# Patterns and Mental Mathematics

In patterns and mental mathematics we will learn to find patterns and solve questions on mental math.

‘Mathematics is a dull subject’.

But the mathematical mind says 'the most interesting subject is mathematics'.

The teacher can discover some pastime facts in mathematics and make the class joyful. In this topic some interesting facts are given. We gather here some rich mathematical ideas to enrich the intelligent mind.

Here are the counting numbers from 1 to 100 given in groups of 10. A student may discover some patterns regarding numbers.

1. Numbers in each column increase by 1.

All the numbers from 1 to 100 continuously increase by 1.

2. Numbers in rows increase by 10.

3. Each two of the diagonally situated numbers from left to right from the lowest to the highest have a difference of 9. As seen in 10, 19, 28, 37, 46, 55, 64, 73, 82, 91.

4. Every two of the diagonally situated numbers from left to right from top to bottom have the difference of 11. As: 1, 12, 23, 34, 45, 56, 67, 78, 89, 100.

5. All numbers in the first row end with 1, in the second row with 2, in the third row end with 3 and so on. All numbers in the last row end with 0.

6. The sum of the digits of each number on the dotted lines is the same, being 1, 2, 3, …, 10 respectively.

First line 1,

Second line 1 + 1 = 2, 2,

Third line 2 + 1 = 3, 1 + 2 = 3, 3

7. The sums of the numbers in different columns form a pattern.

As:

 1 + 2 + 3 + ……. + 10 = 55 11 + 12 + 13 + .......... + 20 = 155 21 + 22 + 23 + …….. + 30 = 255 31 + 32 + 33 + ……. + 40 = 35593 ….. 91 + 92 + ....... + 100 = 955 or (10 x 11)/2 = 55or (20 x 21)/2 – (10 x 11)/2 = 155or (30 x 31)/2 – (20 x 21)/2 = 255 or (40 x 41)/2 – (30 x 31)/2 = 355 or (100 x 101)/2 – (90 x 91)/2 = 955

We see that the sum of numbers from 1 to 10 = 55

 from 11 to 20 = 155from 21 to 30 = 255

The sum of numbers of the continued from 71 to 80 = 755

 column increases by 100. As:55, 155, 255, …… from 91 to 100 = 955 from 101 to 110 = 1055

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