[New 2025-26] Chapter 1 - Patterns in Mathematics NCERT Solution | Worksheet | Extra Questions for Class 6 Maths Ganita Prakash.
Class 6 maths chapter 1 full chapter : Patterns in mathematics.
'Patterns in Mathematics' is an important topic to understand in mathematics. In this chapter, we will explore some of the most basic ideas of mathematics including sequences of numbers and sequences of shapes and their remarkable and often surprising interrelations. These ideas form the building blocks of ‘mathematics’, and will help us in understanding more advanced topics in mathematics such as the numbers and analysis of different shapes...
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# THIS PAGE INCLUDES :
# Notes : Patterns in Mathematics
Patterns in Mathematics class 6 notes
# Patterns in Numbers :
Among the most basic patterns that occur in mathematics are patterns of numbers. Table given below shows some key number sequences that are studied in Mathematics.
All 1's : Every number in the pattern is one (1).
Counting numbers : Numbers in the pattern are increased by 1.
E.g. 1, 2, 3, 4, 5, 6, 7, ...
Odd numbers : Numbers in the pattern are increased by 2. starting with one (1).
E.g. 1, 3, 5, 7, 9, 11, 13, ...
Even numbers : Numbers in the pattern are increased by 2. starting with two (2).
E.g. 2, 4, 6, 8, 10, 12, 14, ...
Triangular numbers : Numbers in the pattern are obtained by adding the natural numbers. starting with 2.
E.g.
01 + 2 = 3
03 + 3 = 6
06 + 4 = 10
10 + 5 = 15
15 + 6 = 21
21 + 7 = 28
Squares : Numbers in the pattern are the squares of natural numbers.
E.g.
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
Cubes : Numbers in the pattern are the cubes of natural numbers.
E.g.
1 x 1 x 1 = 1
2 x 2 x 2 = 8
3 x 3 x 3 = 27
4 x 4 x 4 = 64
5 x 5 x 5 = 125
6 x 6 x 6 = 216
Virahanka numbers : Each number is the sum of two preceding numbers in the sequence.
E.g.
00 + 1 = 1
01 + 1 = 2
02 + 1 = 3
03 + 2 = 5
05 + 3 = 8
08 + 5 = 13
13 + 8 = 21
Power of 2 : Each term in the sequence is obtained by multiplying the preceding number by 2.
E.g.
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
Power of 3 : Each term in the sequence is obtained by multiplying the preceding number by 3.
E.g.
30 = 1
31 = 3
32 = 9
33 = 27
34 = 81
35 = 243
# Visualising Number Sequences :
Many number sequences can be visualized using pictures. Visualising mathematical objects through pictures or diagrams can be a very fruitful way to understand mathematical patterns and concepts.
Let us represent the number sequences using the following pictures.
Patterns in Mathematics Class 6 Notes Maths Chapter 1.
# Relation among Number Sequences :
Sometimes, number sequences can be related to each other in surprising ways. like when you start adding counting numbers you will end up getting triangular numbers and when you start adding counting numbers up and down you will end up getting square numbers.
⏺ Adding Counting numbers :
1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15
1 + 2 + 3 + 4 + 5 + 6 = 21
The sequence is 1, 3, 6, 10, 15, 21, .... which are triangular numbers.
Pictorial explanation :
⏺ Adding counting numbers up and down :
1 = 1
1 + 2 + 1 = 4
1 + 2 + 3 + 2 + 1 = 9
1 + 2 + 3 + 4 + 3 + 2 + 1 = 16
1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 25
1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 36
The sequence is 1, 4, 9, 16, 25, 36, ... which are square numbers in the form of 12, 22, 32, 42, 52, 62, ...
Pictorial explanation :
Class 6 Maths Chapter 1 Notes Patterns in Mathematics.
# Patterns in Shapes :
Other important and basic patterns that occur in Mathematics are patterns of shapes. These shapes may be in one, two, or three dimensions (1D, 2D, or 3D)—or in even more dimensions. The branch of Mathematics that studies patterns in shapes is called geometry.
