Headstart - Math Coursebook 3

MATHS COURSEBOOK

Aligned with NEP 2020

Headstart Maths Coursebook - Class 3

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ISBN 978-81-967554-5-4

First Edition

Preface

Dear Parents, Educators, and Guardians,

In the ever-evolving landscape of education, the National Education Policy (NEP) 2020 is a pivotal milestone, emphasizing the critical role of ages 3 to 6 in shaping a child’s mental faculties. Moving away from the traditional method of memorization, it highlights the significance of key learning goals, places a greater emphasis on multidisciplinary education, and aims to nurture the creative talents of every learner.

Aligned with the visionary NEP 2020, we proudly introduce the “HeadStart Programme” by Infinity Learn— an innovative educational initiative meticulously designed to fortify your child’s foundation during their most formative years. Tailored for Grades 1 to 5, this program aims to instil a passion for learning and establishes a formidable academic base.

The HeadStart Program unfolds a tailored educational experience, commencing with Grades 1 and 2, where the focus lies on making numbers (Math) comprehensible and fostering exploratory learning in Environmental Studies (EVS). Progressing into Grades 3, 4, and 5, the program expands to encompass critical mathematical thinking, exploration of Science, and a nuanced understanding of society, environment, and global citizenship in Social Studies.

Equipped with thoughtfully crafted course books, home reinforcement workbooks, and a cutting-edge learning app, the HeadStart Program leverages both traditional and digital tools to ensure a comprehensive educational experience.

What is the HeadStart Advantage?

We firmly believe that enhancing creativity, logical and critical thinking in the early years will pave the way for a robust foundation in Mathematics and Science during the middle years. This, in turn, positions learners for success in senior-grade challenges, differentiating them in high-stakes exams such as JEE, NEET, and CUET.

For educators, we provide meticulously designed lesson plans and in-class videos, ensuring uniform and effective teaching methodologies. Our mission encapsulates the question ‘Baccha Seekha ki Nahi’—did the child learn?—as we are dedicated to ensuring that each child’s learning journey is not merely a progression but a meaningful and enriching experience.

We invite you to join us in this exciting new chapter of your child’s education. The “HeadStart Programme” is more than a curriculum; it’s a pathway to nurturing a lifelong passion for learning. Let’s provide our children with the optimal start in their educational journey.

Warm regards,

The Infinity Learn Team

Numbers 1

My Study Plan

• 4-digit numbers and their place values

• Compare and order 4-digit numbers

• Round off 4-digit numbers to the nearest tens and hundreds

• Roman numerals and their basic principles

Let’s Recall

1. Identify the number based on the given diagram.

2. Fill in the boxes.

(a) 789 = hundreds, tens, ones

(b) 357 = hundreds, tens, ones

(c) 279 = hundreds, tens, ones

999 is the greatest 3-digit number. Fact Zone

100 is the smallest 3-digit number.

3. Write the numbers in figures.

(a) Three hundred fifty-two

(b) Seven hundred seventy-five

(c) Five hundred eighty-eight

4. Arrange the numbers.

(a) Ascending order

(b) Descending order 230, 256, 928, 672 635, 764, 851, 697

Thinking Zone

I am a 4-digit number. My thousands place is 6, my hundreds place is 2, my tens place is 7, and my ones place is 9. What number am I? Find out.

Let’s Learn

4-Digit Numbers

We know that

• 10 Ones = 1 Ten = 10

• 10 Tens = 1 Hundred = 100

Similarly, 10 Hundreds = 1 Thousand = 1000.

10 Hundreds 1 Thousand

1000 is the smallest 4-digit number. We read it as one thousand.

Counting by Thousands

Observe the table given below. Each represents 1000.

Similarly,

10 one thousand blocks represents the number 10,000. We read 10,000 as ten thousand. It is the smallest five-digit number.

Forming and Reading Four-Digit Numbers

Look at the following blocks.

3 Thousands + 2 Hundreds 4 Tens 8 Ones

Let us find out the number formed by these blocks. The number formed is 3000 + 200 + 40 + 8 = 3248

We read it as three thousand two hundred forty-eight.

To read a four-digit number, we first read the Thousands, then the Hundreds and finally we read the last two digits together, that is, the Tens and the Ones digits.

Fact Zone

1. Write the number names for the following:

a. 6754 = ______________________________________________________

b. 3029 = ______________________________________________________

c. 9985 = ______________________________________________________

d. 5097 = ______________________________________________________

e. 4639 = ______________________________________________________

2. Write the numerals for the following:

a. Six thousand ten = ________________

b. Nine thousand five hundred eighty-two = _____________

c. Two thousand nine hundred ninety-one = ______________

d. Eight thousand four hundred seventy-five = _______________

e. Three thousand nine hundred four = _________________

Numbers on the Abacus

Abacus is one of the oldest tools used to represent numbers. Let us represent 1000 on the abacus.

The given abacus represents the number 999.

We can put maximum 9 beads in any spike.

On adding 1 to 999, it becomes 999 and one more, that is, 999 + 1 or one thousand or 1000.

Let us represent 5084 on the abacus.

H T O

We do not put any beads in the spike having the digit 0 in that place.

Let’s Practise - 2

1. Write the number represented by each abacus.

Place Value and Face Value

The place value of a digit in a number depends on its place within the number. It is obtained by multiplying the digit with the value of the place it occupies. The face value of a digit in a number is the digit itself, irrespective of the place it occupies.

The place value and face value of digits in 2563 can be written as:

Example: Write the place value and face value of the digits in 6703.

Solution:

The face value and place value of 0 are always 0.

Expanded Form and Short Form

The expanded form of a number is the sum of the place values of all its digits.

Let us write the place value of each digit of 5298.

H T O 5 2 9 8

Place value of 8 = 8 × 1 = 8

Place value of 9 = 9 × 10 = 90

Place value of 2 = 2 × 100 = 200

Place value of 5 = 5 × 1000 = 5000

Thus, the expanded form of 5298 = 5000 + 200 + 90 + 8.

To write the number in standard form, write the face value of each digit at its correct place.

For example, 5298 is the standard (or short) form of 5000 + 200 + 90 + 8.

Successor and Predecessor

The successor of any number is the number that comes just after it.

Look at the number 2478 shown on the following number line.

• We need not show the place value of 0 in the expanded form. For example, 3407= 3000 + 400 + 0 + 7 = 3000 + 400 + 7

• The successor of any number can be found by adding number 1 to it. For example, 3245 + 1 = 3246.

Fact Zone

Fact Zone

2478 is followed by 2479 on the number line. So, 2479 is called the successor of 2478.

The predecessor of a number is the number that comes just before it. On the given number line, 2474 comes before 2475. So, 2474 is called the predecessor of 2475.

The predecessor of any number can be found by subtracting 1 from it. For example, 1098 - 1 = 1097.

Let’s Practise - 3

1. Find the predecessor of:

2354 __________

2. Find out the successor of:

4208 ________

Comparison of Numbers

2030 __________

9791 _________

Comparing numbers helps us find which one is larger or smaller. As we know:

• the > sign stands for ‘greater than’.

• the < sign stands for ‘less than’.

• the = sign stands for ‘equal to’.

7385 ___________

5609 ____________

If the given numbers have the same number of digits, start comparing them from the leftmost place. A number having more digits is greater than the other.

Let’s compare two numbers: 7389 and 7388, and represent them using their respective digits in a place value chart:

The number 7389 is formed using the digits 3, 7, 8, and 9.

The number 7388 is formed using the digits 3, 7, and 8.

Step 1: Write the digits of the two numbers in a place value chart as shown below.

Step 2: Look at the digits in the thousands place. They are the same.

Step 3: Look at the digits in the hundreds place. They are the same.

Step 4: Look at the digits in the tens place. They are the same.

Step 5: Look at the digits in the ones place. Here, 9 > 8.

So, the number 7389 is greater than the number 7388 or 7389 > 7388.

Let’s Practise - 4

1. Fill in the correct sign <, >, or =.

a. 4562______4652

b. 8822_____2288

2. Arrange 3896, 8986, 2698, and 9849 in ascending and descending order.

Ascending Order: ___________, __________, ____________, ____________

Descending Order: ___________, __________, ____________, ____________

Ascending and Descending Order

Ascending order means arranging numbers in increasing sequence, from the smallest number to the greatest number.

Let’s arrange the numbers 7491, 8219, and 7652 in ascending order.

Step 1: Compare the digits at the thousands place. The number 8219 has the greatest thousands digit.

Step 2: Compare the remaining two numbers, 7491 and 7652. Since thousands place digits are the same, compare the digits at the hundreds place. The number 7491 has 4 at the hundreds place, while 7652 has 6 at the hundreds place. Therefore, 7491 is the smallest of the three numbers.

Ascending order: 7491 < 7652 < 8219.

Descending order means arranging the numbers in decreasing sequence, from the greatest to the smallest number.

Example: Arrange the numbers in descending order: 6749, 7896 and 2438

Solution: Arrange the given numbers in order from the greatest to the smallest: 7896 > 6749 > 2438 .

Forming the Greatest and the Smallest Numbers

We can arrange the digits of the given numbers in increasing or decreasing order to form the greatest and the smallest numbers.

Example 1: Form the (a) greatest number and (b) smallest number using the digits 8, 6, 2, and 1 without repetition.

Solution:

a. To form the greatest 4-digit number with digits 8, 6, 2, and 1, without repeating, we arrange the digits in decreasing order.

8 6 2 1

b. To form the smallest 4-digit number with digits 8, 6, 2, 1, without repeating, we arrange the digits in increasing order.

1 2 6 8

Example 2: Form the smallest 4-digit number with the digits 4, 6, 1, and 0, without repetition.

Solution:

We arrange the digits in the increasing order.

0 1 4 6

But, the digit 0 at the beginning of a number has no value. So, this is a 3-digit number, that is 146.

So, to make it the smallest 4-digit number, place the digit 0 after the secondsmallest digit, that is, 1.

Therefore, the smallest number that can be formed with the digits 4, 6, 1, and 0 without repeating is 1046 .

Let’s Practise - 5

1. Form the greatest and smallest 4-digit numbers using the given digits only once.

Digits Smallest Number Greatest Number

2, 8, 0, 5

2, 4, 8, 3

4, 7, 3, 8

8, 6, 9, 0

Rounding Off

Sometimes, the answer is not the actual number but a figure just close to that number.

For example, there are around 3000 students in our school. Such numbers are called estimated numbers. Rounding off is a way of estimating. Rounding means changing a given number to the nearest tens, hundreds, thousands, and so on.

Rounding off helps us remember the numbers and perform calculations easily.

Rounding

off Numbers to the Nearest 10

To round a number to the nearest 10, we observe the digit at the ones place. We round up the number when the digit at the ones place is either 5 or greater than 5.

For example, 28 is rounded up to 30 and 75 is rounded up to 80. We round down the number when the digit at the ones place is less than 5.

For example, 34 is rounded down to 30 and 81 is rounded down to 80.

Let’s Practise - 6

1. Round off the following numbers to the nearest tens. 15 ________ 263 _________ 45 _________ 824 ________

Roman Numerals

Roman numeral is an ancient numeral system that uses combinations of letters to represent numbers. These were used in earlier days by the Romans. In the present time, we see the Roman numerals being used in some analog clocks and watches.

Roman numerals with their corresponding Hindu-Arabic numerals are given below:

Rules for Writing Roman Numerals

• The letters I, X, C, and M can be repeated up to three times in a row.

• The letters V, L, and D are never repeated.

• Smaller numerals placed before larger numerals are subtracted from the larger ones.

There is no symbol to represent 0 in the Roman numeral system.

For example, IV represents 4 (V – I), IX represents 9 (X – I), and XL represents 40 (L – X).

• Smaller numerals placed after larger numerals are added to the larger ones. For example, VI represents 6 (V + I), XI represents 11 (X + I), and LX represents 60 (L + X).

• Combine the Roman numerals following the rules mentioned above to form larger numbers. For instance, 37 is represented as XXXVII (10 + 10 + 10 + 5 + 1 + 1).

were used in ancient Rome for counting and recording numbers.

Roman numerals

Fact Zone

1. Write the Roman numerals for the following numbers: a. 12 b. 38 c. 23 d. 31 Let’s Practise - 7

Let’s Sum Up

• 10 ones form 1 ten, 10 tens form 1 hundred, 10 hundreds form 1 thousand.

• 2345 is the standard form of a number. Its expanded form would be 2000 + 300 + 40 + 5. Hence, we use place values, and not face values to form the expanded form of a number.

• We use greater than (>), less than (<), and equal to (=) signs to compare numbers.

• Arranging numbers from the smallest to the largest is known as ascending order. When numbers are arranged from the largest to the smallest, it is called descending order.

• Rounding off a 3-digit number to its nearest tens helps in estimation.

• Roman numerals use various combination of letters to show HinduArabic numerals.

Cross-Curricular Connections

Science

In which year did the famous scientist Albert Einstein win the Nobel Prize in Physics? Find out and write the year in words.

Social Studies

Arrange the heights of the mountains listed below in ascending order:

Mount Everest: 8848 metres

K2: 8611 metres

Kangchenjunga: 8586 metres

Life Skills

During a community clean-up event, students collected 3548 pieces of litter from the park. Suppose, the community plans to reduce the litter collected next year by half. How many pieces of litter would they aim to collect during the next clean-up event? Represent the reduced number in words.

21st Century Skills

Following are the lengths of some popular dams in India:

a. Sardar Sarovar Dam: 1210 m b. Krishna Raja Sagar Dam: 2621 m

c. Tungabhadra Dam: 2441 m

• Which of these dams is the longest?

• Which of these dams is the shortest?

• Arrange these lengths in ascending order.

Tips for the Parent

• Encourage your child play sudoku or other easier number games.

Addition 2

My Study Plan

• Addition of 3-digit numbers

• Addition of 4-digit numbers

• Addition of three numbers

• Properties of addition

• Estimating the sum

• Stories based on addition

Let’s Recall

1. Add the numbers and write down the correct answer in the given blanks.

2. Rewrite as vertical addition and solve.

24 + 24 + 24

13 + 31 + 46

Word Zone

Pair: A set of two similar things

Thinking Zone

Find the pair of equal numbers whose sum is: a. _____ + _____ = 80 b. _____ + _____ = 120

Let’s Learn

Addition of 3-Digit Numbers

Adding means putting things together. Addition of 3-digit numbers means adding numbers that have 3 digits each.

Addition without regrouping

Let’s consider the numbers 364 and 531. Add them to find the total.

Step 1: Arrange the addends according to their place values, i.e., ones, tens, and hundreds.

Step 2:

Add the digits in the ones place (4 + 1 = 5). Write the sum under the ones place.

Step 3: Add the digits in the tens place (6 + 3 = 9). Write the sum under the tens place.

Step 4: Add the digits in the hundreds place (3 + 5 = 8). Write the sum under the hundreds place.

Hence, the sum of 364 and 531 is 895.

Addition with regrouping

When adding the numbers, if the sum of the digits in one column is greater than nine, then we regroup the provided numbers and move the excess digit to the following column.

Regrouping for 3-digit numbers begins in the ones column and proceeds to the left, toward the tens column and then the hundreds column.

Word Zone

Excess: An extra quantity of something

Let us understand this with an example by adding the numbers 456 and 239.

Step 1:

Step 2:

Arrange the addends according to their place values, i.e., ones, tens, and hundreds.

Add the digits in the ones place. Here, 6 + 9 = 15.

Since 15 is greater than 9, we carry forward 1 to the tens column and write 5 as the sum in the ones column.

Step 3:

Step 4:

While adding the digits in the tens place, including the number that is carried forward from the ones column.

1 (carry forward) + 5 + 3 = 9

Write the sum under the tens column.

Add the digits in the hundreds place. 4 + 2 = 6

Write the sum under the hundreds column.

Hence, the sum of 456 and 239 is 695.

1. Add the numbers.

2. Rewrite as vertical addition and solve.

Let’s Learn

Addition of 4-Digit Numbers

A 4-digit number is made up of thousands, hundreds, tens, and ones digits. The addition of 4-digit numbers means adding numbers that each have 4 digits.

Addition without regrouping

Let us consider the numbers 1068 and 4511. Add them to find the total.

Step 1: Arrange the addends according to their place values, i.e., ones, tens, hundreds, and thousands.

Step 2:

Step 3:

Add the digits in the ones place (8 + 1 = 9). Write the sum under the ones place.

Step 4:

Add the digits in the tens place (6 + 1 = 7). Write the sum under the tens place.

Step 5:

Add the digits in the hundreds place (0 + 5 = 5). Write the sum under the hundreds place.

Add the digits in the thousands place (1 + 4 = 5). Write the sum under the thousands place.

Hence, the sum of 1068 with 4511 is 5579.

