Text Book Solutions All Class

Introduction

Imagine a world full of measuring tools and colorful adventures! In this chapter, we’ll learn how to measure using our hands, feet, and special tools like metre ropes. Get ready to compare lengths, guess distances, and have a fun as we explore the exciting world of measurement together!

Let’s Understand With a Story

Once there were two friends, Riya and Aryan. They loved playing cricket. One day, they wanted to know how long their cricket bat was.

Riya & Aryan

Aryan tried to measure it using his hands and said it was 4 hand lengths long. 

Then, Riya tried and said it was 6 hand lengths long for her.

They were confused why the bat was different lengths for each of them. 

Their mom explained, “Your hands are different sizes, so using hand length isn’t a good way to measure. You should use a ruler or a measuring tape. They give the same answer for everyone.”

Riya and Aryan understood and learned that using the right tools helps us measure things correctly. 

From that day on, they always used a ruler or measuring tape to measure things accurately.

Ruler & Measuring Tape

Now that we know why and how measurement is important, let’s understand different types of measurements.

Try yourself:

What is the most accurate way to measure the length of an object?

• A.Using hand lengths
• B.Using a ruler or measuring tape
• C.Guessing the length
• D.Comparing with other objects

View Solution

Measurement of Length – “How long?”

Have you ever wondered how people measured things long ago? They didn’t have rulers like we do now. Instead, they used parts of their bodies! Here are some of the parts they used:

• A hand span is the distance from the tip of the thumb to the tip of the little finger when the fingers are spread apart.
• A cubit is the distance from the elbow to the tip of the middle finger when the hand is stretched out.

But here’s the thing: everyone’s hand span and cubit are different like we saw in the story given above.
So when they measure something, they don’t always get the same answer. That’s why mathematicians decided to create standard units of length.Foot Scale

• In many parts of the world, people used units like inches, feet, and yards. 
• 12 inches make one foot and 3 feet (plural of foot) make 1 yard.
• But now, we mostly use the Metric system. 
• The standard unit for measuring length is called a meter, and we write it as ‘m’. 
• Longer distances are measured in kilometers (km), and smaller lengths in centimeters (cm).

So, even though people used to measure with their hands and arms, now we use meters and centimeters to measure things accurately!

For measuring lengths, we use:

• a Meter rod,
• a Measuring tape
• a Ruler.

Different tools for Measuring Lengths

A cloth merchant measures cloth by iron rod called the meter rod.

Metre Rod

15 cm Ruler

Here, the distance from the floor to a door knob is about 1 meter and the height of the plant is also about 1 meter.
There are certain things such as the following that are more than a meter long.
There are certain things like those shown below that are less than a meter long.
We use meter to measure long length and centimeter to measure short length.

Measurement of Length Using Centimeter Scale

Your finger is about 1 centimeter wide.
This will help you to estimate length in centimeter. A 15 cm or 30 cm ruler is used to measure lengths in centimeter.
To measure the length of an object, say, a sharpener, line up one of the sharpener end at the 0 mark of the ruler. The other end, touches the 2 cm mark of the ruler, so it is 2 cm long.
Similarly, we can measure the length of the following objects

• The length of the pencil is 12 cm.
• The length of the crayon is 6 cm.
• The length of the board pin is 1 cm. 
  

Try yourself:

What is the standard unit for measuring length in the Metric system?

• A.Inch
• B.Foot
• C.Meter
• D.Yard

View Solution

Measuring Distances – “How far?”

Measuring distance is like counting steps or jumps to find out how far things are from each other on a grid or map. We use units of distance, like meters, feet, km to measure the length or distance between two points.

Long distances measured using kilometers that is represented by km.

1 kilometer is about 1000 meters.

Measuring Heights – “How Tall?”

“How Tall?” is about measuring how high or tall something or someone is, like a tree or a person. We use units of measurement, like meters or feet, to find out the height from the ground to the top of the object or person.

Story Time: How tall we are?

Once upon a time in a park, there were boxes of flowers piled up high, forming a huge tower. 

• All the kids gathered around to see how tall they were compared to the tower. 
• Rajat stood next to the tower and found out he was 4 boxes tall.
  Rajat is 4 boxes tall
• Richa then stood beside Rajat and discovered she was 5 boxes tall. 
  Richa is 5 boxes tall
• Finally, Disha joined them and realized she was 3 boxes tall.
  Disha is 3 boxes tall
• The kids were amazed to see how the tower helped them understand their heights in a fun way. 
• They learned that comparing our height to something else, like a tower or a tree, can show us how high or tall we are.
  Height is usually measured in meters. 
  1 m = 100 cm

Let’s Practice

Question: Look at the picture of the flower below.  Can you guess the height of the flower with the help of the ruler given:  View Answer

Question: Upon looking at the following image, can you tell which one of the following kid is taller?  View Answer

Question: Look at the strings and help Arjun choose the longest one. How did you find out? Discuss.  View Answer

In Summary, Measurement helps us find out how long, heavy, or full something is. We use units like centimeters (cm), meters (m) and kilometers (km) to measure lengths. Always remember that:

• 1 m = 100 cm
• 1 km = 1000 m

Introduction

Welcome to the “House of Hundreds,” where we learn about three-digit numbers. In this chapter, we’ll learn about counting, make fun number patterns, and solve puzzles together. Get ready to discover the secrets of numbers and become counting champions!

Let’s Know the number neighbours

Imagine you have the number 234. We’re going to find the numbers that are close to 234, but in terms of hundreds, 50s, and 10s. Let’s break it down step-by-step.Neighbouring Hundreds

Neighbouring hundreds are the closest multiples of 100 around your number. For 234, we look for the nearest hundreds before and after it.

• Lower neighbouring hundred: The closest multiple of 100 before 234 is 200.
• Upper neighbouring hundred: The closest multiple of 100 after 234 is 300.

So, the neighbouring hundreds of 234 are 200 and 300.

Try yourself:

What are the neighboring hundreds of the number 589?

• A.500 and 600
• B.400 and 700
• C.550 and 650
• D.450 and 550

View SolutionNeighbouring 50s

Neighbouring 50s are the closest multiples of 50 around your number. For 234, we look for the nearest 50s before and after it.

• Lower neighboring 50: The closest multiple of 50 before 234 is 200. (Though 200 is also a neighboring hundred, it can also be considered here.)
• Upper neighboring 50: The next multiple of 50 after 234 is 250.

So, the neighbouring 50s of 234 are 200 and 250.

Neighbouring 10s

Neighbouring 10s are the closest multiples of 10 around your number. For 234, we look for the nearest 10s before and after it.

• Lower neighbouring 10: The closest multiple of 10 before 234 is 230.
• Upper neighbouring 10: The closest multiple of 10 after 234 is 240.

So, the neighbouring 10s of 234 are 230 and 240.

Different Ways of Representing Numbers

Let’s explore different ways to represent the numbers. 

Let’s take a number, 456. Here are various ways to write or represent it:Using “more than” a base number:

• 156 more than 300

Breaking it down into place values:

• 4 hundreds, 5 tens, 6 ones

As a single number:

• 456

As a sum of its place values:

• 400 + 50 + 6

Using “less than” a base number:

• 44 less than 500

As a subtraction from a nearby higher number:

• 500 – 44

Try yourself:

What are the neighboring 100s of the number 789?

• A.700 and 800
• B.650 and 850
• C.750 and 850
• D.700 and 900

View SolutionLet’s Practice: 

1. 68 more than 300:
   • 368 (68 + 300)
2. Breaking it down into place values:
   • 3 hundreds, 6 tens, and 8 ones
3. As a single number:
   • 368
4. As a sum of its place values:
   • 300 + 60 + 8
5. 32 less than 400:
   • 32 less than 400 is 368
6. As a subtraction from a nearby higher number:
   • 400 – 32

By understanding these different representations, you can see how the number 456 can be expressed in multiple ways, making it easier to understand its value and position within different contexts.

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What Are Number Patterns?

Number patterns are sequences of numbers that follow a specific rule or set of rules. These rules can involve adding or subtracting a certain number repeatedly to get the next number in the sequence.

Example 1: Adding 20 each time or Skip by 20 

• Starting number: 450
• Rule: Add 20

Sequence: 450, 470, 490, 510, 530, 550, …

Here’s how it works:

• Start with 450.
• Add 20 to 450 to get 470
• Add 20 to 470 to get 490
• Add 20 to 490 to get 510
• Continue this pattern to get the next numbers.

Example 2: Adding 50 each time or Skip by 50

• Starting number: 300
• Rule: Add 50

Sequence: 300, 350, 400, 450, 500, 550, …

Here’s how it works:

• Start with 300.
• Add 50 to 300 to get 350
• Add 50 to 350 to get 400
• Add 50 to 400 to get 450
• Continue this pattern to get the next numbers.

Number Patterns with Subtraction

When creating a number pattern using subtraction with bigger numbers, we’ll subtract a fixed number of tens each time to get the next number in the sequence.

Example 1: Subtracting 30 each time

• Starting number: 600
• Rule: Subtract 30

Sequence: 600, 570, 540, 510, 480, 450, …

Here’s how it works:

• Start with 600.
• Subtract 30 from 600 to get 570
• Subtract 30 from 570 to get 540
• Subtract 30 from 540 to get 510
• Continue this pattern to get the next numbers.