Shape sequences are one important type of shape pattern that mathematicians study. Table given below shows a few key shape sequences that are studied in Mathematics.
# Relation to Number Sequences :
⏺ Regular Polygon :
In a regular polygon, number of sides are represented by counting numbers.
E.g.
● 03 sided - Triangle
● 04 sided - Quadrilateral
● 05 sided - Pentagon
● 06 sided - Hexagon
● 07 sided - Heptagon
● 08 sided - Octagon
● 09 sided - Nonagon
● 10 sided - Decagon
π Note : The word ‘regular’ refers to the fact that these shapes have equal-length sides and also equal ‘angles’.
⏺ Stacked Squares :
In stacked squares, each square is related to square numbers (1, 4, 9, 16, ...), where each step in the sequence add another row and column of squares.
Numbers in the pattern are the squares of natural numbers.
E.g.
1 x 1 = 01
2 x 2 = 04
3 x 3 = 09
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
----- The End -----
# Key Points :
● Mathematics may be viewed as the search for patterns and for the explanations as to why those patterns exist.
● Among the most basic patterns that occur in mathematics are number sequences.
● Some important examples of number sequences include the counting numbers, odd numbers, even numbers, square numbers, triangular numbers, cube numbers, VirahΔnka numbers, and powers of 2.
● Sometimes number sequences can be related to each other in beautiful and remarkable ways. For example, adding up the sequence of odd numbers starting with 1 gives square numbers.
● Visualizing number sequences using pictures can help to understand sequences and the relationships between them.
● Shape sequences are another basic type of pattern in mathematics. Some important examples of shape sequences include regular polygons, complete graphs, stacked triangles and squares, and Koch snowflake iterations. Shape sequences also exhibit many interesting relationships with number sequences.
# NCERT Solutions :
Ganita Prakash class 6 maths chapter 1 Patterns in mathematics figure it out ncert page 2.
Patterns in Mathematics Class 6 NCERT Solutions Ganita Prakash Maths Chapter 1
Q1.
Can you think of other examples where mathematics helps us in our everyday lives?
Solution :
Shopping : For calculating total cost of goods, amount of Tax and discount.
At Home : Measuring ingredients for cooking, calculating monthly budget/expenses.
Travelling : Estimating travel time, Distance and Expenses.
Ganita Prakash Class 6 Maths Chapter 1 Solutions Patterns in Mathematics.
Q2.
How has mathematics helped propel humanity forward?
Solution :
Economy : Helps in investment, Money distribution, budget planning, etc.
Infrastructure : For designing and developing Bridges, houses, highways, etc.
Science and Technology : Helps in developing machine learning and Artificial intelligence.
Ganita Prakash class 6 maths chapter 1 Patterns in mathematics figure it out ncert page 3.
NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 1 Patterns in Mathematics
Q1.
Can you recognize the pattern in each of the sequences in Table 1?
Solution :
Yes, we can recognize the pattern in each of the sequence.
All 1's : Every number in the pattern is one (1).
Counting numbers : Numbers in the pattern are increased by 1.
E.g. 1, 2, 3, 4, 5, 6, 7, ...
Odd numbers : Numbers in the pattern are increased by 2. starting with one (1).
E.g. 1, 3, 5, 7, 9, 11, 13, ...
Even numbers : Numbers in the pattern are increased by 2. starting with two (2).
E.g. 2, 4, 6, 8, 10, 12, 14, ...
Triangular numbers : Numbers in the pattern are obtained by adding the natural numbers. starting with 2.
E.g.
01 + 2 = 3
03 + 3 = 6
06 + 4 = 10
10 + 5 = 15
15 + 6 = 21
21 + 7 = 28
Squares : Numbers in the pattern are the squares of natural numbers.
E.g.
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
Cubes : Numbers in the pattern are the cubes of natural numbers.
E.g.
1 x 1 x 1 = 1
2 x 2 x 2 = 8
3 x 3 x 3 = 27
4 x 4 x 4 = 64
5 x 5 x 5 = 125
6 x 6 x 6 = 216
Virahanka numbers : Each number is the sum of two preceding numbers in the sequence.
E.g.
