating.

Here, 3 is repeated with a turn.

3, 6, 9, 12, 15 – Here 3 is being added each time. 2 4 2 4 Example 9

What will come next in this number pattern? This pattern repeats 2 and 4. So, the next 2 numbers will be 2 and 4.

Do It Together

Fill in the next numbers to complete the pattern. 1

3 9 3 9

1 3 5 7

Do It Yourself 12F Which options show a number pattern? a

2, 4, 6, 8

Write if true or false.

1, 3, 1, 2, 3, 1, 3

5 4 5 4 5 4 is a pattern.

The next number in the pattern 5, 10, 15, 20 is 25.

1, 2, 3, 4, 5, 6 is a pattern.

0 1 2 0 1 2 0 1 2 is not a pattern.

Fill in the blanks to complete the pattern. a

4 8 12 16

10 9 8 7

2, 3, 4, 2, 3, 4

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Fill in the missing number in the pattern. 7

3 5 4 3 ___ ___ 3 5 4 3 5 4

0 2 0 2 ___ 2 0 ___ 0 2

9 0 2 1 ___ ___ ___ ___ 9 0 2 1

What will be the next 3 numbers in the number patterns? 1, 3, 2, 1, 3, 2,

1, 4, 7, 10,

Word Problems 1

Binu remembers his father’s number. It is 99 68 599 685. Is it in a pattern?

Roy arranged a few number cards in this way: 5

Is this making a pattern? If not, arrange them to make a number pattern.

Points to Remember •

Lines can be straight (

) or curved (

•

Straight lines can be sleeping, standing, or slanting.

•

Cube, cuboid, cylinder, cone, and sphere are all solid shapes.

• •

Square, rectangle, circle, triangle, oval are all flat shapes. Patterns can be repeating, turning, growing, or number.

Math Lab Setting: Groups of 4. What to do? 1

Collect pens, crayons, erasers or any other such small objects in your group.

One member will choose and arrange these objects to make a pattern.

You may create a repeating or a growing pattern.

The other members will draw the pattern in their notebooks.

Take turns in your groups. Create as many patterns as you can.

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Make a Pattern

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Chapter Checkup 1

Choose the correct name from the box for each line and write it in the box below. Sleeping line

Standing line

Look at the pictures. Count the number of squares, rectangles, triangles, circles, and ovals. b

Look at the solid shapes.

Cuboid

Trace to draw the flat shape. Then, write the name of the shape you get. a

Curved line

Write the kinds of lines you see in these letters – standing, sleeping, slanting and curved. a

Slanting line

Cylinder

Cube

Which of these solid shapes will give us a square, each time when it is traced?

Which of these solid shapes can give us a circle, when traced?

Which of these solid shapes can give us a rectangle, when traced?

What comes next in the pattern? Draw and colour to fill in. a

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Draw and colour the shapes to complete the next part of the pattern. a

Write ‘GROW’ if it is a growing pattern. Write ‘NO’ if it is not. a b c d

Draw the next part of the growing pattern. a

10 a

Draw a pattern of these shapes.

Draw a growing pattern with these shapes.

Word Problem 1

Rani traced an object and she got a square each time. Which of these objects did she trace?

Cap

Chapter 12 • Shapes and Patterns

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Pencil case

Cube

Book

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Time

Let's Recall We know that the sun is a big bright ball in the sky. We can understand what time it is by observing the sun. The sun rises early in the morning. We wake up every morning and start our day. The sun keeps rising slowly and gets brighter and hotter. This is afternoon. The sun then slowly starts setting in the evening. It gets cooler and pleasant. This is when we come out and play with friends! Finally it is night! And there is no sun in the sky anymore! This is when we go off to bed.

Let's Warm-up

Let us match the pictures to the correct time of the day.

Playing in the park.

Morning

Going to bed.

Noon

Eating lunch.

Evening

Waking up.

Night I scored __________ out of 4.

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Reading Time on a Clock Real Life Connect

Mia was getting ready for her drawing class. It starts at 5 o’clock in the evening. Mia: Mother, am I on time?

Mother: Yes, it is not yet 5 o’clock. It is half past 4.

Mia: Mother, what do you mean by half past?

Mother: Let me show you how to read the half past time.

Time on a Clock We use a clock to read time. A clock has numbers 1 to 12 written on it. The short hand tells us the hour and the long hand tells us the minutes.

Minute hand Hour hand

The minute hand is on 12.

The hour hand is on 5.

The hour hand is on 10.

This is 5 o’clock.

This is 10 o’clock.

The time can be written in 2 ways:

5 o’clock or 5:00.

10 o’clock or 10:00.

Chapter 13 • Time

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Now, let us see how to read time to half hour.

Hour hand Minute hand

The minute hand is on 6.

So, this is 4:30.

So, this is 7:30.

The hour hand is between 4 and 5. 4:30 can also be written as half past 4.

The hour hand is between 7 and 8. 7:30 can also be written as half past 7.

So, the minute hand tells us if the time is on the hour or half past. When the time is half past: •

30 minutes have passed.

•

the hour hand will be between 2 numbers.

• •

the minute hand will be on 6.

the number before the hour hand tells the hour.

We can also find the time taken for an activity.

Mia’s mother goes to drop Mia at school. She starts at 8:00 and reaches the school at 9:00. She then goes to the market and gets there at 9:30.

