Class 6 Maths Chapter 1 Extra Questions Patterns in Mathematics
Class 6 Maths Patterns in Mathematics Extra Questions
NCERT Class 6 Maths Chapter 1 Patterns in Mathematics Extra Questions and Answers
Question 1.
How is math used in GPS technology?
Solution:
Math is used in GPS technology to calculate distances and plot the most efficient routes using geometric principles.
Question 2.
What is ‘Virahanka numbers’?
Solution:
A sequence of numbers in which each number (starting from the third term) is the sum of the two preceding ones. For example: 1, 2, 3, 5, 8, 13, 21, 34, 55, …
1, 2,
1 + 2 = 3,
2 + 3 = 5,
3 + 5 = 8,
5 + 8 = 13,
8 + 13 = 21,
13 + 21 = 34,
Question 3.
Visualise the square number 64.
Solution:
64 can be writen as 8 × 8. Thus, it can be shown by dots as:
Question 4.
Visualize cube number 1000.
Solution:
1000 can be writen as 10 × 10 × 10. Thus,
Question 5.
What is hexagonal number? Represent it pictorially.
Solution:
The numbers that can represent by a hexagon with a dot in the centre and all other dots surrounding the centre dot in a hexagonal shape.
For example: 1, 7, 19, 37, 61, 91, ……
Pictorial representation:
Question 6.
Complete the following number sequences:
(a) 1 + 3 + 5 + ___ + 9 + 11 = ____.
(b) 1 + ___ + 3 + 4 + 3 + 2 + 1 = ____.
(c) 1 + 2 + 3 + __ + 5 + __ + 7 +…..+ 11 + __+ …. + 7 + ___ + 5 + 4 + 3 + 2 + 1 = 121 Solution:
(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 + 9 + 10 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 121
Question 7.
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, …, …, ….
Solution:
(a) The given pattern is as follows:
1, 1 + 2 = 3, 1 + 2 + 3 = 6, 1 + 2 + 3 + 4 = 10, 1 + 2 + 3 + 4 + 5 = 15; a pattern of triangular numbers. Therefore, 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; a pattern of square numbers.
Therefore, 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; a pattern of cubes.
Therefore, the next three numbers of this pattern are: 6 × 6 × 6 = 216, 7 × 7 × 7 = 343, 8 × 8 × 8 = 512.
Question 8.
Assertion: 15 is both a triangular number and a square number.
Reason: If dots arrangement of a number is represented in triangle as well as in square, then the number is called both triangular as well as square number or square- triangular number.
In the given question, a statement of Assertion is followed by a statement of Reason. Choose the correct option as:
(a) Both assertion and reason arp true and the reason is the correct explanation of assertion.
(b) Both assertion and reason are true but the reason is not the correct explanation of the assertion.
(c) Assertion is true and the reason is false.
(d) Assertion is false and the reason is true.
Solution:
(d) Since, 15 dots can be arranged in a triangle, but cannot be arranged in a square.
Hence, assertion is false, but the reason is true.
Question 9.
Represent first 7 centered hexagonal numbers pictorially.
Solution:
The first six centered hexagonal numbers are as follows: 1, 7, 19, 37, 61, 91, 127.
Pictorial representation:
Question 10.
Case Based Question
Rima and Diva are playing with square counters.
Rima arranges her counters as follows:
Diva arranges the counters as follows:
One of their friends, Rohan, says these are showing the number patterns.
Based on the above information, answer the following questions.
(a) What are the number patterns they are showing?
(b) If Rima’s arrangement is representing the triangular numbers, then what will be her next two arrangements if she follows the same pattern?
(c) What is Diva’s next arrangement with counters if she follows the same pattern?
Solution:
(a) The number pattern represented by Rima’s arrangement is: 1, 3, 6, …, which are triangular numbers.
Diva’s arrangement represents the pattern: 1,4,9,…, which are square numbers.
(b) The next triangular numbers are 10 and 15. So, Rima’s arrangement for these triangular numbers is as follows:
(c) The next square number is 16. So, Diva’s arrangement for the number 16 is as follows:
