Class 6 Maths Chapter 1: Patterns in Mathematics Worksheet

Class: 6  Subject: Mathematics (Ganita Prakash)  Chapter: Patterns in Mathematics
This worksheet is based on the chapter “Patterns in Mathematics”.

Section A – Fill in the Blanks (10 × 1 = 10)

1. Mathematics is the search for __________.
2. The study of whole number patterns is called __________.
3. The sequence 2, 4, 6, 8, … is called __________ numbers.
4. The sequence 1, 3, 5, 7, … is called __________ numbers.
5. 25 is a __________ number.
6. 64 is a __________ number.
7. The next number after 21 in the Virahānka sequence is __________.
8. The next number in the sequence 1, 2, 4, 8, 16 is __________.
9. Shapes having equal sides and equal angles are called __________ polygons.
10. The branch of Mathematics that studies shapes is called __________.

Section B – Multiple Choice Questions (10 × 1 = 10)

1. Which of the following is an odd number?
2. A) 10
   B) 18
   C) 21
   D) 40
3. Which sequence represents square numbers?
4. A) 1, 3, 6, 10…
   B) 1, 4, 9, 16…
   C) 2, 4, 6, 8…
   D) 1, 2, 3, 5…
5. Which number comes next?

1, 8, 27, 64, 125, _____

1. A) 144
   B) 196
   C) 216
   D) 225
2. Which sequence is known as triangular numbers?
3. A) 1, 2, 3, 4…
   B) 1, 3, 6, 10…
   C) 2, 4, 6, 8…
   D) 1, 4, 9, 16…
4. What is the next number?

1, 2, 3, 5, 8, 13, 21, _____

1. A) 29
   B) 31
   C) 34
   D) 35
2. Which shape has 8 equal sides?
3. A) Pentagon
   B) Hexagon
   C) Octagon
   D) Heptagon
4. Which branch of Mathematics studies shapes?
5. A) Algebra
   B) Geometry
   C) Arithmetic
   D) Statistics
6. What is the next power of 2?

1, 2, 4, 8, 16, _____

1. A) 18
   B) 24
   C) 32
   D) 64
2. Which of the following is NOT a square number?
3. A) 25
   B) 36
   C) 45
   D) 49
4. Which shape has 5 sides?
5. A) Hexagon
   B) Pentagon
   C) Octagon
   D) Triangle

Section C – Complete the Patterns (10 × 1 = 10)

1. 1, 2, 3, 4, 5, ___, ___, ___
2. 2, 4, 6, 8, 10, ___, ___
3. 1, 3, 5, 7, 9, ___, ___
4. 1, 4, 9, 16, 25, ___
5. 1, 8, 27, 64, ___
6. 1, 3, 6, 10, 15, ___
7. 1, 2, 4, 8, 16, ___
8. 1, 3, 9, 27, 81, ___
9. 1, 7, 19, 37, ___
10. 1, 2, 3, 5, 8, 13, ___

Section D – Match the Following (5 × 1 = 5)

Column A	Column B
Square Numbers	Geometry
Cube Numbers	1, 8, 27
Geometry	1, 4, 9
Odd Numbers	1, 3, 5
Even Numbers	2, 4, 6

Section E – True or False (10 × 1 = 10)

1. Mathematics is only about calculations. ______
2. Number theory studies whole numbers. ______
3. 36 is a square number. ______
4. 36 is also a triangular number. ______
5. 64 is a cube number. ______
6. A hexagon has 6 sides. ______
7. A pentagon has 7 sides. ______
8. Geometry studies shapes. ______
9. Regular polygons have equal sides and equal angles. ______
10. The sequence 1, 2, 4, 8… is called Powers of 2. ______

Section F – Short Answer Questions (5 × 2 = 10)

1. What is Mathematics?
2. What are number sequences?
3. Why are 1, 4, 9, 16 called square numbers?
4. What are triangular numbers?
5. Write any four examples where Mathematics is used in daily life.

Section G – Long Answer Questions (5 × 3 = 15)

1. Explain the difference between odd numbers and even numbers with examples.
2. Write any six important number sequences given in the chapter.
3. Explain why Mathematics is useful in everyday life.
4. What are regular polygons? Give four examples.
5. Explain the relation between odd numbers and square numbers using examples.

Section H – Higher Order Thinking Skills (HOTS) (5 × 2 = 10)

1. Find the next number:
   1, 7, 19, 37, ____
2. If the first 10 odd numbers add up to a square number, what is the square number?
3. Which number is both a triangular number and a square number?
4. Find the next number:
   1, 3, 9, 27, 81, ____
5. Create your own number pattern using at least six numbers.

 

Class 6 Maths Chapter 1: Patterns in Mathematics Worksheet Solutions

 

The solutions follow the number sequences, shape patterns and relationships explained in the chapter.

Section A – Fill in the Blanks

1. Mathematics is the search for patterns.
2. The study of whole number patterns is called number theory.
3. The sequence 2, 4, 6, 8, … is called even numbers.
4. The sequence 1, 3, 5, 7, … is called odd numbers.
5. 25 is a square
6. 64 is a cube
7. The next number after 21 in the Virahānka sequence is 34.
8. The next number in the sequence 1, 2, 4, 8, 16 is 32.
9. Shapes having equal sides and equal angles are called regular
10. The branch of Mathematics that studies shapes is called geometry.