00 + 1 = 1
01 + 1 = 2
02 + 1 = 3
03 + 2 = 5
05 + 3 = 8
08 + 5 = 13
13 + 8 = 21
Power of 2 : Each term in the sequence is obtained by multiplying the preceding number by 2.
E.g.
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
Power of 3 : Each term in the sequence is obtained by multiplying the preceding number by 3.
E.g.
30 = 1
31 = 3
32 = 9
33 = 27
34 = 81
35 = 243
Patterns in Mathematics Class 6 Solutions Question Answer.
Q2.
Rewrite each sequence of Table 1 in your notebook, along with the next three numbers in each sequence! After each sequence, write in your own words what is the rule for forming the numbers in the sequence.
Solution :
All 1's : Every number in the pattern is one (1).
Counting numbers : Numbers in the pattern are increased by 1.
E.g. 8, 9, 10.
Odd numbers : Numbers in the pattern are increased by 2. starting with one (1).
E.g. 15, 17, 19.
Even numbers : Numbers in the pattern are increased by 2. starting with two (2).
E.g. 16, 18, 20.
Triangular numbers : Numbers in the pattern are obtained by adding the natural numbers. starting with 2.
E.g.
28 + 8 = 36
36 + 9 = 45
45 + 10 = 55
Squares : Numbers in the pattern are the squares of natural numbers.
E.g.
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
Cubes : Numbers in the pattern are the cubes of natural numbers.
E.g.
7 x 7 x 7 = 343
8 x 8 x 8 = 512
9 x 9 x 9 = 729
Virahanka numbers : Each number is the sum of two preceding numbers in the sequence.
E.g.
21 + 13 = 34
34 + 21 = 55
55 + 34 = 89
Power of 2 : Each term in the sequence is obtained by multiplying the preceding number by 2.
E.g.
27 = 128
28 = 256
29 = 512
Power of 3 : Each term in the sequence is obtained by multiplying the preceding number by 3.
E.g.
36 = 729
37 = 2187
38 = 6561
Ganita Prakash class 6 maths chapter 1 Patterns in mathematics figure it out ncert page 5.
Class 6 Maths Ganita Prakash Chapter 1 Patterns in Mathematics Question Answers.
Q1.
Copy the pictorial representations of the number sequences in Table 2 in your notebook, and draw the next picture for each sequence!
Answer :
Class 6 Maths Chapter 1 Patterns in Mathematics Solutions.
Q2.
Why are 1, 3, 6, 10, 15, … called triangular numbers? Why are 1, 4, 9, 16, 25, … called square numbers or squares? Why are 1, 8, 27, 64, 125, … called cubes?
Solution :
Triangular numbers : 1, 3, 6, 10, 15, ... are called triangular numbers because they can be represented in the form of an equilateral triangle.
Square numbers : 1, 4, 9, 16, 25, ... are called Square numbers because they can be represented in the form of Square.
Cube numbers : 1, 8, 27, 64, 125, ... are called Cube numbers because they can be represented in the form of Cube.
Patterns in Mathematics Class 6 question answer.
Q3.
You will have noticed that 36 is both a triangular number and a square number! That is, 36 dots can be arranged perfectly both in a triangle and in a square. Make pictures in your notebook illustrating this!
This shows that the same number can be represented differently, and play different roles, depending on the context. Try representing some other numbers pictorially in different ways!
Answer :
Chapter 1 patterns in mathematics class 6.
Q4.
What would you call the following sequence of numbers?
That’s right, they are called hexagonal numbers! Draw these in your notebook. What is the next number in the sequence?
Answer :
The following sequence of number is called Hexagonal Numbers. The next number in this sequence is 61.
chapter 1 patterns in mathematics class 6 solutions.
Q5.
Can you think of pictorial ways to visualize the sequence of Powers of 2? Powers of 3?
Answer :
Power of 2 :
We can visualize the sequence of power of 2 as squares made of dots where each subsequent square has twice the number of dots as of the previous one.
Power of 3 :
We can visualize the sequence of power of 3 as triangles made of dots where each subsequent triangle has thrice the number of dots as of the previous one.
