मराठी
Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 5
पाठ्यपुस्तक उत्तरे३९९२
संकल्पना स्पष्टीकरण१२०
अभ्यासक्रम

Mathematical Patterns

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Topics

  • Definition: Pattern
  • Example
  • Square Numbers and Their Formation
  • Triangular Numbers and Their Formation
  • Key Points Summary
CISCE: Class 6

Definition: Pattern

A pattern is a sequence of numbers, shapes, or figures that follow a specific rule. Once we identify the rule, we can predict the next numbers or shapes in the sequence.

CISCE: Class 6

Examples

1. Number Pattern:

  • The sequence is 1, 4, 7, 10, 13, ...
  • This is an arithmetic pattern where each number increases by 3.
    (1 + 3 = 4, 4 + 3 = 7, and so on.)

2. Shape Pattern:

  • .........
  • ......
Maharashtra State Board: Class 5

Square Numbers and Their Formation

A square number is simply a number that you get when you multiply a number by itself. For example:

  • 2 × 2 = 4
  • 3 × 3 = 9
  • 4 × 4 = 16
  • 5 × 5 = 25

Imagine you have a set of dots and want to arrange them in a square shape. For instance:

  • If you have 4 dots in each row and 4 rows, you’ll get 4 × 4 = 16 dots, arranged in a 4 × 4 square.

  • If you have 3 dots in each row and 3 rows, you’ll get 3 × 3 = 9 dots, arranged in a 3 × 3 square.

So, the number of dots you get from multiplying a number by itself will always form a perfect square shape, and those numbers are called square numbers.

Maharashtra State Board: Class 5

Triangular Numbers and Their Formation

Triangular numbers are numbers that can be arranged in a triangle shape.

Consider the sum of numbers from 1 to 6 as follows:

  • 1 dot forms a single dot.
  • 1 + 2 = 3 dots can be arranged in two rows:
  • 1 + 2 + 3 = 6 dots can be arranged in three rows:
  • 1 + 2 + 3 + 4 = 10 dots can be arranged in four rows.
  • 1 + 2 + 3 + 4 + 5 = 15 dots can be arranged in five rows. 
These numbers (3, 6, 10, 15, 21, etc.) are called triangular numbers because they can be arranged to make an equilateral triangle, where all three sides of the triangle are equal.

Triangular numbers are simply the sums of the numbers from 1 upwards, and these sums create triangles when the dots are arranged properly!

CISCE: Class 6

Key Points Summary

  • Arithmetic sequence: nth term = a + (n-1)d

  • Square numbers: 1², 2², 3², 4², 5²...

  • Triangular numbers: 1, 3, 6, 10, 15...

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