Topics
Patterns in Mathematics
- Mathematical Patterns
- Patterns in Numbers
- Patterns in Shapes
Mathematics
Lines and Angles
Number Play
- Fundamentals of Numbers
- Supercells
- Number Line
- Working with Number Digits
- Palindromic Patterns
- Kaprekar Number
- Clock and Calendar Numbers
- Mental Math
- Patterns in Numbers
- The Collatz Conjecture
- Basic Concept of Estimation and Approximation of Numbers
Data Handling and Presentation
- Mathematical Data Collection and Organisation
- Pictographs
- Bar Graphs
- Artistic and Aesthetic Considerations
Prime Time
- Multiples and Common Multiples
- Factors and Common Factors
- Prime and Composite Numbers
- Eratosthenes’ Method of Finding Prime Numbers
- Co-prime Numbers
- Prime Factorisation
- Tests for Divisibility of Numbers
- Divisibility by 10
- Divisibility by 5
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Exploring Special Numbers & Logical Reasoning
Perimeter and Area
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of Triangle
- Problems based on Perimeter
- Perimeter of a Regular Polygon
- Perimeter of an Equilateral Triangle
- Concept of Area
- Problems based on Area
- Area of a Triangle
- Exploring Shapes Through Perimeter and Area
Fractions
Playing with Constructions
- Basic Concept of Construction
- Squares and Rectangles
- Constructing Squares and Rectangles
- An Exploration in Rectangles
- Constructing Complex Figures
- Exploring Diagonals of Rectangles and Squares
- Points Equidistant from Two Given Points
Symmetry
The Other Side of Zero
- Fundamentals of Numbers
- Negative and Positive Numbers
- Tracking Movement: Using Positive and Negative Numbers
- Comparison of Integers
- Number Line
- Conversion between Addition and Subtraction
- The Token Model
- Integers in Other Places
- Explorations with Integers
- Integers
- Definition
- Steps
Maharashtra State Board: Class 6
Kaprekar Number
Indian mathematician Dattatreya Ramchandra Kaprekar discovered this amazing trick.
Steps:
- Select any 4-digit number (where no digits are the same).
Example: 8531 - Arrange the digits:
In descending order (big to small): 8531 → 8531
In ascending order (small to big): 8531 → 1358 - Subtract the smaller number from the bigger one:
8531 - 1358 = 7173 - Repeat the steps with the new number (7173):
Descending: 7731
Ascending: 1377
7731 - 1377 = 6354 - Continue repeating the same steps:
6354 → 6543 - 3456 = 3087
3087 → 8730 - 0378 = 8352
8352 → 8532 - 2358 = 6174 - Once you reach 6174, you will continue to receive 6174 repeatedly.
531 → 7173 → 6354 → 3087 → 8352 → 6174 → 6174 → 6174...
Therefore, we refer to the number 6174 as the Kaprekar Number.
