# Concept of Pattern

Concept of pattern will help us to learn the basic number patterns and table patterns.

Animals such as all cows, all lions, all dogs and all other animals have dissimilar features. All mangoes have similar features and shapes. Leaves of the same tree have similar pattern of shape. The doors and windows of a house have similar patterns. We may search for similar patterns in mathematics also.

The study of patterns helps students to observe relationships and find continuous connections, to deduce generalizations and predictions.

In everyday life we observe dress pattern, carpet pattern, wall-paper pattern, sari-design pattern as well as number pattern in arithmetic.

Examples of patterns are given below:

2     4      6     8     10     12    …………….;

5    10    15    20    25    30    …………….

The learner has to recognize a pattern and expand it. He must analyze it and then create new patterns to study the subject matter. The teacher should develop in the students the concept of pattern.

(i) To get better idea on the concept of pattern let us look at the following pictures:

Using the numbers the sequence is:

The rule to go from one number to the next number is ‘add 2’

(ii) In the pattern 1, 3, 5, 7, ……. the number of footballs go on increasing and the number becomes larger each time.

Sometimes the numbers i8n a pattern go on decreasing. Suppose there are 16 footballs in the basket. A person gives two footballs to each group of players for the football match. The number of footballs in the basket goes on decreasing by each group.

The pattern is:

The missing numbers are 8, 6 and 4. The rule of the pattern is to take away 2 each time.

(iii) The numbers becomes larger and larger very rapidly.

The missing number is 16. The rule to go from one term to the next is multiply by 2.

Here are some examples of designs having the same pattern:

Number Patterns:

1 + 2 + 3 + 4 + 5 + ……. + 10 = 55

Sum of the numbers from 1 to 10 is 55

Hence, the sum of the numbers from 11 to 20 will be 10 × 10 = 100 more than 55

11 + 12 + 12 + ……. + 20 = 155

Look at the following pattern that grows when you add triangles.

The pattern can be represented in numbers as 1, 2, 3.

A pattern like given above will form a sequence 1, 4, 9, 16, 25, …..

Table Patterns:

(i) 2, 4, 6, 8, 10, …….

In table 2, we see every forward number is 2 more than its previous one.

(ii) 2, 8, 14, 20, 26, …….

Every forward number is 6 more than the previous one.

 (iii) 1 + 2 + 3 + 4 + 5 = 15 Sum of first 5 consecutive numbers = 15 2 + 3 + 4 + 5 + 6 = 20 Sum of 2 to 6 consecutive numbers = 15 + 5 = 20 3 + 4 + 5 + 6 + 7 = 25 Sum of 3 to 6 consecutive numbers = 15 + 2 × 5 = 25 11 + 12 + 13 + 14 + 15 = 65 Sum of 11 to 15 consecutive numbers = 15 + (11 - 1) × 5             = 15 + (10 × 5)             = 15 + 50             = 65

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