Patterns and Symmetry

# Patterns and Symmetry

Patterns

A pattern is a definite sequence of shapes, numbers or letters repeated over and over again.

Types of Patterns

Repeating Pattern

In this type of pattern, the objects repeat in a certain order.

Example: Draw three more images to complete the pattern.

Natural Patterns

In nature, patterns are visible in flowers, leaves, honeycombs, snowflakes, etc.

Apart from nature, patterns can also be seen in man-made things. Following are the examples of patterns in man-made things.

Growing or Increasing Pattern

In this type of pattern, the numbers or shapes grow or increase in value and size.
Example:
1.  25, 50, 75, 100, 125, 150, 175 is a number pattern which increases by 25 at each step.
2. 1, 3, 6, 10, .... are the triangular number pattern.

Decreasing Pattern

In this type of pattern, the numbers or shapes decrease in value and size.
Example: 99, 98, 97, 996, 95, 94, 93 is a number pattern which decreases by 1 at each step.

Tiling Patterns

Tiling is the process of creating a pattern using the repetition of geometric shapes with no overlaps and no gaps.

Tessellation

Tessellation is the process of creating a design using the repetition of geometric shapes without leaving any gaps. A honeycomb is an example of a natural tessellation and a floor tile pattern is an example of a man-made tessellation.

Patterns in Numbers

Patterns can also be seen in numbers. See the pattern of numbers given below.

120, 140, 160, 180, 200, 220, 240, 260, 280, 300

The difference between every two consecutive numbers is 20.
Example: Fill in the missing numbers in these patterns.
a. ___, ___, ___, 60, 70, 80
b. ___, ___, ___, 18, 20, 22
c. 1, 3, 5, ___, ___, ___, 13, 15
d. 5, 10, ___, ___, ___, 30, 35
e. 17, 27, ___, ___, ___, 67, 77

f. 50, 100, 150, ___, ___, ___, 350, 400

Solution:

a. 30, 40, 50, 60, 70, 80
b. 12, 14, 16, 18, 20, 22
c. 1, 3, 5, 7, 9, 11, 13, 15
d. 5, 10, 15, 20, 25, 30, 35
e. 17, 27, 37, 47, 57, 67, 77

f. 50, 100, 150, 200, 250, 300, 350, 400

Addition patterns help us to find the solution without calculation.

 0 + 1 + 2 = 3 5 + 6 + 7 = 18 1 + 2 + 3 = 6 6 + 7 + 8 = 21 2 + 3 + 4 = 9 7 + 8 + 9 = 24 3 + 4 + 5 = 12 8 + 9 + 10 = 27 4 + 5 + 6 = 15 9 + 10 + 11 = 30

The sum differs by 3 in each statement or we can say that the pattern follows the multiplication table of 3.

Subtraction Patterns

In subtraction patterns, a rule can be applied to form the pattern sequence.

 70 – 50 = 20 65 – 45 = 20 69 – 49 = 20 64 – 44 = 20 68 – 48 = 20 63 – 43 = 20 67 – 47 = 20 62 – 42 = 20 66 – 46 = 20 61 – 41 = 20

You can see that when 1 is taken away from both the subtrahend and the minuend, the difference remains unchanged.

Multiplication Patterns

Table of 9
 1 × 9 = 9 6 × 9 = 54 2 × 9 = 18 7 × 9 = 63 3 × 9 = 27 8 × 9 = 72 4 × 9 = 36 9 × 9 = 81 5 × 9 = 45 10 × 9 = 90

The patterns that can be seen in the table of 9 are as follows:
·        The ones place has numbers from 9 to 0 in decreasing order.
·        The tens place has numbers from 0 to 9 in increasing order.
·        The sum of the digits of each product is always 9.

Division Patterns

Look at the following patterns.

a.      12 ÷ 12 = 1
120 ÷ 12 = 10
1200 ÷ 12 = 100
12000 ÷ 12 = 1000
120000 ÷ 12 = 10000

b.      400000 ÷ 2 = 200000
40000 ÷ 2 = 20000
4000 ÷ 2 = 2000
400 ÷ 2 = 200
40 ÷ 2 = 20

Symmetry

A shape is symmetrical when one-half of the shape is exactly like the other half. Symmetry is everywhere around us.

The line dividing these images into two identical halves is called the line of symmetry.

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