Example 2: Subtracting 40 each time

• Starting number: 800
• Rule: Subtract 40

Sequence: 800, 760, 720, 680, 640, 600, …

Here’s how it works:

• Start with 800.
• Subtract 40 from 800 to get 760
• Subtract 40 from 760 to get 720
• Subtract 40 from 720 to get 680
• Continue this pattern to get the next numbers.

Identifying the Rule in Larger Number Patterns

To identify the rule in a number pattern with larger numbers, look at the differences between consecutive numbers:

Example 1:  Pattern: 450, 470, 490, 510, 530, …

• Find the difference between each pair of numbers:
  • 470 – 450 = 20
  • 490 – 470 = 20
  • 510 – 490 = 20
  • 530 – 510 = 20

The rule here is to add 20 each time.

Example 2:  Pattern: 900, 870, 840, 810, 780, …Find the difference between each pair of numbers:

• 900 – 870 = 30
•  870 – 840 = 30
• 840 – 810 = 30
• 810 – 780 = 30

The rule here is to subtract 30 each time.

Try yourself:

What is the next number in the pattern 700, 680, 660, 640, …?

• A.620
• B.600
• C.610
• D.630

View SolutionCreating Your Own Patterns

You can create your own number patterns with larger numbers by choosing a starting number and a rule (either addition or subtraction by tens). For example:

1. Starting number: 650, Rule: Add 40
   • Sequence: 650, 690, 730, 770, 810, …
2. Starting number: 1000, Rule: Subtract 50
   • Sequence: 1000, 950, 900, 850, 800, …

By understanding and practicing number patterns with addition and subtraction using larger numbers, you’ll be able to recognize and create sequences that follow specific rules.

Learn with Story

Once upon a time in the town of Mathville, there lived a young detective named Noah. Noah was not an ordinary detective; he was a number detective, solving mysteries using his keen understanding of numbers and patterns.

One sunny day, Noah received a mysterious letter with a series of number riddles. Each riddle presented a clue about a specific number, and Noah’s task was to decipher these clues and find the hidden numbers. Excited for the challenge, Noah put on his detective hat and got to work.

Riddle 1: “I have 2 zeroes as digits and am very close to 99.”

Noah quickly realized that a number with two zeroes and close to 99 had to be 100. The zeroes in 100 act as placeholders, making it very close to 99.

Riddle 2: “I have 1 nine as a digit and is just 2 less than 300.”

This clue pointed to the number 298. It has one zero in the tens place and is just 2 less than 300.

Riddle 3: “I have 2 hundreds, 9 tens, and 8 ones.”

Noah recognized this as the number 298, as it has 2 hundreds (200), 9 tens (90), and 8 ones (8).

Riddle 4: “I have 2 tens and 5 ones, I am between 500 and 550, and my hundreds digit is 5.”

This described the number 525. It has 5 tens and 2 ones, is between 500 and 550, and the hundreds digit is 5.

Noah continued solving each riddle with enthusiasm, using his knowledge of place value and number sense to crack the codes. After solving all the riddles, he realized that the final mystery number was hidden in a clue about centuries and half centuries.

Riddle 5: “I am century + half century.”

This clue referred to the number 150. A century is 100, and half a century is 50. When you add them together, you get 150.

Noah felt proud of his detective skills and decided to share his solutions with the people of Mathville. 

You can also solve the number riddles just by understanding numbers more. 

Making numbers

To create a number in the hundreds using different numbers, we can break down the number into its place values and then fill in the blanks with appropriate numbers. Let’s use the example of making the number 789 using six different numbers:

1. Identify the Place Values of the Number:
   • Hundreds place: 700
   • Tens place: 80
   • Ones place: 9
2. Fill in the Blanks with Different Numbers:
   • To make 700, we can use 300 + 200 + 200
   • To make 80, we can use 40 + 40
   • To make 9, we can use 4 + 4 + 1

Putting these numbers together: 

• 700=300+200+200
• 80=40+40
• 9=4+4+1

So, to create the number 789 using six different numbers, we can use: 300+200+200+40+40+4+4+1=789300+200+200+40+40+4+4+1=789

This breakdown shows how we can represent a number in hundreds using various numbers that add up to the desired value. You can do similar to all numbers. 

In summary, we explored how numbers can be represented in various ways and learned about number patterns. We also discussed how to create number patterns using operations such as addition and subtraction. You are encouraged to try additional examples to deepen your understanding and become more familiar with these concepts.

Let’s Practice Question 1: Milin and Aditya are resting. Shubh asks them to complete the number patterns. Let us help them fill in the empty boxes.

  View Answer

Introduction

Imagine you have a yummy chocolate bar, and you want to share it with your friend. But wait! How do you make sure you both get an equal piece? That’s what we’ll learn in our exciting chapter on “Fair Share.” We’ll explore fun ways to divide treats like chocolates and parathas equally, making sharing fair and enjoyable for everyone. Sharing Things Equally

Imagine your summer vacations are going on and your best friend came to your house for a visit. Your mom prepared you a pizza and asked to share the yummy pizza with your friend. But how would you do so?

Yes, you guessed right! You’ll cut the pizza in a way that you and your friend get equal share of the pizza.

• When you cut the pizza right down the middle, you make two parts that are exactly the same size. 
• Each of these parts is called a “half” because it’s one of the two equal pieces.
  
• Now, if you take one of these halves, you have half of the pizza. But what about the other half? It’s still there, right? That’s what we call the “full” pizza. 
• When you put both halves together, you have the full pizza again!

So, what do we learnt from here?  When 1 whole is shared equally between 2 people, each share is called a half!

Try yourself:

What do we call each share when 1 whole is divided equally between 2 people?

• A.Quarter
• B.Half
• C.Full
• D.Third

View Solution

That’s how we understand the concepts of half and full—dividing things equally and knowing how the parts fit together to make the whole.

Let’s Practice!

1. You’ve  been given some shapes and you’re required to divide each shape into two equal halves using a line.

After dividing the shapes into equal halves, they would look something like :2. You’ve been given some shapes with some of their part shaded. You’re identify which one is equally shared and circle them.

The circled shapes below are the ones which are equally shared (equally halved):

Here, we haven’t circled the pizza and the paratha because:

• Pizza is not equally halved, but contains more than half of the whole.
• Paratha is not exactly halved, one half is bigger than the other half.

Great job! Now you know how to share things fairly and understand what halves are all about. You also learned how to tell when exactly half of something is shaded.Understanding Halves and Doubles 

Imagine you and your friend have some marbles. You count them and find that you have 3 marbles, while your friend has 6. That’s a lot more!

Now, let’s see what’s happening here. 

• When you have 3 marbles and your friend has 6, you can say that your 3 marbles are half of your friend’s 6 marbles.
• It’s like saying your friend has double the number of chocolates you have—twice as much!

Understanding halves and doubles helps us compare quantities. It shows how things can be divided equally or doubled up.

Learn with Stories

Once upon a time, there were two best friends named Mia and Leo. They loved spending time together, especially when it involved yummy treats. One sunny afternoon, Mia’s mom baked a delicious round cake for them to share.

• Mia and Leo sat down at the table, excited to enjoy the cake. Mia said, “Let’s cut the cake into halves so we both get an equal piece.”
• Leo asked, “What does cutting the cake into halves mean?”
• Mia smiled and explained, “Cutting the cake into halves means we divide it into two equal parts. It’s like drawing a line down the middle so we each get the same amount.”
• Mia carefully took a knife and cut the cake straight down the middle, creating two equal halves. Each half looked exactly the same, and Mia and Leo each got one half of the cake.
• Later, Mia’s mom brought out another cake, but this time it was a rectangular cake. Leo said, “Let’s try doubling this cake!”
• Mia was curious and asked, “What do you mean by doubling the cake?”
• Leo explained, “Doubling the cake means we take what we have and make it twice as big. If we have one cake, doubling it would give us two cakes.”
• Mia and Leo pretended they had another identical rectangular cake. They placed the two cakes side by side and noticed that the area covered by both cakes together was double the area of one cake.
• Leo said, “So, halving means cutting something into two equal parts, like when we split the round cake into halves. And doubling means making it twice as big, like imagining we have two rectangular cakes instead of one.”

Try yourself:

What does it mean to double a quantity?

• A.Dividing it into two equal parts
• B.Making it twice as big
• C.Adding one more to it
• D.Subtracting half of it

View Solution

Mia and Leo enjoyed their cakes, feeling happy and full, and they both learned a fun and delicious lesson about halves and doubles.

Understanding Halves and Quarters 

Imagine you have big pile of oranges.

• A half means dividing them into two equal parts. It is written as 1/2.

So, if you have 8 oranges and want to find half of them, you just need to share them equally. That means each half will have 8/2 =4 oranges.Now, let’s say you need to share your oranges with a friend, and you have to give a quarter of them.

•  A quarter means dividing them into four equal parts. It is written as 1/4.

So, if you have 8 oranges, you divide them into 4 equal parts. Each part will have 8/4 =2 oranges.  So, when you give your friend a quarter of your oranges, you’re giving them 2 oranges.
Understanding about halves and quarters helps us share things fairly and divide them equally. Whether it’s sharing oranges or anything else, learning about halves and quarters makes numbers more fun to understand!

