5th Class Mental Ability Shapes and Patterns Patterns

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.