Addition with regrouping

When adding the numbers, if the sum of the digits in the ones column is greater than nine, then we regroup the numbers and move the excess digit to the following column.

Regrouping for 4-digit numbers begins in the ones column and proceeds to the left, toward the tens column, hundreds column, and then thousands column. Let us understand this with an example.

Add 2556 and 1637.

Step 1:

Arrange the addends according to their place values, i.e., ones, tens, hundreds, and thousands.

Add the digits in the ones place.

Here, 6 + 7 = 13.

Step 2:

Step 3:

Since 13 is greater than 9, we carry forward 1 to the tens column and write 3 as the sum in the ones column.

While adding the digits in the tens place, include the number that is carried forward from the ones column.

1 (carry forward) + 5 + 3 = 9

Write

Add the digits in the hundreds place.

5 + 6 = 11

Step 4:

Step 5:

Since 11 is greater than 9, we carry forward 1 to the thousands column and write 1 as the sum in the hundreds column.

While adding the digits in the thousands place, include the number that is carried forward from the hundreds column.

1 (carry forward) + 2 + 1 = 4

Write the sum under the thousands column.

Hence, the sum of 2556 and 1637 is 4193.

Let’s Practise - 2

1. Add the numbers.

2. Rewrite as vertical addition and solve.

a. 1145 + 2121

b. 2437 + 3175 + +

Let’s Learn

Addition of Three Numbers

Sometimes, we have to add more than two numbers. Look at the example given below.

Example 1: Add 126, 234, and 349.

Solution:

Step 1: Arrange the addends according to their place values, i.e., ones, tens, and hundreds.

Step 2: Add the digits in the ones place of all three numbers.

Here, 6 + 4 + 9 = 19.

Since 19 is greater than 9, we carry forward 1 to the tens column and write 9 as the sum in the ones column.

Step 3: While adding the digits in the tens column, include the number that is carried forward from the ones column.

1 (carry forward) + 2 + 3 + 4 = 10

Again 10 is greater than 9, we carry forward 1 to the hundreds column and write 0 as the sum in the tens column.

Step 4: While adding the digits in the hundreds column, include the number that is carried forward from the tens column.

1 (carry forward) + 1 + 2 + 3 = 7

Write the sum under the hundreds column.

Hence, the sum of 126, 234, and 349 is 709.

Example 2: Add 2136, 5423, and 1744.

Solution:

Step 1:

Step 2:

Arrange the addends according to their place value, i.e., ones, tens, hundreds, and thousands.

Add the digits in the ones place of all three numbers.

Here, 6 + 3 + 4 = 13.

Since 13 is greater than 9, we carry forward 1 to the tens column and write 3 as the sum in the ones column.

Step 3: While adding the digits in the tens column, include the number that is carried forward from the ones column.

1 (carry forward) + 3 + 2 + 4 = 10

Again, 10 is greater than 9, so we carry forward 1 to the hundreds column and write 0 as the sum in the tens column.

Step 4: While adding the digits in the hundreds column, include the number that is carried forward from the tens column.

1 (carry forward) + 1 + 4 + 7 = 13

Here, 13 is greater than 9, so we carry forward 1 to the thousands column and write 3 as the sum in the hundreds column.

Step 5: While adding the digits in the thousands column, include the number that is carried forward from the hundreds column.

1 (carry forward) + 2 + 5 + 1 = 9

Write the sum under the thousands column.

Hence, the sum of 2136, 5423, and 1744 is 9303.

Rewrite as vertical addition and solve.

1.

Let’s Learn

Properties of Addition

Property 1: The sum of two numbers remains the same even if we change the order of the numbers. This is called the order property of addition or commutative property.

For example,

H T O 3 8 4 1 + 2 1 4 1 5 9 8 2

Thus, 3841 + 2141 = 5982 and 2141 + 3841 = 5982.

Hence, 3841 + 2141 = 2141 + 3841.

Property 2: While adding three or more numbers, the numbers can be grouped in any way. The sum always remains the same. This is called grouping property of addition or associative property.

For example, 3045 + (2981 + 2442) = Th H T O 1 1 2 9 8 1 + 2 4 4 2 5 4 2 3

(3045 + 2981) + 2442 =

Thus, 3045 + (2981 + 2442) = 8468 and (3045 + 2981) + 2442 = 8468.

Hence, 3045 + (2981 + 2442) = (3045 + 2981) + 2442.

Word Zone

Order: Arrangement or sequence of things or objects

Property 3: When we add 1 to a number, the sum is the successor of the number. For example,

Thus, 6706 + 1 = 6707. Therefore, 6707 is the successor of 6706.

Property 4: If 0 is added to any number, the sum is the number itself.

For example, Thus, 8901 + 0 = 8901.

Let’s Learn

Estimating the Sum

Estimating the sum means rounding off the addends and then adding them.

Example 1: Estimate the sum of 327 and 453 to nearest tens.

Add 327 and 453 together through estimation.

Step 1: Round off numbers to the nearest tens.

If the digit in the ones place is 5, 6, 7, 8, or 9, replace the ones place digit with 0, and add 1 to the tens place digit.

If the digit in the ones place is 0, 1, 2, 3, or 4, replace the ones place digit with 0, and the tens place digit remains unchanged.

327 is closer to 330 when rounded to the nearest tens.

453 is closer to 450 when rounded to the nearest tens.

Step 2:

Now, add the rounded numbers:

330 + 450

So, 330 + 450 = 780.

Hence, the estimated sum of 327 and 453 to the nearest tens is 780.

Example 2: Estimate the sum of 3412 and 2356 to nearest hundreds.

Add 3412 and 2356 together through estimation.

Word Zone

Successor: Follows or comes after

Step 1: Round off the numbers to the nearest hundreds.

If the digit in the tens place is 5, 6, 7, 8, or 9, replace the tens and ones place digits with 0, and add 1 to the hundreds place digit.

If the digit in the tens place is 0, 1, 2, 3, or 4, replace the tens and ones place digit with 0, and the hundreds place digit remains unchanged.

3412 is closer to 3400 when rounded to the nearest hundreds.

2356 is closer to 2400 when rounded to the nearest hundreds.

Step 2:

Now, add the rounded numbers.

3400 + 2400

So, 3400 + 2400 = 5800.

Hence, the estimated sum of 3412 and 2356 to nearest hundreds is 5800.

Let’s Practise - 4

1. Fill in the blanks.

a. The successor of 1648 is ____________.

b. When we add ________ to a number, the number remains unchanged.

c. 2334 + 1484 = 1484 + ______________.

d. While adding three or more numbers, the numbers can be grouped in any way and the sum always remains the ____________.

2. Solve using estimation to nearest hundreds.

3432 + 2365

3. Solve using estimation to nearest tens.

567 + 874

Let’s Learn

Stories Based on Addition

In our daily life, we often need to add things together. When you read stories with numbers and see words like ‘total,’ ‘together,’ ‘in all,’ ‘altogether,’ or ‘sum of,’ it means you should use addition to find the answer.

Example 1: A library has 2,436 books in one bookshelf and 1,295 books in another. How many books does the library have in total?

Solution:

Number of books in one bookshelf of a library = 2436

Number of books in another bookshelf of a library = 1295

Total number of books in the library = 2436 + 1295

Hence, the total number of books in the library is 3,731.

Example 2: In a large farm, there are 3,456 cows and 2,198 sheep. How many animals are there in the farm in total?

Word Zone

Bookshelf: A storage unit that holds books

Solution:

Number of cows in the farm = 3456

Number of sheep in the farm = 2198

Total number of cows and sheep in the farm = 3456 + 2198

Hence, the total number of cows and sheep in the farm is 5,654.

Let’s Practise - 5

1. Solve the following problems.

a. A classroom has 1,367 crayons and 1,798 markers. How many supplies does the classroom have in total?

b. Seema spent ₹ 2,347 on groceries and ₹ 1,568 on clothes. How much money did she spend in total?

c. There are 4,789 books in the library’s fiction section and 1,245 books in the non-fiction section. How many books are there in the entire library?

Groceries: The food and the other items purchased by people for their daily needs Fiction: Stories created from imagination

Let’s Sum Up

• Adding 3-digit numbers and 4-digit numbers in column method involves arranging the addends according to their place value and then finding the sum.

• The sum of two numbers remains the same even if we change the order of the numbers. This is called the order property of addition or commutative property.

• The sum of three or more numbers always remains the same when they are grouped in any way. This is called grouping property of addition or associative property.

• Adding 1 to a number gives the successor of the number.

• Adding 0 to a number gives the same number.

• Estimating the sum means rounding off the addends and then adding them.

On October 2nd, the day of Gandhi Jayanti, the students were asked to collect litter. The 3rd grade students picked up 376 items, the 4th grade students picked up 274 items, and the 5th grade students picked up 393 items. How many items did all three classes collect in total?

Life Skills

Cross-Curricular Connections

Arts:

You are making a collage with pictures from three magazines. The first magazine has 1,234 pictures, the second has 2,345 pictures, and the third has 3,456 pictures. How many pictures do you have for your collage in total?

Social Studies:

The following are the 3 largest national parks in India.

National Parks in India Area (sq.km.)

Hemis National Park 4,400

Desert National Park 3,162

Gangotri National Park 2,390

What is the total area covered by these 3 largest national parks in India?

English:

Pihu bought a novel which consisted of two volumes. There were 289 pages in the 1st volume and 175 pages in the 2nd volume. Find out the total number of pages the novel was comprised of.

21st Century Skills

To maintain a good health status, a person needs to drink 30004000 ml of water per day. Aayu wanted to assess how much water he would be able to drink on 2 days of the weekend. On Saturday, he drank 2705 ml of water, and on Sunday, he drank 3075 ml of water. Find out the total volume of water consumed by Aayu in those 2 days.

Extend Your Knowledge

Partial Sums:

It is a method for adding numbers.

For example, let us add the numbers 2458 and 3177 using partial sums:

Th H T O

2 4 5 8 + 3 1 7 7

1 5 = 8 ones + 7 ones

1 2 0 = 5 tens + 7 tens

5 0 0 = 4 hundreds + 1 hundred

5 0 0 0 = 2 thousands + 3 thousands

5 6 3 5

Hence, the sum of 2458 and 3177 using partial sums is 5635.

Tip for the Parent

• Encourage your child to practise addition regularly by incorporating it into everyday activities like calculating the total price of grocery items.

Subtraction 3

My Study Plan

• Subtraction of 3-digit and 4-digit numbers with and without regrouping

• Verification of Subtraction using Addition

• Subtraction using Estimation Method

• Word Problems based on Addition and Subtraction

Let’s Recall

In a zoo, there were 48 plants. Some were eaten by the animals. Now, there are 35 plants left. How many plants did the animals eat?

Number of plants animals ate is _____.

Thinking Zone

Imagine, you had saved Rs.3,874 to buy a bicycle. Then, your grandparents gave you some money for your birthday. After counting, you had Rs.4,905. How much money did you get from your grandparents for your birthday, and how did you find it out?

Subtraction of 3-Digit Numbers

Subtraction means taking away a smaller number from a bigger one.

Look at the subtraction problem given below:

Example 1: Let us subtract 342 from 597.

Solution: 597 - 342 = ________

Step 1: Arrange the digits in the correct column:

• Greater number must be written above the smaller number.

• Digit at hundreds place are 5 and 3. So, 597 > 342.

Step 2: Subtract the digits in the ones place.

Step 3: Subtract the digits in the tens place.

9 tens – 4 tens = 5 tens

Step 4: Subtract the digits in the hundreds place.

5 hundreds – 3 hundreds = 2 hundreds

Therefore, 597 – 342 = 255

Example 2: Subtract 449 from 687.

Solution: 687 – 449 = _________

Step 1: Arrange the digits in the correct column:

• Greater number must be written above the smaller number.

• Digit at hundreds place are 6 and 4. So, 687 > 449.

Step 2: Subtract the digits in one’s place.

• 7 < 9, so, 7 – 9 is not possible.

• Borrow 1 from ten’s place.

• 1 tens = 10 ones. So, 10 + 7 = 17 ones.

• 17 ones – 9 ones = 8 ones

Step 3: Subtract the digits in the tens place.

• 1 ten is borrowed from ten’s place, so 7 tens are left.

• 7 tens – 4 tens = 3 tens

Step 4: Subtract the digits in the hundreds place.

• 6 hundreds – 4 hundreds = 2 hundreds

Therefore, 687– 449 = 238

Let’s Practise-1

Subtract:

(a) 641 – 345 (b) 769 – 546

(c) 541 - 282

(d) 753 – 682 (e) 835 – 651 (f) 967 - 535

Let’s Learn

Subtraction of 4-Digit Numbers

Look at the subtraction problem given below:

Example 1: Let us subtract 1332 from 5947.

Solution: 5947 - 1332 = ________

Step 1: Arrange the digits in the correct column:

• Greater number must be written above the smaller number.

• Digit at thousands place are 5 and 1. So, 5947 > 1332.

Step 2: Subtract the digits in the ones place.

Step 3: Subtract the digits in the tens place.

Step 4: Subtract the digits in the hundreds place.

Step 5: Subtract the digits in the thousands place.

Therefore, 5947 – 1332 = 4615

Example 2: Subtract 4549 from 6187.

Solution: 6187 – 4549 = _________

Step 1: Arrange the digits in the correct column:

• Greater number must be written above the smaller number.

• Digit at thousands place are 6 and 4. So, 6187 > 4549.

Step 2: Subtract the digits in one’s place.

• 7 < 9, so, 7 – 9 is not possible.

• Borrow 1 from ten’s place.

• 1 tens = 10 ones. So, 10 + 7 = 17 ones.

• 17 ones – 9 ones = 8 ones

Step 3: Subtract the digits in the tens place.

• 1 ten is borrowed from ten’s place, so 7 tens are left.

• 7 tens – 4 tens = 3 tens

Step 4: Subtract the digits in the hundreds place.

• 1 < 5, so, 1 – 5 is not possible.

• Borrow 1 from thousands place.

• 1 thousand = 10 hundreds. So, 10 +1 = 11 hundreds.

• 11 hundreds – 5 hundreds = 6 hundreds

Step 5: Subtract the digits in the thousands place.

• 1 thousand is borrowed from thousands place, so 5 thousands are left.

• 5 thousands – 4 thousands =1 thousand

Therefore, 6187 - 4549 = 1638

Let’s Practise-2

Subtract:

a. 9282 – 5411

7532 – 6825

c. 8354 – 6517

6521 – 5329

Let’s Learn

Checking Subtraction Using Addition

To check whether we have subtracted two numbers correctly or not, we add the difference to the subtrahend. If we get minuend, that is, the greater number as the sum, the answer is correct.

For example, 7894 – 4281 = 3613

(Minuend) – (Subtrahend) = (Difference)

Now let us check our subtraction: 4281 + 3613 = 7894 (Subtrahend) + (Difference) = (Minuend)

Difference: The answer when you take away one number from another. Minuend: The big starting number in subtraction. Subtrahend: The smaller number you subtract. Word Zone

Let’s Learn

Properties of Subtraction

Property 1: If we subtract 0 from a number, the difference is the number itself.

For example, 3487 − 0 = 3487

Property 2: If we subtract 1 from a number, we get the predecessor of the number.

For example, 8776 − 1 = 8775

Property 3: If we subtract a number from itself, the difference is 0.

For example, 7645 - 7645 = 0

Let’s Learn

Estimating the Difference

Estimating differences means finding a close or approximate answer to a subtraction problem without doing the exact calculation. It helps in many reallife situations.

For example, when you are shopping and want to know roughly how much something costs after a discount, or when you are planning a trip and want to estimate the travel time.

We use rounding off to make the numbers easier to work with.

Predecessor: The number before.

Example 1:

You are shopping and want to buy a toy for 285 rupees and a book for 148 rupees. With 500 rupees, estimate how much money you will have left after buying both items.

Solution:

Step 1: Rounding off the cost of toy to the nearest tens.

285 can be rounded off to 290

Step 2: Rounding off the cost of book to the nearest tens. 148 can be rounded off to 150

Step 3: Adding the rounded prices to estimate the total cost.

Step 4: Subtracting the estimated total cost from the money you have.

Example 2:

Subtract 357 from 593 through estimation.

Solution:

Step 1: Rounding off the greater number to the nearest tens.

290 + 150 = 440

500 – 440 = 60

593 can be rounded off to 590

Step 2: Rounding off the smaller number to the nearest tens. 357 can be rounded off to 360

Step 3: Subtracting the rounded off numbers.

590 – 360 = 230 A. Fill in the blanks:

from 8346 through estimation.

When we subtract the same number from each number to find the next one, it creates a special pattern. It’s like a fun rule that helps us figure out the next numbers in a sequence.

For example-

Find the missing number in the sequence:

49 42 35 28 21 14 ?