Understanding Quarters and Wholes

Imagine you have a delicious pizza. 

As you’ve already understood about quarters,

• When we talk about quarters, we’re talking about cutting that pizza into 4 equal parts, just like four slices.

 Each slice is called a quarter. So, if you cut your pizza into four slices, each slice is one quarter of the whole pizza.Now, when we say “wholes,” we mean the complete pizza i.e. 4 slices put together. So, if you have all four quarters of the pizza, you have the complete pizza—a whole pizza!

And mathematically, we can say that:
1 quarter + 1 quarter + 1 quarter + 1 quarter = 4 quarters = 1 whole

So, 4 quarters make a whole pizza!

Edurev Tip: 

Let’s Practice 

Question: Use the clues to find the correct option. Also, Tick the correct option:
“I have less than double of 3 marbles.
I have more than half of 8 marbles.”

  View Answer

Question: You’ve  been given some shapes and you’re required to make a quarter of a whole using a line.  View Answer

Question: You’ve  been given some shapes and you’re required to tick mark the shapes which show three-quarters.  View Answer

Question: Show quarters and halves in different ways in the grids given below.   View Answer

Understanding Multiplication

Imagine you have a basket full of colourful marbles. You want to find out how many marbles are in the basket. You see that there are 4 rows of marbles as given in picture below, with each row containing 5 marbles:

1. 5 marbles in the first row,
2. 5 marbles in the second row,
3. 5 marbles in the third row, and
4. 5 marbles in the fourth row.

Instead of counting each row individually, you can use multiplication to find the total number of marbles. Multiply the number of rows (4) by the number of marbles in each row (5): 4 × 5, which equals 20.

So, there are 20 marbles in the basket!

Seeing Patterns in Multiplication Tables

Multiplication is not just about memorizing numbers—it’s also about spotting patterns.

Let’s take the 5-times table as an example:

• 1 × 5 = 5
• 2 × 5 = 10
• 3 × 5 = 15
• 4 × 5 = 20
• 5 × 5 = 25

What patterns do you see?

• The last digits keep repeating: 5, 0, 5, 0, 5, 0…
• All the answers end in either 0 or 5.

Now, can you guess the last digits of 11 × 5 and 12 × 5?

• 11 × 5 = 55 → ends in 5
• 12 × 5 = 60 → ends in 0

By noticing patterns, we can predict answers without fully calculating. This makes multiplication easier and more logical.

Try yourself:

What is the result of 6 multiplied by 3?

• A.12
• B.18
• C.15
• D.24

View SolutionUnderstanding Division

Division is a method of sharing things equally among a specific number of people. It also helps us find out how many times one number goes into another.

• Imagine you have a big box of delicious kaju katlis to share with your friends.
• Suppose you have 20 kaju katlis and 5 friends to share with.
• Instead of giving them out one by one, we can use division to see how many each friend gets.
• We start with the total number of kaju katlis, which is 20, and divide it by the number of friends, which is 5, i.e., 20 ÷ 5 = 4.
• This division can also be seen as repeated subtraction. We subtract 5 kaju katlis each time until we have none left. After the first subtraction, we have 15 kaju katlis: 20 – 5 = 15. Then, subtracting another 5 leaves us with 10 kaju katlis: 15 – 5 = 10.
• This continues until we subtract the last 5 kaju katlis, resulting in 0 kaju katlis.
• Each time we subtract 5, we count it as one friend’s share. So, from 20 shared by 5, each person gets 4 kaju katlis.

Remainders in Division

• Sometimes, if the total doesn’t divide evenly, we might have a remainder. For instance, if you had 22 kaju katlis and 5 friends, each friend would still get 4, but there would be 2 kaju katlis left over.

This is how division helps us share items fairly among a group, ensuring everyone receives their fair portion.

Learning with Story: Raksha Bandhan

Once upon a time, during the festive occasion of Raksha Bandhan, in a cosy little house, there lived a girl named Sara. Sara loved her four cousins: Alex, Ben, Clara, and David. One sunny afternoon, their grandma gave Sara a bag of 12 toffees to share equally with her cousins. Sara wanted to make sure each cousin got the same number of toffees, so she needed to figure out how to do this.

Sara decided to use a method she learned in school called division. Division helps us find out how to split something into equal parts. Here’s how Sara did it:

1. Count the Total Number of Toffees: Sara counted the toffees in the bag and found there were 12 toffees.
2. Count the Number of Cousins: Sara counted her cousins: Alex, Ben, Clara, and David. There were 4 cousins.

Sara realised she needed to divide the total number of toffees (12) by the number of cousins (4) to ensure fairness in sharing. She remembered the division symbol (÷) and set up her problem:

12 ÷ 4 = ?

To figure this out, Sara thought about it like this: if she gives 1 toffee to each cousin, she would have given out 4 toffees in total (because there are 4 cousins). She kept giving each cousin 1 toffee until all the toffees were gone.

Here’s how she did it step-by-step:

1. She gave 1 toffee to each cousin, so 4 toffees were given out (12 – 4 = 8).
2. She gave another 1 toffee to each cousin, so another 4 toffees were given out (8 – 4 = 4).
3. She gave 1 more toffee to each cousin, giving out the remaining 4 toffees (4 – 4 = 0).

Sara saw that each cousin received 3 toffees. She checked her work: 3 toffees per cousin times 4 cousins equals 12 toffees.

So, the division was correct:

12 ÷ 4 = 3

Sara was happy that each of her cousins got an equal share of toffees, and they all enjoyed their sweet treat together.

Try yourself:What is the result of dividing 16 cookies equally among 4 friends?

• A.3
• B.4
• C.5
• D.6

View SolutionWays of Grouping

Let’s talk about a fun way to count things! Imagine you have a bunch of your favorite candies. How would you count them? There are many ways, and we’ll explore some exciting methods together!

• Think about your candies . You can put them in groups to count them easily. For example, let’s say you have 12 toys. You can make 3 groups with 4 candies in each group. So, you have 3 groups of 4 candies each. That’s one way to count them! 
• Now, let’s try another way. Instead of 3 groups, let’s make 4 groups, each with 3 candies. So, now you have 4 groups of 3 candies each. That’s another way to count them! 
• Whether you make 3 groups of 4 candies or 4 groups of 3 candies, you still have the same total number of candies, which is 12.

This shows us that we can count things by grouping them in different ways, but the total remains the same! It makes counting even more fun!Number Line Skip

In the evening, the family visits the playing field. Maya and her mother discover an exciting game called “Number Line Skip.” Atya uses a stick to draw a winding number path on the ground. She asks Dhara to write the numbers starting from 0. Dhara is SKIP JUMPING BY 3.

As they played, they noticed something amazing! Starting from 0, Dhara jumps to 3. From 3, she goes to 6. From 6, she continues to 9. They realised that by adding the same number, they could predict the next jump. Let’s look at Dhara’s jumps:

• 1 jump → 3
• 2 jumps → 3 + 3 = 6 = 2 x 3
• 3 jumps → 3 + 3 + 3 = 9 = 3 x 3
• 4 jumps → 3 + 3 + 3 + 3 = 12 = 4 x 3, and so on.

They also had a fun challenge: “Guess and write the next number she will jump to.” Atya places a flower on 12. “Skip jump with equal steps to reach the flower,” she instructs. No direct jumping to the flower is allowed.

Now, they hopped and laughed, discovering the wonders of numbers. The one who reaches the flower in the smallest number of jumps wins!Writing Tables

In the Fun Way of Writing Tables game, a little boy Aryan and his friends found a cool way to learn their times tables using sticks. They made a grid with sticks and counted where they crossed to figure out the answers.

Here’s how they did it:

• Aryan lined up sticks in rows and columns to make a big square grid. 
• Then, he counted where the sticks crossed to find the answer to different multiplication questions. For example, to find out what 5 times 3 is, she counted where the row labelled “3” and the column labelled “5” crossed.
• He noticed a pattern in the answers, like how the last numbers repeated in some of them. This helped her understand how numbers work together.
• Following the same pattern, they discovered some other tables as well,which are shown below: 
• Aryan and his friends also saw something cool when they looked at the tables for 2, 3, and 5. They noticed that some numbers had a special connection with others. This made them curious, and they wanted to explore more!
• As you can see, when we multiply 1 with 2, we get 2; when we multiply 1 with 3, we get 3 and when we multiply 1 with 5, we get 5.
• So, we can say that any number multiplied to 1 results in the same number.

By playing this game, Aryan and his friends had fun while learning about multiplication tables and discovering new patterns in numbers. Math became an exciting adventure for them!

Try yourself:

What is the result when 4 is multiplied by 7?

• A.24
• B.28
• C.30
• D.32

View SolutionWord Problems

Word problems play a crucial role in mathematics as they enable students to use their knowledge of basic arithmetic like addition, subtraction, multiplication, and division in everyday situations. Here are some examples of these types of problems.

Examples of Word Problems

1. There are 5 fruits in each basket. If there are 9 baskets filled with fruits, how many fruits are there in total?
Solution: Number of fruits in one basket = 5
Number of baskets = 9
Total fruits = Fruits per basket × Number of baskets = 5 × 9 = 45
Therefore, there are 45 fruits altogether.

