Class 6
Mathematics

Chapter 1 Patterns in Mathematics

Welcome to the complete tutorial of Chapter 1. In this lesson you will learn how mathematics is connected with patterns around us. You will also understand number patterns, shape patterns and their applications in daily life through simple explanations and examples.

Introduction

Mathematics is one of the most useful subjects in our daily life. From counting money to measuring distance, from designing buildings to using mobile phones, mathematics is present everywhere.

One of the most interesting ideas in mathematics is the study of patterns. Whenever numbers, shapes or objects follow a rule, they form a pattern.

Did You Know?

Patterns are found in flowers, leaves, honeycombs, buildings, music, computer programming and even in the stars.

Daily Life

Shopping, banking, travelling and sports all use mathematical patterns.

Technology

Computers, Artificial Intelligence and Mobile Apps depend upon mathematical patterns.

Engineering

Bridges, roads, houses and machines are designed using mathematics.

Nature

Nature itself follows beautiful mathematical patterns like flowers, shells and snowflakes.

Learning Objectives

After studying this chapter, you will be able to:

  • Understand the meaning of patterns.
  • Recognize different number patterns.
  • Identify shape patterns.
  • Find the next term in a sequence.
  • Understand square, triangular and cube numbers.
  • Observe mathematical patterns in nature.
  • Improve logical thinking and reasoning skills.

What are Patterns?

A pattern is an arrangement of numbers, shapes, letters or objects that follows a particular rule.

Once we understand the rule, we can easily predict the next term in the sequence.

Pattern = Rule + Sequence

Examples of Patterns

Number Pattern

2, 4, 6, 8, 10...

Rule: Add 2 every time.

Alphabet Pattern

A, C, E, G...

Rule: Skip one letter.

Shape Pattern

▲ ■■ ⬟ ⬢ Every new figure has more sides.

Colour Pattern

Red Blue Red Blue Red Blue The colours repeat in order.

Patterns Around Us

Patterns are present everywhere around us. We observe them every day, even without noticing.

  • Flower petals
  • Honeycomb
  • Chessboard
  • Building tiles
  • Traffic signals
  • Calendar
  • Clock
  • DNA structure
  • Computer programming
  • Music beats
The ability to recognize patterns is one of the most important mathematical skills.

Fun Fact

Mathematics is often called the Science of Patterns because every branch of mathematics studies different kinds of patterns.

The better you understand patterns, the easier algebra, geometry and programming become.

Number Patterns

A Number Pattern is a sequence of numbers arranged according to a particular rule. Every number is related to the previous number using a mathematical operation like addition, subtraction, multiplication or division.

Remember

Every number pattern follows a rule. If you know the rule, you can always find the next number.

Increasing Pattern

2, 4, 6, 8, 10...

Rule
Add 2

Decreasing Pattern

20,18,16,14,12...

Rule
Subtract 2

Multiplication Pattern

2,4,8,16,32...

Rule Multiply by 2

Division Pattern

64,32,16,8,4...

Rule Divide by 2

Counting Numbers

Counting numbers are the first numbers that we learn.

Counting Numbers

1 2 3 4 5 6 7 8 9 10 ....

These numbers continue forever.

Even Numbers

Even numbers are divisible by 2.

Numbers Observation
2 4 6 8 10 Every number is divisible by 2.
Rule

Next Even Number = Previous Number +2

Odd Numbers

Odd numbers are not divisible by 2.

Numbers Observation
1 3 5 7 9 Remainder becomes 1 after dividing by 2.

Square Numbers

Square numbers are obtained by multiplying a number by itself.

Number Calculation Square
1 1 × 1 1
2 2 × 2 4
3 3 × 3 9
4 4 × 4 16
5 5 × 5 25

Triangular Numbers

Triangular numbers are formed by arranging dots in the shape of a triangle.

1
1 +2 =3
1+2+3 =6
1+2+3+4 =10
1+2+3+4+5 =15
Triangular Numbers

1 3 6 10 15 21 28 ....

Cube Numbers

Cube numbers are obtained by multiplying a number three times.

Number Calculation Cube
1 1×1×1 1
2 2×2×2 8
3 3×3×3 27
4 4×4×4 64
5 5×5×5 125

Shape Patterns

A Shape Pattern is formed when different shapes are arranged according to a fixed rule. The rule may depend upon the number of sides, size, colour or position of the shapes.

Shape Patterns help us understand Geometry and improve logical thinking.

Repeating Pattern

■ ▲ ■ ▲ ■ ▲

The same shapes repeat again and again.

Growing Pattern

■ ■■ ■■■ ■■■■
Each figure becomes larger.

Rotating Pattern

▲ ▶ ▼ ◀
The shape rotates every time.

Colour Pattern

🟥 🟦 🟥 🟦
Colours repeat in order.