Solution: 49 42 35 28 21 14 ? 14 – 7 = 7 –7 –7 –7 –7 –7 –7

Let’s Learn

Subtraction in Real Life

In our daily life, we often need to subtract smaller numbers from greater number. When you read stories with numbers and come across words like ‘difference,’ ‘less,’ ‘subtract,’ or ‘how much is left,’ it means you should use subtraction to find the answer.

Look at this example.

Example 1: A toy costs 805. A child has only 480. How much more money does he need to buy the toy?

Solution:

Cost of the toy = 805

Amount of money the child has = 480

The amount of money the child needs = 805 – 480

Hence the child needs 325 more to buy the toy.

Example 2: There are 5290 children in the ABC School. 2458 are boys. Find out the number of girls in the ABC School.

Solution:

Total number of children in school = 5290

Total number of boys in school = 2458

Number of girls in school = 5290 – 2458

Hence, the number of girls in ABC school is 2832.

Word problems on Addition and Subtraction

Example 1: There are 708 houses in a colony. 590 of them have no electricity and the rest have solar powered electricity. How many houses have solar powered electricity?

Solution:

Total number of houses = 708

Number of houses without electricity = 590

The number of houses with solar powered electricity = 708 – 590

Hence, the number of houses with solar powered electricity is 118.

Example 2: There are 2354 academic books and 1210 children books in a library. Find the total number of books in the library?

Solution:

Total number of academic books = 2354

Number of children books = 1210

The total number of books in the library = 2354 + 1210

Hence, the total number of books in the library is 3564.

Let’s Practise-4

Solve:

a. A classroom has 3,364 crayons and 3,784 markers. How many supplies does the classroom have in total?

b. Seema spent Rs.4,343 on groceries and Rs.4,569 on clothes. How much money did she spend in total?

c. You had 708 candies, and you gave away 625 to the needy. How many candies do you have now?

d. You had 7234 marbles, and you gave away 4132 marbles to your friend. How many marbles are left with you now?

e. You had 5544 stickers, and you used up 2329 stickers. How many stickers are left with you now?

Let’s Sum Up

• When all the digits of the Minuend are bigger than all the digits of the Subtrahend, we can perform subtraction without regrouping.

Ex: 456 - 343

• When one or more digits of the Minuend are smaller than the Subtrahend digits, we need to borrow tens/hundreds/thousands from the respective place values. In this case, subtraction is calculated by regrouping.

Ex: 456 - 368

• Minuend - Subtrahend = Difference

Subtrahend + Difference = Minuend

• Subtraction through estimation is calculated by rounding off to the nearest tens for 3-digit numbers and nearest hundreds for 4-digit numbers.

Cross-Curricular Connections

Geography

The Amazon River in South America is about 6,400 kilometers long, while the Nile River in Africa is approximately 6,650 kilometers long. Which river is longer between the two and by how much?

Life Skills

Imagine you have 528 saved for a special toy. Your parents gave you an extra 275 as a reward. How much money do you have now to buy the toy? The special toy costs 650. How much money will you have at the end?

21st Century Skills

The table below shows the production of pencil boxes in a week in a factory.

Day

Number of Pencil Boxes

Monday 4376

Tuesday 2321

Wednesday 5591

Thursday 6999

Friday 6610

Saturday 1981

Answer the following questions based on the data given in the table. How many more pencil boxes were produced on?

y Friday than Monday

y Wednesday than Saturday

y Monday than Tuesday

• Thursday than Tuesday

• Thursday than Friday

Extend Your Knowledge

KenKen is a fun puzzle game with math. You get a grid with special sections, and each section has a number you’re supposed to make by adding or subtracting.

For example, if you see the number 7 and a minus sign in a 4x4 grid, you have to find numbers to subtract so they equal 7. You’ll need to think carefully to fill in the right numbers and complete the puzzle. It’s like a math adventure!

Tip for the parent

Encourage your child to solve real life problems based on sum and difference of 3-digit numbers and 4-digit numbers like finding total of monthly expenditure, etc.

My Study Plan

Multiplication

• Multiplication of 3-digit numbers by 1-digit numbers

• Multiplication of 4-digit numbers by 1-digit numbers

• Multiplication of 2/3-digit numbers by 2-digit numbers with and without regrouping

• Properties of multiplication

• Multiplication in real-life situations and problem-solving

• Lattice multiplication methods

Let’s Recall

1. Write the repeated additions given below as multiplications.

2. Multiply the following.

Thinking Zone

A box has 32 chocolates. How many chocolates will 4 boxes have?

Let’s Learn

Multiplication

Multiplication is a method of adding the same number repeatedly. It is one of the basic and most used mathematical operation in our daily lives. We use the symbol ‘×’ to represent multiplication. In multiplication, the number to be multiplied is called the multiplicand. The number by which we multiply is known as the multiplier. The answer of the multiplication sum is called the product. For example,

If we multiply 312 × 2, we place them as shown below. Here, 312 is the multiplicand and 2 is the multiplier. After multiplying these numbers, we get the product as 624.

Therefore, Multiplicand × Multiplier = Product

3- Digit Multiplication

3-digit multiplication involves multiplication of 3-digit numbers with 1-digit, 2-digit, or 3- digit numbers by placing them at their correct place values. For a 3-digit number, these place values are ones, tens, and hundreds.

Multiplication of a 3-digit number with a 1-digit number

In this type of multiplication, we multiply the digits by placing the 3-digit number on the top and the 1-digit number below it. This can be performed in two ways:

3-digit multiplication without regrouping

In this multiplication, a 3-digit number is multiplied by a 1-digit number without any carry-overs to give the product.

Example: Multiply 314 by 2.

Solution:

Step 1

Arrange the numbers correctly

Step 2

Multiply 2 with 4 2 × 4 = 8

Thus, the product of 314 and 2 is 628.

3-digit multiplication with regrouping

Step 3

Multiply 2 with 1 2 × 1 = 2

Step 4

Multiply 2 with 3 2 × 3 = 6

In this multiplication, a 3-digit number is multiplied by a 1-digit number and the extra digit of the product is carried over to the next column.

Example: Multiply 169 by 3.

Solution:

Step 1

Arrange the numbers correctly

Step 2

Multiply 3 with 9 3 × 9 = 27

Write 7 in the ones place of the answer and carry over 2 to the tens place.

Thus, the product of 169 and 3 is 507.

Step 3

Multiply 3 with 6 3 × 6 = 18

Add carried over 2 to 18.

18 + 2 = 20

Write 0 in the tens and carry over 2 to the hundreds place.

Step 4

Multiply 3 with 1 3 × 1 = 3

Add carried over 2 to 3.

3 + 2 = 5

Write 5 in the hundreds place of the answer.

Let’s Practise - 1

1. Multiply the following numbers.

Let’s Learn

Multiplication of 4-Digit Number with a 1-Digit Number

4-digit multiplication is similar to 3-digit multiplication, but it involves 4-digit numbers. It also involves arranging the numbers according to their place values (ones, tens, hundreds, thousands) and then multiplying them.

4-digit multiplication without regrouping

Example: Multiply 1321 by 3.

Solution:

Step 1

Multiply 3 with 1

3 × 1 = 3

Write 3 in the ones place of the answer.

Step 2 Step 3 Step 4

Multiply 3 with 2

3 × 2 = 6

Write 6 in the tens place of the answer.

Thus, the product of 1321 and 3 is 3,963.

Multiply 3 with 3

3 × 3 = 9

Write 9 in the hundreds place of the answer.

Multiply 3 with 1

3 × 1 = 3

Write 3 in the thousands place of the answer.

4-digit multiplication with regrouping

Example: Multiply 1456 by 7.

Solution:

Step 1

Multiply 7 with 6

7 × 6 = 42

Write 2 in the ones place of the answer and carry over 4 to the tens place.

Step 2

Multiply 7 with 5

7 × 5 = 35

Add carried over 4 to 35.

35 + 4 = 39

Write 9 in the tens place of the answer and carry over 3 to the hundreds place.

Thus, the product of 1456 and 7 is 10,192.

Step 3

Multiply 7 with 4

7 × 4 = 28

Add carried over 3 to 28.

28 + 3 = 31

Write 1 in the hundreds place of the answer and carry over 3 to the thousands place.

Step 4

Multiply 7 with 1

7 × 1 = 7

Add carried over 3 to 7.

7 + 3 = 10

Write 0 in thousands place and 1 in ten thousands place of the answer.

When you multiply any whole number by 10, the result is the same number with a zero added at the end. For example, 7 × 10 = 70.

Fact Zone

1. Find the product.

Multiplication of 2-Digit Number with Another 2-Digit Number

Without regrouping

Example: Let’s calculate the product of 22 and 31.

Solution:

Step 1

Arrange the digits in the multiplicand and multiplier correctly.

Step 2

Multiply the multiplicand with the digits in the ones place of the multiplier.

Multiply 31 with 2

Step 3

Multiply the multiplicand with the digits in the tens place of the multiplier.

Multiply 31 with 20

Step 4

Add the products. Add 62 from step 2 and 620 from step 3

Thus, the product of 22 and 31 is 682. With Regrouping

Example: Let’s calculate the product of 76 and 14.

Solution:

Step 1

Arrange the digits in the multiplicand and multiplier correctly.

Step 2

Multiply the multiplicand with the digits in the ones place of the multiplier.

Multiply 76 with 4

Step 3 Step 4

Multiply the multiplicand with the digit in the tens place of the multiplier.

Multiply 76 with 10

Add the products. Add 304 from step 2 and 760 from step 3

Thus, the product of 76 and 14 is 1,064.

Multiplication of a 3-Digit Number with Another 2-Digit Number

Without Regrouping

Example: Let’s calculate the product of 132 and 12 using the following steps

Solution:

Step 1

Arrange the digits in the multiplicand and multiplier correctly.

Step 2

Multiply the multiplicand with the digits in the ones place of the multiplier.

Multiply 132 with 2

Step 3 Step 4

Multiply the multiplicand with the digits in the tens place of the multiplier.

Multiply 132 with 10

Thus, the product of 132 and 12 is 1,584. With Regrouping

Example: Let’s calculate the product of 113 with 48.

Solution:

Step 1

Arrange the digits in the multiplicand and multiplier correctly.

Add the products.

Add 264 from step 2 and 1320 from step 3

Step 2 Step 3 Step 4

Multiply the multiplicand with the digits in the ones place of the multiplier.

Multiply 113 with 8

Multiply the multiplicand with the digits in the tens place of the multiplier.

Multiply 113 with 40

Add the products.

Add 904 from step 2 and 4520 from step 3

Thus, the product of 113 × 48 is 5,424.

Let’s Practise - 3

1. Find the product.

Let’s Learn

Properties of Multiplication

There are several important properties of multiplication that we should understand:

Multiplication by 0

When we multiply any number with 0, the product is always 0. For example, 4 × 0 = 0

Similarly, 182 × 0 = 0 and 5434 × 0 = 0.

Multiplication by 1

When we multiply a number with 1, the product is always the number itself. For example: 90 × 1 = 90

Similarly, 979 × 1 = 979 and 6528 × 1 = 6528.

Order property of multiplication

The product of two numbers always remains the same, even if we change the order in which we multiply them. This is known as order property of multiplication of numbers.

For example,

4 × 5 = 20 and 5 × 4 = 20. Therefore 4 × 5 = 5 × 4.

Similarly,

211 × 3 = 633 and 3 × 211 = 633. Therefore, 211 × 3 = 3 × 211.

Also, 1117 × 5 = 5585 and 5 × 1117 = 5585. Therefore, 1117 × 5 = 5 × 1117.

Grouping property of multiplication

When we multiply three or more numbers, we can group the numbers in any manner, and the product remains unchanged. This property of multiplication is known as the grouping property or associative property.

Let us take an example:

129 × 4 × 5, we can rearrange these numbers using brackets in three different ways:

(129 × 4) × 5 = 516 × 5 = 2580

129 × (4 × 5) = 129 × 20 = 2580

(129 × 5) × 4 = 645 × 4 = 2580

Regardless of how we group the numbers, the product remains the same in all three cases, which is 2580.

Let’s Practise - 4

1. Fill in the blanks to solve the following.

a. 119 × 1 = ________

b. 354 ×0 = ________

c. 113 × 43 = ___ × 113 = 4859

d. 1243 x ____ = 0

e. 5324 x _______ = 5324

Let’s Learn

Multiplication in Real Life

In our daily lives, we often need to multiply numbers. When you read stories with numbers and come across words like ‘times,’ ‘product,’ ‘multiplied by,’ or ‘double,’ it means you should use multiplication to find the answer.

Example 1:

Aayu played 6 games. He scored 20 runs in each game. How many runs did Aayu score in total?

Solution:

Number of runs Aayu scored in each game = 20

Number of games Aayu played = 6

Total number of runs scored by Aayu = 20 × 6

Therefore, the total number of runs scored by Aayu is 120.

Example 2:

A factory produces 672 boxes of chocolates each day. If each box contains 8 chocolates, how many chocolates does the factory produce daily?

Solution:

Number of chocolate boxes produced daily = 672

Number of chocolates in each box = 8

Number of chocolates produced daily by the factory = 672 × 8

Therefore, the factory produces 5,376 chocolates daily.

Example 3:

A bakery sold 736 cakes in a week. If each cake had 12 slices, how many slices were sold in total?

Solution:

Number of cakes sold = 736 cakes

Number of slices in each cake = 12 slices

Total number of slices sold = Number of cakes sold × Number of slices in each cake = 736 × 12

Therefore, a total of 8,832 slices were sold in the bakery during the week.

Let’s Practise - 5

1. Solve the following real-life questions.

a. A bookstore has 4321 books in its inventory. If each book costs Rs 8, what is the total value of all the books in the store?

b. A car factory produced 3750 cars in a month. If each car requires 4 tyres, how many tyres did the factory use for these cars?

c. A toy store has 894 toy cars in stock. If each toy car costs Rs. 50, what is the total cost of all the toy cars?

d. A hotel has 456 rooms, and each room has 2 beds. How many beds are there in the hotel in total?

Let’s Learn

Lattice Multiplication

Lattice multiplication is a visual and systematic method for multiplying multidigit numbers.

Let’s understand multiplication of 23 by 16 through lattice method.

The steps to perform lattice multiplication:

Word Zone

Visual: Seeing

Multi-digit numbers: Numbers with more than one digit, like 25 or 354

Step 1: Create a lattice grid:

• The number of rows and columns should be equal to the number of digits in the two numbers being multiplied.

• In this case, we have 2 digits for 23 and 2 digits for 16, so the grid will be 2 × 2.

Step 2: Draw diagonal lines:

• Draw diagonal lines from the upper right corner to the lower left corner of each box.

Step 3: Label the lattice:

• Split the numbers to be multiplied into their digits and write them on the top and on the right.

Step 4: Multiply the numbers:

• Multiply the numbers on the top of the grid with the number on the right of the grid and write the answer in the grid.

• First, multiply 1 and 2 to get 2, and then write it in the first box above and below the diagonal.

• Likewise, multiply other digits.

Step 5: Add the numbers:

• Add the numbers in the grid diagonally.

• Start from the topmost left diagonal.

• As 8 is alone at the bottom most right diagonal, write 8 below it.

Step 6: Write the answer:

• To get the answer, write the numbers starting from the leftmost one at the top and moving to the right.

• In this case, you would read from 3 on the left to 8 on the right to get 368.

Therefore, 23 multiplied by 16 is equal to 368.

Let’s Practise - 6

1. Solve the following using lattice multiplication.

a. 43 × 12

b. 27 × 31

Life Skills

A school organized a visit to a beach. There were 25 students. The students were asked to collect garbage on the beach and put it in garbage bags. If each student collected 450 grams of garbage, how many grams of garbage were collected by 25 students?

Let’s Sum Up

• Multiplication is a process that involves adding the same number repeatedly. It is represented by the symbol ‘×’.

• Multiplicand x multiplier = Product.

• During multiplication, the numbers are arranged in columns according to their place values: ones, tens, hundreds, thousands.

• To multiply the multiplicand with the multiplier, multiply each digit of the multiplicand with the multiplier, starting from the right.

• When you multiply any number by 0, the product is always 0.

• When you multiply any number by 1, the product is the same as the original number.

• Changing the order of the multiplicand and multiplier does not change the product.

• When multiplying three or more numbers, you can group them in different ways and the product will remain the same.

Cross-Curricular Connections

Science:

If a plant needs 6 hours of sunlight per day to grow properly, how many hours of sunlight would it need in a week?

Social Studies:

India is known for its rich cultural heritage and has 28 states. If each state has 5 major cultural festivals, how many major cultural festivals are there in total across all the states in India?

Extend Your Knowledge

Heritage of Vedic Maths

In the ancient vedic maths of India, there is a very simple method for multiplying any number by 11.

