CBSE Notes Class 6 Maths Chapter 1 Patterns in Mathematics

1.0Patterns in Mathematics: Class 6th Mathematics

Patterns are arrangements of numbers, shapes, or objects that follow a particular rule or set of rules. Understanding patterns helps students develop reasoning and problem-solving skills. Let’s explore the different types of patterns in Class 6 Mathematics. 

2.0What is Mathematics?

Mathematics is the study of numbers, shapes, and structures, governed by logic and reasoning. It provides tools to analyze and solve problems, and its applications extend far beyond calculations into understanding the world around us. Patterns in mathematics not only simplify complex problems but also reveal deep relationships among mathematical concepts.

3.0Patterns in Numbers

Patterns in numbers are sequences or arrangements that follow a specific rule. Recognizing these patterns helps us predict future elements in a sequence and understand underlying mathematical relationships.

Examples of Number Patterns

1. Addition/Subtraction Patterns:

• Example: 2, 4, 6, 8, 10 (Add 2 each time).
• Rule: $\text{Next term}=\text{Current term}+2.$

2. Multiplication Patterns: 

• Example: 3, 6, 12, 24 (Multiply by 2 each time).
• Rule: $\text{Next term}=\text{Current term}\times 2.$

3. Odd and Even Numbers:

• Odd: $1,3,5,7,\dots .$
• Even: $2,4,6,8,\dots .$

4.0Visualising Number Sequences

Visual representation of number sequences can enhance understanding. Dots, grids, or geometric shapes are commonly used to depict patterns.

Example:

This visualization makes it easier to derive formulas and understand the progression of the sequence.

5.0Relations Among Number Sequences

Many number sequences are interrelated, often sharing common rules or properties.

Examples:

1. Square Numbers and Odd Numbers:
   The difference between consecutive square numbers forms a sequence of odd numbers.

$\begin{array}{rl}& 1=1\\ & 1+3=4\\ & 1+3+5=9\\ & 1+3+5+7=16\\ & 1+3+5+7+9=25\\ & 1+3+5+7+9+11=36\end{array}$

6.0Patterns in Shapes

Patterns are not confined to numbers; they appear in shapes, symmetry, and spatial arrangements.

Types of Shape Patterns:

Tiling and Tessellations

Patterns in shapes often involve tiling, where shapes are repeated without gaps.

• Example: Floor tiles using hexagons or squares.

7.0Relation to Number Sequences

Shape patterns and number sequences often overlap, providing deeper connections.

Example:

1. Square Numbers and Grids:
   Square numbers ($1,4,9,16,\dots$) correspond to the total number of dots in square grids:

$2\times 2=4,3\times 3=9,4\times 4=16.$