Start at 8:00

Reach school at 9:00

Reach market at 9:30

How much time did Mia’s mother take to reach the school? 1 hour

At what time did Mia and her mother leave their house? 8:00

At what time did Mia’s mother reach the market? 9:30

If they started at 9:00, at what time would they reach the school? 10:00

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Example 1

Look at the clock and tell the time.

Hour hand Minute hand

Do It Together

The minute hand is on 6. The hour hand is between 11 and 12. So, the time is half past 11 or 11:30.

Read the time on the clocks. Write the time in 2 different ways.

12:30

Error Alert! Look at the hands carefully! The time is 12:30

Minute hand

The time is 6:00

Hour hand

Remember! The long hand is the minute hand and the short hand is the hour hand.

Do It Yourself 13A 1

Read and write the correct time.

Chapter 13 • Time

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Draw the hour hand and minute hand to show the time.

3 o’clock 3

8 o’clock

Write if true or false. a

The long hand is the hour hand.

The minute hand will be on 12 when the time is 12 o’clock.

The hour hand will be on 4 when the time is 2 o’clock.

How much time did it take Rina to take the exam? Exam Begins

Half past 11

1 o’clock

Exam Ends

Look at the time and fill in the blank with before or after.

Half past 1 is __________

Half past 9 is __________

Half past 3 is __________

1 o’clock.

10 o’clock.

3 o’clock.

Word Problem 1

Rashi goes to the market at 5 o’clock. She comes back at 8 o’clock. How much time did Rashi spend in the market?

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Reading The Calendar Real Life Connect

Mili was excited about her summer vacation.

Mili: Mom, when will the vacation start?

Mother: One more month is left.

Mili: When are we leaving on our trip?

Mother: We are going in May. Mili: What day is it?

Mother: It is a Tuesday.

Days and Months

APRIL

Mili’s birthday is in April.

Mili: Will my birthday come after the trip?

Mother: No. May comes after your birthday. Mili: And when does Tuesday come?

Mother: It comes after Monday.

Let us help Mili understand the days of the week and the months of the year. Days of the week There are 7 days in a week.

Let us understand yesterday, today, and tomorrow using the days of the week.

Yesterday Sunday

Today Monday

Tomorrow Tuesday

If today is a Monday, tomorrow will be a Tuesday. If yesterday was a Sunday, today is a Monday. Chapter 13 • Time

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Example 2

Do It Together

Look at the train above and fill in the blanks. 1

Tuesday comes after Monday.

Thursday comes before Friday.

The day after Tuesday is Wednesday.

The day before Sunday is Saturday.

There are 7 days in a week.

The table below shows the sweet available in a shop each day. Look at the table and fill in the blank. Monday

Tuesday

Cupcake Ice cream cone

Wednesday

Thursday

Friday

Saturday

Laddoo

Gulab jamun

Pudding

Fruit Cake Cupcake

_____________ is available on Friday.

Laddoo is available on _____________.

Cupcake is available on _____________ and Sunday.

Gulab Jamun is available on _____________.

Sunday

Months of the year There are 12 months in a year. The year starts in January and ends in December.

JANUARY

FEBRUARY

MARCH

APRIL

MAY

JUNE

JULY

AUGUST

SEPTEMBER

OCTOBER

NOVEMBER

DECEMBER

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Look at the calendar. A calendar shows year, months, days, and dates.

There are 30 days in April, June, September, and November.

2023

There are 31 days in January, March, May, July, August, October, and December.

February has 28 days.

There are 30 + 31 = 61 days in November and December.

Did You Know? • There are 365 days in a year and 366 days in a leap year. • A leap year comes after every 4 years. February has 29 days in a leap year.

Chapter 13 • Time

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We take different time to do different activities. Some activities take hours, some take days, and some take months. Months

Days

Seed to grow into a plant

Winter Holidays

Doing homework

Brushing Teeth

Hours

Example 3

Read the calendar given above. Answer the questions. 1 2 3 4 5

Example 4

Example 5

Minutes

Which is the first month of the year? January

Which is the last month of the year? December Which month comes after March? April

Which month comes before September? August How many months are there in a year? 12

Fill in the blanks. 1

The months with 30 days are April, June, September, and November.

There are 28 days in February 2023.

There are 7 months with 31 days.

Write if the given activities take minutes, hours, days, or months. 1 2 3 4

Having a bath

_________________ minutes

Summer vacations

_________________ months

Watching a movie

day changing from morning to evening

hours _________________ hours _________________

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Do It Together

Colour the months with only 30 days in yellow and the months with 31 days in green.

Which months are coloured in yellow?

Which months are coloured in green?

How many days are there in January and February?

Write 2 activities that takes hours, days, and months.

Do It Yourself 13B 1

Fill in the blanks with the correct answer.

[Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday] a

Thursday comes after ________________.

________________ comes before Friday.

________________ lies between Monday and Wednesday.

Write the correct day. a

Today is Monday.

What day is tomorrow?

________________________

What day was yesterday? ________________________ b

Today is Thursday.

What day is tomorrow?

________________________

What day was yesterday? ________________________ Chapter 13 • Time

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Look at the calendar given above and write if true or false. a

There are only 30 days in the month of August.

________________

January and December have 31 days.

________________

February only has 28 days.

________________

There are 7 months with 31 days.

________________

Write the correct month. a

This month is January. The month that comes after January is The month that comes before January is

________________. ________________.

This month is April. The month that comes after April is The month that comes before April is

________________. ________________.

Twisha’s birthday is in the last month of the year. This year her birthday is before Sunday and after Friday. a

Which month is Twisha’s birthday?