Let’s understand this with an example:

Example: Multiply 682 by 11.

Step 1: Write the number 682.

Step 2: Working from right to left, first write the digit at ones place, which is 2.

Step 3: From the ones digit, add each pair of digits and write the sum and carry over, if there is any.

Add 2 and 8 to get 10; write 0 and carry over 1.

Add 8 and 6 to get 15; add the carry over 1 to get 15; write down 5 and carry over 1.

Add the carry over 1 to 6 to get 7.

So, 682 x 11 = 7502.

Now multiply 445 with 11.

21st Century Skills

Consider the following scenarios involving the number of fruits in different baskets:

a. A basket of apples contains 5 apples.

b. A basket of oranges contains 7 oranges.

c. A basket of mangoes contains 3 mangoes.

Now, suppose you have 4 baskets of each type of fruit.

i. How many apples do you have in total?

ii. How many oranges do you have in total?

iii. How many bananas do you have in total?

Tip for the Parent

• Make multiplication a part of your child’s everyday life. For example, if you’re at the grocery store, ask your child to calculate the total cost of multiple items. If each apple costs Rs.50 and you’re buying 6, how much will that cost?

Division

My Study Plan

• Terms associated with division

• Division facts

• Division using multiplication tables

• Division as repeated subtraction

• Long division method

• Properties of division

• Division by 10 and 100

• Division in real life

Let’s Recall

a. There are 15 carrots. Make groups of 5.

How many groups are there?

b. There are _____ daisies. Make groups of 6.

How many groups are there?

Thinking Zone

Aayu had 12 straws. First, he used the straws to create 4 triangles. Then, he used the same 12 straws to make 3 squares. Figure out why he was able to make more triangles with the 12 straws than squares.

Let’s Learn

Terms Associated with Division

Division means sharing things equally. When we share things equally, it means we have divided them.

For example, 30 ÷ 6 = 5

In the above division sentence:

• ‘÷’ is the sign or symbol used for division.

• The number that we want to divide is called dividend. Here, the dividend is 30.

• Divisor is the number by which the dividend is to be divided or the number of parts into which the dividend is to be shared. Here, 6 is the divisor.

• Quotient is the result or the answer. Here, 5 is the quotient.

Let’s Learn

Division Facts

Division facts are like mathematical sentences for dividing numbers. Division is the opposite of multiplication. When we multiply, we go forward on the number line by taking equal steps. However, with division, we go backwards on the number line by taking equal steps.

For example,

× 4 = 24

× 6 = 30

÷ 6 = 5 8 × 9 = 72

Example: Write division fact for 5 × 9 = 45

Solution:

There are two division facts for 5 × 9 = 45

45 ÷ 9 = 5

45 ÷ 5 = 9

÷ 8 = 9

÷ 9 = 8

For every multiplication fact, there are two related division facts. Fact Zone

Let’s Learn

Division Using Multiplication Tables

We can also divide numbers using multiplication tables. Let us use an example to understand.

Example 1: Divide 24 ÷ 6.

Solution:

Recall multiplication table of 6 till you get 24 as an answer.

6 × 1 = 6

6 × 2 = 12

6 × 3 = 18

6 × 4 = 24

Therefore, 24 ÷ 6 = 4

This means that there are 4 sixes in 24.

Example 2: Divide 42 ÷ 7.

Solution:

Recall multiplication table of 7 till you get 42 as an answer.

7 × 1 = 7

7 × 2 = 14

7 × 3 = 21

7 × 4 = 28

7 × 5 = 35

7 × 6 = 42

Therefore, 42 ÷ 7 = 6

This means that there are 6 sevens in 42.

Word Zone

Related: Belonging to same family or group

Let’s Practise - 1

1. Use the numbers 4, 12 , and 48 to form a division statement. _____ ÷ _____ = _____

2. Write the division facts for the following multiplication facts.

Multiplication Facts Division Facts

7 × 10 = 70

9 × 8 = 72

4 × 5 = 20

7 × 6 = 42

3. Divide the following using multiplication tables.

a. 35 ÷ 7 = _____ b. 27 ÷ 3 = _____

c. 64 ÷ 8 = _____

Let’s Learn

Division as Repeated Subtraction

d. 48 ÷ 6 = _____

Repeated subtraction is the process of subtracting the same number from the large number until the remainder is 0 or smaller than the number being subtracted.

Let’s understand this with an example: 60 divided by 15 equals what number?

60 – 15 = 45

45 – 15 = 30

30 – 15 = 15

15 – 15 = 0

We can see that 15 can be subtracted 4 times from 60. So, there are four groups of 15 in 60. or 60 ÷ 15 = 4

Here, 60 is the dividend, 15 is the divisor, and 4 is the quotient. Hence, 60 divided by 15 equals 4.

Let’s Practise - 2

1. Divide the following numbers by repeated subtraction in the given space.

a. 75 ÷ 25

75 – 25 = ___

So, 75 ÷ 25 = ___ – 25 = ___ ___ – ___ = ___

b. 108 ÷ 18

108 – 18 = ___

So, 108 ÷ 18 = ___ – 18 = ___ ___ – ___ = ___ ___ – ___ = ___ ___ – ___ = ___

– ___ = ___

Let’s Learn

Long Division with/without Remainder

It is used for dividing large numbers by breaking down a division problem into a series of easier steps. Let us understand long division by solving an example.

Example 1: Solve 126 ÷ 9.

Solution: Here, the dividend = 126 and the divisor = 9.

Let us divide this by using the following steps.

Step 1:

Step 2:

Since the first digit of the dividend is smaller than the divisor, consider the first 2 digits to proceed with the division.

12 is not divisible by 9 but we know that 9 × 1 = 9. So, write 1 in the quotient and subtract 12 – 9 = 3.

Step

Step

Hence, 126 ÷ 9 = 14.

Example 2: Solve 753 ÷ 6.

Solution: Here, the dividend = 753 and the divisor = 6.

Let us divide this by using the following steps.

Step 1: Consider the first digit of the dividend and divide it by 6. Here, it will be 7 ÷ 6.

Step 2: 7 is not divisible by 6, but we know that 6 × 1 = 6.

So, write 1 in the quotient and subtract 7 – 6 = 1.

Step 3:

Step 4: 15 is not divisible by 6 but we know that 6 × 2 = 12.

Step

Step 6:

Step 7: Now, 3 < 6. Thus, remainder = 3 and quotient = 125.

Let’s Practise - 3

1. Divide the following numbers using long division method.

346 ÷ 3

865 ÷ 5

Let’s Learn

Properties of Division

Property 1

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

For example:

22 ÷ 1 = 22

99 ÷ 1 = 99

Property 2

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

For example:

19 ÷ 19 = 1

87 ÷ 87 = 1

Property 3

0 divided by any number gives the quotient 0.

For example:

0 ÷ 7 = 0

0 ÷ 27 = 0

Property 4

Division by 0 is undefined.

For example:

17 ÷ 0 = undefined

28 ÷ 0 = undefined

Let’s Learn

Division by 10 and 100

Let’s learn to divide a number by 10 and 100 to find the quotient and the remainder.

Division by 10

When a number is divided by 10, the digit at the ones place becomes the remainder, and the number formed by the other digits is the quotient.

For example,

• 31 ÷ 10: Quotient = 3 and Remainder = 1

• 156 ÷ 10: Quotient = 15 and Remainder = 6

• 224 ÷ 10: Quotient = 22 and Remainder = 4

• 56 ÷ 10: Quotient = 5 and Remainder = 6

Division by 100

When a number is divided by 100, the digits at the tens and ones places become the remainder, and the number from of the remaining digits is the quotient. For example,

y 906 ÷ 100: Quotient = 9 and Remainder = 6

y 325 ÷ 100: Quotient = 3 and Remainder = 25

y 1242 ÷ 100: Quotient = 12 and Remainder = 42

y 1634 ÷ 100: Quotient = 16 and Remainder = 34

Let’s Practise - 4

1. Divide the following numbers.

a. 124 ÷ 10: Quotient = ____ and Remainder = ____

b. 1024 ÷ 100: Quotient = ____ and Remainder = ____

c. 1400 ÷ 100: Quotient = ____ and Remainder = ____

d. 45 ÷ 10: Quotient = ____ and Remainder = ____

2. Fill in the blanks.

a. 12 ÷ 12 = ______

b. 0 ÷ 18 = ________

c. 2468 ÷ _____ = 2468

d. 451 ÷ ______ = 1

Let’s Learn

Division in Real Life

In our daily lives, we often need to divide things into groups or share them equally. When you read stories with numbers and see words like ‘share,’ ‘divide,’ ‘equally,’ ‘among,’ or ‘each,’ it means you should use division to find the answer. Look at the following examples.

Example 1: In a library, 72 books are to be equally shared among 6 children. How many books will each child get?

Solution:

Total number of books = 72

Number of children = 6

Number of books each child will get = 72 ÷ 6

Hence, each child will get 12 books.

Example 2: If you have 134 mangoes and want to share them with 5 friends, how many mangoes will each friend get, and how many mangoes will be left?

Solution:

Number of mangoes = 134

Number of friends = 5

Total number of mangoes each friend will get: 134 ÷ 5

Here quotient = 26 and remainder = 4

Therefore, each friend will get 26 mangoes and 4 mangoes will be left after equal distribution.

a. There are 168 crayons that need to be placed into 7 boxes with an equal number of pencils in each box. How many pencils will be in each box?

b. There are 54 ice cream cones that need to be shared equally among 9 children. How many ice cream cones will each child get?

c. There are 112 pizza slices that need to be divided equally among 8 families. How

each family get?

1. Solve.

Let’s Sum Up

• Division means sharing things equally. Dividend, divisor, and quotient are the terms in the division statement.

• Division facts are division number sentences. For example: 35 ÷ 5 = 7.

• Repeated subtraction is the process of subtracting the same number from the large number until the remainder is 0 or smaller than the number being subtracted.

• Long division is used for dividing large numbers by breaking down a division problem into a series of easier steps.

• A number is divided by 1; the quotient is the number itself.

• A number is divided by itself gives the quotient as 1.

• 0 divided by any number gives the quotient 0.

• Division by 0 is undefined.

• Dividing a number by 10, the digit at the ones place becomes the remainder, and the number formed by the other digits is the quotient.

• Dividing a number by 100, the digits at the tens and ones places become the remainder, and the number made from the remaining digits is the quotient.

Life Skills

Aayu bought 180 cupcakes on his birthday and wanted to distribute cupcakes to 30 poor kids. How many cupcakes would each kid get?

English:

A novel of 536 pages contains 8 chapters in it. Find out how many pages each chapter contains if each chapter has an equal number of pages.

Social Studies:

Imagine Delhi is divided into 10 equal districts. If there are 9000 people living in Delhi, how many people, on average, live in each district of Delhi?

Science:

A honeybee gathers nectar from 161 flowers in a week to produce honey. How many flowers does it visit in one day?

Cross-Curricular Connections

21st Century Skills

Green tea is beneficial for health as it can help you remain alert and focused, and it contains antioxidants that help keep your body strong.

In a factory, 759 green tea bags are produced in an hour. Each green tea box can hold 11 bags. Find how many boxes can be packed in one hour.

Extend Your Knowledge

Dividing the number 311 by 4 using long division method:

Here, dividend = 311, divisor = 4, quotient = 77 and remainder = 3

To check the answer is correct or not, verify it by using the below statement:

Dividend = Divisor × Quotient + Remainder

Consider, Divisor × Quotient + Remainder

= 4 × 77 + 3

= 308 + 3 = 311 = Dividend

Hence, the given answer is correct.

Tip for the Parent

• Encourage your child to practise division with real-world scenarios. Ask them to share a certain number of items equally among their siblings or friends.

Fractions 6

My Study Plan

• Fraction

• Writing a fraction

• Fraction as a part of collection

• Real life problems on fractions

Let’s Recall

Which of the following shapes is divided into 4 equal parts?

Thinking Zone

Imagine you have a cake and wish to distribute it evenly among 6 people. How many slices should you cut the cake into to ensure everyone receives an equal share? Discuss your answer with your teacher.

Let’s Learn

Fraction

Fractions are parts of a whole, representing how something is divided into equal parts.

Whole: A complete unit Word Zone

For example: a pizza is divided into 3 equal parts.

So, each slice represents a part or fraction of the whole pizza.

Let’s Learn

Writing a Fraction

A fraction has two parts – Numerator and Denominator.

The numerator and the denominator are separated by a dividing line or fraction bar.

For example, 1 7

Numerator is the number above the fraction bar.

Denominator is the number below the fraction bar.

Let’s consider an example where two friends are sharing a pizza, dividing it into two equal parts.

How many parts each friend will get?

Each friend gets 1 part out of 2 equal parts of the pizza.

The fraction of pizza each friend gets = Parts each friend gets Total parts

Hence, the fraction of each friend’s pizza = 1 2

This is called as one-half or half.

Now, let us divide the pizza equally amongst four friends.

One-half

So, each friend’s share of pizza is 1 part out of 4 equal parts.

Fraction of each friend’s pizza = 1 4

This is called one-fourth or a Quarter.

Now, let us divide the pizza equally amongst three friends.

Quarter or One-fourth

So, each friend’s share of pizza is 1 part out of 3 equal parts.

Fraction of each friend’s pizza = 1 3

This is called one-third.

One half: One part out of two equal parts of an object

Quarter: One part out of four equal parts of an object

One third: One part out of three equal parts of an object Word Zone

One-third

Note: The numerator tells us how many parts we are looking at, and the denominator shows the total number of equal parts in a whole.

Example 1: Find the fraction for coloured part. Also, identify the numerator and denominator in the fraction.

Solution:

This box is divided into three equal parts and two parts out of three are coloured.

Fraction for coloured part = Coloured parts

Total parts

Fraction for coloured part = 2 3 which is also called two-third.

In this fraction, 2 is numerator and 3 is denominator.

Example 2: Find the fraction for coloured part.

Solution:

This box is divided into four equal parts and three parts out of four are coloured.

Fraction for coloured part = Coloured parts

Total parts

Fraction for coloured part = 3 4 which is also called three-quarters.

Example 3: Find the portion of the shape that is yellow and the portion that is green.

Solution:

Number of parts coloured in yellow = 5

Total number of equal parts = 10

Fraction for yellow coloured part = Yellow coloured parts

Total parts

Fraction of the part coloured in yellow = 5 10

Number of parts coloured in green = 5

Total number of equal parts = 10

Fraction for green coloured part = Green coloured parts

Total parts

Fraction of the part coloured in green = 5 10

Example 4: What fraction of figure is uncoloured?

Solution:

Number of parts uncoloured = 5

Total number of equal parts = 8

Fraction for uncoloured part = Uncoloured parts

Total parts

Fraction for uncoloured part =

Practise - 1

1. Colour the part of the figure that has been written next to it. The first one has been done for you.

2. Complete the following table.

Fraction showing the coloured part Numerator Denominator

Let’s Learn

Fraction as Part of a Collection

Imagine you have 6 colourful pens in your hand.

If you share these pens with your three friends equally, what will be the fraction of pens each friend gets?

To distribute pens equally, divide the pens into equal groups.

With three friends, pens are divided into 3 equal groups.

Group 1

Group 2

Group 3

Or, you can calculate by dividing the total number of pens by the total number of friends, that is, 6 ÷ 3 = 2

So, each friend will have 2 pens. Therefore, the fraction of pens each friend gets

= Number of pens each friend get

Total pens = 2 6

Let us see some examples to understand this better.

Example 1: Two friends want to share 6 balloons equally. Find the fraction of balloons each friend will get.

Solution:

Divide the 6 balloons into two equal parts.

Group 1

Group 2

Divide total number of balloons by total number of friends i.e., 6 ÷ 2 = 3

So, each friend will have 3 balloons.

Therefore, the fraction of balloons each friend gets

= Number of balloons each friend get

Total balloons = 3 6

Example 2: Find the fraction of the boxes that are coloured in:

1. blue

2. red

3. yellow

Solution:

Fraction for coloured part = Coloured parts Total parts

Number of parts coloured in blue = 3

Total number of equal parts = 8

Fraction of the part coloured in blue = 3 8

Number of parts coloured in red = 4

Total number of equal parts = 8

Fraction of the part coloured in red = 4 8

Number of parts coloured in yellow =1

Total number of equal parts = 8

Fraction of the part coloured in yellow = 1 8

Let’s Practise - 2

1. What fraction of the collection does each person get?

a. 4 people sharing 8 balloons. Fraction =

b. 2 people sharing 16 cupcakes. Fraction =

c. 5 people sharing 15 cups. Fraction =

d. 3 people sharing 3 candies. Fraction =

2. Write the fractions of the fruits in the basket.

Fraction of apples in the basket is .

Fraction of oranges in the basket is .

Fraction of bananas in the basket is .