2. Donald, the duck can see 60 legs in a cow shed. How many cows are there in the shed?
Solution: Total number of legs = 60
Number of legs per cow = 4
Total number of cows in the shed = 60 / 4 = 15
So, there are 15 cows in the shed.

By working through these examples, you can become more comfortable with division and multiplication.

Let’s Practice

Question: Each cycle needs 2 wheels. How many cycles can be fitted with 12 wheels?

  View Answer

Introductions

Let’s Understand with Story

On a bright sunny day at the busy carnival, Ajit, Tom, and Joy came across a stall filled with yummy toffees. Joy quickly picked up two toffees, which led to a fun guessing game among the friends. “Guess how many toffees are in the boxes. Count and check.” This began a sweet journey of counting and discovery.

To count the toffees easily, they began with these numbers: 10, 20, 30, … 100, 110, 120, … 190, 200, 210, … 290, 291, 292, 293, 298. Jojo has 2 toffees in his hand. How many toffees do they have altogether? 298 plus one more makes 299; 299 plus one more makes 300.

• How many more triangles are needed to make 300?
• How many bangles are there less than 300?
• Which is more: bangles or triangles?

Guessing and Counting Toffees

• Jojo starts with two toffees in his hand and checks the boxes.
• They counted: 10, 20, 30, … 100, 110, 120, … 190, 200, 210, … 290, 291, 292, 293, 298.
• In total, they counted 298 toffees; adding one gives 299.
• Joy smiled and said, “299 and one more is 300!”
• They celebrated reaching the magical number of 300 toffees.

1. Joy is hopping on the tiles at the fair. Can you guess the missing numbers below:

Have you tried guessing the numbers yet? If not, that’s okay! The missing numbers have been given below for you:

2. Imagine there are some ants on the ground that found some food. Can you guess how many ants there might be? After making a guess, let’s count them together to see if our guess was correct.

Hint:

Well done! You’ve guessed the right number. So, the total number of ants are 127. 

Try yourself:Joy has 4 boxes of candies. If the first box has 72 candies, the second box has 85 candies, and the third box has 67 candies, how many candies are in the fourth box if the total number of candies is 282?

• A.40
• B.75
• C.86
• D.58

View SolutionWriting Number Sentences

To help children in developing a method for counting accurately, we can use matchsticks to visualise numbers. For instance, we can create large numbers using matchsticks or any other common materials found at home and bring them to school.

Consider two large bundles of matchsticks. Each large bundle contains 10 smaller bundles, and each of these smaller bundles has 10 matchsticks. To calculate how many matchsticks are in one large bundle, we multiply: 10 (small bundles) x 10 (matchsticks in each small bundle) = 100 matchsticks in one large bundle. Since we have two large bundles, we multiply 100 (matchsticks in one large bundle) x 2 (large bundles) = 200 matchsticks in total from the large bundles.

Now, we have 3 small bundles left over along with 5 extra matchsticks. Each of these small bundles has 10 matchsticks, so we multiply: 3 (extra small bundles) x 10 (matchsticks in each small bundle) = 30 matchsticks from the extra small bundles. Adding the 5 extra matchsticks gives us 30 + 5 = 35 matchsticks. Therefore, in total, we have 200 matchsticks from the large bundles and 35 matchsticks from the small bundles and extra matchsticks, resulting in a total of 235 matchsticks.

We can express the number 235 in the following ways:

• 200 and 35 more (200 + 35)
• 15 less than 250 (250 – 15)

Number Fun: Up and Down We Go!

Once upon a time, there were five friends named Jack, Lily, Ben, Mia, and Sam. They were all going on a camping trip together.

• Jack brought 5 apples for everyone to share. He gave one apple to Lily, so they had 5 apples in total. Adding 1 made the number of apples bigger.
• Meanwhile, Ben had 10 marshmallows to roast over the campfire. But Sam accidentally dropped 2 into the fire, leaving them with only 8 marshmallows. Taking away 2 made the number of marshmallows smaller.

By adding more or taking some away, the number of items they had changed during their camping adventure! Now, let’s explore numbers! We’ll learn how to increase or decrease them.

Increasing and Decreasing Numbers

• 285 – increase the number by one
  Sol: To make the number bigger, we add one: 285 + 1. This gives us 286.
• 147 – increase the number by ten
  Sol: To increase the number, we add ten: 147 + 10. This results in 157.
• 367 – decrease the number by 2
  Sol: To make the number a bit smaller, we take away 2: 367 – 2. This gives us 365.
• 289 – decrease the number by 10
  Sol: To reduce the number, we take away 10: 289 – 10. This results in 279.
• 290 – increase the number by 20
  Sol: To make the number bigger, we add 20: 290 + 20. This gives us 310.

Now, let’s compare some numbers using the signs (> or <) to=”” see=”” which=”” is=”” greater=”” or=””>

• 199 < 221
• 285 > 275

Yay! You’ve learnt how to make numbers bigger and smaller. Well done!

Counting the Number of Letters in Number Names

Counting the letters in number names is an enjoyable way to practise counting. Here’s how you can do it:

• Write Down the Number: Begin by writing the number you want to count the letters for. For example, let’s use the number “Eleven.”
• Spell Out the Number: Write the number in words. “Eleven” is spelled E-L-E-V-E-N.
• Count the Letters: Count each letter in the word. “Eleven” has six letters: E-L-E-V-E-N.
• Repeat for Other Numbers: You can do this for other numbers too. For instance, “three” has five letters (T-H-R-E-E), “seven” has five letters (S-E-V-E-N), and “twenty” has six letters (T-W-E-N-T-Y).

Magical Count: Write down any number name. Count the letters in that name and then write down the new number name. Keep repeating. 

Writing Numbers in Sentences

• When we count or discuss numbers, we use special words known as number names.
• These help us express numbers in words rather than just digits. Let’s explore how to write number names for three-digit numbers.
• Three-digit numbers consist of three digits. We read them from left to right, just like reading words in a book.
• The number 123 contains three digits: 1, 2, and 3. Each digit has its own place: hundreds, tens, and ones.
• To write three-digit numbers in words, we start by stating how many hundreds, then how many tens, and finally how many ones. For example: The number 123 is written as “one hundred twenty-three.”
• We say (i) “one hundred” for the hundreds place , (ii) “twenty” for the tens place , and (iii) “three” for the ones place.

Let’s look at some examples of three-digit numbers:

• 256: This is read as “two hundred fifty-six.”
• 378: This is read as “three hundred seventy-eight.”
• 429: This is read as “four hundred twenty-nine.”

Counting the Letters

• In the colorful land of Numerica, there were three best friends: Two-hundred and Thirteen, Three Hundred and Sixty Seven, and One Hundred and Ten. They wanted to know whose name was the longest, so they decided to count the letters in their names
• They gathered around a magical counting tree, where each leaf had a letter written on it. (i)  Two-hundred and Thirteen suggested they count the letters in their names. (ii)Three Hundred and Sixty Seven suggested they take turns counting each other’s letters to make sure they didn’t miss any.
• They started with Number Two-hundred and Thirteen and counted 21 letters.
• Then, they counted 23 letters in Number Three hundred and Sixty Seven. 
• Finally, they counted 16 letters in Number One Hundred and Ten. 
• They discovered that Number Three hundred and Sixty Seven had the longest name with 25 letters.

They agreed that each of their names was unique and special. They were happy to learn how to count the letters in their names.

Try yourself:Which number name has the most letters in it?

• A.Two hundred and thirteen
• B.Three hundred and sixty seven
• C.One hundred and ten
• D.Four hundred and fifty two

View SolutionCounting Numbers on a Number Line

Number Line

A number line is a helpful way to show numbers in order from the smallest to the largest. It helps us see how numbers relate to one another. The number line includes positive numbers, negative numbers, and zero.

Picture yourself at one end of the number line. As you move along it, you’ll notice the numbers increase. If you go the opposite way, the numbers decrease.

Counting on a number line is similar to taking steps. For instance, if we count from 100 to 110:

• Start at 100
• Step to 101
• Then to 102
• Next to 103
• Finally, reach 110

The number line also includes zero, an important number that acts as a middle point. To the left of zero, we have negative numbers which are less than zero, such as:

• -1
• -2
• -3

So, number lines help us understand how numbers are arranged and how we can move between them. Grasping both positive and negative numbers on the number line is essential for understanding basic mathematical ideas.Understanding Place Value

• In maths, every number consists of different parts known as digits.
• Each digit has a specific value depending on its position in the number, which we call place value.
  For example, consider the number 786. In this number:
• 
  • The digit 7 is in the hundreds place, giving it a value of 700.
  • The digit 8 is in the tens place, making its value 80.
  • The digit 6 is in the ones place, so its value is just 6.

Together, these values add up: 700 (from 7 hundreds) + 80 (from 8 tens) + 6 (from 6 ones) equals 786. Understanding place value helps us grasp the value of larger numbers.

Now let’s take the number 24 as an example.

• It has two digits.
• The digit 4 represents four single items, and it’s placed in the ones position.
• The digit 2 in the tens place represents two bundles of ten items each, which makes twenty.
• So, when we combine the value of 20 with the value of 4, we get the number 24.

