Patterns In Whole Numbers

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Unit: Number System

Chapter: Patterns in Whole Numbers

Reference: – Introduction to Patterns, Visual Patterns (Line, Triangle, Rectangle, Square), Number Sequences (Odd, Even, Square, Triangular, Cube, Fibonacci), Arithmetic Patterns, Special Patterns (Magic Squares, Repeating Digits), Observing and Extending Patterns

After studying this chapter, you should be able to understand:

• Introduction to Patterns & Their Importance
• Visual Patterns with Dots (Line, Triangle, Rectangle, Square)
• Number Sequences: Odd, Even, Square, Triangular, Cube, Fibonacci
• Recognizing Rules & Extending Patterns
• Special Patterns (Magic Squares, Repeating Digits)
• Patterns in Everyday Life

Pattern in Whole Number

 

Pattern can be in the form of whole number, fractions and decimals. Pattern of numbers refers to the arrangement of numbers and pictures that follows specific rules. Under this topic we learn to form the pattern of numbers with the help of dots. Basic numbers are representing with the help of dots.

Like, 3 can be represented with the help of triangle.

4 can be represented with the help of square by making 2 rows and 2 columns.

 

6 can be represented with the help of rectangle 2 rows and 3 columns or by making 3 rows and 2 columns. It can also be represented as triangle.

For Example:

1. Represent the following numbers 8 and 9 with the help of specific figures.

Solution: 8 can be represented with the help of rectangle by making 4 columns and 2 rows or by making 2 columns and 4 rows.

Represent the number 9 with the help of suitable figure.

Solution: 9 can be represented with the help of square. This is because square has equal sides and 9 is a square of 3. So, 3 numbers of rows and 3 numbers of columns can be drawn with the dots.

Observe the following table:

 

There are some more patterns relating to the whole numbers. Though not related to the figures or dots but related to mathematical operations and numbers. It is easy to find the pattern of certain numbers. In further classes we will study the pattern and sequence of the numbers in more detailed way. Each number has some pattern.

 

For Example:

1. Multiply 3 to 8, 98, 998 and 9998.

On seeing the numbers we will first think of direct multiplication of the numbers.

But on applying such method it will be a lengthy process. We can solve the above question by merely understanding the pattern of the numbers.

3 ×8=3 10-2 = 30-6=24

3 ×98=3100-2=300-6=294

3 ×998=3 1000-2 = 3000-6=2994

3 ×9998=3 10000-2=30000-6=29994

On observing, we have found a new and easier way of calculating tough numbers.

 

1. Multiply 22 by 5, 10, 15and 20 with using direct multiplication.

Solution-

Now we have to multiply large number to small different numbers. This can be done with the observation of the same pattern. It is always easy to multiply any number with the multiples of 10 and 11. So to make the calculation easy we will also convert the multiples of 5 to multiples of 10 by multiplying and dividing by 2.

22 ×5=22 × 102=11 ×10=110

22 ×10=22 × 202=11 ×20=220

22 ×15=22 × 302=11 ×30=330

22 ×20=22 × 402=11 ×20=440

 

1. Write the next two steps of the following series by observing them:

0×9+1=0+1=1

1×9+2=9+2=11

12 ×9+3=108+3=111

123 ×9+4=1107+4=1111

Solution: As the pattern is based on multiples of 9,

First 9 is multiplied by 0 then 1 then 12 and then 123, and the number is also added by increasing natural numbers,

So the next steps will be:

1234 ×9+5=11106+5=11111

12345 ×9+6=111105+6=111111