Fraction of strawberries in the basket is .

Fraction of mangoes in the basket is .

Let’s Learn

Fractions in Real Life

The word ‘fraction’ comes from the Latin word ‘fractus’ which means broken.

We use fractions in our daily life to solve many problems. Fractions help us understand parts of a whole and make sharing, cooking, and many other things easier. Let us look at some examples based on fractions in real life.

Example 1: You and your friends had pizza. If you both ate 3 slices out of 8, what fraction of the pizza did you eat?

Solution:

Total number of slices of pizza = 8

Number of slices you and your friends ate = 3

Fraction of pizza eaten by you and your friend is = Number of slices eaten

Total number of slices = 3 8

Example 2: In art class, 34 students used red crayons, and 16 used blue crayons. What fraction of students used red crayons? What fraction of students used blue crayons?

Solution:

Total number of students in class = 34 + 16 = 50

Number of students who used red crayons = 34

Fraction of students who used red crayons =

Fact Zone

Number of students who used red crayons

Total number of students = 34 50

Therefore, the fraction of students who used red crayons = 34 50

Number of students who used blue crayons = 16

Fraction of students who used blue crayons =

Number of students who used blue crayons

Total number of students = 16 50

Therefore, the fraction of students who used blue crayons = 16 50

Let’s Practise - 3

1. Jitu has 10 candies, and he wants to distribute it to two of his friends equally. What fraction of candies will each friend get?

2. Amit has 15 toy cars. 5 of them are blue, and the rest are red. What fraction of the cars are red? What fraction of the cars are blue?

3. Emily has 12 candies. She gave 3 of them to her friend and kept the rest. What fraction of the candies did Emily give to her friend? What fraction of the candies did she keep for herself?

4. Emma has 12 seashells, and she wants to equally distribute it to 6 of her cousins. What fraction of seashells will each cousin get?

Let’s Sum Up

• When an object or a group of objects is divided into equal parts, each part is called a fraction of the whole.

• A fraction has two parts – Numerator and Denominator.

• The numerator and the denominator are separated by a dividing line or fraction bar.

• 1 2 is called as half.

• 1 4 is called as quarter.

• We can use fractions in our daily life to solve various problems.

Life Skills

Imagine your family of four is having a party, and you have a cake with 8 slices. You know that sharing is important. Use fractions to make sure each family member gets a fair share of the cake.

Cross-Curricular Connections

Science:

If a plant has 20 leaves and 5 of them are yellow, what fraction of the leaves are yellow?

Social science:

In your class election for head girl, there were two candidates. The first candidate received 23 votes, while the second received 21 votes. If everyone in your class voted, find the election’s winner and the fraction of votes they received?

21st Century Skills

Imagine you are a contractor working on a housing project, and you have completed constructing 35 houses out of 52. Express this as a fraction.

Now, if you had to explain to your team what fraction of the work is left, how would you do it?

Extend Your Knowledge

y Fractions with the same denominators are called like fractions.

For example: 2 5 , and 3 5 are like fractions because both have same denominator 5.

y Fractions with different denominators are called unlike fractions.

For example: 1 4 , and 1 3 are unlike fractions because both have different denominators 4 and 3 respectively.

Tip for the Parent

Encourage your child to practise fractions in everyday situations, like sharing snacks, and show how parts make up a whole to reinforce their understanding with everyday objects, like fruits, chapatis and pizzas.

Geometry and Patterns

My Study Plan

• Point, line, ray, and line segment

• Measuring and drawing a line segment

• Maps

• Tangrams

• Tiling

• Symmetry

Let’s Recall

1. Match the following shapes with their correct names.

2. Identify the patterns in the following series and write the next two terms. a. 3, 5, 7, 9, __, __

Thinking Zone

Observe your surroundings and list four objects with straight lines and four with curved lines in the respective columns.

Straight lines

Curve lines

Let’s Learn

A point, a Line, a Ray, and a Line Segment

Point

A point represents the exact position of an object. It is dimensionless, meaning it has no length, breadth, or depth.

A point is denoted by a dot symbol, “.”

We use capital letters of the alphabet to name a point. For example, ‘P’ represents a point.

This can be read as “Point P”.

Line

A line is a set of points that extends in both directions. It has no endpoint and no breadth and thickness.

A line is often represented as a straight line with arrows at both ends, indicating that it can extend indefinitely.

We use two different capital letters of the alphabet to name a line. For example, a line can be represented as ‘MN’ with an arrow over it.

This is read as “Line MN “.

Ray

It is a part of a line that has one endpoint, and the other part is infinitely long. That is why it is visualised with a single-headed arrow.

A ray is represented by two capital letters of the alphabet with a pointed arrow on top of it.

where, A is the starting fixed point of the ray.

This is read as “Ray AB.”

Example: The rays of a torch originate from a point and extend to infinity. That is why it is called a ray.

Line segments

A line segment is a straight path that has two endpoints. It lies between two fixed points, so it has a finite length.

This is read as “Line segment AB”.

Example: A pencil, a piece of chalk, an edge of paper, etc.

Measuring line segments

We measure the length of a line segment with the help of a ruler or a 15 cm scale. Suppose we have to measure the length of a line segment AB.

We put the ruler along the line in such a way that one of its edges touches both points A and B.

R ay

A torch

Place the zero mark of the ruler at A, and read the ruler mark at B.

The reading of the scale at B gives the length of the line segment AB in cm. Here, it reads 6 cm.

Therefore, the length of AB = 6 cm.

Drawing line segments

Suppose we must draw a line segment with a length of 6 cm. We proceed as follows:

Step 1: Put the ruler on a piece of paper. Hold it firmly.

Step 2: With the help of a sharp pencil, mark point A against the 0 mark of the ruler and point B against the 6 cm mark of the ruler.

Step 3: Move the pencil from A to B along the edge of the ruler.

Thus, we obtain the line segment AB whose measurement is 6 cm.

Let’s Practise - 1

1. Identify the given representations and provide their names.

a. X Y

b. O K

c. E F

d. G

2. Read the statements and tick ‘True’ or ‘False’.

a. A line-segment is a part of line. True False

b. A ray has no definite endpoint. True False

c. A line segment has no endpoints. True False

Let’s Learn

Plane Shapes

A plane shape is a closed figure that has no thickness. Triangles, circles, and squares are a few examples of plane shapes.

Triangle

A triangle is a shape formed by three line segments. The three line segments of a triangle are called its sides. The point at which two sides of a triangle meet is called a vertex of the triangle. A triangle has 3 sides and 3 vertices.

We name a triangle by its vertices.

In the given figure, PQR is a triangle. This triangle has the following:

(a) Three vertices, namely P, Q, and R.

(b) Three sides namely PQ, QR, and RP.

Quadrilateral

A quadrilateral is a shape made up of four line segments. These line segments forming a quadrilateral are called its sides. The corner where two sides of a quadrilateral meet is known as its vertex. So, a quadrilateral has 4 sides and 4 vertices.

For example, consider a quadrilateral named PQRS. This quadrilateral has:

(a) Four corners or vertices, which are P, Q, R, and S.

(b) Four sides, which are PQ, QR, RS, and SP.

Rectangle

A rectangle is a special type of quadrilateral. It is formed by two horizontal line segments and two vertical line segments. The opposite sides of a rectangle are always of the same length. For example, in the given figure, PQRS is a rectangle.

In this rectangle, PQ equals SR, and QR equals PS.

PQ = SR and QR = PS

Square

A rectangle with all four sides equal is called a square. For example, PQRS is a square. Therefore, the lengths of PQ = QR = RS = SP.

Circle

When we place a bangle on a piece of paper and move a pencil around it, we get a figure shown alongside. We call it a circle. It is curved and has no sides and no vertices.

Let’s Practise - 2

1. Match the following.

Column A

a. Triangle

b. Quadrilateral

c. Rectangle

d. Square

e. Circle

Column B

i. Shape with no sides or vertices

ii. Shape with three sides and three vertices

iii. Shape with four sides of equal length

iv. Shape with four sides and four vertices

v. Shape with two pairs of equal sides

Let’s Learn

Solid Shapes

Objects that occupy space are called solids. Solids can come in various shapes. The outer part of a solid is known as its surface. This surface can be flat (plane) or curved.

A flat surface is termed as a plane. The surface of a book is an example of a plane surface. Objects like a ball or a globe have curved surfaces.

Few objects have both curved surfaces and plane surfaces. For example, a water bottle, food can, etc.

Some solid shapes are:

Cuboid

Each of the solids given below, a wooden box, a matchbox, a brick, a book, a pencil box, etc., is in the shape of a cuboid.

A cuboid has six faces, each of which is a rectangle in shape.

Two adjacent faces of a cuboid meet at a line segment, which is called an edge of the cuboid.

A cuboid has 12 edges.

Three edges of a cuboid meet at a point called a vertex.

A cuboid has 8 vertices.

Cube

Solids like dice, Rubik’s cubes, ice-cubes, etc. are all examples of a cube.

Cuboid

Cube

Cylinder Sphere

Cone

Wooden box Matchbox

Brick

Book

Pencil box

Face

Edge

Vertex

Dice

Rubik’s Cube

Ice-cube

A cuboid with 6 identical faces is called a cube.

Thus, each face of a cube is a square.

A cube has 6 faces, 12 edges, and 8 vertices.

Cylinder

Things like water bottles, gas cylinders, coffee mugs, etc. are in the shape of a cylinder.

A cylinder has two plane faces and one curved face.

A cylinder has two edges, both of which are circular. It has no vertex.

The base and the top of a cylinder are of the same size and same shape.

Sphere

Objects that are in the shape of a ball are known to have the shape of a sphere.

Example: A football and a watermelon.

A sphere has only one curved face. It no vertex and no edge.

Water Bottle

Gas Cylinder

Coffee Mug

Cone

Objects, such as ice cream cones, traffic cones, birthday caps, etc., are in the shape of a cone.

A cone has one plane face, which is its base. A cone has one curved face, one vertex, and one circular edge, where the curved face meets the plane face.

1. Match the object to the shape. Let’s Practise - 3

Vertex

Curved face

Curved edge

Plane face

Ice cream

Traffic Cone

Birthday cap

2. Fill in the table.

Let’s Learn

Maps

A map is a drawing or picture that shows a place or an area. It helps us understand where things are located, like streets, buildings, parks, and rivers. Most maps are drawn on a flat surface. A map displayed on a round surface is called a globe.

A Map

A Globe

Maps can be used to find directions and navigate from one place to another. For example, they are used in daily life to find a friend’s house or plan a trip. Let us explore an example:

Look at the map below and answer the following questions.

1. When you begin your journey at the bank, on which side will you find Station Square?

Solution:

The map tells us that Station Square is in the south.

2. Which of these would be farthest in distance from the bank - Hill Road or City Road?

Solution:

The map tells us that the City Road would be farthest in distance from the bank.

Let’s Practise - 4

1. Observe the map and answer the following questions.

Write north, south, east, or west to complete the sentences.

a. The rowboats are to the ______ of the campfire.

b. The camping trailers are to the ______ of the tents.

c. The cabins are to the ______ of the tents.

d. The tents are to the ______ of the campfire.

Let’s Learn

Tangrams

Tangram is a fun and ancient Chinese puzzle game. It consists of seven flat pieces called “tans,” which are put together to form various shapes and pictures.

The seven tans are usually made up of five triangles (two large, one medium, and two small), one square, and one parallelogram. We can give each tan a number from 1 to 7. This helps us talk about the pieces and their positions. In the figure given above, the pieces labelled with the numbers 1, 2, 4, 6, and 7 are triangles. The piece labelled as number 3 is a parallelogram, and the one with number 5 is a square. We can use these geometric shapes to make various designs of people, animals, and things. The following pictures are examples:

With tangrams, you can dive into a delightful world of geometric puzzles, creating over 6,000 different shapes! Not only does this spark creativity, but it also gives your problem-solving skills a fun workout.

Cat Sailboat House Rocket

Let’s Practise - 5

1. Use appropriate tangram pieces (7) to complete the following images.

Let’s Learn

Tiling

Tessellations or tiling are patterns created by repeating shapes without any gaps or overlaps. It’s like covering a surface with flat shapes in a way that they fit together perfectly. You can often find tessellations on walls using tiles. You can find the examples of tiling or tessellation in the following figures:

Overlaps: When one thing covers part of another Word Zone

House Swan Boat

Take a look at the picture below. In this case, even though the circles are arranged without overlapping, there are spaces or gaps in between them. Therefore, this figure does not form a tessellation.

Let’s Practise - 6

1. A tessellation should be free of gaps and ______.

a. triangles

b. single shapes

c. overlaps

d. curved shapes

2. Tick the boxes that show tessellations.

Symmetry

When a shape can be folded in half, and both sides look the same, it is called symmetrical. The line on which we fold it is called the line of symmetry or the axis of symmetry.

If we place a mirror along the line of symmetry, we will observe that the mirror reflects the other half of the figure.

The dotted line in each of the following figures is the line of symmetry. They are called symmetrical figures.

Shapes that can’t be divided into two identical halves are called asymmetrical figures.

Here are some examples of asymmetrical figures:

GIf the line of symmetry goes from left to right, then we say the shape has horizontal symmetry.

Example: English alphabets like C and D have horizontal lines of symmetry.

If the line of symmetry goes from top to bottom, then we say the shape has vertical symmetry.

Symmetrical: When both sides look the same Axis: A line around which you can spin something Word Zone

Example: The English alphabet A has vertical line of symmetry.

Some shapes have both horizontal and vertical lines of symmetry. Examples include the English alphabets, ‘H’ and ‘O’.

The plane figures given below have more than one line of symmetry.

A line of symmetry helps you find balance and harmony in shapes. It is like a secret code for making things look beautiful and even! Fact Zone

1. Draw the line of symmetry in each of the following figures.

Let’s Learn

Pattern

When you repeat shapes, numbers, or letters following a certain rule, you create a sequence. This sequence is known as a pattern. Patterns can be of various types—increasing, decreasing, logical, skipping, changing directions, or a combination of these.

Patterns in nature

The arrangement of petals on a flower, the stripes on the body of animals, and the leaves on a tree branch all follow specific patterns. These are examples of natural patterns.

Pattern in numbers

A number pattern is a list of numbers that follows a certain rule. For example, look at these numbers: 4, 7, 10, 13, 16, ….

In this pattern, each number is increasing by 3. So, to find the next number, we add 3 to the last number in the sequence, which is 16. So, 16 + 3 = 19.

Therefore, the next number in the sequence is 19. Here is another example: 13, 11, 9, 7, ….

In this pattern, the numbers are decreasing by 2 each time. To find the next number, subtract 2 from 7. So 7 - 2 = 5.

Therefore, the next number is 5.

Pattern in shapes

Patterns in shapes are sequences or arrangements of shapes that follow specific rules, such as colours, sizes, shapes, or sequences.

Let us examine the following picture pattern:

In this pattern, we observe that the number of squares increases by two with each step. Therefore, the next shape will be:

Thinking Zone

Draw an object that has an infinite number of lines of symmetry.

Let’s Practise - 8

1. Identify the patterns and write the next two terms for each sequence.

a. 5, 11, 17, 23, ___, ___

b. 25, 21, 17, ___, ___

2. Draw the pictures that come next in each growing pattern.

a.

Let’s Sum Up

• A point is a location with no size or shape, often represented as a dot.

• A line is a straight path with no endpoints, represented by a double-headed arrow.

• A ray is a part of a line with one endpoint, visualised with a single-headed arrow.

• A line segment is a straight path with two endpoints, having a finite length.

• Maps help understand locations and are used for navigation and trip planning.

• Tangrams consist of seven flat pieces (tans) used to form various shapes and pictures.

• Tessellation involves covering a surface with shapes without gaps or overlaps.

• Symmetry is when a shape can be folded in half, and both sides look the same.

• Patterns exist in nature, numbers, and shapes.

Life Skills

Imagine you have a fun project where you get to draw tangram shapes to create four different ocean creatures. Take out your drawing book and draw these ocean creatures using tangram pieces. To make them extra special, use different colours to colour each piece.

English:

List the English alphabets that do not have a single line of symmetry.

Science:

Identify some animals or insects that exhibit symmetry.

Identify the pattern in the clocks given below. Complete the pattern by drawing the time in the next three clocks. 21st Century Skills

Extend Your Knowledge

Examine a city map, carefully observe the symbols used, and draw each symbol while identifying its meaning. Additionally, explain why symbols are important in a map. Consider how using symbols helps people understand and navigate the map more easily, and discuss any creative ideas you might have for designing new symbols that could be useful on a map.

Tips for the Parent

Encourage your child to play with tangram puzzles. Also, ask your child to identify and draw patterns they observe around the house or in nature. This could be patterns in floor tiles, wallpaper, or the arrangement of leaves on a plant.