Comparing Numbers

 ‘=’ is the symbol used for ‘equal to‘.

• 3 = 3 is read as ‘3 is equal to 3’.
• Look at the numbers from 11 to 20 in order.  The number 13 is to the left of 14. So, 13 < 14. The number 14 is to the right of 13. So, 14 > 13. Every number is equal to itself. 14 = 14, 15 = 15, 16 = 16, etc.

Note:

• When comparing two numbers, help children focus on the quantities that the numbers represent.
• Use Dienes block representation to show that 1 H is more than 1 T and 1 O. Similarly, 1 T is more than 1 O.

Comparing 3-digit Numbers

• To compare numbers, we check their hundreds, tens, and ones places.
• If the hundreds places are the same, we move to the tens. If those are equal, we then look at the ones place.
• Encourage children to think about what the numbers actually represent.
• Use Dienes blocks to illustrate that 1 H is greater than 1 T and 1 O, and that 1 T is greater than 1 O.
• Examples: (i) 329 and 392: Both have three hundreds, but 329 has 2 tens while 392 has 9. Thus, 392 is greater. (ii) 235 and 523: 235 has 2 hundreds and 3 tens, while 523 has 5 hundreds. So, 523 is greater. (iii) 157 and 153: 157 has 7 ones, while 153 has 3. Therefore, 157 is greater. (iv) 432 and 423: Both have four hundreds, but 432 has 3 tens compared to 2 in 423. Thus, 432 is greater.

Ascending and Descending Orders

When it comes to numbers, putting them in order from the largest to the smallest is called descending order or decreasing order. On the other hand, putting them in order from the smallest to the largest is called ascending order or increasing order.

• Moving from the largest number to the smallest is known as descending order.
• Moving from the smallest number to the largest is known as ascending order.

For instance, the numbers 2, 4, 5, 8, and 9 are arranged in ascending order, while 9, 8, 5, 4, and 2 are in descending order.

To compare numbers, we use the symbols > (greater than) and < (less= than)=”” to=”” indicate=”” their=”” relationships.=”” for=””>

• 199 < 201, which means 199 is less than 201.
• 285 > 275, indicating that 285 is greater than 275.

Now, let’s compare the following numbers and use the symbols > and <>

1. 185 < 211.
2. 295 > 265.

Consider these examples:

• 432 is > 423 because both have four hundreds, but 432 has 3 tens while 423 has 2 tens.
• 329 is < 392 because both have three hundreds, but 329 has 2 tens while 392 has 9 tens.
• 110 is > 11 because 110 has 1 hundred while 11 has no hundreds (zero hundreds).

Try yourself:What is the ascending order of the numbers 456, 564, 645, and 546?

• A.456, 546, 564, 645
• B.456, 564, 546, 645
• C.645, 564, 546, 456
• D.546, 564, 645, 456

View SolutionUse of > or < in Forward and Backward Counting

• Jiya starts climbing the stairs from stair number 11. She has to reach stair number 20 to pick up her pencil pouch that she dropped there.
• As she climbs up, she counts upwards as 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. On her way down with the pencil pouch, she counts backwards as 20, 19, 18, 17, 16, 15, 14, 13, 12, and 11.
• 11 < 12 < 13 < 14 < 15 < 16 < 17 < 18 < 19 < 20 shows the ascending order of numbers from 11 to 20. 20 > 19 > 18 > 17 > 16 > 15 > 14 > 13 > 12 > 11 shows the descending order from 20 to 11.

Numbers get “bigger/greater” when counting forward and “smaller/lesser” when counting backward.Forming 3-Digit Numbers

Sometimes, we are given certain digits and asked to make the smallest and greatest 3-digit numbers without using any digit more than once.

Forming the Greatest Number

• To create the greatest number, arrange the digits in descending order, starting from the hundreds place.
• Select the largest digit for the hundreds place, the next largest for the tens place, and the smallest for the ones place.

Forming the Smallest Number

• To create the smallest number, arrange the digits in ascending order, starting from the hundreds place.
• Choose the smallest non-zero digit for the hundreds place, the next smallest for the tens place, and the largest for the ones place.

Examples:

• Digits: 3, 7, 2
  Greatest 3-digit Number: 732 (Descending order: 7 > 3 > 2)
  Smallest 3-digit Number: 237 (Ascending order: 2 < 3=””><>
• Digits: 5, 6, 2
  Greatest Number: 652 (Descending order: 6 > 5 > 2)
  Smallest Number: 256 (Ascending order: 2 < 5=””><>

Let’s Practice!

Question 1: Fill these:

  View Answer

Question 2: Write down any number name. Count the number of letters in that number name and write the name of that new number down. Keep repeating — what happens?

  View Answer

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Have you ever noticed the door in your classroom, a slice of pizza, or your school clock?

• All of these are shapes—the building blocks of everything around us!
• Today we will look, draw, and play with four shapes:
  1. Rectangle
  2. Square
  3. Triangle
  4. Circle

Let’s begin our shape adventure!

Rectangle

A rectangle is a shape with four sides where opposite sides are the same length, and all the angles are right angles.

Try yourself:

Which of the following objects is most likely to be in the shape of a rectangle?

• A.Soccer Ball
• B.Book
• C.Clock
• D.Pizza

View Solution

Parts of a Rectangle:

• Sides: Rectangles have four sides. The longer sides are called the length, and the shorter sides are called the breadth.
• Corners & Angles: Rectangles have four corners where two sides meet at right angles, giving the shape a sharp and clear look.

Common objects that are rectangles include a blackboard, a TV screen, and a ruler. These items are often found in our daily lives and have specific uses.

Rectangles Around Us

Square

A square is a unique kind of rectangle and also a four-sided shape where all four sides are the same length.

Parts of a Square:

• Sides: Squares have four equal sides, meaning each side is the same length.
• Corners: The corners of a square form right angles (90 degrees).

For Example– Chess Board, Carrom Board , Clock

Squares around us

Similarities and Differences in Rectangle and SquareA rectangle and a square are both flat shapes with four straight sides and four corners. In fact, a square is just a rectangle that has all its sides the same length! Here’s what they share:

• Four sides
  Both shapes have exactly four straight sides.
• Opposite sides the same length
  In each shape, the top and bottom sides match in length, and the left and right sides match too.
• Four right-angle corners
  Every corner in a rectangle or a square is a “right angle” (just like the corner of a book).
• Remember:
  Every square is a rectangle because it follows all these rules.
  But not every rectangle is a square, since rectangles only need their opposite sides to be equal—not all four.

Triangle

A triangle is a shape with three sides and three corners. It looks like a slice of pizza or a traffic sign.

Parts of a Triangle:

• Sides: Triangles have three sides. Each side is a straight line that connects two corners.
• Corners (Vertices): Triangles have three corners where the sides meet. These corners are called vertices. Each vertex is where two sides come together.
  
  
• For Example: Slice of Pizza, Pyramid, Slice of watermelon

Triangles around us

Circle

Think of a circle as a round cookie. It’s a shape with no corners, and when you draw it, you start at one point and go all the way around until you return to the start.

• Centre of a circle: The centre of a circle is the dot in the middle that is the same distance from every point on the edge of the circle.

• Radius of Circle: If you draw lines from the centre to the edge, they will all be equal in length. This distance is known as the radius.
  
• The diameter is two times the radius and is the longest line that passes through the centre. 
  
• The total distance around the circle is called the circumference.
  

Try yourself:

What is a shape with three sides and three corners called?

• A.Rectangle
• B.Circle
• C.Square
• D.Triangle

View Solution

Combination of Shapes

We can make all sorts of things by combining different shapes creatively. Here are a few examples:

1. House: A house can be made using rectangles for the walls, a triangle for the roof, squares or rectangles for windows, and circles for doorknobs or windows.

2. Car: A car might have rectangles for the body, circles for wheels, and triangles for headlights or the hood.

3. Tree: A tree can be made using a rectangle for the trunk, circles for leaves, and triangles for branches.

4. Robot: A robot could have rectangles for the body and limbs, circles for eyes or buttons, and triangles for decorations or parts of its design

5. Rocket: A rocket might use cylinders for the body, cones for the top or nose, rectangles for fins, and circles for windows or portholes.

By combining shapes in different ways, we can create all sorts of objects, from everyday things like houses and cars to imaginative creations like robots and rockets! It’s like putting together pieces of a puzzle to build something new and exciting.

How Do We Draw Shapes?

Take a pencil and paper—let’s make some shapes! There are two kinds of lines you can draw:

Two Main Types of Lines

• Straight lines are like the edges of a square or a rectangle. They don’t bend or curve; they just go straight from one point to another.
• Curved lines are like the edges of a circle or an oval. They bend and are not straight. They can be round or stretched out like an oval.

Try yourself:

What type of lines are like the edges of a circle or an oval?

• A.Straight lines
• B.Curved lines
• C.Dotted lines
• D.Wavy lines

View Solution

Shapes can also have different angles, which are important for classifying them. For example:

• A triangle has three angles.
• A rectangle has four right angles.

When you combine straight and curved lines in various ways, you can create all sorts of shapes like triangles, circles, squares, and rectangles. It’s like using building blocks to create different structures!

