Double Century Chapter Notes | Mathematics for Class 3 (Maths Mela) PDF Download

Introduction

• Tens of thousands of years ago, people began counting to keep records of their things.
• They used marks on cave walls and tree barks to record numbers.
  

Ancient Methods of Counting

• People grouped items into sets of 5, 10, 20, and 60 to keep track of larger quantities.
• This helped them manage their belongings and trade goods.
• Thousands of years ago, ancient Indians developed a system using ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
• This invention was crucial for writing any number, no matter how large, using just these symbols.

The Power of Zero

• The introduction of the symbol "0" as a placeholder for "nothing" was a revolutionary concept.
• It made the numerical system efficient and allowed for complex calculations.
• The numerical system laid the foundation for inventions like TVs, computers, and mobile phones.
• It is used globally in every country, showcasing its universal importance.

Let's help Sachin to do his homework to understand how numbers work.

Sachin's Number Adventure

• Once upon a time, there was a young boy named Sachin who loved numbers. 
• One day, he had a homework assignment to add 1 to numbers in his book.
  
• He started with easy numbers like 1+1=2, 56+1=57, and so on. Sachin was doing great until he reached number 99. 
• He scratched his head, wondering what comes after 99.
• Just then, his older brother Vivek walked into the room. Seeing Sachin's confusion, Vivek asked, "What's the matter, Sachin?"
• Sachin replied, "I don't know what comes after 99. I'm stuck!"
  
• Vivek smiled and said, "Don't worry, Sachin. Let me teach you about the number 100."
• Vivek explained, "When we add 1 to 99, we get 100. It's like when you count from 1 to 99 and then start over at 1 but add a new set of tens. So, after 99 comes 100."
  
• Sachin's eyes lit up with understanding. He exclaimed, "Oh, I get it now! 99+1 equals 100!"
• Vivek nodded proudly and said, "That's right! Numbers keep going on and on, and there's always something new to learn about them."

From that day on, Sachin had no trouble with numbers. He sailed through his homework and became even more fascinated by the endless possibilities of mathematics.

Making 100

• In mathematics, we can make the number 100 using different sets of numbers.
• Let's explore some combinations that add up to 100.
  

Examples:

1. 90 + 10 = 100
2. 80 + 20 = 100
3. 70 + 30 = 100
4. 60 + 40 = 100
5. 50 + 50 = 100

Explanation:

• When we add 90 and 10, we get 100 because 90 + 10 = 100.
• Similarly, 
  • 80 + 20 
  • 70 + 30 
  • 60 + 40
  • and 50 + 50 all equal 100.
• These examples show that there can be many ways to make 100 using different numbers.
• By combining numbers in different ways, we can explore the flexibility and possibilities of mathematics.

Let's Learn by Practicing- 1

Tanya and Reema, two friends who loved math, discovered a fun game one day. Tanya had learned in class how to make 100 by adding different numbers together. She couldn't wait to show Reema.

Tanya & Reema

• Excitedly, Tanya explained, "We can write down any five numbers between 1 and 99. Then, I'll add another number to each of yours to make it 100!"
• Reema nodded eagerly and quickly jotted down her five numbers: 20, 35, 42, 68, and 75.
• Tanya smiled and said, "Let's start!" She took Reema's first number, 20, and added 80 to it, making it 100. "20 + 80 = 100!"
  
• Next, Tanya looked at 35. She added 65 to it, and voila! "35 + 65 = 100!"
• They continued playing, combining numbers in creative ways. Tanya added 58 to 42, 32 to 68, and 25 to 75, successfully making each combination equal 100.
• Reema clapped her hands in delight. "This is so much fun, Tanya! I never knew math could be this exciting."
  
• Tanya grinned. "Math is like a puzzle, and we are the puzzle solvers! There are endless ways to explore and play with numbers."

Just like the combinations Tanya made in the story, there are many other ways to make 100 using different numbers. We can continue exploring beyond 100 to see how numbers can be combined creatively. Moreover, we can continue the counting even after reaching 100. Let's see how:

Counting After 100

After reaching 100, counting continues using a similar pattern as before. Here's an explanation of how counting continues after 100:

1. Using Hundreds: Once we reach 100, we start counting with the next hundred. For example:

• 100 + 1 = 101
• 100 + 2 = 102
• 100 + 3 = 103

2. Hundreds and Tens: We can also combine hundreds and tens. For instance:

• 100 + 10 = 110
• 100 + 20 = 120
• 100 + 30 = 130

3. Hundreds and Ones: Additionally, we can combine hundreds and ones to continue counting:

• 100 + 5 = 105
• 100 + 8 = 108
• 100 + 15 = 115

4. Beyond Hundreds: The same pattern continues as we go beyond 100:

• 110 + 1 = 111
• 120 + 2 = 122
• 130 + 3 = 133

This pattern of adding one to the previous number continues indefinitely, creating an endless sequence of counting. 

Number Names

• Just like numbers below 100, numbers above 100 also have names.
• Let's explore how number names work beyond 100.

Naming Numbers Above 100:

• When we count beyond 100, we start with the hundreds place followed by the remaining digits.
• For example, 101 is "one hundred one," 102 is "one hundred two," and so on.

Understanding Place Value:

• In numbers like 101, the "one" represents the hundreds place, "zero" in the tens place, and "one" in the ones place.
• Similarly, in 123, the "one" is in the hundreds place, "two" in the tens place, and "three" in the ones place.  

Let's See how this works:

Let's Learn by Practicing- 2

• Rahul felt a little frustrated, but then his older sister Anju noticed his confusion. Anju was very good at explaining things in simple ways.
  Rahul & Anju
• 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 said, "When we have 100 and add 1, it becomes One Hundred One. See? We just say 'One Hundred' and then add the number after that."
  
• 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."
  
• Rahul practiced saying the names of numbers like 100 and 7, 100 and 9, and even 100 and 10.

Example - 

• 109
• 123
• 150
• 157
• 159

Explanation  - 

• 109 , Here we have a Hundred and a Nine , so its number name will be one hundred + nine , which is One Hundred Nine

Similarly, 

• 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 Nine

From that day onwards, Rahul was confident in naming numbers above 100, thanks to his sister's simple explanations and patient teaching.

Let's Learn by Practicing- 3

Once upon a time, there was a clever little dog named Bingo. Bingo loved playing with numbers on a number line. One day, Bingo decided to help his friends learn how to add numbers to reach a target. He invited his friends to play a fun game.

Bingo said, "Let's see if we can make some big numbers by adding smaller ones. Our first goal is to make 100."

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

Next, Bingo kept the game going. "How about making 200?" Bingo asked excitedly. One friend said, "We can add 140 and 60 because 140 + 60 equals 200!" Bingo smiled and said, "Correct! You could also add 150 and 50 or 120 and 80 to make 200. See how many ways we can reach our goal?"

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

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.