Class 5 Exam  >  Class 5 Notes  >  Mathematics for Class 5  >  Chapter Notes: Patterns

Patterns Class 5 Notes Maths

What is a Pattern?

  • Have you ever noticed the cool designs on your clothes, the way tiles fit perfectly on a floor, or the way numbers follow a special order in a puzzle? 
  • These are all examples of patterns
  • Patterns are like puzzles that repeat in a smart way, making things look neat, fun, and organized.

A pattern is formed by repeating a unit, which may be a set of numbers or shapes, according to a rule.

Understanding Number Patterns

1. Square Numbers

Patterns of squares using dots can be made in two different ways
I. Rita uses coloured dots to make patterns of squares as follows:

Patterns Class 5 Notes Maths

  • 1 x 1 = 1
  • 2 x 2 = 4
  • 3 x 3 = 9
  • 4 x 4 = 12

The number of dots in each square contains a square number and this is so called because the dots are arranged in a square shape.

A square number is obtained by multiplying the number by itself.

Now, can you name the next two square numbers and draw the square patterns?

Patterns Class 5 Notes Maths

II. Abhinav makes the square patterns as:

Patterns Class 5 Notes Maths

  • 1 × 1 = 1
  • 2 × 2 = 4 = 1 + 3
  • 3 × 3 = 9 = 1 + 3 + 5
  • 4 × 4 = 16 = 1 + 3 + 5 + 7

Thus, we observe that,
First square number = 1 = First odd number
Second square number = 4 = 1 + 3 = Sum of first two odd numbers
Third square number = 9 = 1 + 3 + 5 = Sum of first three odd numbers
Fourth square number = 16 = 1 + 3 + 5 + 7 = Sum of first four odd numbers

2. Triangular Numbers

  • Triangular patterns using dots can be made as given below.
  • The number of dots in each triangle is known as a triangular number.
  • Look at the following triangular pattern by using dots.

Patterns Class 5 Notes Maths

Thus, we observe the pattern as:
First triangular number = 1 = First natural number.
Second triangular number = 3 = 1 + 2 = Sum of first two natural numbers.
Third triangular number = 6 = 1 + 2 + 3 = Sum of first three natural numbers and so on.
Now, see what happens if you add two consecutive triangular numbers?
1 + 3 = 4
3 + 6 = 9
6 + 10 = 16
10 + 15 = 25
Square numbers

EduRev Tips: We get a square number by adding two consecutive triangular numbers. The square numbers are shown in a multiplication square as given alongside. They lie on a diagonal line.

Patterns Class 5 Notes Maths

Border Patterns

  • Observe the following patterns around you. Patterns in the border of dupatta, bedsheets, floors, etc.

Patterns Class 5 Notes Maths

  • These are called border patterns. We see that border patterns enhance the original beauty.
  • These border patterns are formed by repeating a certain shape or unit in one direction.
  • Following a basic symmetry repetition, maybe of translation, vertical reflection or horizontal reflection.

To understand better, let us take an example.
Consider the symbol Patterns Class 5 Notes Maths as the basic unit or shape in the border pattern. We can get the following patterns when Patterns Class 5 Notes Maths follows the different symmetries as shown below.

Patterns Class 5 Notes Maths

What are Tiling Patterns?

The most familiar examples of translations are the patterns formed by pairing stones or bricks and the cross-section of beehives.

A tiling pattern is formed by the repetition of a single unit or shape which when repeated, fills the plane with no gaps and no overlaps.

Look at the following patterns.

Patterns Class 5 Notes Maths

Now, observe these patterns. Are they tiling patterns? If not, then why not?

Patterns Class 5 Notes Maths

Thus, the above patterns are not tiling patterns.

Tiling Patterns Around Us

Tiling patterns are found in things around us.

Patterns Class 5 Notes Maths

Multiple tiling patterns can be made using a single shape as shown.

Patterns Class 5 Notes Maths

The document Patterns Class 5 Notes Maths is a part of the Class 5 Course Mathematics for Class 5.
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FAQs on Patterns Class 5 Notes Maths

1. What is a pattern in mathematics?
Ans. A pattern in mathematics is a sequence or arrangement that follows a specific rule or formula. It can be seen in numbers, shapes, or colors, where the elements repeat or change in a predictable way.
2. How can we identify number patterns?
Ans. To identify number patterns, we look for a sequence of numbers and determine the rule that governs the pattern. This could involve addition, subtraction, multiplication, or division. For example, in the pattern 2, 4, 6, 8, the rule is that each number increases by 2.
3. What are border patterns and how are they used?
Ans. Border patterns are decorative designs that are created along the edges of a surface. They often repeat in a uniform manner and are used in art, architecture, and textiles to enhance visual appeal and create a sense of order.
4. What is tiling pattern and how can it be created?
Ans. A tiling pattern is formed by arranging shapes, such as squares or triangles, in a way that covers a surface completely without any gaps or overlaps. To create a tiling pattern, one can use geometric shapes and repeat them in a systematic way.
5. Why are patterns important in mathematics?
Ans. Patterns are important in mathematics because they help us understand relationships and predict outcomes. Recognizing patterns aids in problem-solving and enhances critical thinking skills, allowing us to make connections between different mathematical concepts.
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