Introduction

Today, let’s explore how we add and take away numbers, and why these are super useful.

Addition is like putting things together. Imagine you have a pile of marbles. If you add more marbles to that pile, you end up with a bigger pile. For example, if you have 3 marbles and you add 2 more marbles, you will have 3 + 2 = 5 marbles in total.

Subtraction is like taking things away. Let’s go back to our marbles. If you have 5 marbles and you take away 2 marbles, you will have 5 – 2 = 3 marbles left.

So, addition makes things bigger by adding more, and subtraction makes things smaller by taking away. They’re like the opposite of each other!

Try yourself:

What does addition do to a number?

• A.Makes it smaller
• B.Makes it bigger
• C.Keeps it the same
• D.None of the above

View Solution

Learn with Story- Addition & Subtraction

Once upon a time, there were two kids named Suman and Aditya. They had six plant seeds that they wanted to plant in their garden. So, they decided to ask their grandpa for help. 

• Grandpa was very happy to see the kids doing something good, so he gave them four more seeds. 
• This is like adding because now they had 6 + 4 = 10 seeds in total.
• Excitedly, Suman and Aditya went to their garden. 
• They first planted two seeds next to the mango tree. 
• Now, they had 10 – 2 = 8 seeds left. 
• Then, they planted four seeds near the flowers. 
• Subtracting these, they had 8 – 4 = 4 seeds left. 
• Finally, they planted the remaining four seeds near the lemon tree. 
• This left them with 4 – 4 = 0 seeds, which meant they had used up all their seeds.

The kids were so happy to see their garden full of newly planted seeds, all thanks to their teamwork and Grandpa’s help!

Try yourself:What is the result of adding 7 and 5?

• A.12
• B.11
• C.13
• D.14

View Solution

Tens Frame

A tens frame is a simple math tool used to understand numbers in groups of ten. It consists of a rectangular frame with ten boxes or squares arranged in rows of five. Each box can hold one object, like a counter or a dot.

Addition using Tens Frame

Let’s say you have a tens frame with 6 counters placed in it. 

• This means that 6 out of the 10 boxes are filled, and there are 4 empty boxes.
• Now, if you add 4 more counters to the tens frame, you’ll fill up the remaining 4 empty boxes. 
• Counting all the counters, you’ll find that there are now 6 + 4 = 10 counters in total, filling the entire tens frame.

Subtraction using Tens Frame

Starting with a full tens frame of 10 counters, each box containing one counter, if you take away 2 counters, you’ll remove them from the filled boxes. 

• Now, you’ll have 8 counters remaining, filling 8 out of the 10 boxes on the tens frame.
• Continuing with subtraction, if you take away 4 more counters, you’ll remove them from the filled boxes. Now, you’ll have 4 counters remaining, filling only 4 out of the 10 boxes on the tens frame.
• Finally, if you take away the last 4 counters, you’ll remove them from the filled boxes, leaving the tens frame completely empty with 0 counters.
• Using the tens frame helps us see how adding fills up spaces, and subtracting takes away from those filled spaces, making it easier to understand addition and subtraction with numbers.

Try yourself:

In a tens frame with 8 counters placed, how many more counters are needed to fill it completely?

• A.2 counters
• B.10 counters
• C.5 counters
• D.3 counters

View Solution

Learn with Story- Using Number Line

Once upon a time, two kids named Maya and Arjun were sitting together, trying to solve a math problem that involved adding numbers bigger than 10. 

• They had a tens frame in front of them, which they were using to understand smaller numbers easily. 
• However, when it came to bigger numbers like 24 + 32, they started feeling confused.
• Just then, their elder brother Rahul walked into the room. 
• Seeing their puzzled faces, Rahul asked what they were working on. 
• Maya and Arjun explained that they were trying to add 24 and 32 using the tens frame but were finding it difficult.
• Rahul smiled and said, “Let me show you an easier way to do this using a number line.” 
• He drew a long line on a piece of paper and marked 24 on it. 
• “First, we start with 24,” Rahul explained. “Now, to make it easier, let’s add 6 steps to reach 30.” He marked 30 on the number line.
• “Next,” Rahul continued, “we add 10 more steps to reach 40.” 
• He marked 40 on the number line. “Then, another 10 steps to reach 50,” he added, marking 50 on the line. 
• “Finally, we add the remaining 8 steps to reach 58, which is our answer.”
• Maya and Arjun looked amazed. 

They could visually see each step of adding, making the process less confusing and more enjoyable.

Using number lines makes calculations easy because it breaks down the process into smaller, manageable steps that are visually represented. This helps in understanding the concept of addition or subtraction by visually seeing the progression of numbers, making it less daunting and more intuitive for learners.

Now, let’s help Arjun and Maya in subtracting 22 from 54 using the same method of the number line:

1. Start with 54 on the number line.
2. Subtract 10 to reach 44.
3. Subtract 10 more to reach 34.
4. Subtract 2 more to reach 32.

So, 54 – 22 = 32.

From that day on, Maya, Arjun, and Rahul always used the number line for bigger calculations, finding it to be a helpful and fun way to solve math problems.

Try yourself:

What is the missing number in the grid below?

Grid:
1 4 ?
2 5 8
3 6 9

• A.7
• B.10
• C.11
• D.12

View Solution

Number Grid

A number grid is like a map of numbers arranged in rows and columns. It’s similar to the grid used in games like Snake and Ladders, where each square in the grid contains a number. 

For example, a number grid from 1 to 100 would have 10 rows and 10 columns, with numbers ranging from 1 to 100 distributed across the grid.

• Using a number grid can help us visualize and understand mathematical operations like addition, subtraction, and movement in a structured way. Let’s take the example you mentioned:
• If we start at 8 on the number grid and move 2 steps up, we land on 28. This is because each step up in the grid adds 10 to the number. So, from 8, going up 2 steps means adding 10 twice (8 + 10 + 10 = 28).
• Similarly, if we start at 28 and move 2 steps to the right, we land on 30. This is because each step to the right adds 1 to the number. So, from 28, moving right 2 steps means adding 1 twice (28 + 1 + 1 = 30).
• Conversely, if we move to the left, each step subtracts 1 from the number. For example, if we start at 30 and move 2 steps to the left, we land on 28 (30 – 1 – 1 = 28).

In this way, a number grid helps us visualize and perform calculations by understanding the patterns of addition and subtraction associated with movement in different directions on the grid. It’s a useful tool for learning and practicing mathematical operations in a structured and interactive manner.

Solving Puzzle- Magic Sum

Imagine you have a 3×3 grid, like a small square divided into 3 rows and 3 columns. Each box in the grid has a number in it, but some boxes are blank. You also know the total sum for each row and column.

Let’s solve it step by step:

Horizontal Sum

1. First row: The given sum is 15, and you have 2 and 8 already. Adding them gives 10, so the blank box should be 15 – 10 = 5.
2. Second row: The given sum is 10, and you have 3 already. Subtracting 3 from 10 gives 7 for the first blank box. Then, the second blank box must be 0 to make the sum correct.
3. Third row: The given sum is 20, and you have 4 already. Subtracting 4 from 20 gives 16 for the first blank box. Then, the second blank box must be 0.

Vertical Sum

1. First column: The given sum is 17, and you have 3 already. Subtracting 3 from 17 gives 14 for the first blank box. Then, the second blank box must be 0.
2. Second column: The given sum is 7, and you have 2 already. Subtracting 2 from 7 gives 5 for the blank box.
3. Third column: The given sum is 21, and you have 7 already. Subtracting 7 from 21 gives 14 for the first blank box. Then, the second blank box must be 0.

So, the completed grid looks like this:

Now that we’ve learned how to add, subtract, and solve grid puzzles with bigger numbers, let’s keep practicing getting even better at math!

Try yourself:

What is the result of 37 – 15?

• A.22
• B.20
• C.18
• D.14

View Solution

Bundle

• A bundle is a group or collection of items put together.
• In mathematics, we often make bundles to count more easily.
• A common example is bundling 10 sticks.
• Together to form one group or bundle of 10.

Why Do We Use Bundles?

• Helps in counting large numbers.
• Easy to count when we group things in bundles, especially in tens.
• It helps in understanding place value(tens and ones).

Example:

Suppose you have 14 pencils.

• First, make a bundle of 10 pencils.
• Then, you will have 1 bundle of 10 pencils and 4 loose pencils left.
• So, 14 pencils = 1 bundle of 10 + 4 pencils.

Counting in 10s:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100. 

Example: You have 10 apples in a basket. If Nani Maa adds 10 more apples each time, how many apples will you have after counting by 10s?

• Start with 10 apples.
• Add 10 more to get 20 apples.
• Add 10 more to get 30 apples.

Let’s do Addition to find total number of sticks:

                                                                                                           85 sticks + 67 sticks =  Total 152 sticks

Nisha and Nandni both collected sticks. Who collected more Nisha or Nandni? How much more?

Total no of Nisha’s stick = 85
Total no of Nandni’s stick = 67    

       85 sticks – 67 sticks =  18 sticks

       Nisha collected 18 sticks more than Nandni.

Try yourself:Raju sold 45 books on Monday and 68 books on Tuesday. How many books did he sell in two days?

