Class 4 Exam  >  Class 4 Notes  >  Mathematics for Class 4  >  Chapter Notes: Patterns & Symmetry

Patterns and Symmetry Class 4 Notes Maths

What is Pattern? 

A Pattern means repetition in a proper sequence. Patterns can be formed by drawing an image and its reflected image. They can be formed using any Shapes

What is Symmetry? 

Symmetry means an object that can be divided exactly into two identical halves of the same size and shapes.

Look at the figures given below and the dotted lines

Patterns and Symmetry Class 4 Notes Maths

Patterns and Symmetry Class 4 Notes MathsIf you fold the above figures along the vertical line, you will find that one half exactly covers the other half. Such figures are called the symmetrical figures.

An object is said to have symmetry if it can be divided into two identical halves. The line that divides the object into its identical halves is called the line of symmetry. For example, in the given image, the line passing through the middle of the flower is its line of symmetry.

What do you think are all objects symmetrical?

No, some objects like the ones given below are not symmetrical. They are called non-symmetrical objects or things.


Patterns and Symmetry Class 4 Notes MathsPatterns and Symmetry Class 4 Notes Maths

Question for Chapter Notes: Patterns & Symmetry
Try yourself:
What is the definition of symmetry?
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Reflection Like a Mirror Image

When you look into a mirror, you see your reflection. The mirror image is the reflection of the image.
We can see that a symmetrical shape can be split in half by the line of symmetry. If we put a small mirror on the dotted line, we will see the whole shape. Thus, you can see that a shape has line symmetry when one half of it is the mirror image of the other half.
Patterns and Symmetry Class 4 Notes Maths
Patterns and Symmetry Class 4 Notes MathsThus, reflectional symmetry is also known as mirror symmetry.
Look at the reflection of some numbers and letters.
Patterns and Symmetry Class 4 Notes Maths
Patterns and Symmetry Class 4 Notes Maths

Symmetry in Some Geometrical Shapes

  1. A square has four lines of symmetry.
    Patterns and Symmetry Class 4 Notes Maths
  2. A rectangle has two lines of symmetry.
    Patterns and Symmetry Class 4 Notes Maths
  3. An isosceles triangle has only one line of symmetry.
    Patterns and Symmetry Class 4 Notes Maths
  4. An equilateral triangle has three lines of symmetry.

Patterns and Symmetry Class 4 Notes Maths

Symmetry in Letters and Numbers

Here are some capital letters and numbers which have lines of symmetry.
Patterns and Symmetry Class 4 Notes Maths
Patterns and Symmetry Class 4 Notes MathsHowever, there are some letters and numbers which are not symmetrical.Patterns and Symmetry Class 4 Notes Maths

Patterns

Patterns are shapes, designs and a group of numbers that repeat themselves in a predictable manner.
Let us look at some examples.
Patterns and Symmetry Class 4 Notes Maths

Patterns in Addition

Patterns of the sum of three consecutive numbers
1 + 2 + 3 = 6, 6 is a multiple of 3 and 3 × 2 = 6.
2 + 3 + 4 = 9, 9 is a multiple of 3 and 3 × 3 = 9.
3 + 4 + 5 = 12, 12 is a multiple of 3 and 3 × 4 = 12.
4 + 5 + 6 = 15, 15 is a multiple of 3 and 3 × 5 = 15.
5 + 6 + 7 = 18, 18 is a multiple of 3 and 3 × 6 = 18.

Rule
The sum of three consecutive numbers is a multiple of 3. Also, the sum is three times the middle term.

Patterns in Multiplication

I. Multiplication of a number ending in 5 by itself.

Patterns and Symmetry Class 4 Notes Maths
Patterns and Symmetry Class 4 Notes Maths

Rule
Every product ends in 25 and the remaining digits are obtained by multiplying the digit at the tens place by its next higher number.

II. Multiplying the same number having all digits as 1.
We have,
1 × 1 = 1
11 × 11 = 121
111 × 111 = 12321
1111 × 1111 = 1234321

Patterns and Symmetry Class 4 Notes Maths

Rule
The middle digit in the product is the sum of the digits of one factor.

III. To multiply factors like 19 and 21.
19 × 21 = 399 = 400 – 1 = 20 × 20 – 1
29 × 31 = 899 = 900 – 1 = 30 × 30 – 1
39 × 41 = 1599 = 1600 – 1 = 40 × 40 – 1
Observing the above pattern, we can write
49 × 51 = 50 × 50 – 1 = 2500 – 1 = 2499    
59 × 61 = 60 × 60 – 1 = 3600 – 1 = 3599

IV. To multiply a number by 11.
Patterns and Symmetry Class 4 Notes Maths
Patterns and Symmetry Class 4 Notes Maths

Observing the given pattern,
Patterns and Symmetry Class 4 Notes Maths

Patterns and Symmetry Class 4 Notes Maths

Patterns in Division

Observe the given patterns.
Patterns and Symmetry Class 4 Notes Maths
Patterns and Symmetry Class 4 Notes Maths
These patterns show that as the dividend increases (divisor remaining the same), the quotient also increases. As the dividend decreases, the quotient also decreases.
Now, keeping the dividend same, let us increase or decrease the divisor and observe the effect on the quotient.
Patterns and Symmetry Class 4 Notes Maths
Patterns and Symmetry Class 4 Notes Maths

Now, look for the pattern in the following sequence of numbers and find the missing number. 3125, 625, 125, , 5, 1
The missing number is 25, as per the rule for this pattern, the number is divided by 5, each time.

Geometrical Patterns Based on Symmetry

Rangoli patterns are drawn as decorations during the festival of Diwali. The pictures given here show two such patterns.
Patterns and Symmetry Class 4 Notes MathsNow, look at the following patterns.
Patterns and Symmetry Class 4 Notes Maths

This pattern is symmetrical.

It can be folded in half, so all the lines and colours in each half fit exactly on top of each other.

Quilt patterns based on symmetry.
Patterns and Symmetry Class 4 Notes Maths
Patterns and Symmetry Class 4 Notes MathsThis pattern is not symmetrical.

When it is folded in half, some of the lines and colours do not match.

The document Patterns and Symmetry Class 4 Notes Maths is a part of the Class 4 Course Mathematics for Class 4.
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FAQs on Patterns and Symmetry Class 4 Notes Maths

1. What is a pattern?
Ans. A pattern is a repeated decorative design or arrangement of shapes, colors, or lines that creates a visual effect.
2. What is symmetry?
Ans. Symmetry is the quality of being made up of exactly similar parts that are arranged in a balanced way.
3. How can patterns be used in everyday life?
Ans. Patterns can be used in everyday life for various purposes such as in clothing designs, interior decoration, architecture, and even in nature like the patterns on a leaf or a shell.
4. What are the different types of patterns?
Ans. Some common types of patterns include geometric patterns, floral patterns, striped patterns, polka dot patterns, and abstract patterns.
5. Why is symmetry important in art and design?
Ans. Symmetry is important in art and design as it creates a sense of balance, harmony, and aesthetic appeal in the composition. It helps in organizing elements in a visually pleasing way.
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