Table of Contents

## What are Patterns?

Patterns – Different Types and Solved Questions: Patterns are typically sequences of related data elements. They can be found in many places, including in nature, in music, in mathematics, and in everyday life. Some patterns are obvious and easy to see, while others are more subtle. In **CBSE maths syllabus Class 4** the patterns chapter is like a doorway for students to explore the interesting world of math order and symmetry. In this chapter, kids not only figure out how to spot patterns but also learn to make, continue, and study them. We focus on helping them get better at finding repeats, sequences, and shapes in math, so they can really see the cool designs hiding in numbers. It’s all about understanding the beauty in how math things are put together.

- Patterns can be used for many purposes, including for predicting future events, for understanding how something works, for creating artwork, and for solving problems. Mathematicians and scientists often use patterns to develop theories and models.
- Patterns can be described in many ways. Some common ways to describe patterns include by their shape, by their size, by the type of data they contain, by the way they are repeated, and by the rules that govern them.

## Pattern Definition

Pattern definition is a method for specifying the structure of a repeating object. A pattern is typically described in terms of a template, which is then used to generate a specific instance of the pattern. The template may be a simple description of the object’s structure, or it may be a more detailed description that includes specific instructions for assembling the object.

## Number Patterns

A number pattern is a sequence of numbers that are generated based on a specific rule. The numbers in a number pattern can be consecutive or non-consecutive. Some number patterns can be generated by starting with a certain number and then adding a certain number to that number each time. Other number patterns can be generated by multiplying a certain number by a certain number each time. There are also number patterns that can be generated by taking a certain number and dividing it by a certain number each time.

## Types of Number Patterns

There are many different types of number patterns. Some of the most common types are:

### Sequences

- A sequence is a pattern of numbers that are ordered in a specific way. The numbers in a sequence usually increase or decrease by a certain amount.
- One common type of sequence is the Fibonacci sequence. The Fibonacci sequence is a sequence of numbers where each number is the sum of the previous two numbers.
- 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …
- The Fibonacci sequence is named after Leonardo Fibonacci, who discovered the sequence in the 1200s.
- Another common type of sequence is the harmonic sequence. The harmonic sequence is a sequence of numbers where each number is the reciprocal of the previous number.
- 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/13, 1/14, 1/15, 1/16, 1/17, 1/18, 1/19, 1/20, 1/21, 1/22, 1/23, 1/24, 1/25, 1/26, 1/27, 1/28, 1/29, 1/30

## Types of Modes of Number Patterns

There are six types of modes of number patterns.

### 1. Ascending Mode

The ascending mode of number patterns starts with the smallest number and increases by a certain amount with each number in the sequence.

For example, the ascending mode of the sequence 1, 2, 3, 4, 5 would be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

### 2. Descending Mode

The descending mode of number patterns starts with the largest number and decreases by a certain amount with each number in the sequence.

For example, the descending mode of the sequence 10, 9, 8, 7, 6 would be 10, 9, 8, 7, 6, 5, 4, 3, 2, 1.

### 3. Even Mode

The even mode of number patterns starts with the smallest even number and increases by a certain amount with each even number in the sequence.

For example, the even mode of the sequence 2, 4, 6, 8, 10 would be 2, 4, 6, 8, 10, 12, 14, 16, 18.

### 4. Odd Mode

The odd mode of number patterns starts with the smallest odd number and increases by a certain amount with each odd number in the sequence.

For example, the odd mode of the sequence 3, 5, 7, 9, 11 would be 3, 5, 7, 9,

## Rules for Patterns in Maths

There are a few basic patterns that you should be aware of when studying mathematics.

1. The pattern of addition is:

1 + 2 = 3

2 + 3 = 5

3 + 4 = 7

4 + 5 = 9

5 + 6 = 11

6 + 7 = 13

7 + 8 = 15

8 + 9 = 17

9 + 10 = 19

2. The pattern of subtraction is:

1 – 2 = -1

2 – 3 = -1

3 – 4 = -1

4 – 5 = -1

5 – 6 = -1

6 – 7 = -1

7 – 8 = -1

8 – 9 = -1

9 – 10 = -1

3. The pattern of multiplication is:

1 x 2 = 2

2 x 2 = 4

3 x 2 = 6

4 x 2 = 8

5 x 2 = 10

6 x 2 = 12

7 x 2 = 14

8 x 2 = 16

9 x 2 = 18

10 x 2 = 20

4. The pattern of division is:

1 ÷ 2 = 0.5

2 ÷ 2 = 1

3 ÷ 2 = 1.5

4 ÷ 2 = 2

## Solved Questions

What is a quorum?

A quorum is a set number of members of a group that must be present for a meeting to take place, or for a vote to be cast.