Category : 5th Class
Patterns
Objectives
· Students will learn to develop and extend patterns.
· Students will learn to discover how patterns arise in a variety of mathematical and everyday contexts, and to establish the rules which govern them.
Introduction
Patterns are
· repeated designs or recurring sequences.
· an ordered set of letters, words, numbers, shapes or other mathematical objects, arranged according to a particular rule.
Type I: To find the missing term or next term (number or letter)
· Identify the rule followed in rest of the given terms using mathematical operation: addition, subtraction, multiplication, division, skip counting and reverse counting.
· Identify the order of alphabetical series either from A to Z or Z to A.
· Skipping letters.
Type II: To find the missing part in the figure pattern.
· Complete the figure pattern by drawing its incomplete part in the pattern.
Example 1:
In the number pattern below, what are the values of A and B respectively?
(a) 9, 49 (b) 49, 9
(c) 9, 64 (d) 81, 49
Ans. (a)
Explanation: Pattern followed in the above series is
\[2\times 2=4,\text{ }\,\,\,\,\,\,3\times 3=9,\text{ }\,\,\,\,\,\,\,\,\,4\times 4=\text{ }16,\text{ }\,\,\,\,\,\,\,\,\,5\times 5=\text{ }25,\]
\[6\times 6=36,\text{ }\,\,\,\,\,\,7\times 7=49~\]
Example 2:
Which is the missing square?
(a) (b)
(c) (d)
Ans. (b)
Explanation: Sum of circles in each row or column is 10.
Example 3:
Which one will replace the question mark?
(a) 2 (b) 3
(c) 4 (d) 5
Ans. (c)
Explanation: As, \[5\times 6=30~\]
and \[4\times 7=42\]
Similarly, \[9\times ?=36~~\]
\[?=\frac{36}{9}~\,\]
? = 4
Example 4:
Find the missing pair of letters in the series.
(a) KL (b) LM
(c) KM (d) MN
Ans. (b)
Explanation: The pattern is as follows:
Example 5:
Which figure will replace the question mark in the figure pattern below?
(a) (b)
(c) (d)
Ans. (d)
Explanation:
Example 6:
Which figure will replace the question mark in the series?
(a) (b)
(c) (d)
Ans. (c)
Explanation: The figure repeats itself after two steps.
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