Ganita Prakash class 6 maths chapter 1 Patterns in mathematics figure it out ncert page 8.
Class 6 maths chapter 1 new book patterns in mathematics.
Q1.
Can you find a similar pictorial explanation for why adding counting numbers up and down, i.e., 1, 1 + 2 + 1, 1 + 2 + 3 + 2 + 1, …, gives square numbers?
Answer :
1
1 + 2 + 1 = 4
1 + 2 + 3 + 2 + 1 = 9
1 + 2 + 3 + 4 + 3 + 2 + 1 = 16
1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 25
1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 36
The sequence is 1, 4, 9, 16, 25, 36, ... which is in the form of 12, 22, 32, 42, 52, 62, ...
Pictorial explanation :
Q2.
By imagining a large version of your picture, or drawing it partially, as needed, can you see what will be the value of 1 + 2 + 3 + ... + 99 + 100 + 99 + ... + 3 + 2 + 1?
Solution :
1 + 2 + 3 + ... + 99 + 100 + 99 + ... + 3 + 2 + 1 = 100 x 100 = 10,000.
Patterns in Mathematics NCERT Solutions.
Q3.
Which sequence do you get when you start to add the All 1’s sequence up? What sequence do you get when you add the All 1’s sequence up and down?
Solution :
(i) Adding all 1's sequence up.
1
1 + 1 = 2
1 + 1 + 1 = 3
1 + 1 + 1 + 1 = 4
1 + 1 + 1 + 1 + 1 = 5
∴ The sequence is 1, 2, 3, 4, 5, ... which are natural numbers.
(ii) Adding all 1's sequence up and down.
1
1 + 1 = 2
1 + 1 + 1 = 3
1 + 1 + 1 + 1 = 4
1 + 1 + 1 + 1 + 1 = 5
∴ The sequence is 1, 2, 3, 4, 5, ... which are again natural numbers.
Q4.
Which sequence do you get when you start to add the Counting numbers up? Can you give a smaller pictorial explanation?
Answer :
1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15
1 + 2 + 3 + 4 + 5 + 6 = 21
The sequence is 1, 3, 6, 10, 15, 21, .... which are triangular numbers.
Pictorial explanation :
Patterns in mathematics class 6 cbse.
Q5.
What happens when you add up pairs of consecutive triangular numbers? That is, take 1 + 3, 3 + 6, 6 + 10, 10 + 15, … ? Which sequence do you get? Why? Can you explain it with a picture?
Answer :
1 + 3 = 4
3 + 6 = 9
6 + 10 = 16
10 + 15 = 25
15 + 21 = 36
The sequence is 4, 9, 16, 25, 36, .... which consists of square numbers. This is because the sum of two consecutive triangular numbers are Square numbers.
Pictorial explanation :
Class 6 maths chapter 1 patterns in mathematics solutions.
Q6.
What happens when you start to add up powers of 2 starting with 1, i.e., take 1, 1 + 2, 1 + 2 + 4, 1 + 2 + 4 + 8, … ? Now add 1 to each of these numbers—what numbers do you get? Why does this happen?
Answer :
1
1 + 2 = 3
1 + 2 + 4 = 7
1 + 2 + 4 + 8 = 15
1 + 2 + 4 + 8 + 16 = 31
The sequence is 1, 3, 7, 15, 31, ... On adding 1 to each term.
01 + 1 = 2
03 + 1 = 4
07 + 1 = 8
15 + 1 = 16
31 + 1 = 32
The new sequence is 2, 4, 8, 16, 32, ... which can also be written as 21, 22, 23, 24, 25, ... This sequence represent power of 2.
Patterns in mathematics class 6 ncert solutions.
Page 9 : Figure it out.
Q7.
What happens when you multiply the triangular numbers by 6 and add 1? Which sequence do you get? Can you explain it with a picture?
Answer :
On multiplying triangular numbers by 6 and adding 1 we get -
(01 x 6) + 1 = 7
(03 x 6) + 1 = 19
(06 x 6) + 1 = 37
(10 x 6) + 1 = 61
The sequence is 7, 19, 37, 61, .... which are hexagonal numbers.
