NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 1
Ganit Prakash class 6 Maths
Patterns in Mathematics class 6
Important NCERT Questions Based on new NCERT Books for Session 2024-2025
Working with the Text
Find your own patterns or relations in and among the sequences in Table 1. Can you explain why they happen with a picture or otherwise?
Share
Uses of Mathematics in Everyday Life:
1 Cooking: When we measure ingredients to cook a recipe, we use math to ensure the quantities are correct.
2 Shopping: Calculating the total cost of items and figuring out discounts involves basic math.
3 Traveling: We use Maths to determine distances, travel time, and fuel usage.
4 Sports: Keeping track of scores, calculating averages, and determining player statistics all involve math.
5 Banking: Simple mathematics is used when managing money, such as saving, spending, and calculating interest.
Pattern: Connection Between Square Numbers and Odd Numbers
Sequence of Square Numbers: 1, 4, 9, 16, 25, 36, …
Sequence of Odd Numbers: 1, 3, 5, 7, 9, 11, …
Relation: Each square number is the sum of the first 𝑛 odd numbers.
For example:
1 = 1
4 = 1 + 3
9 = 1 + 3 + 5
16 = 1 + 3 + 5 + 7
Explanation with a Picture: If we imagine forming a square by placing dots. Start with 1 dot, then add a row of 3 dots to form a 2 x 2 square, then add a row of 5 dots to make a 3 x 3 square, and so on. This shows that each square is built by adding the next odd number of dots, demonstrating why square numbers are the sum of consecutive odd numbers.
This pattern occurs because each new square is formed by extending the previous square by an L-shaped layer of dots, where the number of dots in the layer equals the next odd number.
To see the complete Chapter 1, Visit here:
https://www.tiwariacademy.com/ncert-solutions-class-6-maths-ganita-prakash-chapter-1/