Which day is Twisha’s birthday?

Word Problem 1

Saina goes for her dance classes every Saturday. She goes for her art class every Sunday. Which are the days in the week that Saina does not go for her dance or art class?

Seasons and Festivals Mili was packing her bag for the trip. Mili: Do I have to take a sweater for the trip? Mother: No, it is summer. We do not need sweaters. Mili: Which months are summer? Let us help Mili with the seasons throughout the year. There are 5 different seasons in India. They are winter, spring, summer, monsoon, and autumn. 234

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January

February

March

April

Winter May

Winter June

Spring July

Spring August

Summer September

Summer October

Monsoon November

Monsoon December

Autumn

Winter

Mili also wants to know about the different festivals that come in different seasons: Summer

Mahavir Jayanti Ram Navami

Autumn

Spring

Diwali

Baisakhi

Dussehra

Holi

Monsoon

Raksha Bandhan

Christmas

Janmasthami

Makar Sankranti

Independence Day

Did You Know? A festival like Eid is not seasonal and does not fall in a particular season. It’s timing keeps changing every year.

Do It Together

Winter

Vasant Panchami Republic Day

Did You Know? New year is celebrated on the first day of January.

Look at the table on the previous page and answer the questions. 1 2

Which months are monsoon season? July and August How many months are there in autumn?

Chapter 13 • Time

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3 4 5

Which season comes after winter? Which season comes before summer? Which season comes after summer?

Think and Tell

Is there any other festival you celebrate at home? Which season does it fall in?

Do It Yourself 13C 1

Match the correct months with the seasons.

a c

Autumn

Spring

May

October

August

March

December

Independence Day is celebrated in the ________________ season. ________________ season comes after spring. Autumn comes after the ________________ season. Christmas is celebrated in the ________________ season. Spring comes after summer. Dussehra is celebrated in the summer season. Winter comes after autumn.

Answer the following questions. a

b c

Monsoon

Write if true or false. b

Summer

Fill in the blanks. b

Winter

Are Independence Day and Republic Day celebrated in the same season? __________ How many months of winter are there? ________________ From which month does summer start? ________________

Lily visits her grandmother every year before the school starts in April. She celebrates Holi every year with her grandmother. She visits her right after winter. Which month does Lily visit her grandmother?

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Word Problem 1

Era spends her summer vacation with her grandparents every year. Which are the months that Era spends with them?

Story Problems on Time It is Thursday! Noni is happy. She has Art class at school! This is Noni’s timetable at school. There are 6 periods every day at school. PERIODS

DAYS

Monday

English

Science

EVS

Maths

Craft

Sports

Tuesday

Sports

English

Science

Computer

Maths

Wednesday

Maths

Art

English

Music

EVS

Science

Thursday

Maths

Art

English

Science

Hindi

Friday

Dance

Science

Maths

EVS

English

Hindi

BREAK

Saturday

HOLIDAY

Sunday

HOLIDAY

Noni has to pack her bag for Thursday. She will take her Maths book, Art book, English book, Science book and Hindi book to school that day. Example 6

Look at the timetable on the previous page. Choose the correct answer. 1

On which day of the week does Noni have her Computer class? a

Monday

Friday

Wednesday

Saturday

Friday

Math On Friday, Noni has ____________ class in Period 3. a

Science

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Noni has her dance class on ____________. Friday a

Tuesday

Maths

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Do It Together

Manoj made a timetable for his daily schedule from Monday to Friday. Look at the table and fill in the blanks. Monday

Tuesday

Wednesday

Thursday

Going to school

Friday

Going to school

8:00

Going to school

4:00

Coming back from school

Dinner time

Bed time

5:00

Swimming class

9:00

Story time

8:30

9:30

Art Class

Story time

Sports

Chess

Story time

Manoj goes to school at ________________ every day.

Manoj goes for his ________________ class on Monday.

Manoj goes for Music class on ________________.

Manoj goes for ________________ class on Tuesday.

Music

Story time

Do It Yourself 13D 1

Read Noni’s time table given on page 16 and answer the questions. a

How many Math classes does Noni have on Tuesday?

How many days in the week does Noni have the Science class?

How many Sports classes does Noni have in a week?

Read Manoj's time table given on page 238. Match the day with the class that he has. a

Sports

Monday

Chess

Tuesday

Swimming

Wednesday

Music

Thursday

Art Class

Friday

The table below shows the timetable of a train. Look at the table and answer the questions. Station A 9:00

Station B 10:30

Station C 11:00

Station D 12:30

Station D 2:00

Station E 3:30

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The train reaches Station D at ______.

The train reaches Station ______ at 2:00.

The train reaches Station C at ______ o’clock.

The train reaches Station B at half past ______.

Complete the table by making your class timetable.

DAYS Monday

Wednesday Thursday

BREAK

Tuesday

PERIODS

Friday

Saturday Sunday

Answer the questions based on your class timetable.

b c

What is the first period on Monday?

What is the last period on Thursday?

What is the third period on Wednesday?

Word Problem 1

Jia wakes up at 7 o’clock in the morning every day. She takes around 2 hours to get ready for school. What time does Jia go to school every day?

Points to Remember • • • • • • •

The long hand is called the minute hand and the short hand is called the hour hand of a clock. There are 7 days in a week. Monday is the first day of a week. There are 12 months in a year. January is the first month of the year. January, March, May, July, August, October, and December have 31 days. April, June, September, and November have 30 days. February has 28 days. There are 5 seasons India – Winter, Spring, Summer, Monsoon and Autumn. A calendar shows the year, months, days and date.