My Study Plan

Measurement

• Length of objects with standard units

• Addition and subtraction of length

• Real life applications of length

• Mass of objects with standard units

• Addition and subtraction of mass

• Real life applications of mass

Let’s Recall

1. Measure the following things using a hand span.

a. Notebook b. Desk

2. Measure the following things using an arm span. a. Blackboard b. Width of the room

3. Do you remember these machines? What do they measure? They measure _______________.

Measure: To find out how big or long something is Word Zone

Thinking Zone

Imagine you have to measure the length or weight of something in your daily life. How will you do it and why? Discuss in the class.

Let’s Learn

Length

The length of something is how long it is when measured from one end to the other along the longest side. It helps us to identify the size of an object. When the size of an object is measured horizontally, it is known as length and when the size of an object is measured vertically, it is known as height of the object. For example:

Measuring Length

Measuring Height

Earlier we used things like arm spans, hand spans, and foot spans to measure the length of objects. These are called non-standard units. Non-standard units are not very accurate because everyone’s hand span or foot size is different.

So, to make things less confusing, we use standard units of length now.

Word Zone

Non-standard: Something not normal or something different

Standard units

These are pre-defined and do not change from person to person or object to object. Some examples of measurements of length using standard units are centimetres, metres, and kilometres.

Centimetre

This is a small unit we use to measure things. The short form of centimetre is written as cm. If you look at the ruler, you will see these little marks, and each mark is one centimetre.

For example:

In the image above, the length of the pencil is 7 cm.

Metre

A metre is a unit we use to measure things that are not too small, like a pencil, and not too big, like a mountain. The short form of metre is m. We generally measure metre from metre stick or measuring tape.

For example:

In the image above, the length of the wall is measured using a measuring tape.

Kilometre

A kilometre is a unit which is used to measure very long distances. It can be the distance between two cities or places, the distance between your school and your home, and so on.

For example:

In the image above, the distance between the two places is 2 km.

Relation between metre, centimetre, and kilometre

One metre is equal to one hundred centimetres.

1 m = 100 cm

One kilometre is equal to one thousand metres.

1 km = 1000 m

The distance between Kashmir and Kanyakumari, two opposite corners of India, is about 3,600 kilometres.

Fact Zone

Let’s Practise - 1

1. Check out the pictures below and fill in the blanks with the correct unit of length (metre/centimetre) for each of them.

Objects

Units of measurement

2. Pihu wants to know the distance between her house and her grandmother’s house. The distance would be in _______. (Encircle the correct one)

Metre Centimetre Kilometre

3. Measure the length of the following using your ruler.

Objects

Measurement (in cm) Pencil

Sharpener

Length of your notebook

Addition and Subtraction of Length

Addition

We can easily add two lengths with the same units.

We can add km and km, m and m, cm and cm.

Let us understand this better with the help of the following examples.

Example 1:

Add: 22 km and 23 km.

Solution:

Arrange the given numbers in columns as shown and add.

So, 22 km + 23 km = 45 km.

Example 2:

Add: 231 cm and 569 cm.

Solution:

Arrange the given numbers in columns as shown and add.

So, 231 cm + 569 cm = 800 cm.

Example 3:

Add: 4 km 500 m and 2 km 290 m.

Solution:

There are two steps to be followed in order to solve this problem.

Step 1:

Write the numbers so that km and m are in the correct column, as shown in the table.

Step 2:

Add km with km and m with m.

So, 4 km 500 m + 2 km 290 m = 6 km 790 m.

Subtraction

We can easily subtract two lengths with the same units.

We can subtract km and km, m and m, cm and cm.

Look at the following example.

Example 1:

Subtract 42 cm from 68 cm.

Solution:

Arrange the given numbers in columns as shown and subtract.

So, 68 cm – 42 cm = 26 cm.

Example 2:

Subtract 14 km 125 m from 56 km 250 m.

Solution:

These are two steps to be followed in order to solve this problem.

Step 1:

Write the numbers so that km and m are in the correct column, as shown in the table.

Step 2:

Subtract km from kmand m from m.

1. Solve the following.

2. Subtract 65 km 350 m from 87 km 430 m.

Let’s Learn

Real Life Applications

Example 1:

Pihu has a red ribbon and a green ribbon. The red ribbon is 44 m 16 cm long. The green one is 25 m 35 cm long. What is the total length of the ribbons that Pihu has?

Solution:

Step 1: Read the word problem and note down the given information.

Length of red ribbon = 44 m 16 cm

Length of green ribbon = 25 m 35 cm

Step 2: We need to find the total length of Pihu’s ribbons means we must add them.

Write the numbers so that m and cm are in the correct column, as shown in the table.

Step 3: Now, let us calculate. Add m with m and cm with cm.

Hence, the total length of Pihu’s ribbons is 69 m 51 cm.

Example 2:

Aayu’s house is 44 km 670 m from his school. He has already covered a distance of 29 km 480 m. How far is he from home?

Solution:

Step 1: Read the word problem and note down the given information.

Distance between Aayu’s house and his school = 44 km 670 m

Distance covered by Aayu = 29 km 480 m.

Step 2: We need to find the difference between the two distances. Write the numbers so that km and m are in the correct column, as shown in the table.

Step 3: Now, let us calculate.

Subtract km from km and m from m.

Hence, Aayu is 15 km 190 m away from his home.

Fact Zone

Apart from cm, m, and km, several other units of length are also used. These include units like inches, yards, and miles.

Let’s Practise - 3

1. Solve

a. Rahul has a 31 m 205 cm long wire. His father bought 34 m 450 cm more wire for him. What is the total length of the wire Rahul has now?

b. David goes on an evening walk on Monday and covers a distance of 2 km 54 m. On Tuesday, he covers a distance of 3 km 300 m. What is the total distance he covers in these two days?

c. Sara goes to buy a cloth in the market. She buys a cloth which is 5 m 63 cm. If she gives 3 m 49 cm to the tailor for stitching a dress, then how much cloth is left?

d. Jaspreet is a cyclist. He is in a cycle race currently and he needs to cover 23 km 784 m to win the race. If he has covered 16 km 457 m till now, then how much distance is left to be covered?

Let’s Learn

Mass

Mass is a measure that tells how heavy or light an object is. Some things can be very heavy, such as a big rock, while others are very light, like a feather.

Lifting a big rock

Lifting a feather

To find out how heavy or light an object is, we need to measure its weight. We can use lighter objects to measure the weight of heavier objects. We can use stones, marbles, nails, bricks, etc, to measure the weight of the other objects.

For example, the weight of the apple = 2 stones.

And, the weight of the tennis ball = 10 marbles.

Using objects, such as pebbles and stones can lead to confusion, so, we use standard units to measure weight.

Standard units

One standard unit of weight is gram. It can also be written as ‘g’.

We can measure the weight of spices, such as cumin and chilli powder in grams.

500 grams

Another standard unit of measurement of weight is kilogram. It can also be written as ‘kg’.

We can measure the weight of rice, sugar and fruits like watermelon in kilograms.

5 kilograms

Kg is a bigger unit and g is a smaller unit. We use kg to weigh heavier objects and use g to measure lighter objects.

5 kg

We use balance and weights to weigh things. Some of the known weights of measures are as below: 50 g, 100 g, 200 g, 500 g, 1 kg, 2 kg, 5 kg, 10 kg, 50 kg, and 100 kg.

In an electronic weighing balance, we have only one pan. We can see the weight directly on the screen.

Relation between gram and kilogram

One kilogram is equal to one thousand grams.

1 kg = 1000 g

Let’s Practise - 4

1. Look at the pictures and write an appropriate unit of measurement of mass (kilogram/gram) for each of them in the given space.

Images

Unit of measurement of mass

Addition and Subtraction of weight

Addition

We can easily add two weights with the same units.

We can add kg and kg and g and g.

Example 1: Add: 150 g and 100 g.

Solution:

Arrange the given numbers in columns as shown and add.

Therefore, 150 g + 100 g = 250 g.

Example 2: Add 2 kg 750 g and 2 kg 150 g.

Solution:

There are two steps to be followed in order to solve this problem.

Step 1:

Write the numbers so that kg and g are in the correct column, as shown in the table.

Step 2:

Add kg with kg and g with g.

Therefore, 2 kg 750 g + 2 kg 150 g = 4 kg 900 g.

Subtraction

Example 1:

Subtract 3 kg 151 g from 8 kg 387 g.

Solution:

There are two steps to be followed in order to solve this problem.

Step 1:

Write the numbers so that kg and g are in the correct column, as shown in the table.

Step 2:

Subtract kg from kg and g from g.

Thus, 8 kg 387 g – 3 kg 151 g = 5 kg 236 g.

Example 2:

Subtract 27 kg 650 g from 41 kg 716 g.

Solution:

There are two steps to be followed in order to solve this problem.

Step 1:

Write the numbers so that kg and g are in the correct column, as shown in the table.

Step 2:

Subtract kg from kg and g from g.

Thus, 41 kg 516 g – 27 kg 650 g = 14 kg 66 g.

Let’s

Learn

Real Life Application of Mass

Example:

Arun brought 4 kg 500 g of tomatoes on Monday and 3 kg 150 g of tomatoes on Saturday. What is the total amount of tomatoes that he bought on Monday and Saturday?

Solution:

Step 1: Read the word problem and note down the given information.

Weight of tomatoes brought by Arun on Monday = 4 kg 500 g

Weight of tomatoes brought by Arun on Saturday = 3 kg 150 g

Step 2: Try to understand, what we need to find. We need to find the total weight of tomatoes bought on Monday and Saturday. 4 kg 5 0 0 g + 3 kg 1 5 0 g

So, Arun bought 7 kg and 650 g of tomatoes in total.

The unit of weight that is smaller than a gram is called a milligram. We measure very small weights, such as weight of medicines.

Let’s Practise - 5

1. Solve the following.

a. Add 13 kg 350 g and 12 kg 450 g.

b. Add 76 kg 350 g and 23 kg 950 g.

c. Subtract 34 kg 650 g from 75 kg 900 g.

d. Subtract 65 kg 450 g from 96 kg 750 g.

e. A vegetable seller had 54 kg 500 g potatoes. He sold 34 kg 250 g potatoes over the day. How many potatoes are left with him?

Let’s Sum Up

• Length means how long a thing is when measured from one end to the other along the longest side.

• The measurement of length using standard units are centimetre, metre, and kilometre.

• One metre is equal to one hundred centimetres.

• One kilometre is equal to one thousand metres.

• Addition and subtraction of lengths with the same units as km and km, m and m, cm and cm can be easily solved by arranging the digits in proper columns.

• Weight of an object tells how heavy or light an object is.

• The measurement of weight using standard units are gram and kilogram.

• One kilogram is equal to one thousand grams.

• Addition and subtraction of weight with the same units as kg and kg, g and g is also done by arranging the digits in the proper place value columns.

Cross-Curricular Connections

Arts:

Here are various art and craft supplies: Unused chalk Unused colored pencil Hole punch Ruler

Arrange the given objects in ascending order based on their weight.

Arrange the given objects in ascending order according to their length.

Life Skills

Use a measuring tape or a measuring chart to measure the height of different members of your family. Find the difference in height between the tallest and the shortest family member.

21st Century Skills

Mickey is planning to make a school garden, and he needs to measure the length of two different plots to determine the best one for his project. Plot A is 5 metres long, and Plot B is 400 centimetres long. Explain which plot is longer and why. Additionally, he has a bag of soil weighing 2 kilograms. He needs to distribute this soil equally into four pots. How much soil will each pot receive?

Extend Your Knowledge

Conversion of units:

We know that 1 km = 1000 m.

19 km 45 m can be written as:

= 19 × 1000 m + 45 m

= 19000 m + 45 m = 19045 m

So, 19 km 45 m is equal to 19045 m. Similarly, 4 kg 3 g can be written as:

= 4 × 1000 g + 3 g = 4000 g + 3 g = 4003 g

Tip for the Parent

• Encourage your child to make comparisons using everyday objects. For example, ask them to find something in the house that is longer or shorter than their shoe, or heavier or lighter than a book.

My Study Plan

• Telling time

• AM and PM

• Conversion of units of time

• Calendar

• Time duration

Let’s Recall

1. Look at the clock and write the time below each clock.

2. Draw the minute and hour hands on the clock face. 8:00 10:15 4:30 2:45

Thinking Zone

Long ago, people used a sundial to measure time of the day. Do you think the method was accurate? Find out more about this by having a discussion with your teacher and classmates.

Let’s Learn

Telling Time

The time of a day is measured using a clock. A clock has 12 numbers. The minute hand on a clock takes 5 minutes to go from one number to the next. So, when the minute hand moves from one number to the next, it means 5 minutes have passed. This means we can use the table of 5 to tell time in 5-minute chunks. For example, look at this clock.

Let us learn how to tell time step by step:

Step 1: Start by looking at the hour hand. It is between numbers 7 and 8. Step 2: Next, check the minute hand. It is pointing at the number 4. As we know:

× 3 = 15 minutes 4

× 4 = 20 minutes

In this clock, the hour hand is between 7 and 8, and the minute hand is at 4. So, the time is 20 minutes past 7 or 7:20.

Now consider the time on the clock to be 7:15. In this case, we can also say that the time is 15 minutes past 7 or quarter past 7.

Let us learn from one more example.

Step 1: Start by looking at the hour hand. It is between numbers 2 and 3.

Step 2: Next, check the minute hand. It is pointing at the number 8.

As we know:

= 40 minutes

In this clock, the hour hand is between 2 and 3, and the minute hand is at 8.

So, the time is 40 minutes past 2 or 2:40.

Note: We only use past until half past (30 minutes past). After that, we start to use ‘to.’

As we know, 1 hour = 60 minutes.

In 2:40, there are 20 minutes (60 – 40 = 20) left until 3 o’clock. So, another way to express 2:40 is twenty to three (2:40).

Now consider the time on the clock to be 2:45, in this case we can also say that the time is fifteen to three or quarter to 3.

AM and PM

A day has 24 hours. When it is 12 o’clock at night, we call it midnight. When it is 12 o’clock during the day, we call it noon.

From midnight until 12 noon, we say ‘AM’ in the time, like 5:00 AM. From 12 noon until midnight, we say ‘PM’ in the time, like 5:00 PM.

Let’s Practise - 1

1. Look at the clock and fill in the blanks.

a. The time in the first clock is twenty-five to ____.

b. The time in the second clock is 20 minute past ___.

c. The time in the third clock is ____ to four.

2. Match the following:

It’s ten to nine 9:15

2. Match the following.

It’s ten to nine 9:15

It’s quarter past nine 8:50

It’s five to twelve 12:05

It’s five past twelve 11:55

3. Circle the correct option.

a. Aayu often go to play football in the evening.

AM PM

b. Pihu sleeps in the afternoon.

AM PM

Let’s Learn

Conversion of Units of Time

Converting units of time involves converting between seconds, minutes, and hours.

To do this, we need to know how different units of time are related to each other:

Let us look at how we can convert time from one unit to another.

Hours to minutes

To convert 2 hours to minutes, think of how many minutes are there in each hour.

We know that:

1 hour = 60 minutes

So, 2 hours = 2 × 60 = 120 minutes

Minutes to seconds

To convert 5 minutes to seconds, think of how many seconds are there in each minute.

We know that, 1 minute = 60 seconds

So, 5 minutes = 5 × 60 seconds = 300 seconds.

Some clocks also have a third hand known as, the second hand.

Let’s Practise - 2

Fact Zone

1. Convert 5 hours into minutes.

2. Convert 3 minutes into seconds.

3. Convert 4 hours and 25 minutes into minutes.

4. Match the following to their correct pairs.

Let’s Learn

Calendar

A calendar is a series of pages that shows the days, weeks, and months of a particular year.

It helps us keep track of time. It has twelve months, and each month has a different number of days.

Some important points about a calendar are as follows:

1. All months other than February have 30 or 31 days.

2. February has 28 days in most of the years.

3. But every fourth year there are 29 days in February.

4. The year February has 29 days, we call it a leap year.

5. A leap year has 366 days instead of 365 days.

Word Zone

Leap Year: A year with an extra day every four years

Let’s Learn

Time Duration

The length of time it takes to complete something is called the duration of an activity. Activities can vary in length; some are short, like making a cup of tea, while others are long, like sleeping.

Example 1: Imagine you leave for school at 7:00 AM and reach home at 7:20 AM. How much time do you take to reach school?

Solution:

Let us solve it step by step:

Step 1: Start with the time you leave for school and the time you arrive. You leave for school at 7:00 AM

You arrive at school at 7:20 AM

Step 2: Find out how long it took to reach school.

• Look at the numbers in the start and end times. In this case, it is 7:00 AM and 7:20 AM. The hours are the same, which is 7. This means your journey took place during the 7th hour of the day.