Section B – Multiple Choice Questions

1. C) 21
2. B) 1, 4, 9, 16…
3. C) 216
4. B) 1, 3, 6, 10…
5. C) 34
6. C) Octagon
7. B) Geometry
8. C) 32
9. C) 45
10. B) Pentagon

Section C – Complete the Patterns

1. 1, 2, 3, 4, 5, 6, 7, 8
2. 2, 4, 6, 8, 10, 12, 14
3. 1, 3, 5, 7, 9, 11, 13
4. 1, 4, 9, 16, 25, 36
5. 1, 8, 27, 64, 125
6. 1, 3, 6, 10, 15, 21
7. 1, 2, 4, 8, 16, 32
8. 1, 3, 9, 27, 81, 243
9. 1, 7, 19, 37, 61

The differences are 6, 12, 18 and 24.

10. 1, 2, 3, 5, 8, 13, 21

Section D – Match the Following

Column A	Correct Match
Square Numbers	1, 4, 9
Cube Numbers	1, 8, 27
Geometry	Study of shapes
Odd Numbers	1, 3, 5
Even Numbers	2, 4, 6

Section E – True or False

1. Mathematics is only about calculations. — False
2. Number theory studies whole numbers. — True
3. 36 is a square number. — True
4. 36 is also a triangular number. — True
5. 64 is a cube number. — True
6. A hexagon has 6 sides. — True
7. A pentagon has 7 sides. — False
8. Geometry studies shapes. — True
9. Regular polygons have equal sides and equal angles. — True
10. The sequence 1, 2, 4, 8… is called Powers of 2. — True

Section F – Short Answer Questions

 

1. What is Mathematics?

Mathematics is the search for patterns and the explanations for why those patterns exist. Patterns can be found in numbers, shapes, nature, technology and everyday activities.

2. What are number sequences?

A number sequence is a list of numbers arranged according to a particular rule or pattern.

For example:

• 2, 4, 6, 8, … follows the pattern of even numbers.
• 1, 4, 9, 16, … follows the pattern of square numbers.

3. Why are 1, 4, 9 and 16 called square numbers?

They are called square numbers because their dots can be arranged in the form of perfect squares.

• 1 = 1 × 1
• 4 = 2 × 2
• 9 = 3 × 3
• 16 = 4 × 4

4. What are triangular numbers?

Triangular numbers are numbers whose dots can be arranged in the shape of a triangle.

Examples are:

1, 3, 6, 10, 15, 21…

Each triangular number is formed by adding the next counting number:

• 1
• 1 + 2 = 3
• 1 + 2 + 3 = 6
• 1 + 2 + 3 + 4 = 10

5. Write four examples where Mathematics is used in daily life.

Mathematics is used in:

1. Shopping and calculating bills
2. Cooking and measuring ingredients
3. Reading clocks and calendars
4. Constructing houses and bridges

Section G – Long Answer Questions

1. Explain the difference between odd and even numbers.

Odd numbers are numbers that cannot be divided equally into groups of two.

Examples:

1, 3, 5, 7, 9, 11…

Even numbers are numbers that can be divided equally into groups of two.

Examples:

2, 4, 6, 8, 10, 12…

An even number is divisible by 2, while an odd number leaves a remainder of 1 when divided by 2.

2. Write any six important number sequences from the chapter.

Six important number sequences are:

1. Counting numbers:
   1, 2, 3, 4, 5…
2. Odd numbers:
   1, 3, 5, 7, 9…
3. Even numbers:
   2, 4, 6, 8, 10…
4. Triangular numbers:
   1, 3, 6, 10, 15…
5. Square numbers:
   1, 4, 9, 16, 25…
6. Cube numbers:
   1, 8, 27, 64, 125…

Other sequences in the chapter include Virahānka numbers and powers of 2 and 3.

3. Explain why Mathematics is useful in everyday life.

Mathematics is useful because it helps us understand and solve everyday problems. We use it while shopping, calculating money, measuring objects, cooking food and reading time.

Mathematics is also used in science, technology, transport, construction and medicine. It helps people build houses and bridges, create mobile phones and computers, study planets and design vehicles.

4. What are regular polygons? Give four examples.

Regular polygons are closed shapes in which all sides are equal in length and all angles are equal.

Four examples are:

1. Equilateral triangle
2. Square
3. Regular pentagon
4. Regular hexagon

The chapter explains that regular polygons can be arranged according to the number of their sides: 3, 4, 5, 6, 7 and so on.

5. Explain the relationship between odd numbers and square numbers.

When consecutive odd numbers starting from 1 are added, the result is always a square number.

Examples:

• 1 = 1²
• 1 + 3 = 4 = 2²
• 1 + 3 + 5 = 9 = 3²
• 1 + 3 + 5 + 7 = 16 = 4²
• 1 + 3 + 5 + 7 + 9 = 25 = 5²

Therefore, the sum of the first n odd numbers is n².

Section H – HOTS Solutions

1. Find the next number:

1, 7, 19, 37, 61

Explanation:

• 7 − 1 = 6
• 19 − 7 = 12
• 37 − 19 = 18

The differences increase by 6.

Therefore:

37 + 24 = 61

2. What is the sum of the first 10 odd numbers?

The sum of the first n odd numbers is n².

Therefore:

10² = 100

3. Which number is both triangular and square?

36

It is a square number because:

6 × 6 = 36

It is also a triangular number because:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

4. Find the next number:

1, 3, 9, 27, 81, 243

Each number is multiplied by 3:

81 × 3 = 243

5. Create your own number pattern.

Sample answer:

5, 10, 15, 20, 25, 30

Rule: Add 5 to each number.

Other correctly formed patterns are also acceptable.