We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only repeat. Such patterns are known as repeating patterns. A pattern has a group of units that follow a rule while repeating or changing. Let us have a quick review of what we have learnt earlier about patterns.
I. Complete the series by drawing the next figure:
Answer:
A pattern can also be created with numbers. The set of
numbers which follow a common rule form a pattern. For example, the sequence 2,
4, 6, 8, …… can be extended by using the rule of even numbers. Patterns with
numbers can also be created using mathematical operations like addition,
subtraction, multiplication and division.
For example:
1. Write the next 3 terms of the pattern 11, 15, 19, 23, ……..
The first term is 11. The common difference is 4. The next 3 terms are 27, 31, 35.
Here are some patterns. Follow them and extend them:
(i)
1 × 9 + 2 = 11
12 × 9 + 3 = 111
123 × 9 + 4 = 1111
1234 × 9 + 5 = 11111
12345 × 9 + 6 = _______
123456 × 9 + 7 = _______
(ii)
1 × 8 + 1 = 9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
1234 × 8 + 4 = 9876
12345 × 8 + 5 = _______
123456 × 8 + 6 = _______
(iii)
111 ÷ 3 = 37
222 ÷ 6 = 37
333 ÷ 9 = 37
444 ÷ 12 = 37
555 ÷ 15 = _______
666 ÷ 18 = _______
(iv)
9 + 1 = 10
90 + 10 = 100
900 + 100 = 1000
9000 + 1000 = _______
90000 + 10000 = _______
900000 + 100000 = _______
Follow the pattern of the following products and extend them further:
(i)
5 × 5 = 25
55 × 5 = 275
555 × 5 = 2775
5555 × 5 = 27775
_ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _
55555555 × 5 = 277777775
_ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _
(ii)
404 × 404 = 163216
505 × 505 = 255025
606 × 606 = 367236
707 × 707 = 499849
808 × 808 = 652864
_ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _ _ _ _ _ _
In patterns in numbers here are some unsolved questions for the students to understand and complete the questions on patterns.
I. Complete the given series:
(i) 1, 3, 5, 7, …….., …….., …….., ……..
(ii) 5, 10, 15, 20, …….., …….., …….., ……..
(iii) 10, 20, 30, 40, …….., …….., …….., ……..
(iv) 3, 5, 8, 12, 17, …….., …….., …….., ……..
(v) 10, 20, 35, 55, 80, …….., …….., …….., ……..
(vi) 2, 2, 3, 3, 3, 4, 4, 4, 4, …….., …….., …….., ……..
(vii) 1, 3, 6, 8, 11, 13, 16, …….., …….., …….., ……..
(viii) 35, 45, …….., 65, 75, …….., 95
(ix) 100, 90, 80, …….., 60, 50 ……..
(x) 1, 3, 5, 7, 9, …….., …….., …….., ……..
Answer:
I. (i) 9, 11, 13, 15
(ii) 25, 30, 35, 40
(iii) 50, 60, 70, 80
(iv) 23, 30, 38, 47
(v) 110, 145, 185, 230
(vi) 5, 5, 5, 5, 5
(vii) 18, 21, 23, 26
(viii) 55, 85
(ix) 70, 40
(x) 11, 13, 15, 17
II. Complete the series:
(i) 1, 4, 7, 10, 13, 16, …….., …….., …….., ……..
(ii) 12, 17, 22, 27, 32, …….., …….., …….., ……..
(iii) 6, 16, 26, 36, 46, …….., …….., …….., ……..
(iv) 10, 30, 50, 70, …….., …….., …….., ……..
(v) 38, 35, 32, 29, …….., …….., …….., ……..
(vi) 54, 50, 46, 42, …….., …….., …….., ……..
(vii) 53, 49, 45, 41, …….., …….., …….., ……..
(viii) 23, 30, 37, 44, …….., …….., …….., ……..
Answer:
II. (i) 19, 22, 25, 28
(ii) 137, 42, 47, 52
(iii) 56, 66, 76, 86
(iv) 90, 110, 130, 150
(v) 26, 23, 20, 17
(vi) 38, 34, 30, 26
(vii) 37, 33, 29, 25
(viii) 51, 58, 65, 72
III. Complete the following series:
(i) 7, 14, 21, 28, …….., …….., …….., ……..
(ii) 25, …….., 75, 100, …….., …….., …….., ……..
(iii) 10, 100, …….., 10000, 100000, ……..
(iv) 2, 10, …….., 250, 1250
(v) 500000, 50000, …….., 500, …….., 5
(vi) 64, 32, 16, …….., 4, …….., 1
(vii) 5, 10, 20, …….., 80, …….., 320
(viii) 8, 16, 24, 32, …….., …….., …….., ……..
(ix) 45, 54, 63, …….., …….., …….., ……..
(x) 2, 6, 18, 54, ……..
Answers:
III. (i) 7, 14, 21, 28, …….., …….., …….., ……..
(ii) 25, …….., 75, 100, …….., …….., …….., ……..
(iii) 10, 100, …….., 10000, 100000, ……..
(iv) 2, 10, …….., 250, 1250
(v) 500000, 50000, …….., 500, …….., 5
(vi) 64, 32, 16, …….., 4, …….., 1
(vii) 5, 10, 20, …….., 80, …….., 320
(viii) 8, 16, 24, 32, …….., …….., …….., ……..
(ix) 45, 54, 63, …….., …….., …….., ……..
(x) 2, 6, 18, 54, ……..
Related Concept
● Patterns and Mental Mathematics
● Counting Numbers in Proper Pattern
● Puzzle
● Patterns
4th Grade Math Activities
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