• Now, look at the minutes in the start and end times. In this case, it is 00 (for 7:00) and 20 (for 7:20). You can see that 20 is more than 00.

• So, subtract 00 from 20, which is 20.

So, you took 20 minutes to reach school.

Example 2: Aayu left from school at 3 PM and reached home one hour later. What time did he reach home?

Solution:

If Aayu left from school at 3 PM, and reached home one hour later, you can find out the time by adding 3 + 1 hour = 4

Therefore, Aayu reached home at 4:00 PM.

Big Ben in London is like a giant clock tower. It is very tall and can be seen from far away in the city. Fact Zone

Let’s Practise - 3

1. Which month has the least number of days? Tick the correct answer.

a. January b. February c. April d. December

2. List the months with 30 days and the months with 31 days.

Months with 30 days

Months with 31 days

3. A man leaves Delhi at 12:30 AM and reaches Lucknow at 8:30 AM. Find the time taken by the man to reach Lucknow.

4. An aeroplane took off at 2:30 PM and landed at its destination after 2 hours. At what time did the aeroplane land?

Let’s Sum Up

• The minute hand on a clock takes 5 minutes to go from one number to the next.

• We use past until half past (30 minutes past). After that, we start to use ‘to.’

• When it is 12 o’ clock at night, we call it midnight. When it is 12 o’ clock during the day, we call it noon.

• A leap year has 366 days instead of 365 days.

• 1 minute = 60 seconds

• 1 hour = 60 minutes

• 1 day = 24 hours

• The length of time it takes to complete something is called the duration of an activity.

Life Skills

We have different units of time, like seconds, minutes, hours, and days, to help us understand time better. Name some activities you do in a minute. Now, name some activites you do in an hour.

Cross-Curricular Connections

Science:

The Earth is like a big spinning ball. When it spins, one side faces the Sun, and it is daytime; the other side faces away, and it is nighttime. So, the Earth’s rotation is what makes day and night happen. Take a ball and a torch. Imagine the ball as our planet Earth and the torch as the Sun. Place the ball on a surface and flash the torch light on it. See which face of the ball glows up and which face appears dark.

21st Century Skills

Using alarm clock and timer can help you with your schedule and learning. Think about your day-to-day activities where you can make use of alarm clock or timer like for your playing time, screen time, study time, etc. Then, start making use of these tools!

Extend Your Knowledge

Clocks and watches are used to measure time. Some clocks are analog, with hands that point to numbers, while others are digital, displaying numbers on a screen.

A stopwatch is a special timer used for measuring short periods of time, like in a race.

Tips for the Parent

• Ask your child questions like, “What time is it?” and “What day is it today?” to reinforce their understanding of time.

• Play games that involve time and calendars, such as setting a timer for a fun activity or playing calendar-related board games.

Money

My Study Plan

• Rupees in words and figures

• Conversion of money

• Addition, subtraction, multiplication and division of money

• Real life problems on Money

• Bills

Let’s Recall

Roy is saving some money from his pocket money in his piggy bank.

(i) How much money has Roy saved in his piggy bank?

(ii) If Roy gave away 75, how much money does he have left in his piggy bank?

Thinking Zone

Suppose you want to buy a toy that costs 19 rupees. You have coins of 1 rupee and 5 rupees. How can you use these coins to pay for the toy using as few coins as possible? Explain your answer.

Let’s Learn

Expressing Money in Words and Figures

We all need money in daily life to buy things.   Money is available in two forms — coins and notes.

Each coin or note has a certain value. This value is expressed in rupees or paise.

Look at these notes and coins and see if you can recognise these.

Different types of Coins and Notes

But almost all of the paise coins are not in use now. Nowadays the coins of 1, 2, 5 and 10 are mostly used. Some coins and notes share the same value.

For example: 10 and , here both the coin and note have value ` 10.

The symbol for a rupee is “`” and paisa is “p”.

For example 10 rupees can be written as `10, and 50 paise can be written as 50p.

Sometimes, the price of items that we want to buy is in the combination of rupees and paise.

While writing rupees and paise together, we put a dot (.) to separate rupees from paise. The number to the left of the dot shows the amount in rupees and that on its right shows the paise part.

Note: When we use the dot, we don’t need to write paise separately.

For example,

(i) 9 rupees and 50 paise is written as ` 9.50.

(ii) Five rupees and twenty-five paise is written as ` 5.25.

When the paise are less than 10, that is only a single digit, then to complete 2 digits in the right side of the dot we write a zero after putting the dot followed by the single digit.

For example: Two rupees and five paise is written as `2.05.

Look at the price of the product given below.

45.50

To read the price, the number written in left side of the dot is ` and the right side of the dot is paise.

This means that in ` 45.50, 45 is the rupees part and 50 is the paise part.

So, we read and write `45.50 in words as forty-five rupees and fifty paise.

Look at another example.

99.05

To read the price, the number written in left side of the dot is ` part and the right side of the dot is paise part.

Word Zone

Price: cost

This means that in ` 99.05, 99 is the rupees and 05 is the paise.

So, we read and write ` 99.05 in words as ninety-nine rupees and five paise.

Let’s Practise - 1

1. Take a look at the toy’s price and, write ₹ and p separately. One has been done for you.

2. Write in words. One has been done for you.

(a) ₹ 33.25 Thirty-three rupees and twenty-five paise

(b) ₹ 21.75

(c) ₹ 39.50

(d) ₹ 64.55

3. Write the following in figures. One has been done for you.

(a) Sixty-two rupees and twenty paise ₹62.20

(b) Forty-one rupees and sixty paise

(c) Ninety-nine rupees and thirty paise

(d) Seventy-eight rupees and eight paise

Early Romans used salt as money and the word “salary” comes from “sal,” meaning salt in Latin.

Let’s Learn

Conversion of Money

The relation between rupee and paise is as follows: `1 = 100 Paise

Suppose we have two coins of 50p each:

Now if we combine these two 50p coins, we will get 100p which is equal to `1.

Or conversely, we can say, we will get two 50 p coins in exchange of `1.

Similarly, if we have four coins of 25p each, we will get 100p which is equal to `1

Or conversely, we can say, we will get four 25p coins in exchange of `1.

The act of converting paise to rupee or rupee to paise is known as Conversion.

Converting rupees ( ) into paise (p)

Step 1 - Identify the value of Rupee.

Step 2 - Multiply that value by 100.

Step 3 - The final answer would be in Paise.

Example 1: Convert `213 into paise.

Solution:

To convert rupees into paise, we multiply the amount in rupees by 100.

Hence, `23 = 23 × 100 p = 2300 p

Example 2: Convert `12 and 25 paise into paise.

Solution:

We can write `12 and 25 paise as `12.25

` 12.25 = `12 + 25 p = 12 x 100 p + 25 p = 1200 p + 25 p = 1225 p

Alternative Method:

To convert the money in rupees and paise into paise, remove ` and the dot (.) Write p for paise at the end.

Therefore, 12 rupees and 25 paise = `12.25 = 1225 p

Converting paise (p) into rupees ( )

Steps to convert:

1. Identify the value of Paise.

2. Count the two digits from the right and put a dot (.) after the second digit.

3. Remove paise or p and write ` at the beginning.

Example 3 : Convert 300 paise into rupees.

Solution:

Count the two digits from right.

3 0 0 p 2 1

Now put a dot and remove paise or p and write ` at the beginning.

So, 300 p = `3.00 or `3

Alternative Method:

We know, 100 p = `1.00

300 p = 3 × 100 p = 3 × ` 1.00 = ` 3.00

Example 4: Convert 345 paise into rupees.

Solution:

Count the two digits from right.

3 4 5 p 2 1

Now put a dot and remove paise or p and write ` at the beginning.

So, 345 p = `3.45

Alternative Method:

345 p = 300 p + 45 p

= 3 × 100 p + 45 p = ` 3.00 + 45 p

= ` 3.45

The term ‘rupee’ is derived from the Sanskrit word “rupyah,” which translates to “shaped silver,” just like a silver coin.

Let’s Practise - 2

1. Convert the following money from rupees to paise.

a. ` 144

b. ` 57.30

c. ` 29.05

d. ` 34.45

2. Convert the following money from paise into rupees.

a. 9700 paise =___________

b. 5710 paise =___________

c. 8200 paise =___________

d. 710 paise =___________

Learn

Addition and Subtraction of Money

Addition of Money

Adding money is like adding regular numbers, but we have to be careful about the different parts of money.

Money has two main parts: rupees and paise. Rupees are like the bigger part, and paise are like the smaller part.

To add money first put the rupees under rupees and the paise under paise. And don’t forget the dot, it’s important! The dot helps us know where the rupees end and the paise start.

Example 1: Add ` 523.50 + `41.75.

Step 1:

Arrange the money in ` and p in columns such that the dots are exactly one below the other.

Step 2: First add the paise.

But in paise we have 125p. Now we need to regroup paise (p) in rupees (`).

125 p = 100p + 25 p = ` 1 + 25p

Carry 1 to the rupees column and write 25 in the paise (p) column.

Step 3: Now, add the rupees.

Total = `565.25 or five hundred sixty-five rupees and twenty-five paise.

Subtraction of Money

Just like adding money, first we need to put the rupees under rupees, the paise under paise and the dot under the dot. Then, we subtract the numbers just like regular numbers.

Example 2: ` 412.25 - 311.75

Step 1: Arrange the money in ` and p in columns such that the dots are exactly one below the other.

But we can’t take out 75 paise from 25 paise. So, we borrow 1 = 100 p from 412 leaving 411 in column.

In paise column, we now have 100 p + 25 p = 125 p

Step 2: First, subtract the paise.

Step 3: Now, subtract the rupees.

Total = `100.50 or hundred rupees and fifty paise.

Let’s Practise - 3

1. Add the following: 2. Subtract the following:

a. 110.05 + 29.45 = _________.

b. 304.50 + 108 = _________.

c. 230.25 + 175.25 = _________.

d. 450.20 + 101.50 = _________.

Let’s Learn

Multiplication and Division of Money

Multiplication of Money

a. ₹ 125.00 - ₹ 10.50 = _________.

b. ₹ 169.50 - ₹ 76.45 = _________.

c. ₹ 445.50 - ₹ 344 = _________.

d. ₹ 209.25 - ₹ 87.25 = _________.

Money can be multiplied by a given number just like we multiply ordinary numbers.

To multiply money by number, multiply the amount with the number and after multiplication put a dot at second place from right.

Example 1: Multiply ` 36.25 × 8

Step 1: Arrange the money in ` and p in columns.

Step 2: Multiply money as you multiply ordinary numbers.

Just remember to place the dot in the product after two places from the right.

Total = ` 290.00

Example 2: Multiply ` 16.25 by 5.

Step 1: Arrange the money in ` and p in columns.

Step 2: Multiply money as you multiply ordinary numbers. Just remember to place the dot in the product after two places from the right.

Total = ` 81.25

Division of Money

Money can be divided by a given number just like we multiply ordinary numbers.

To divide money by number, convert the rupees into paise and divide it by the number and after division put a dot at second place from right.

Example 3: Divide ` 9.60 by 8

Solution:

Step 1: Change ` 9.60 into paise, i.e., 9.60 × 100 = 960 p

Step 2: Divide 960 by 8. 960 ÷ 8 = 120

Step 3: To convert the quotient 120 p back into rupees, put a decimal point in the quotient after two places from the right and put ` symbol at the beginning and remove paise (p).

120 p = ` 1.20

Thus, ` 9.60 ÷ 8 = ` 1.2

Example 4: Divide ` 38.25 by 5.

Solution:

Step 1: Change ` 38.25 into paise, i.e., 38.25 × 100 = 3825 p

Step 2: Divide 3825p by 5. 3825 ÷ 5 = 765

Step 3: To convert the quotient 765 p back into rupees, put decimal point in the quotient after two places from the right and put ` symbol at the beginning and remove paise (p).

765 p = ` 7.65

Thus, ` 38.25 ÷ 5 = ` 7.65

Money can have unique marks to check if it’s real and not fake.

For example, a special security thread on rupee notes helps us check if it’s real or fake.

Fact Zone

Let’s Practise - 4

1. Multiply the following amounts:

2. Divide the following:

(a) ₹ 14.05 × 9 = _________. (a) 648 p ÷ 8 = _________.

(b) ₹ 20.25 × 8 = _________.

(c) ₹ 16.06 × 7 = _________.

(d) ₹ 32.25 × 3 = _________.

Let’s Learn

Application of Money in Real Life

(b) ₹ 85.00 ÷ 5 = _________.

(c) ₹ 25.50 ÷ 4 = _________.

(d) ₹ 32.44 ÷ 4 = _________.

We use money for different purposes like buying things, paying bills and saving for the future.

Application of money using addition

Example 1: Pihu purchased a T-shirt, a frock and a pair of socks for ` 150.50, ` 170.25 and ` 30 respectively. How much did Pihu pay to the shopkeeper for this?

Solution:

Price of the T-shirt = ` 150.50

Price of the frock = ` 170.25

Price of the socks = ` 30

To find how much Pihu paid to shopkeeper, we need to add all the price.

Total money to be paid to shopkeeper = ` 150.50 + ` 170.25 + ` 30

Step1: Arrange the money in ` and p in columns such that the dots are exactly one below the other.

Step2: Add rupees to rupees and paise to paise.

Total price to be paid to the shopkeeper = ` 350.75

Application of money using subtraction

Example 2: How much money did the shopkeeper return to Alex if he purchased items worth ` 240.50 and gave a ` 500 note to the shopkeeper?

Solution:

Total cost of items purchased by Alex = ` 240.50

Amount given by Alex to the shopkeeper = ` 500

To find how much money the shopkeeper returned, we need to subtract cost of items from the amount paid by Alex.

Amount returned by the shopkeeper = ` 500 - ` 240.50

Step1: Arrange the money in ` and p in columns such that the dots are exactly one below the other.

But we can’t subtract 50 p from 0 p, so we need to take 1 carry from ` 500.

Step2: Subtract rupees from rupees and paise from paise.

Amount returned by the shopkeeper = `

Application of money using multiplication

Example 3: One bottle of jam cost ` 40.25. Find the cost of 4 such bottles.

Solution:

Cost of 1 bottle = ` 40.25

Cost of 4 bottles = ` 40.25 × 4

To find the cost of four bottles, we need to multiply 4 with cost of one bottle of jam:

Cost of 4 bottles = ` 40.25 x 4

Step 1: Arrange the money in ` and p in Columns.

Step 2: Multiply money as you multiply ordinary numbers. Just remember to place the dot in the product after two places from the right.

Hence, cost of 4 bottles = ` 161.00.

Application of money using division

Example 4: An amount of ` 884.80 is divided equally among 4 students. How much money did each student get?

Solution:

Amount to be divided = ` 884.80

Number of students = 4

To find out how much money each student received when `884.80 is divided equally among 4 students, divide the total amount by the number of students.

Money each student received = `884.80 ÷ 4

Step 1: Change ` 884.80 into paise, i.e., 884.80 × 100 = 88480 p

Step 2: Divide 88480 ÷ 4 = 22120.

Step 3: To convert the quotient 22120 p back into rupees, put decimal point in the quotient after two places from the right and put ` symbol instead of p. 22120 p = ` 221.20

So, money each student received is ` 221.20.

Let’s Practise - 5

1. Mohit bought a pack of chocolate bars for ` 109.50 and a pack of candies for ` 204.75. How much did he spend in total?

2. Reena bought items worth ` 418.75. She gave ` 500 note to the shopkeeper. How much should the shopkeeper return?

3. Robert bought 16 notebooks, each costing ` 23.50. How much money did he pay?

4. If Riya distributes ₹ 48.36 among 6 boys, how much will each boy get?

Let’s Learn

Bills

A “bill” is a slip of paper that tells you how much money you need to pay for something you bought or a service you used.

For example, take a look at the bill of a stationary shop that sold a unit of English and Math book along with 2 pieces of pen sets.

Bill Rijwan Bookstore

Let’s prepare a bill of our own.

Here is a list of items for which we need a bill. Two bottles of jam for `65.25 each, a packet of soup for `45, and two packets of pasta for `35.50 each.

The bill will look like,

Now to find the total cost of each item we need to multiply the Rate and Quantity, So,

Now add all the cost prices, to find the total amount, ` 130.50 + ` 45 + ` 71 = ` 246.50

Total Amount = 246.50

So, we spent ` 246.50 today on shopping.

Let’s Practise - 6 Purchase: to buy Word Zone

1. Mr. Alam bought the following items from store:

(a) 3 lamps costing ₹ 51.25 each

(b) 1 toy bike costing ₹ 180

(c) 4 packets of cream costing ₹ 54.50 each

Prepare the bill for the above purchase. Calculate the total amount paid by Mr. Alam.