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Math Lab Time Travel

Material required: One sheet of white Chart paper, crayons, pencil, ice-cream sticks, time chits with half past and o’clock time. Setting: Classroom, In groups of 5 Instructions: 1 2 3 4 5

Students cut the white paper to form a circle. Mark the numbers like a clock on the circle. Make an hour hand and minute hand with the ice-cream sticks. Each child picks up a chit one by one. Move the ice-cream sticks on the clock to show the time.

Chapter Checkup 1

Choose the correct time from the box and write below the clocks showing the same time. 4:00 a

2:00 b

10:30 c

11:30 d

Fill in the blanks with the time in numbers and words. In numbers

In words

4:30

________________

Seven o’clock

________________

Half past eight

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Draw the hands of the clock to show the time. a

7:30 4

2:30

10:00

3:30

The table below shows Neha’s father’s schedule. Read and follow the instructions.

Has breakfast every day at 9 o’clock. Leaves for the office every weekday at 10:30. Goes for a walk every Monday, Wednesday and Friday. Goes to the market every Sunday.

Show the breakfast time on the clock.

On which days does Neha’s father NOT go for a walk? ________________________

What does Neha's father go every Sunday? ________________________

Does he go for a walk on Thursday? Yes/No

Draw hands to show the time he leaves for the office.

Read the calendar and answer the questions: a

How many Saturdays are there in this month?

How many days are there in this month?

How many Mondays are there in this month?

Calender

Look at the pictures given below and answer the questions.

January- February (End of Winter Season) Chapter 13 • Time

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March- April (Spring Season)

May- June (Summer Season) 241

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July- August (Monsoon Season)

September-November (Autumn Season)

The year begins with the _________________ season.

Which season comes after the summer season? _________________

Which months do the spring season fall in? _________________

_________________ and _________________ months are the monsoon season.

Write if true or false. a b c d

There are 12 months in a year. _________________ There are 8 days in a week. _________________

Monday comes before Tuesday. _________________ Sunday comes after Saturday. _________________

Write 2 activities that take hours, days, and months.

Read Sunita’s daily timetable and answer the questions. 7:00 8:30

4:30

Have tea

10:00

b c

Have breakfast

Leave for office

8:30

Wake up

9:30 1:30

December (Winter Begins)

Come home

Have dinner Go to bed

At what time does Sunita have her dinner? What does Sunita do at 9:30?

What time does Sunita go to bed?

If Tanya goes to school at 9 o’clock and comes back at 12 o’clock, how much time is she at school?

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Word Problems 1

Raj lives in a boarding school. Look at his timetable and fill in the blanks. Timetable Event Wake up time Has breakfast Goes to school Cricket class Homework time Dinner time

a b c d e

Time 6:30 7:00 8:00 5:30 6:30 8:00

Days Every day Every day Every day Monday and Wednesday Every day Every day

Raj wakes up at _________________ in the morning. Raj eats breakfast at _________________.

His cricket class starts at _________________.

Raj has his cricket classes on _________________ and _________________. Raj does his homework at _________________ every day.

The calendar below shows the annual plan of a school. Read the calendar and answer the questions. January

Sports Day July

February Revision for Final Exam August

March

Final Exam September

April New Session begins

October

November December

Parent Teachers’ Independence Half-Yearly Navaratri meeting Day celebration Exam Celebration a b c d

Diwali Break

School Trip

When does the new session start at school? Which month is the Sports Day? When is the school trip? Which event happens in the month of September?

The table shows Seema's weekly timetable. Read the timetable and complete the table.

Chapter 13 • Time

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May- June Summer Holiday

Seema wakes up.

Seema has breakfast.

Seema goes to school.

Seema gets back home.

Seema goes out to play.

6:00

7:00

______________

4:00

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Money

Let's Recall How do we buy things? When we go to the market we take money with us. We give money to the shopkeeper. He gives us what we want to buy.

Money is what we give for buying chocolates, books, crayons, clothes, etc. But do we give the same amount of money for all these items?

No! Some things are expensive and some are cheap. For example, our clothes are more expensive than a chocolate.

Let's Warm-up

Read the following sentences and state True (T) or False (F). 1

We do not need money to buy things.

________

We pay more money to buy a pen than for shoes.

________

All coins and notes have the same value.

________

A shopkeeper takes money to sell things.

________

I scored ___________ out of 4.

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Indian Currency Real Life Connect

Riya goes to a shop with her mother. She wants to buy a storybook. Riya: I like this book. How much does it cost? Shopkeeper: 100 rupees Riya’s mother pays for the book. Riya is very happy. Jane's Bookshop

#0's5 11-5*12

Indian Coins and Notes

Indian money comes in notes and coins. They can be rupees or paise. Paise come only in the form of coins. Rupees come both in the form of notes and coins. Coins:

50 paise 50 p

1 rupee `1

2 rupees `2

5 rupees `5

10 rupees `10

20 rupees `20

Notes:

10 rupees `10

20 rupees `20

50 rupees `50

100 rupees `100

200 rupees `200

500 rupees `500

Chapter 14 • Money

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There are some coins that were used in the olden days. They are no longer in use. Let us see some of those.

5 paise 5p

10 paise 10p

20 paise 20p

25 paise 25p

1 rupee is equal to 100 paise.

So, 1 rupee is equal to two 50-paise coins.