• A.103 books
• B.113 books
• C.120 books
• D.23 books

View Solution

We practiced our math skills while playing games and enjoyed every moment with our family. Nani’s house was a special place where numbers and fun came together, making each day an exciting new lesson.

Until next time, keep counting, keep learning, and remember that every day can be an exciting new math adventure!

Chapter notes

A long time ago, people did not have number symbols like we do today. Instead, they made little marks on cave walls and tree bark to count things. Now, we use just ten digits—0, 1, 2, 3, 4, 5, 6, 7, 8, and 9—to write any number, big or small. Let’s see how this amazing system works!Ancient Methods of Counting

Counting with Groups

• Long ago, people counted things by grouping them into 5s, 10s, 20s, or even 60s. This made it easier to keep track of their things and trade with others.
• Thousands of years ago, ancient Indians created a special system using just ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This was one of the greatest inventions in history!
  
• Thanks to this number system, we now have TVs, computers, mobile phones, and many other technologies!

The Importance of Zero

• A long time ago, people had no way to write “nothing.” Then, they invented zero (0)!
• This small number made a big difference! It helped make counting and math easier. Because of zero, we can do big calculations and solve tricky problems.

Now, this number system is used all over the world!

Sachin’s 99→100 SurpriseOne day, Sachin’s homework was to add 1 to every number:

• 1 + 1 = 2
• 2 + 1 = 3
• 23 + 1 =24
• 56 + 1 = 57
• … he kept going until he saw 99 + 1 = ?

Sachin scratched his head.
Just then his brother Vivek popped in.

Vivek: “What’s up, Sachin?”
Sachin: “I’m stuck at 99—what comes next?”
Vivek: “Easy—100!”

Sachin’s eyes lit up: “Oh—I get it now! 99 + 1 is 100!”

Vivek (smiling): “Numbers keep going forever. There’s always more to learn!”

Making 100

In math, we can make 100 in different ways by adding two numbers together. Let’s look at some examples:

• 90 + 10 = 100
• 80 + 20 = 100
• 70 + 30 = 100
• 60 + 40 = 100
• 50 + 50 = 100

This means there are many ways to make 100.

Using Matchsticks to Make 100

We can also use matchsticks to understand numbers.

If we take 10 bundles of matchsticks, with 10 sticks in each bundle, we get 100 matchsticks in total.

Try this:

• Count 10 matchsticks and make a bundle.
• Keep making bundles until you have 100 matchsticks.
• How many bundles do you need? (Answer: 10)

You can also try this with seeds, beads, or buttons to practice counting and making 100 in different ways.

Try yourself:

What is the result of 75 + 25?

• A.95
• B.100
• C.110
• D.120

View Solution

Let’s Learn by Practicing

Tanya and Reema, two friends who loved math, found a fun game one day. Tanya had learned in class how to make 100 by adding different numbers together. She was excited to share it with Reema.  

Tanya & Reema

• Tanya excitedly explained, “We can write down any five numbers between 1 and 99. Then, I’ll add another number to yours to make it 100!”
• Reema smiled and wrote down her five numbers: 20, 35, 42, 68, and 75.
• Tanya smiled and said, “Let’s begin!” She took Reema’s first number, 20, and added 80 to it, making it 100. “20 + 80 = 100!”
• Next, she looked at 35, added 65, and said, “35 + 65 = 100!”
• They kept playing, mixing numbers in fun ways. Tanya added 58 to 42, 32 to 68, and 25 to 75, making each one equal 100.

Exploring Other Ways to Make 100

• Besides the combinations Tanya made, we can use matchstick bundles and a number line to visualise making 100 in various ways. For example, using 10 matchsticks for tens and 1 for units can help us understand reaching 100.
• We can also estimate the number of objects, like oranges or bangles, to see how they can be grouped to make 100. This estimation improves our understanding of quantities.
• Another fun game involves using claps, snaps, and pats to represent numbers. For example, one clap could mean 100, one snap could mean 10, and one pat could mean 1. This interactive game aids in visualising numbers and their combinations.
• Just like the combinations Tanya made, many other ways exist to make 100 using different numbers. Let’s keep exploring creative number combinations!

Counting After 100

After reaching 100, counting continues in a similar way. Here’s how it works:

1. Using Hundreds:

• 100 + 1 = 101 (One Hundred One)
• 100 + 2 = 102 (One Hundred Two)
• 100 + 3 = 103 (One Hundred Three)

2. Hundreds and Tens:

• 100 + 10 = 110 (One Hundred Ten)
• 100 + 20 = 120 (One Hundred Twenty)
• 100 + 30 = 130 (One Hundred Thirty)

3. Hundreds and Ones:

• 100 + 5 = 105 (One Hundred Five)
• 100 + 8 = 108 (One Hundred Eight)
• 100 + 15 = 115 (One Hundred Fifteen)

To express numbers beyond 100, we use ten symbols (0-9) which help us write all numbers, where each place value (hundreds, tens, ones) is important in forming these numbers.

Try yourself:

What comes after 99 when counting?

• A.98
• B.100
• C.97
• D.101

View Solution

Number NamesUnderstanding Numbers Beyond 100

• Just as numbers below 100 have names, numbers above 100 do too.
• We will look at how these number names are structured.

Understanding 100

• Are these 100? 
  Yes, 10 bundles of 10 sticks make one bundle of 100.

Let’s Learn Names!

Once upon a time, there was a boy named Rahul who loved to learn new things. One day, he wanted to learn the names of numbers above 100, but he found it a bit difficult. He struggled to say numbers like 101, 105, or 110.

Names of Numbers Above 100

Rahul & Anju

• Rahul felt a bit frustrated, but then his older sister Anju noticed his confusion. Anju was great at explaining things simply.
• Anju sat down with Rahul and said, “Let me show you how to name numbers above 100, Rahul. It’s easy!”
• She started with 100 and explained, “When we have 100 and add 1, it becomes One Hundred One. We just say ‘One Hundred’ and then add the next number.”
• Rahul’s eyes lit up with understanding. “Oh, so 100 and 2 is One Hundred Two, right?”
• Anju nodded, “Exactly! You’re getting it.”
• Next, she showed him 100 and 5, saying, “When we have 100 and add 5, it’s One Hundred Five.
• Then she explained, “100 and 9 make One Hundred Nine. “
• Finally, she said, “And 100 and 10 makes One Hundred Ten.”

Examples

• 109 – One Hundred Nine
• 123 – One Hundred Twenty Three
• 150 – One Hundred Fifty
• 157 – One Hundred Fifty Seven
• 159 – One Hundred Fifty Nine

Explanation

• 109 – Here we have a Hundred and a Nine, so its name will be One Hundred Nine.
• 123 – One Hundred + Twenty Three = One Hundred Twenty Three
• 150 – One Hundred + Fifty = One Hundred Fifty
• 157 – One Hundred + Fifty Seven = One Hundred Fifty Seven
• 159 – One Hundred + Fifty Nine = One Hundred Fifty Nine

From that day on, Rahul was confident in naming numbers above 100, thanks to his sister’s clear explanations and patient teaching.

Try yourself:

What is the number name for 145?

• A.One Hundred Forty Five
• B.One Hundred Fifty Four
• C.One Hundred Forty Six
• D.One Hundred Forty Seven

View Solution

Let’s Learn Combinations!

Once upon a time, there was a clever little dog named Bingo. Bingo loved playing with numbers. One day, he decided to help his friends learn how to add numbers to reach a target by inviting them to a fun game.

Bingo said, “Just like Bingo and his friends, you can also try more examples to understand how numbers work. Our first goal is to make 100.”

Bingo pointed to the number line and asked, “If we start with 50, what can we add to make 100?” His friends thought for a moment and shouted, “50! Because 50 + 50 equals 100!” Bingo wagged his tail happily.

Bingo continued, “How about making 200?” One friend replied, “We can add 140 and 60 because 140 + 60 equals 200!” Bingo smiled and explained, “You could also add 150 and 50 or 120 and 80. See how many ways we can reach our goal?”

Exploring Combinations

• 60 and 40 make 100
• 45 and 55 make 100

Bingo clapped his paws and said, “Great job, everyone! You’ve learned to add numbers to make bigger numbers!”

Now, let us play a game called “Clap, Snap, and Pat.” One clap represents 100, one snap represents 10, and one pat represents 1. You can play this game in teams where one team shows a number using claps, snaps, and pats, and the other team guesses it.

And so, Bingo and his friends kept playing with numbers, learning new ways to add and reaching their target goals. They had so much fun learning together!

Just like Bingo and his friends, you can also try some more examples and understand how numbers work.

Let’s Practice!

Question 1: 
Write numbers in the blank spaces inside the flower petals so that the numbers in each petal add up to 100.   View Answer

Question 2: 
Look at the picture. Estimate and write the number of each of the following objects.

a. Oranges: …………..

b. Bangles: ………….

c. Laddoos: …………

d. Barfi :……………

e. Bindis: ……………

f. Bananas: …………………


  View Answer

Introduction

Have you ever looked at your toys, snacks, or even the things around your house and wondered, “What shape is that?“

 Shapes are not just fun to look at—they are all around us, and some shapes are even 3D, meaning we can touch and hold them!