Pictorial explanation :
ncert class 6 maths chapter 1 patterns in mathematics.
Q8.
What happens when you start to add up hexagonal numbers, i.e., take 1, 1 + 7, 1 + 7 + 19, 1 + 7 + 19 + 37, … ? Which sequence do you get? Can you explain it using a picture of a cube?
Answer :
1
1 + 7 = 8
1 + 7 + 19 = 27
1 + 7 + 19 + 37 = 64
1 + 7 + 19 + 37 + 61 = 125
1 + 7 + 19 + 37 + 61 + 91 = 216
The sequence is 1, 8, 27, 64, 125, ... Which are cubes of counting numbers.
Pictorial explanation :
Ganita Prakash class 6 maths chapter 1 Patterns in mathematics figure it out ncert page 11.
Patterns in mathematics class 6 ganita prakash
Q1.
Can you recognise the pattern in each of the sequences in Table 3?
Answer :
Regular Polygons : The sequence shows polygons with increasing number of sides, starting with triangle (3 sides) up to decagon (10 sides).
Complete graphs :
The sequence represents complete graph, denoted by Kn (n is number of vertices). In each graph, vertices are connected to each other by straight line starting from k2 (2 vertices) to K6 (6 vertices).
Stacked Squares :
The sequence shows shapes consists of a square grid, with the number of squares in increasing order i.e. 1x1 , 2x2, 3x3, 4x4, 5x5.
Stacked Triangles :
The sequence shows shapes consists of a triangular grid, with the number of triangles in increasing order i.e. each row adds an additional triangle. It grows in triangular numbers (1, 3, 6, 10, 15, etc.)
Koch Snowflake : The sequence shows process of constructing a Koch snowflake, starting with an equilateral triangle, 6 triangles added up to make a star and adds more detailed edges, creating a fractal pattern.
Patterns in Mathematics Class 6 Solutions Questions and Answers.
Q2.
Try and redraw each sequence in Table 3 in your notebook. Can you draw the next shape in each sequence? Why or why not? After each sequence, describe in your own words what is the rule or pattern for forming the shapes in the sequence.
Answer :
class 6 maths patterns in mathematics solutions.
Page 11 : Figure it out.
Q1.
Count the number of sides in each shape in the sequence of Regular Polygons. Which number sequence do you get? What about the number of corners in each shape in the sequence of Regular Polygons? Do you get the same number sequence? Can you explain why this happens?
Answer :
The sequence for sides of regular polygon is 3, 4, 5, 6, 7, 8, 9, 10, ... Here, the sequence is of counting numbers starting from 3.
The sequence for corners of regular polygon is 3, 4, 5, 6, 7, 8, 9, 10, ... Yes, we get the same sequence because in a regular polygon the numbers of sides and corners are equal.
Patterns in mathematics class 6 questions and answers.
Q2.
Count the number of lines in each shape in the sequence of Complete Graphs. Which number sequence do you get? Can you explain why?
Answer :
01 Shape = 01
02 Shape = 03
03 Shape = 06
04 Shape = 10
05 Shape = 15
The sequence we get is 1, 3, 6, 10, 15, ... These are the triangular numbers.
Class 6 maths ch 1 patterns in mathematics.
Page 12 : Figure it out.
Q3.
How many little squares are there in each shape of the sequence of Stacked Squares? Which number sequence does this give? Can you explain why?
Answer :
01 Shape = 01
02 Shape = 04
03 Shape = 09
04 Shape = 16
05 Shape = 25
The sequence we get is 1, 4, 9, 16, 25, ... These are the Square numbers because these numbers can be expressed in the form 12, 22, 32, 42, 52, ...
Class 6 math chapter 1 patterns in mathematics.
Q4.
How many little triangles are there in each shape of the sequence of Stacked Triangles? Which number sequence does this give? Can you explain why? (Hint: In each shape in the sequence, how many triangles are there in each row?)