Did You Know? Indian notes are made of a special paper. It is called ‘rag paper’. This paper is strong and does not tear easily.

2 rupees is equal to four 50-paise coins.

Example 1

Look at the price tag and circle the correct note or coin.

`10

`50

`100 246

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Do It Together

Look at the notes and coins. Write the amount using the rupee symbol.

`10

Do It Yourself 14A 1

Write if true or false. a

There is a 15-rupee coin.

__________

There is a 300-rupee note.

__________

There is a 2-rupee coin.

__________

There is a 10-rupee coin and a note.

__________

Look at the things. Tick () if the correct note or coin shows the cost.

How many 50-paise coins will be needed to make `4?

Write the correct value of each coin.

Chapter 14 • Money

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Read the statement and match it with the correct currency. Riya bought a box of crayons for `100. Raj bought a packet of balloons for `50. Tina bought a red pen for `10.

Operations on Money Real Life Connect

The next day, Riya goes to another shop. She wants to buy a new lunch box. Riya: I like this lunch box. How much does it cost? Shopkeeper: This lunch box costs 50 rupees.

Riya is confused about how she should pay for it. She does not have a 50-rupee note!

Exchange of Money Let us see the different ways in which Riya can pay for the lunch box: 1

Five 10-rupee notes.

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Example 2

Two 20-rupee notes and one 10-rupee note.

Three 10-rupee notes and one 20-rupee note.

Sam’s mother buys a doll for 75 rupees. Write 3 ways in which she can pay? 1

`50

`20

`5 = `75

`50

`10

`5 = `75

`20

`10

Do It Together

`5 = `75

Circle the notes and coins needed to buy these things.

`25

`40

`65

`24

`7 Chapter 14 • Money

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Do It Yourself 14B 1

How will you buy a pencil worth 18 rupees using 10-rupee notes and 1-rupee coins? Draw.

How will you pay for crayons worth 56 rupees, using 10-rupee notes and 1-rupee coins? Draw.

Raj has a 100-rupee note with him. He wants 50-rupee and 10-rupee notes. What notes can he get if he exchanges 100 rupees with his friend?

Fill in the blanks with the correct answers.

For 20 rupees we can exchange _______________ 5-rupee coins.

For 100 rupees we can exchange _______________ 50-rupee notes.

_______________ 10-rupee notes make 70 rupees.

Ruhaan has to buy a crayon worth rupees 200. How can he make it using 20-rupee notes and 10-rupee notes?

Adding and Subtracting Money Do you remember that Riya has to pay 50 rupees for the lunch box? But suddenly, Riya remembers that she also needs to buy a water bottle. The water bottle costs 90 rupees. Riya needs to pay now. Let’s see how she pays!

Remember! `50 for lunch box

Always add the cost of different objects to find the total cost.

`90 for bottle

Cost of lunch box

Cost of water bottle

Total amount

Think and Tell What notes can she use to make the payment of 140 rupees?

Ans: Riya will pay 140 rupees. 250

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The next day, Riya goes to the shop with one 20-rupee note. She buys a packet of biscuits for 15 rupees. She gives the 20-rupee note to the shopkeeper. The shopkeeper gives her 5 rupees back. Let’s understand why. Money Riya paid the shopkeeper: 20 rupees.

Total cost of the packet of biscuits: 15 rupees 20 rupees is more than 15 rupees

–

So we subtract 15 rupees from 20 rupees = 20 – 15 = ?

21 1

010 5 5

Riya gets back 5 rupees from the shopkeeper. Here, 5 rupees is called the change which Riya gets back from the shopkeeper. Example 3

Ram buys a new cap for `35 and crayons for `40. How much money will he pay? Cost of new cap Cost of crayons

Total amount paid

`35 + `40

Ans: Ram pays `75. Example 4

`75

Ram’s father purchased balloons for `72. He gave `80 to the shopkeeper. How much change did he get back? Amount paid to the shopkeeper Cost of balloons

Amount received back

7 10

`80

– `72 `08

Ans: Ram’s father received `8. Error Alert! To find the amount of change, the cost of the item is subtracted from the amount that is paid to the shopkeeper.

Chapter 14 • Money

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–

4 0 5 0 1 0

–

5 0 4 0 1 0

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Do It Together

Look at the price of items. Answer the questions.

`50

`55

`32

`47

Add and tell the total cost 1 bag

1 toy train Total cost

How much will I get back? I give

`55

I will get back

= `_____

Total cost

_ `_____

= `_____

How much will I get back? I give

`50

1 bag

`80

I will buy 1 bag

+ `_____

Add and tell the total cost 1 hat

`22

+ `_____

`55

I will buy 1 box of crayons – `_____

= `_____

I will get back

= `_____

Do It Yourself 14C 14A The pictures show the price of items in a shop. Look at the pictures and answer the questions:

`10

`45

`72

`36

`14

Arun buys 1 ice cream and 1 packet of chips from a shop. How much money will he pay altogether?

Nisha has `87. She buys a cap for `36. How much money will she get back from the shopkeeper?

Tina buys a toy car. She gives `90 to the shopkeeper. How much change will she get back from the shopkeeper?

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Mohan buys an ice cream and a toy car. How much money will he get back, if he pays with `200?

Harish bought a flower vase for `70 and a rose for `10. How much did Harish spend altogether?

Word Problems 1

Read and solve. a

Kartik had `88 with him. He spent `29 to buy a pen. How much money does he have left?