In this lesson, we’ll explore exciting shapes like cubes, cones, spheres, and cylinders. Let’s dive into the magical world of 3D shapes!
We will take a look at how they are identified and what are the common shapes present around us.

What are 3D Shapes?

These are shapes you can feel and hold; they are not just flat like a drawing on paper. Here are some examples:

• Cube: Think of a dice or a Rubik’s Cube. It’s a unique type of cuboid, like a solid box with six square sides.
• Sphere: Imagine a ball or an orange. It is entirely round, similar to a basketball.
• Cylinder: Picture a can of soda or a torch. It’s shaped like a tube with two circular ends.
• Cone: Think of an ice cream cone or a party hat. It resembles a triangle that narrows to a point.

Let’s take a look at some 3D shapes: 

Try yourself:

Which 3D shape can be compared to an ice cream cone or a party hat?

• A.Cube
• B.Sphere
• C.Cylinder
• D.Cone

View Solution

Now that we recognise the different 3D shapes, let’s explore more.Let’s Understand with a Story

Once upon a time, there lived a curious boy named Kunaal. He had just learned all about different 3D shapes in his school, and he was excited to share the new things he learnt with his little sister, Ayushi. Kunaal knew that learning about shapes could be so much fun, especially when you can see them all around you.

• One sunny afternoon, Kunaal called out to Ayushi, “Hey Ayushi, come with me! I want to show you something really cool.” Ayushi, always happy to learn from her big brother, quickly joined him.
• Kunaal took Ayushi on a tour around their house. “Look, Ayushi,” Kunaal said with a smile, “see that box of building blocks? It’s shaped like a cube!” 
• Next, they went to the kitchen, where Kunaal pointed at a cereal box. “This is a cuboid,” he explained. “It’s like a stretched-out cube with rectangular faces. See how it’s longer than it is wide?”  
• As they moved to the living room, Kunaal spotted a party hat from Ayushi’s recent birthday celebration. “Look at this cone,” he exclaimed. “It’s like a triangle that’s getting narrower as it goes up. Remember the ice cream cones we love?” 
• In the garden, Kunaal picked up a ball. “This is a sphere,” he said, rolling it in his hands. “It’s completely round, just like a basketball.” 
• Finally, they went to the garage, where Kunaal showed Ayushi a flashlight. “See this cylinder! It’s like a can of soda or a tube. It has two circular faces and a curved surface.” 
• Ayushi was amazed at how many shapes they could find right in their own home. “Thank you, Kunaal Bhaiya,” she said happily. “Now I understand 3D shapes, all thanks to you!” 

Kunaal was happy and proud to have shared his knowledge with his sister. From that day on, whenever they played or explored, Ayushi would point out different shapes.

More About 3D Shapes

Shapes have different parts. Let’s explore them:

• Face: In geometry, a face is a flat surface on a 3D shape. Think of it like the side of a box or a piece of paper. Faces are what you see when you look at a shape from different angles. For example, if you look at at a cuboid, each of its six sides is a face. Here we can take a look at face of a cuboid. 
• Edge: An edge is like a line where lines of two shapes meet. Imagine the edges of a cuboid—it’s the lines where the faces come together. Here we can take a look at edges of a cuboid (black line is the edge)
• Corner (Vertex): A corner, also called a vertex, is a point where edges meet. It’s like the tip of a pyramid or the corner of a room. In a cube, each of its eight corners is where three edges meet. A vertex can also be defined as a point in space where two or more edges meet.Now we will study how shapes differ from each other.

Cube

• Faces: A cube has 6 square faces.
• Edges: A cube has 12 edges where two faces meet.
• Corners (Vertices): A cube has 8 corners where three edges join.
• Example: Dice (die) used in board games, rubik’s cube, sugar cubes, etc. 

Cuboid

• Faces: A cuboid has 6 faces, all of which are rectangles. If all sides are equal, it is specifically a cube, which is a special type of cuboid.
• Edges: A cuboid has 12 edges, similar to a cube.
• Corners (Vertices): A cuboid has 8 corners where three edges meet.
• Examples: Pencil Box, match-stick box, etc. 

Try yourself:

Which 3D shape has 6 square faces, 12 edges, and 8 corners?

• A.Sphere
• B.Cone
• C.Cube
• D.Cylinder

View SolutionCone

• Faces: A cone has two faces—a circular base and a curved surface that comes to a point at the top.
• Edges: It features one curved edge and one straight edge along the base.
• Corners (Vertices): There is one vertex at the top of the cone.
• Examples: Party hats, Ice-cream cones, etc.

Sphere

• Definition: A sphere is a perfectly round three-dimensional shape where every point on its surface is the same distance from its centre.
• Faces: A sphere has no flat faces.
• Edges: There are no edges on a sphere as it is smooth all around.
• Corners (Vertices): A sphere has no corners or vertices since it has no flat faces.
• Examples: Balls, bubbles, etc. 

Cylinder

• Faces: A cylinder has 2 circular faces and 1 curved surface.
• Edges: A cylinder has 2 edges—one around the circular top and one around the circular bottom, plus 1 curved edge along the side.
• Corners (Vertices): A cylinder has no corners (vertices).
• Examples: Rollers, cans, gas cylinders,etc. 

Let’s Practice!

Ques: Milin went to a shop and bought a toy engine.
Here’s his toy engine, count the shapes which are present in this toy-engine.

(i) Cylinder(s) ………………………………………..
(ii) Cone(s): …………………………………………..
(iii) Cuboid(s) ……………………………………….
(iv) Cube(s) ………………………………………….

Answer:
(i) Cylinder(s) : 1
(ii) Cone(s):2
(iii) Cuboid(s):1
(iv) Cube(s): 1

Introduction

Imagine you have a big jar of candies and you really want to know exactly how many are inside. What would you do?

That’s where counting comes in—a superpower that helps you keep track of everything!

Now, let’s meet two brothers who used counting in a very smart way.

A Cow Story: Deba and Deep Learn to Count

Long ago, in a village, two brothers named Deba and Deep looked after cows. Every day, they took the cows out for grazing and brought them back in the evening.

• One day, Deba asked, “How do we know if all cows have come back?”
• Their friend suggested, “Make a mark on the wall for each cow when it leaves. When it returns, strike the mark. If all marks are gone, all cows are back!”

• Next day, they tried it. And it worked! From that day, they always used counting marks to keep their cows safe.

Try yourself:What did Deba and Deep do to keep track of the cows?

• A.Follow them everywhere
• B.Make marks on the wall
• C.Use a bell
• D.Count them every hour

View Solution

What Happened Later?

• As years passed, Deba and Deep had more cows. One day, before leaving, they made marks on the wall for each cow. When they came back, they started striking out the marks as each cow entered the gate.

Marks on the wall that represent the number of cows

• But two marks were still left! And no cows were outside!
• Why were they worried? Because this meant two cows were missing!
• They quickly went to search and found the missing cows nearby. Thanks to their counting trick, they saved their cows.
• Counting saved the day!

Why Counting Is Important

• To Know How Many: Counting tells us how many toys, sweets, or books we have.
• To Share Fairly: You can count your candies to share them equally with your friends.
• To Solve Problems: Lost something? Count what you have to know what’s missing.
• To Make Plans: If your birthday is in 5 days, you can plan something for each day!

Let’s Count Letters in Names!Let’s take the name “Samantha”.

• Write it out: S-A-M-A-N-T-H-A
• Count each letter: That’s 8 letters!

Now try your own name. How many letters?

You can also:

• Find names that start with the same letter.
• Check which letter is used the most.
• Find the shortest and longest names in your class!

Try yourself:How many letters are there in the word “MATHEMATICS”?

• A.11
• B.5
• C.3
• D.4

View SolutionWho Has the Longer Name?

• Richa and Ayushi were sisters. One day, they argued.
  
• “My name is bigger!” said Richa. “No! Mine is!” replied Ayushi.
• Their brother Rahul said, “Let’s count the letters.”
  
  
• Richa: R-I-C-H-A = 5 letters
  
  Ayushi: A-Y-U-S-H-I = 6 letters
  
  
• Ayushi’s name was longer! They laughed and made up. Counting helped them solve the argument.

So, counting isn’t just about numbers. It’s a way to explore, learn, and solve problems, just like Richa and Ayushi did!

Counting in Number Names

Let’s try the number “Seven”.

• S-E-V-E-N = 5 letters
  Try with other numbers:

• Three = 5 letters
• Eleven = 6 letters
• Twenty = 6 letters

Number names are words for numbers. Instead of 1, we say “One”. 
Below are the number names for the first few natural numbers:

Let’s Practice with Number Friends!

In the land of Numerica, friends Eighty-Nine, Ninety, and Ninety-One wanted to see who had the longest name.
Let’s count the letters in their names to see who has the biggest name!

• “Eighty-Nine” = 10 letters
  
• “Ninety” = 6 letters
  
  
• “Ninety-One” = 9 letters
  

Eighty-Nine had the longest name! But they all learned counting and had fun together.

The friends celebrated their newfound knowledge and friendship, knowing that each of their names was special in its own way.

Just like this, we can count the letters in all the numbers’ names and other words as well. Keep practicing, and you’ll become a pro at counting letters in no time!