House of Hundreds - II Chapter Notes | Mathematics for Class 3 (Maths Mela) PDF Download

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.

Neighboring Hundreds

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

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

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

Neighboring 50s

Neighboring 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 neighboring 50s of 234 are 200 and 250.

Neighboring 10s

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

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

So, the neighboring 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:

1. Using "more than" a base number:
   • 156 more than 300.
2. Breaking it down into place values:
   • 4 hundreds, 5 tens, 6 ones.
3. As a single number:
   • 456.
4. As a sum of its place values:
   • 400 + 50 + 6.
5. Using "less than" a base number:
   • 44 less than 500.
6. As a subtraction from a nearby higher number:
   • 500 - 44.

Summary with Examples:

1. 68 more than 300:

   • 156 more than 300 is 456.

2. Breaking it down into place values:

   • 4 hundreds, 5 tens, and 6 ones.

3. As a single number:

   • 456.

4. As a sum of its place values:

   • 400 + 50 + 6.

5. 32 less than 500:

   • 44 less than 500 is 456.

6. As a subtraction from a nearby higher number:

   • 500 - 44.

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.

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

• 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

• 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 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 Pattern: 900, 870, 840, 810, 780, ...

• Find the difference between each pair of numbers:
  • 870 - 900 = -30
  • 840 - 870 = -30
  • 810 - 840 = -30
  • 780 - 810 = -30

The rule here is to subtract 30 each time.

Creating 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 am 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 5 tens and 2 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 understanig numbers more.