Tanya went to the market to buy a loaf of bread for `25 and butter for `45. How much money did Tanya pay to the shopkeeper altogether?

Arohi bought a pouch for `32. She gave the shopkeeper a 50-rupee note. How much money did Arohi receive back?

Mr. Shah bought a bunch of balloons for `48 and a lion mask for `35. How much money did he spend altogether?

Riya’s uncle has a farm. On the farm there are many animals and they are hungry. How much does each animal’s meal cost? Look at the pictures and answer the questions.

75 rupees

20 rupees

49 rupees

What is the cost of the hen’s meal? __________

How much will Riya’s uncle pay for 2 goats’ meals? __________

Riya went to buy a sheep’s meal. How much did she pay? __________

How much will the meal of 3 hens cost? __________

Rina has three 5-rupee coins and two 2-rupee coins. She wants to buy a pencil for 7 rupees. Can Rina buy the pencil with the coins she has? Will she get back any change from the shopkeeper?

Chapter 14 • Money

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36 rupees

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Points to Remember • • • •

The money in India is called the Indian Rupee. We use the symbol ` for the rupee amount. We have notes and coins for money.

We always get back the change from the shopkeeper if we pay more than the cost of the things. We add the prices of the things to find the total amount.

Math Lab Let’s remember our currency

Material required: Amount cards/chits, pencil, notebook. Setting: Activity to be done pairs. Instructions: 1

Teacher will prepare the amount cards/chits and put them in a bowl.

Students will work in pairs. Each pair will pick one amount chit from the bowl.

The pair will draw the currency notes and coins using the amount and show the amount in different denominations of notes and coins.

Chapter Checkup 1

Rita and her friends were hungry. They went to a nearby food shop to eat. Let’s observe and answer the questions.

Sandwich

French Fries

Ice Cream

Pizza

`35

`15

`42

`80

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Rita and Raj bought one sandwich and one ice-cream. How much did they pay for them? Draw rectangles for the notes and circles for the coins to show the amount.

Tina bought two packs of french fries. How much did she pay? Draw rectangles for the notes and circles for the coins to show the amount.

It’s time for Kriti to prepare yummy hot upma. She goes to the market and buys different ingredients. Look below and answer the questions.

ITEMS PRICE

semolina

vegetables

curd

curry leaves

`70

`65

`22

What is the price of curry leaves?

How much will Kriti pay for the semolina and curd?

Kriti purchases the vegetables and gives `80. How much money will she get back?

Draw rectangles for the notes and circles for the coins to show the amount. a

Show 50 rupees using 10-rupee notes.

Show 10 rupees using 1-rupee coins.

Match the notes with the correct value.

`15

`70

`20

`25

Chapter 14 • Money

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How many 50 paise coins will make ₹5?

Fill in the blanks. a

Three notes of `10 will make _________________.

Tina has five coins of `1 each. She has _________________ rupees in all.

Raj bought a pencil for `10 and an eraser for `7. He paid _________________ rupees to the shopkeeper. My mother gave me `35 and I purchased a candy for `8. Now, I have _________________ rupees left.

Raj has `30. He buys a toy car for `15 and a ball for `10. How much money has Raj spent in total?

Ravi has `15. He wants to save 10 more rupees. How much money will Ravi have after saving?

Your brother had `67. Then he gave `35 to you. How much money does he have left now?

Raj has `20. He buys a toy for `15 and a book for `10. Then, his friend gives him `5. How much money does Raj have now?

Word Problems 1

Priya had `74 and her father gave her `50 more. How much money does she have now?

Anu has `50. She buys two storybooks, each for `18. How much money does Anu have left after buying the books?

Aanya has `25. She wants to buy a toy that costs `15 and a box of chocolates that costs `8. Aanya’s friend offers her a deal: if she helps with some chores, the friend will give her an extra `5. Should Aanya accept the deal? Why or why not?

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15 Data Handling Let's Recall We see a lot of flowers in a garden! How many colours of flowers are there ? Let us count together! There are 13 red flowers in the garden. There are 15 yellow flowers in the garden. We now know the number of flowers in the garden. We also know the types of flowers. We also know the number of each type of flower. This type of information that includes numbers is called 'data'.

Let's Warm-up

Count the number of shapes. Fill in the table. Fill in the blanks.

How many times does

appear?

________

How many times does

appear?

________

How many times does

appear?

________

Which shape appears the most?

________

Which shape appears the least?

________ I scored _________ out of 5.

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Understanding Data Real Life Connect

It is Preeti’s birthday. She went to the market with her father to shop for her birthday party. Father: Please pick the things that you want to take. Preeti: I need all these. Here are the items Preeti took for the birthday party.

Preeti was excited about her birthday!

Counting Data Preeti got home after shopping. Preeti: Hello mother! I am home. Mother: Please count all the items you bought and put them away properly. Let us help Preeti count!

We can help Preeti count by drawing a table to show the number of each item.

A table helps us read the data easily. 258

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Example 1

A farm had four different animals. Count and write down each animal on the farm.

Remember! 3

Do It Together

We count the same kind of objects when counting data.

Ravi bought circle cutouts of different colours. Count the cutouts of each colour and fill in the table.

Colour Number of Cutouts

Do It Yourself 15A 1

An ice-cream seller has these ice creams on Monday. Count and write the number of each type of ice cream.

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Look at the shapes and count each of them.

Shelly went to the zoo with her grandfather on Sunday. She saw the following animals.