Answer :
01 Shape = 01
02 Shape = 04
03 Shape = 09
04 Shape = 16
05 Shape = 25
The sequence we get is 1, 4, 9, 16, 25, ... These are the Square numbers because these numbers can be expressed in the form 12, 22, 32, 42, 52, ...
Class 6 math chapter 1 patterns in mathematics question answer.
Q5.
To get from one shape to the next shape in the Koch Snowflake sequence, one replaces each line segment ‘—’ by a ‘speed bump’ . As one does this more and more times, the changes become tinier and tinier with very-very small line segments. How many total line segments are there in each shape of the Koch Snowflake? What is the corresponding number sequence? (The answer is 3, 12, 48, ..., i.e. 3 times Powers of 4; this sequence is not shown in Table 1)
Answer :
The sequence for the line segment in each shape can be written as 3 x 4n. (where n = 0, 1, 2, 3, 4, 5, ...)
Shape 01 :
= 3 x 40
= 3 x 1
= 03
Shape 02 :
= 3 x 41
= 3 x 4
= 12
Shape 03 :
= 3 x 42
= 3 x 16
= 48
Shape 04 :
= 3 x 43
= 3 x 64
= 192
Shape 05 :
= 3 x 44
= 3 x 256
= 768
The sequence we get is 3, 12, 48, 192, 768, .....
# Worksheet - Extra Questions :
Patterns in Mathematics Class 6 Extra Questions Maths Chapter 1
class 6 maths chapter 1 patterns in mathematics worksheet
# Fill in the blanks :
1. A _______ polygon has all sides and angles equal.
2. A seven sided polygon is called _______ .
3. The sequence 1, 4, 9, 16, 25, ... is known as _______ numbers.
4. The number 1, 8, 27, 64, 125, 216, ... are the _______ of counting numbers.
5. The sequence 7, 19, 37, 61 is called _______ numbers.
Patterns in mathematics class 6 extra questions worksheet.
# True - False :
1. The sequence 1, 4, 9, 16, 25, ... is an example of cube numbers.
2. The sequence 3, 5, 7, 9, ... is an example of odd numbers.
3. A regular pentagon has 5 sides and 4 angles.
4. The number 36 can be both a triangular and a square number.
5. We can use (3 x 4n) for Koch snowflake pattern.
Patterns in maths for class 6 worksheets.
# Multiple Choice Questions :
Q1. If you start with the number 1 and keep adding 2, what sequence will you get?
(a) Sequence of Even numbers
(b) Sequence of odd numbers
(c) Sequence of Prime numbers
(d) Sequence of Square numbers
Q2. How many sides does a Heptagon have?
(a) 04
(b) 05
(c) 06
(d) 07
Q3. What is the sum of first 5 odd numbers?
(a) 25
(b) 35
(c) 55
(d) 45
Q4. Which number is both square and triangular number?
(a) 16
(b) 25
(c) 36
(d) 10
Q5. Which number sequence denotes hexagonal numbers?
(a) 1, 4, 9, 16
(b) 1, 3, 6, 10
(c) 1, 8, 27, 64
(d) 1, 7, 19, 37
Class 6 Maths Chapter 1 Extra Questions Patterns in Mathematics.
# Numerical Question :
Q1.
Complete the following number sequences:
(a) 1 + 3 + 5 + ____ + 9 + 11 = ____.
(b) 1 + ____ + 3 + 4 + 3 + 2 + 1 = ____.
(c) 1 + 2 + 3 + ____ + 5 + ____ + 7 + ____ + 7 + ___ + 5 + 4 + 3 + 2 + 1 = 64
Q2.
Identify the patterns and write the next three numbers to complete the given patterns.
(a) 1, 3, 6, 10, 15, ____, ____, ____.
(b) 1, 4, 9, 16, 25, ____, ____, ____.
(c) 1, 8, 27, 64, 125, ____, ____, ____.
Q3.
Find out the next 3 missing numbers and figure out the pattern rule for each sequence.
(a) 5, 25, 125, 625, ____, ____, ____.
(b) 11, 13, 17, 19, 23, 29, ____, ____, ____.
(c) 3, 9, 27, 81, 243, ____, ____, ____.
(d) 64, 125, 216, 343, ____, ____, ____.
