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.
In nature,
patterns are visible in flowers, leaves, honeycombs, snowflakes, etc.
Man-made Patterns
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
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
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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