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A potter makes some pots. Look at the table and write down how many he makes each day. Monday

= _________

Tuesday

= _________

Wednesday

= _________

Thursday 5

= _________

Rashi loves collecting things from her garden. This is what she has collected on 3 days. Count and write down the number of each item collected by her. Friday Saturday Sunday

= _________ = _________ = _________

Word Problem 1

Rashi wants to count the number of spoons, cups, plates, and glasses in her kitchen. Look at the picture and count each item.

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Organising Data Real Life Connect

Preeti’s mother decided to go and buy some vegetables. She asked Preeti to quickly make a list of vegetables she needed to buy. Here is the list of fruits and vegetables: Items

How much?

Carrots

3 kg

Mangoes

1 kg

Potatoes

5 kg

Apples

Oranges Onions

5 kg

Think and Tell Preeti’s mother needed 3 kg of mangoes. If she had to double the number of all the items needed for the party, how many mangoes would there be?

6 kg

10 kg

The list will help Preeti’s mother to remember all the vegetables she needs to buy from the market. Example 2

Palak wants to go to the grocery store to buy some items for her house. She needs to buy 1 packet of sugar, 2 cakes of soap, 10 spoons, 1 packet of salt and 3 packets of milk. Help her to make a list of all the things. List of items Items

How many

Cakes of soap

Sugar

Spoons Salt

Milk Example 3

1 packet 10

1 packet

3 packets

Manoj wants to buy some fruit for his family. Mother wants 2 mangoes and father wants 1 bunch of grapes. His sister wants 2 apples. His grandmother wants 1 pear. Can you make a list based on this? Fruits

How many?

Grapes

1 bunch

Apples

Mangoes Pears

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Do It Together

Look at the pictures and help Seema make a list of all the things she needs for her camp. Cap

: ______

Umbrella : 1 Coat

: 1

Pants

: ______

Bag

: 1

Bottles

: ______

Chips

: ______

Shoes

: 1 pair

Do It Yourself 15B 1

Make a list of 5 things that you have in your school bag every day. Things

Number of Things

Tina needs to buy a few things for her art class. She needs 1 drawing book, 2 bottles of paint, 3 paint brushes and 5 sheets of white paper. Make a list of all the things she wants.

Meena wants to go the the grocery shop to buy a few things. She needs 1 bottle of shampoo, 1 packet of sugar, 3 plates, 1 packet of chilly powder and 2 packets of biscuits. Help her make a list of these things.

Nisha wants to bake a cake. Look at the pictures and make a list of all the things she has to buy.

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Whisk

Eggs

Flour

Milk

Sugar 263

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Rohit bought two bananas on Monday. On Tuesday, he bought 5 more than what he bought on Monday. On Wednesday, he bought 10 more than what he bought on Monday. Make a list to show how many bananas he bought each day. Days

Number of Bananas

Monday Tuesday Wednesday

Finding Information Remember Preeti’s mother made a list of items she needed to buy from the market for cooking. List of fruits and vegetables: Items

How much?

Mangoes

1 kg

Carrots

3 kg

Potatoes

7 kg

Apples

5 kg

Oranges

6 kg

Onions

10 kg

Let us find some information from the list: 1

How many potatoes are needed?

7 kg

Which is more - apples or potatoes?

Potatoes

How many carrots are needed?

3 kg

Which vegetable is needed the most?

Onions

How many types of fruit are needed? Name them.

3 types of fruit (apples, bananas and mangoes)

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Example 4

The list shows the number of fruit Suraj ate in the entire week. Days

Do It Together

Number of Fruit

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

On which day did Suraj eat the most fruit?

Friday and Sunday

On which day did Suraj eat only one fruit?

Saturday

On which two days did Suraj eat 2 fruit?

Monday and Thursday

The list shows the number of flowers that grew in the garden from January to April. Find the answers. Months

Number of Flowers

January

February

March

April

Which month had the most flowers?

April has the least flowers. True or False?

True

How many flowers are there in January?

________

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

False

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________

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Do It Yourself 15C 1

Mina made a list of different types of books she has at home. Read the table and answer the questions. Book

Fairy tales

Fables

Number of Books

How many comics does Mina have?

What type of books does Mina have the least of?

How many books does Mina have in total?

There was a sport event in the school. Here is a list of how many students participated in the different sports. Read the table and answer the questions. Number of Students

Cricket

Badminton

Hockey

Football

Table Tennis

How many students participated in football?

Which activity had the most students?

Was there any activity with only ten students? Name the activity.

Pooja made a list of pages she read from a book on three days. Read the table and fill in the blanks. Days Pages Read

Sport

Adventure stories Science facts Comics

Day 1

Day 2

Day 3

The most number of pages were read on ___________.

The number of pages read on Day 1 is ________.

The number of pages read on Day 3 is ___________ (more/less) than the number of pages she read on Day 1.

Look at the table and write if true or false. The table shows the number of ice creams sold by an ice-cream seller in four days: a b c d

Day 1

Day 2

Day 3

Day 4

Most ice creams were sold on Day 2.

More ice creams were sold on Day 1 than on Day 4. 16 ice creams were sold on Day 4.

Only 6 ice creams were sold on Day 3.

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Read the table and make a list of all the things Rahul bought for himself. Items

Items Rahul Bought

4 Plates

 

10 Spoons

Items

Number of Items

Name of Friends

Number of Balloons

Sia

5 Cakes of Soap 2 Towels

6 kg Rice

 

1 Bottle

10 Pencils

3 Notebooks



Pictograph On Preeti’s birthday, they played a game, in which all her friends had to blow up as many balloons as they could. Preeti made a table to record the data.

Rohan Rahul

5 2

Prishi

Param

Let us learn how to show the above data using a pictograph. A pictograph shows the data using pictures. 1 Make a table Name Number of Balloons and write the headings. Rohan Sia

Rahul Prishi

Draw pictures in Column 2 to show the total number of balloons. Draw 1 picture for 1 balloon.

Param 2

Write the names in Column 1.

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Now, let us help Preeti read the pictograph. From the table we see: 1

Param blew the greatest number of balloons.

Rahul blew the smallest number of balloons.

Sia blew 3 balloons.

A pictograph helps us to see the data clearly. Example 5

Example 6

Different children like different flavours of ice cream. Read the table and draw a pictograph for the data. Use 1 for 1 ice cream. Flavour

Flavour

Number of Children

Vanilla

Chocolate

Strawberry

Pineapple

Number of Children

Vanilla Chocolate

Read the pictograph showing the number of flowers sold in Anna’s Flower shop. Answer the questions. Flower

Number of Flowers Sold

Roses Daisies Orchids Carnations a

Which flowers were sold the least? - Daisies

Which flowers were sold more than Carnations? - Roses

How many orchids were sold? - 5

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Do It Together

There is a sports event in the school. Students have participated in different sports activities. Let us read the data given in the table. Sport

Number of Students

Hockey

Football

Badminton

Cricket

Tennis

Draw a pictograph to show the above data. 1 Sport

Number of Students

Badminton

= 1 student

Read the pictograph and answer the questions. 1

Hockey 2

Cricket Football

Tennis

How many students participated in Football? Which activity had the most students? - Cricket Was there any activity with only one student? Which activity had the least students?

Do It Yourself 15D 1

The table shows the stationery items bought by students of a class. Draw a pictograph to show the data. [1 = 1 student] Stationary items

Pens

Pencils

Crayons

Erasers

Pencil Boxes

Ask any 5 friends about the number of family members living in their houses. Fill the data in a table. Draw a pictograph to show the data.

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Number of Students

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Sahil went to a market to buy vegetables. Read the pictograph and answer the questions. Vegetables

Number of Students

Tomato Capsicum Carrot Mushroom Potato

Which vegetable did Sahil buy the most of?

How many carrots did he buy?

How many mushrooms did he buy?

Which did he buy more of – mushroom or tomatoes? How many more?

The table shows the number of flowers that grew at Sara’s house from January to April. Month

January

Number of Flowers

February March April 5

Which month had the most flowers?

Which month had the least flowers?

How many flowers grew in January?

What was the total number of flowers in the 4 months?

In the pictograph given in Q4, if 4 more flowers grew in April, how many flowers grew in April in total?

Points to Remember •

When counting data, count the same type of objects.

•

Making lists helps us to remember the things we need.

• •

Count each object only once.

Read the list carefully when looking for information.

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Math Lab Setting: In pairs. Things required: Pencil box of each partner, notebook and pencil. Method: 1

Each partner will check each other's pencil box.

Make a list of all the items in their pencil boxes.

Make the list of this in the notebook.

Chapter Checkup 1

Count the flowers and leaves and fill in the blanks.

_______________ 2

_______________

Class 2 students have these items. Look at the list and answer the questions. Items

Number of Items the Children have

Chalk

Pens

Pencils

Crayons

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_______________

How many children have crayons?

Which item do the children have the least of?

How many children have pencils?

d e

Do the children have more pencils than pens?

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Count the insects in the image and answer the following questions. bug ant snail bee a b c d e

How many bugs are there? How many bees are there?

How many snails are there?

Which insect are there most of?

Which two insects are equal in number?

The list shows the number of fruit with a fruit seller. Look at the list and answer the questions. Fruit

Apples

Mangoes Guavas

Pineapples 5

Number of Fruit 73 20 40 20

a b c d

Which fruit does the fruit seller have the least of? Which two fruits does he have an equal number of?

There are more guavas than pineapples. True or False? Which fruit does he have the most of?

Read the pictograph and answer the questions. Day

Number of Sandwiches Sold

Monday Tuesday Wednesday Thursday Friday a

How many sandwiches were sold on Thursday?

On which day were more sandwiches sold – Monday or Friday? How many more?

How many sandwiches were sold in the week?

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Read the pictograph and fill in the blanks. Year

Number of Medals Won by Joe

2011 2012 2013 2014 2015

Joe won ________ medals in the year 2015.

In 2012 Joe won ________ medals.

Joe won ________ more medals in 2014 than in 2013.

A survey was done on a few students for their favourite colour. The data is given below. Draw a pictograph to show the data. Use to show 1 colour.

blue, red, blue, blue, red, green, blue, yellow, blue, green, blue, blue, green, red, yellow, yellow, green, yellow, green, green, green

Word Problems 1

Mona went to a toy shop. She bought 3 green balls, 4 red balls, 2 dolls and 1 car. Make a table to show the things that she bought. Write the total number of things she bought.

Ram made a list of things he bought. There were a total of 20 things. He bought 3 toys, 5 books and some crayons. How many crayons did he buy? Make a list to show what he bought.

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Imagine Mathematics

About This Book

MATHEMATICS

Singapore

IM_G02_MA_MB_Cover.indd All Pages

Gurugram

Bengaluru

hello@uolo.com `XXX

NEP 2020 based

NCF compliant

CBSE aligned

26/09/23 7:15 PM