(e) 8, 13, 21, 34, 55, ____, ____, ____.
Q4.
What will be the pattern if we starts with 3 sided regular polygon and add 1 side in the shape with each step?
Q5.
Observe the pattern given below. Find the missing number.
Patterns in mathematics class 6 solutions worksheets
Patterns in Mathematics Class 6 Worksheet with answers
# Fill in the Blanks :
1. Regular
2. Heptagon
3. Square
4. Cubes
5. Hexagonal
Class 6 Maths Patterns in Mathematics Extra Questions.
# True - False :
1. False
2. True
3. False
4. True
5. True
Patterns in Mathematics Class 6 Extra Questions.
# MCQ's :
Q1. Sequence of odd numbers (b)
Q2. 7 (d)
Q3. 25 (a)
Q4. 36 (c)
Q5. 1, 7, 19, 37 (d)
worksheet for patterns in mathematics class 6.
# Numerical Questions :
Solution Q1 :
(a) 1 + 3 + 5 + 7 + 9 + 11 = 36 .
(b) 1 + 2 + 3 + 4 + 3 + 2 + 1 = 16 .
(c) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 64
Solution Q2 :
(a) The given pattern is as follows:
1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15
The given number sequence is a pattern of triangular numbers.
The next three numbers of this pattern are:
1 + 2 + 3 + 4 + 5 + 6 = 21
1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
(b) The given pattern is as follows:
1 × 1 = 1
2 × 2 = 4
3 × 3 = 9
4 × 4 = 16
5 × 5 = 25
The given number sequence is a pattern of square numbers.
The next three numbers of this pattern are:
6 × 6 = 36
7 × 7 = 49
8 × 8 = 64
(c) The given pattern is as follows:
1 × 1 × 1 = 1
2 × 2 × 2 = 8
3 × 3 × 3 = 27
4 × 4 × 4 = 64
5 × 5 × 5 = 125
The given number sequence is a pattern of cubes.
The next three numbers of this pattern are:
6 × 6 × 6 = 216
7 × 7 × 7 = 343
8 × 8 × 8 = 512
class 6 maths patterns in mathematics worksheet.
Solution Q3 :
(a) 5, 25, 125, 625, 3125 , 15625 , 78125 .
Rule : Power of 5.
(b) 11, 13, 17, 19, 23, 29, 31 , 37 , 41 .
Rule : Prime numbers
(c) 3, 9, 27, 81, 243, 729 , 2187 , 6561 .
Rule : power of 3
(d) 64, 125, 216, 343, 512 , 729 , 1000 .
Rule : cubes
(e) 8, 13, 21, 34, 55, 89 , 144 , 233 .
Rule : Virahanka numbers
Solution Q4 :
The following patter of polygon will be shown if we starts with 3 sided regular polygon and add 1 side in the shape with each step.
● 03 sided - Triangle
● 04 sided - Quadrilateral
● 05 sided - Pentagon
● 06 sided - Hexagon
● 07 sided - Heptagon
● 08 sided - Octagon
● 09 sided - Nonagon
● 10 sided - Decagon
Solution Q5 :
In the given figure, we can observe that the sum of the four numbers is equal to the number written in the middle of the shape.
In fig 1 :
The number sequence belongs to triangular numbers and the sum of numbers is -
03 + 06 + 10 + 15 = 34
In fig 2 :
The number sequence belongs to Square numbers and the sum of numbers is -
04 + 09 + 16 + 25 = 54
In fig 3 :
The number sequence belongs to Hexagonal numbers and the sum of numbers is -
07 + 19 + 37 + 61 = 124 .
# MCQ Test :
Patterns in mathematics class 6 mcq :
# FAQ's :
Studying patterns in mathematics helps students to develop problem solving skills, logical reasoning and a deep understanding of mathematical concepts.
There are commonly 2 type of patterns in mathematics :
(a) Number pattern
(b) Geometric pattern
Geometric patterns involve shapes, angles and spatial relationships, while number pattern involves sequences of numbers.