Let’s Sum Up

y Money is available in two forms — coins and notes.

y Each coin or note has a certain value. This value is expressed in rupees or paise

y 1 rupee = 100 paisa

y The symbol for a rupee is “₹” and paisa is “p”.

y To add or subtract money first put the rupees under rupees, the paise under paise, the dot under the dot. Then, we add or subtract the numbers just like regular numbers.

y Money can be multiplied or divided by a given number just like ordinary numbers.

y A “bill” is a slip of paper that tells you how much money you need to pay for something you bought or a service you used.

Cross-Curricular Connections

Social Studies

We know that the money or currency we use in India is Rupees. But there are different currencies used around the world. Find out the currencies of atleast 10 different countries.

21st Century Skills

You have 450 rupees, and your mother wants you to divide it equally into three parts: one part for investing, one part for spending, and one part for donation. Then how much money do you have to invest?

Life Skills

Your friend’s little sister’s birthday is coming up, and he wants to buy her a special gift. He’s been saving money each month. He saved ₹35 every month for 5 months.

How much money does he have now, and do you think he’ll have enough money to buy this gift?”

Extend Your Knowledge

In the past, long ago, people didn’t have coins or paper money like we have now. Instead, they used a barter system.   In this system, they traded one thing they had for something else they wanted.

Tip for the parent

Encourage your child to solve real-life problems based on money by involving them  in everyday situations like grocery and stationery shopping.

Barter System: People giving an apple for a hen

My Study Plan

Data Handling

• Recording data using tally marks

• Pitcograph

• Draw and read pictograph

Let’s Recall

1. Look at the pictures below and organise them into two groups:

2. Ask your 10 classmates about their favourite flavour of ice cream and fill the table below:

Apple Carrot Orange

Tomato Banana Capsicum Vegetables Fruits

Ice cream

Thinking Zone

Fill in the details in the following table and count the number of letters.

Your name:

Father’s name:

Mother’s name:

Grandfather’s name:

Grandmother’s name:

Let’s Learn

Recording Data

Data is information or facts that can be collected and organised. It could be numbers, measurements, or descriptions that help us understand and make sense of things.

For example, we can record data about the number of students in a class for their favourite fruits. We can organise this data using graphs or tables to draw conclusions.

Using tally marks

Tally marks are a simple way to count and keep track of numbers. Instead of writing numbers, we use lines or slashes.

A tally mark is represented with the symbol ‘|’. Tally marks are written in groups of five so they can be understood easily. So, for the first four counts, we draw an individual line for each, and for the fifth count, the line goes across the previous four lines to make it a group of five lines.

Let us understand this with the help of an example by organising the given data:

Here is a list of how thirty-five students of class 3 travel to school.

Bus Bus Bus Walk Bus Walk Bike

Bus Walk Bus Car Car Walk Walk

Walk Walk Bus Bus Bike Bus Car

Walk Bus Walk Bus Bike Walk Bike

Bike Car Walk Walk Bike Bus Walk

A tally chart to display the given information:

From the above tally chart, we can say that:

1. A total of 35 students were surveyed about their mode of travel to school.

2. Most students in the class go to school by walking, while the fewest go by car.

3. The number of students walking is one more than those taking the bus.

4. 6 students use a bike to go to school.

1. Below is a list of food options chosen by children in a colony.

Pav Bhaji Maggi Maggi Pani Puri Pav Bhaji

Pasta Maggi Pasta Veg Manchurian Pani Puri

Maggi Pav Bhaji Maggi Pani Puri Pani Puri

Maggi Pani Puri Pasta Pasta Maggi

Complete the tally chart using the given data and answer the following questions.

a. How many children like pasta? _____

b. Which is the most preferred food choice? _______________

c. Which is the least preferred food choice? _______________

d. How many more children like pani puri than pav bhaji? _____

Pav bhaji Maggi Pani puri

2. The tally chart displays the items sold on weekends. Use the details provided in the tally chart to answer the questions.

Food Items

Tally Marks

a. Which item was sold maximum and how many were sold? ____________________ and _______________

b. How many fried rice were sold over the weekend? ______________

c. Which item was the least selling item? ____________________

d. How many more burgers were sold than french fries? _____________

Let’s Learn

Pictograph

Another way to show information is by using pictures, which is called a pictograph. Here, instead of just using numbers, we can draw pictures to make it more fun.

We can use a symbol or a picture to show how many are there or how many were surveyed.

To understand a pictograph, we need a key that tells us what each picture represents.

Burger

Cake

Patty

Ice Cream

French Fry

Fried Rice

Reading a pictograph

Let us understand this through an example.

Below is a pictograph showing the preferred fruit of children surveyed in a colony.

Key: means 1 child

In pictograph, each smiley represents one child.

From the given pictograph, we can say that:

1. A total of 21 children were surveyed.

2. Most of the children like bananas as their favourite fruit.

3. Less number of children like pears as their favourite fruit.

4. Four children like grapes as their favourite fruit.

5. The number of children who prefer apples is two more than the number of children who prefer strawberries.

Now, consider another example in which the key in the pictograph represents more than one number.

The pictograph below shows the favourite beverages of the teachers surveyed in a school.

Word Zone

Prefer: Like or choose one

In this pictograph, 1 cup represents 3 teachers. And, we can see that there are 7 cups representing tea. So, the number of teachers who prefer tea as their favourite beverage = 7 × 3 = 21

Similarly, the number of teachers who prefer coffee as their favourite beverage = 6 × 3 = 18 and so on.

From the above information, we can say that:

1. The total number of teachers surveyed about their favourite beverage = 21 + 18 + 3 + 6 + 12 = 60

2. Most of the teachers prefer tea as their favourite beverage.

3. A very few teachers prefer green tea as their favourite beverage.

4. The number of teachers who prefer coffee is 12 more than the number of teachers who prefer iced tea.

Drawing a pictograph

Given below is the data of the number of books in the library.

Consider the key: one = 10 books.

If there are , then it is equal to 10 + 10 = 20 books. Similarly, = 10 + 10 + 10 = 30 books.

Let us now replace the numbers with the symbols and draw a pictograph.

1. Brain processes images much faster than numerical data.

2. Visually representing data helps to understand the information easily and quickly.

Let’s Practise - 2

1. Observe the data showing the number of trees in the city. Each picture of a tree represents 10 trees.

Answer the following questions.

a. How many trees are there in the city? __________

b. Which type of tree is the least common in the city? __________

c. Which type of tree is the most common in the city? __________

d. What is the difference in the number of peach trees and apple trees?

2. The given pictograph shows the number of cars registered over the period 2016–2020.

Answer the following questions.

a. How many cars were registered in the year 2017? __________

b. In which year was the least number of cars registered? __________

c. In which year was the most number of cars registered?

d. What is the total number of cars registered after the year 2018? __________

3. Fill in the blanks with the correct information. The data shows the number of cookies each child ate.

Number of cookies each child ate

Let’s Sum Up

y Data is information or facts that can be collected and organised.

y Tally marks are a simple way to count and keep track of numbers. The chart that uses tally marks is known as a tally chart.

y A pictograph is a representation of data using images or symbols.

y A key in the pictograph tells us what each picture represents.

Life Skills

The number of members in 30 families of a society is as follows:

2, 3, 6, 5, 6, 4, 4, 4, 8, 4, 3, 3, 2, 4, 6, 4, 5, 3, 2, 5, 6, 4, 8, 5, 4, 3, 2, 4, 5, 3.

Represent the given data using tally marks.

Families

Family of 2 members

Family of 3 members

Family of 4 members

Family of 5 members

Family of 6 members

Family of 8 members

Tally Marks

Total Families

Cross-Curricular Connections

Science:

The tally chart shows some elements in nature. Use the details provided in the tally chart to answer the questions:

a. Which element has 8 letters? _______________

b. Which element has the least number of letters? ______________

c. How many elements have more than 6 letters? _______

d. How many elements have less than 6 letters? _______

Sports:

Find how many FIFA world cups each country has won and create a pictograph based on the information.

Country

Argentina

Brazil

France

Germany

Italy

1 World Cup =

Total World Cups Won

a. Which country has won the most world cups? ___________________

b. Name the two countries that have won equal number of world cups.

21st Century Skills

A gardener bought some flower plants for the garden. Look at the pictograph to see how many sunflower plants, marigold plants, tulip plants, and rose plants the gardener bought.

Answer the following questions.

a. How many marigold plants did the gardener buy? ______

b. Which type of plant did the gardener buy more of? ______

c. How many more tulip plants did the gardener buy than sunflower plants? ______

d. How many plants did the gardener buy in total? ______

Extend Your Knowledge

We now know that data can be visually represented in different ways. One such way is by using a bar graph.

In a bar graph, we use rectangular bars to represent the value. This is how a bar graph looks like. On one side, we take the value, and on the other side, the thing surveyed. You will study more in detail in higher grades.

Tip for the Parent

• Help your child to conduct a simple survey within the colony, asking questions like, “What is your favorite colour in the rainbow”? Let your child collect the responses and represent the data using tally marks and then a pictograph.

ANSWER KEY

CH-01: Numbers

Let’s Practise – 1

1. a. 6754 = Six thousand seven hundred fifty-four

b. 3029 = Three thousand twenty-nine

c. 9985 = Nine thousand nine hundred eighty-five

d. 5097 = Five thousand ninety-seven

e. 4639 = Four thousand six hundred thirty-nine

2. a. Six thousand ten = 6010

b. Nine thousand five hundred eighty-two = 9582

c. Two thousand nine hundred ninety-one = 2991

d. Eight thousand four hundred seventy-five = 8475

e. Three thousand nine hundred four = 3904

Let’s Practise – 2

1. a – 2143, b – 4218, c – 2046

Let’s Practise – 3

1. a – 2353, b – 2029, c – 7384

2. a – 4209, b – 9792, c – 5610

Let’s Practise – 4

1. a. 4562 < 4652

b. 8822 > 2288

2.Ascending Order: 2698, 3896, 8986, 9849

Descending Order: 9849, 8986, 3896, 2698

Let’s Practise – 5

Digits Smallest Greatest Number

2, 8, 0, 5 2058 8520

2, 4, 8, 3 2348 8432

4, 7, 3, 8 3478 8743

8, 6, 9, 0 6089 9860

Let’s Practise – 6

15 – 20, 263 – 260, 45 – 50, 824 – 820

Let’s Practise – 7

a. 12 → XII

b. 38 → XXXVIII

c. 23 → XXIII

d. 31 → XXXI

CH-02: Addition

Let’s Practise – 1

1. (a) 753 (b) 841

2. (a) 695 (b) 459

Let’s Practise – 2

1. (a) 6994 (b) 9130

2. (a) 3266 (b) 5612

Let’s Practise – 3

1. (a) 1438 (b) 7564 (c) 10514 (d) 10144

Let’s Practise – 4

1. (a) 1649 (b) 0 (c) 2334 (d) Same

2. 5800

3. 1440

Let’s Practise – 5

1. (a) 3165 (b) 3915 (c) 6034

CH-03: Subtraction

Let’s Practise – 1

(a) 296 (b) 223 (c) 259 (d) 71 (e) 184 (f) 432

Let’s Practise – 2

(a) 3871 (b) 707 (c) 1837 (d) 1192

Let’s Practise – 3

A. (1) 563 (2) 358 (3) 3498 (4) 0

B. 4930

Let’s Practise – 4

(a) 7148 (b) 8912 (c) 83 (d) 3102 (e) 3215

CH-04: Multiplication

Let’s Practise – 1

1. (a) 1848 (b) 665 (c) 831 (d) 924 (e) 282 (f) 792

Let’s Practise – 2

1. (a) 3693 (b) 8904 (c) 9233 (d) 7761

Let’s Practise – 3

1. (a) 672 (b) 1200 (c) 4028

Let’s Practise – 4

1. (a) 119 (b) 0 (c) 43 (d) 0 (e) 1

Let’s Practise – 5

1. (a) 34568 (b) 15000 (c) 44700 (d) 912

Let’s Practise – 6

1. (a) 516 (b) 837

CH-05: Division

Let’s Practise – 1

1. 48 ÷ 12 = 4

2. Multiplication Facts Division Facts

7 × 10 = 70 70 ÷ 10 = 7 70 ÷ 7 = 10

9 × 8 = 72 72 ÷ 8 = 9 72 ÷ 9 = 8

4 × 5 = 20 20 ÷ 5 = 4 20 ÷ 4 = 5

7 × 6 = 42 42 ÷ 7 = 6 42 ÷ 6 = 7

3. (a) 5 (b) 9 (c) 8 (d) 8

Let’s Practise – 2

1. (a) 3 (b) 6

Let’s Practise – 3

1. (a) Quotient = 115 and Remainder = 1

(b) Quotient = 173 and Remainder = 0

Let’s Practise – 4

1. (a) Quotient = 12 and Remainder = 4

(b) Quotient = 10 and Remainder = 24

(c) Quotient = 14 and Remainder = 0

(d) Quotient = 4 and Remainder = 5

2. (a) 1 (b) 0 (c) 1 (d) 451

Let’s Practise – 5

1. (a) 24 (b) 6 (c) 14

CH-06: Fractions

Let’s Practise – 2

1. (a) 8/4 (b) 16/2 (c) 15/5 (d) 3/3

ANSWER KEY

2. Fraction of apples in the basket is 5/17.

Fraction of oranges in the basket is 3/17.

Fraction of bananas in the basket is 3/17.

Fraction of strawberries in the basket is 4/17.

Fraction of mangoes in the basket is 2/17.

Let’s Practise – 3

1. 10/2

2. 10/15 and 5/15

3. 3/12 and 9/12

4. 12/6

CH-07: Geometry and Patterns

Let’s Practise – 1

1. (a) Line (b) Ray (c) Line Segment (d) Point

2. (a) True (b) False (c) False

Let’s Practise – 2

1.

(a) – (ii) (b) – (iv) (c) – (v) (d) – (iii) (e) – (i)

Let’s Practise – 4

1. (a) East (b) North (c) West (d) North

Let’s Practise – 6

1. overlaps

Let’s Practise – 8

1. (a) 29, 35 (b) 13, 9

CH-08: Measurement

Let’s Practise – 1

1. Metre, Centimetre, Centimetre, Metre

2. Kilometre

Let’s Practise – 2

1. (a) 52 km (b) 31 m (c) 35 km 75 m

(d) 7 km 45 m

2. 22 km 80 m

Let’s Practise – 3

1. (a) 65 m 655 cm (b) 5 km 354 m

(c) 2 m 14 cm (d) 7 km 327 m

Let’s Practise – 5

1. (a) 25 kg 800 g (b) 100 kg 300 g

(c) 41 kg 250 g (d) 31 kg 300 g

(e) 20 kg 250 g

CH-09: Time

Let’s Practise – 1

1. (a) eleven (b) nine (c) five minutes

2. It’s ten to nine – 8:50

It’s quarter past nine – 9:15

It’s five to twelve – 11:55

It’s five past twelve – 12:05

3. (a) PM (b) PM

Let’s Practise – 2

1. 300 minutes

2. 180 seconds

3. 265 minutes

4. 2 days – 48 hours

2 hours – 120 minutes

4 minutes – 240 seconds

180 seconds – 3 minutes

Let’s Practise – 3

1. (b) February

3. 8 hours

4. 4:30 PM

CH-10: Money

Let’s Practise – 1

1.

ANSWER KEY

2. a. Thirty-three rupees and twenty-five paise.

b. Twenty-one rupees and seventy-five paise.

c. Thirty-nine rupees and fifty paise.

d. Sixty-four rupees and fifty-five paise.

3. (a) ₹62.20 (b) ₹41.60 (c) ₹99.30 (d) ₹78.08

Let’s Practise – 2

1. (a) 14400 p (b) 5730 p (c) 2905 p (d) 3445 p

2. (a) ₹97 (b) ₹57.10 (c) ₹82 (d) ₹7.10

Let’s Practise – 3

1. (a) ₹139.50 (b) ₹412.50 (c) ₹ 405.50 (d) 551.70

2. (a) ₹114.50 (b) ₹93.05 (c) ₹101.50 (d) ₹122

Let’s Practise – 4

1. (a) ₹126.45 (b) ₹162 (c) ₹112.42 (d) ₹96.75

2. (a) 81 p (b) ₹17 (c) ₹6.375 (d) ₹ 8.11

Let’s Practise – 5

1. ₹314.25

2. ₹81.25

3. ₹376

4. ₹8.06

CH-11: Data Handling

Let’s Practise – 1

1. (a) 4 (b) Maggi (c) Veg Manchurian (d) 2

2. (a) Ice Cream and 24 (b) 11 (c) Patty (d) 4

Let’s Practise – 2

1. (a) 140 (b) Pear (c) Guava (d) 10

2. (a) 500 (b) 2020 (c) 2018 and 2019 (d) 900