Important Formula: We the Travellers—I | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

1. Place Value System

• This is 1 

•  10 Ones make 1 Ten (10)

• 10 Tens make 1 Hundred (100) 

• 10 Hundreds make 1 Thousand (1,000) 

Place Value Order (Indian System):
Ones → Tens → Hundreds → Thousands → Ten Thousands → Lakhs → Ten Lakhs → Crores

Commas in Large Numbers (Indian System)

• First comma after 3 digits from the right.

• After that, commas after every 2 digits.

• Example: 8045 → 8,045 (Read as Eight thousand forty-five).

Number Naming (Indian System)

Expanded Form

Break a number into place values:

• 1,380 = 1,000 + 300 + 80 + 0

• 9,123 =  9,000 + 100 + 20 + 3

General Rule:
Number = (Thousands × 1000) + (Hundreds × 100) + (Tens × 10) + (Ones × 1)

Number Patterns

A number pattern is a sequence of numbers that follow a fixed rule.
Each number in the sequence is obtained from the previous number using that rule.

Example

456 → 567 → 678
Rule: Add 111 each time.

Types of Rules in Number Patterns

1. Repeated Addition

Add the same number again and again.

• Example: 5, 10, 15, 20, 25 ...
  Rule: Add 5 each time.

2. Repeated Subtraction

Subtract the same number again and again.

• Example: 100, 90, 80, 70, 60 ...
  Rule: Subtract 10 each time.

3. Multiplication by the Same Number

Multiply the previous number by a fixed number.

• Example: 2, 4, 8, 16, 32 ...
  Rule: Multiply by 2 each time.

4. Division by the Same Number

Divide the previous number by a fixed number.

• Example: 256, 128, 64, 32, 16 ...
  Rule: Divide by 2 each time.

Tip for Students:
Always look for what is happening from one number to the next:

• Is the number increasing or decreasing?

• Is it changing by addition, subtraction, multiplication, or division?

Rounding Off Rules

1. Nearest 10:

• Look at Ones digit.

• If Ones ≥ 5 → round up.

• If Ones < 5 → round down.

• Example: 2,346 → 2,350

2. Nearest 100:

• Look at Tens digit.

• If Tens ≥ 5 → round up.

• If Tens < 5 → round down.

• Example: 2,346 → 2,300

3. Nearest 1000:

• Look at Hundreds digit.

• If Hundreds ≥ 5 → round up.

• If Hundreds < 5 → round down.

• Example: 2,346 → 2,000

6. Large Numbers in Daily Life

• Numbers we see daily can range from 1-digit to 5-digit (e.g., distances, money, population).

• Example: A book with 200 pages × 50 words/page = ~10,000 words.

• Units of length: kilometre (km) = 1,000 metres (m).

7. Mathematical Puzzles (Pastime Mathematics)

(a) River Crossing Puzzle

• Objects: Lion, Sheep, Grass with the Boatman.Boatman

• Rules:

  1. Boat carries only 1 item at a time.

  2. Lion & sheep alone → lion eats sheep.

  3. Sheep & grass alone → sheep eats grass.

Solution (7 trips):

• Take sheep across → return alone → take lion → bring sheep back → take grass → return alone → take sheep.

Key Idea: Logical sequencing and safe grouping.

(b) Pile of Pebbles Game

• Two piles, each with 7 pebbles.

• On each turn, a player can take any number of pebbles from one pile only.

• Winning Strategy:

  • If piles are equal → second player wins by copying moves.

  • If piles unequal → first player can win by making them equal.

• Key Idea: Patterns and strategy in game theory.

(c) The Number Puzzle

• Start with any two digits → form two 2-digit numbers → subtract smaller from larger → repeat with digits of result.

• Pattern: Always ends at 9.

• Example:

  • 73 – 37 = 36 → 63 – 36 = 27 → 72 – 27 = 45 → 54 – 45 = 9.

• Why? Differences are always multiples of 9.

• Key Idea: Hidden number patterns and divisibility by 9.

(d) King’s Horses Puzzle

• King has 20 horses, 1 stolen → only 19 left.

• Caretaker arranges horses in a square with horses at corners.

• When king counts each side (5 per side × 4 sides = 20), he double-counts the corner horses.

• Trick: Corner horses counted twice.

• Key Idea: Counting principles and visual tricks.