To identify a pattern in a sequence of numbers, look for consistent difference between two consecutive numbers and then analyze the change between terms to know the rule governing the pattern.
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CBSE Class 6th Mathematics teaches students about the basics, which have a wide range of application in their higher studies. All the chapters given below includes Solutions for all the question available in Class 6th Mathematics NCERT Textbook Ganita Prakash. It also includes some Important Extra Questions related to the Chapters and we have also provided Free Quiz Based Test which is consist of Objective Type Questions which help the students to test their Understanding about the given Chapters. This material is available for Free For the Students So that they can prepare & score good marks in their upcoming exams.
| Chapters | Class 6 Maths Syllabus |
|---|---|
| Chapter 01 : | Patterns in Mathematics |
| Chapter 02 : | Lines and Angles |
| Chapter 03 : | Number Play |
| Chapter 04 : | Data Handling and Presentation |
| Chapter 05 : | Prime Time |
| Chapter 06 : | Perimeter and Area |
| Chapter 07 : | Fractions |
| Chapter 08 : | Playing with Constructions |
| Chapter 09 : | Symmetry |
| Chapter 10 : | The Other Side of Zero |
Curiosity, Textbook of Science for Grade 6, comprises twelve chapters. As the name of the textbook suggests, there are numerous opportunities for the learners to explore the world of science and its nature. Through the chapters, learners will embark on a journey that will connect them to the world around and spark curiosity for further exploration. The hands-on activities embedded within each chapter engages the learners and provide them an opportunity to reflect on learning. The primary aim of Curiosity is to prepare the children for becoming the responsible members of the society, and therefore efforts have been made to raise awareness about various issues, such as gender, region, environment, health and hygiene, water scarcity and energy conservation.
| Chapters | Class 6 Science Syllabus |
|---|---|
| Chapter 01 : | The Wonderful World of Science |
| Chapter 02 : | Diversity in the Living World |
| Chapter 03 : | Mindful Eating: A Path to a Healthy Body |
| Chapter 04 : | Exploring Magnets |
| Chapter 05 : | Measurement of Length and Motion |
| Chapter 06 : | Materials Around Us |
| Chapter 07 : | Temperature and its Measurement |
| Chapter 08 : | A Journey through States of Water |
| Chapter 09 : | Methods of Separation in Everyday Life |
| Chapter 10 : | Living Creatures: Exploring their Characteristics |
| Chapter 11 : | Nature’s Treasures |
| Chapter 12 : | Beyond Earth |
Class 6th English NCERT Poorvi has five thematic units that comprise stories, poems, conversation, narrative and descriptive pieces. Themes such as friendship, wellness, sports, nature, art and culture, etc. have been included. Cross-cutting themes, such as Indian Knowledge Systems, values, heritage, gender sensitivity and inclusion have been integrated in all the units. Each unit has three literary pieces― story or conversation, poem and non-fiction. There are intext questions, ‘Let us discuss’ to assess comprehension of the text. The end-of-the-text questions given in ‘Let us think and reflect’ are designed to encourage critical thinking, reasoning, responding, analyzing, etc. These literary pieces are not only entertaining but also instill valuable life lessons, fostering personal growth and helping children navigate social situations with confidence. The selected pieces will resonate with children’s daily experiences and encourage positive values like resilience, empathy and emotional intelligence that can have a profound impact on their development.
| No. | Class 6 English Syllabus |
|---|---|
| Unit 1 : | Fables and Folk Tales |
| A Bottle of Dew | |
| The Raven and The Fox | |
| Rama to the Rescue | |
| Unit 2 : | Friendship |
| The Unlikely Best Friends | |
| A Friend's Prayer | |
| The Chair | |
| Unit 3 : | Nurturing Nature |
| Neem Baba | |
| What a Bird Thought | |
| Spices that Heal Us | |
| Unit 4 : | Sports and Wellness |
| Change of Heart | |
| The Winner | |
| Yoga - A Way of Life | |
| Unit 5 : | Culture and Tradition |
| Hamara Bharat - Incredible India! | |
| The Kites | |
| Ila Sachani : Embroidering Dreams with her Feet | |
| National War Memorial |