Matchstick Patterns

Many interesting mathematical patterns can be made using matchsticks. Observe the figures carefully and try to discover the rule.

Pattern 1


□

□□

□□□

□□□□

Every new figure requires three additional matchsticks.

Question How many matchsticks are required to make 10 connected squares?

Dot Patterns

Dot patterns help us understand square numbers, triangular numbers and many other mathematical concepts.

Example


•

• •

• • •

• • • •

Each row contains one more dot than the previous row.

This is called a triangular arrangement of dots.

Patterns in Nature

Nature is one of the greatest creators of mathematical patterns.

Snowflakes

Every snowflake has beautiful symmetry.

Flowers

Many flowers have petals arranged in mathematical patterns.

Honeycomb

Honey bees build hexagonal cells because they use space efficiently.

Shells

Sea shells often grow in beautiful spiral patterns.

Virahanka (Fibonacci) Pattern

One famous mathematical pattern is

1 1 2 3 5 8 13 21 34 55

Every number is obtained by adding the previous two numbers.

Example 2 + 3 = 5 3 + 5 = 8 5 + 8 = 13

Activity

Observe the floor tiles of your classroom. Can you identify a repeating pattern? Draw the pattern in your notebook.

Try these:
  • Window grills
  • Brick walls
  • Floor tiles
  • Notebook design
  • Clothing designs
  • Rangoli

Think & Answer

1. What is a pattern?

2. Name any two patterns found in nature.

3. What comes next? 2,4,6,8,___

4. Which number comes after 1,1,2,3,5,8,13,___

5. Draw any repeating pattern.

Key Takeaways

  • Mathematics is the study of patterns.
  • Patterns follow a fixed rule.
  • Patterns may be numerical or geometrical.
  • Nature is full of mathematical patterns.
  • Recognising patterns improves logical thinking.
  • Patterns are widely used in science and technology.

Solved Examples

Let's understand mathematical patterns using simple examples.

Example 1

Find the next number.

2, 4, 6, 8, __

Solution

The rule is Add 2

Answer = 10


Example 2

Find the next number.

5, 10, 15, 20, __

Every number increases by 5.

Answer = 25


Example 3

Find the next square number.

1, 4, 9, 16, 25, __

6 × 6 = 36

Answer = 36

Practice Yourself

Try solving these questions before checking the answers.

  1. 3, 6, 9, 12, ___
  2. 10, 20, 30, 40, ___
  3. 1, 3, 5, 7, ___
  4. 4, 8, 12, 16, ___
  5. 2, 4, 8, 16, ___

Important Points to Remember

Point 1

Every mathematical pattern follows a rule.

Point 2

Patterns help us predict future values.

Point 3

Patterns are found in both numbers and shapes.

Point 4

Patterns improve observation and logical thinking.

Chapter Summary

  • Mathematics is the science of patterns.
  • Patterns follow a fixed rule.
  • Number patterns may increase or decrease.
  • Shape patterns are based on figures.
  • Square numbers come from multiplying a number by itself.
  • Cube numbers come from multiplying a number three times.
  • Triangular numbers are formed by arranging dots.
  • Patterns are present everywhere around us.

Multiple Choice Questions

1. Which of the following is an even number?

A. 7
B. 11
C. 14
D. 15

Answer : C

2. What comes next? 2,4,6,8,...

A. 9
B. 10
C. 12
D. 14

Answer : B

3. Which number is a square number?

A. 15
B. 18
C. 25
D. 27

Answer : C

4. Patterns help us

A. Sleep
B. Predict
C. Forget
D. Draw only

Answer : B

5. Mathematics is called

A. Science of Colours
B. Science of Patterns
C. Science of Games
D. Science of Cooking

Answer : B

Practice Questions

  1. Define a mathematical pattern.
  2. Write five even numbers.
  3. Write five odd numbers.
  4. Find the next term: 12,15,18,21,__
  5. Find the next square number after 49.
  6. Explain triangular numbers with an example.
  7. Write any five patterns found in nature.
  8. Differentiate between square and cube numbers.
  9. Create your own number pattern.
  10. Create your own shape pattern.

Chapter Quiz

Test your understanding of this chapter.

1. Which pattern is increasing?




2. Which is a square number?




3. Mathematics is the study of




Assertion & Reason

A. Patterns help us predict future terms.

R. Every mathematical pattern follows a rule.

A. Every odd number is divisible by 2.

R. Odd numbers always leave remainder 1.

Worksheet

  1. Write first twenty counting numbers.
  2. Write ten even numbers.
  3. Write ten odd numbers.
  4. Write first ten square numbers.
  5. Write first five cube numbers.
  6. Create one repeating pattern.
  7. Create one growing pattern.
  8. Draw a triangular dot pattern.
  9. Draw any shape pattern.
  10. Find the missing number: 4 8 12 __ 20

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Continue Learning

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