One of the inherent beauties of mathematics is the logic and order. This logic can be seen “physically” as a pattern or as a series. The mathematician uses patterns  to solve problems in geometry as well as in many other fields. In addition, there are some examples of applying finding a pattern strategy in everyday life problem solving situation, such us: searching for an address, the police looks for modus operandi that might lead them to a particular criminal by finding a pattern of crimes, then scientists involved in medical research about the particular virus or bacteria.

More importantly, there are some ways to recognize the pattern in applying the finding a pattern strategy to solve Mathematics problems, they are: (1) different point of view; (2) organizing the data; (3) solving a simpler version; and (4) visual representation.

The following is example of problem in Mathematics solved by finding pattern.

(1)     different point of view

Problem: Find the sum of the first 100 even number.

Solution: 2 + 4 + 6 + … + 196 + 198 + 200.

This can be done with calculator, or they can be clever and add in pairs. Recognizing that there is a pattern: 2 + 200 = 202, 4 + 198 = 202, 6 + 196 = 202 and so on. There will be 50 pairs whose sum is 202. Thus, the sum of the first 100 even numbers would be 50 . 202 = 10.100. We also can solve this problem with different point of view.

Number of Even Numbers to be Added

Sum

1

2

3

4

.

.

.

n

22 + 42 + 4 + 62 + 4 + 6 + 8

.

.

.

2 + 4 + 6 + 8 + … + n

= 2         = 1 . 2= 6         = 2 . 3= 12       = 3 . 4= 20       = 4 . 5

= n (n + 1)

 So, the sum is 100 . 101 = 10.100

 (2)     organizing data

Problem:

If you take the digit sum of a number, that is you add the digits in the number, how many three digit numbers will have a digit sum of 10? (For example, 262 is one, since 2 + 6 + 2 = 10; 505 is another, since 5 + 0 + 5 = 10.)

Solution:

We can make use of our organizing data strategy to help set up the lists of numbers with a digit sum of 10 and then see if a pattern exists:

100s: 109, 118, 127, 136, 145, 154, 163, 172, 181, 190 = 10

200s: 208, 217, 226, 235, 244, 253, 262, 271, 280         = 9

300s: 307, 316, 325, 334, 343, 352, 361, 370                 = 8

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.

.

800s: 802, 811, 820                                                         = 3

900s: 901, 910                                                                 = 2

Our pattern is confirmed. There are 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 = 54 numbers between 100 and 999 that have a digit sum of 10.

Reference: Posamentier, Alferd S. and Krulik, Stephen. 1998. Problem Solving Strategies for Efficient and Elegant Solution. Corwin Press Inc. California.