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Problem Solving: Tips For Teachers Author(s): Phares G. O'Daffer Source: The Arithmetic Teacher, Vol. 32, No. 5 (January 1985), pp. 34-35 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41192525 . Accessed: 10/06/2014 07:13 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Arithmetic Teacher. http://www.jstor.org This content downloaded from 195.34.79.45 on Tue, 10 Jun 2014 07:13:40 AM All use subject to JSTOR Terms and Conditions

Problem Solving: Tips For Teachers

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Problem Solving: Tips For TeachersAuthor(s): Phares G. O'DafferSource: The Arithmetic Teacher, Vol. 32, No. 5 (January 1985), pp. 34-35Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192525 .

Accessed: 10/06/2014 07:13

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

http://www.jstor.org

This content downloaded from 195.34.79.45 on Tue, 10 Jun 2014 07:13:40 AMAll use subject to JSTOR Terms and Conditions

Problam totolng Tip3 For Taachao

By Phares G. O'Daffer Illinois State University, Normal, IL 6I761

4P 4AOA

1985

Table 1

Day Pay

1 1С 2 2C 3 4C 4 8C 5 16C

X /3_ 3 /strategy

Spotlight Jl ^ Find a Pattern

F/nof a pattern is a useful strategy for solving certain types of problems or for dealing with a part of a problem. (See the use of this strategy in the "koala bear" problem in the October 1984 "Tips.") Consider the following problem to see how this strategy might be used.

Problem: A rich neighbor (obviously interested in mathematics!) gave Samantha a choice of $600 for a 16-day house-painting job or 1 cent the 1st day, twice as much the 2d day, and so on, doubling the amount each day. Which arrangement should Samantha choose?

It is natural for children first to record the information in a table (table 1) and extend it according to the "double each day" pattern. Often they find a solution to the problem by extending the ta- ble to the 16th day and add- ing up the pay column. As children solve this problem, or as you discuss solutions, you might ask, "Can you make a 'total pay' column and find a pattern that would save work?"

When following up on this Г question, children often dis- . cover the pattern shown in table 2 and conclude that the total pay for 16 days is 1 cent less than the pay for the 17th day!

Once given the suggestion to write the pay as a product of 2s, many children find an- other pattern that makes their work even easier. One child said, "To find the pay, I use 2 as a factor 1 less time i than the number of days." I Using this pattern, the pay ' for the 1 7th day is 2 • 2 • 2 • 2-2-2-2-2-2-2-2- 2 .2-2-2 -2= 65 536C, or $655.36.

Table 2

Day Pay Total

1 1С ^riC 2 2C^3C 3 4CX^7C 4 8с'ж15С 5 16CX

Using the pattern in table 2, we find that the total pay for 16 days is $655.35. Samantha should choose the "doubling cents" plan!

Tabie 3 i /tffiř' Day Pay Factors liknti^bJ

2 2C 2 r'?5ři 3 40 2-2 'ú4^bl 4 8C 2-2-2 4^Sf' 5 16C 2-2-2-2 Г^Т?г 5 : | 16C I 2-2-2-2 ; | km/ Г^Т?г

Looking for patterns helps children develop their inductive reasoning and problem-solving skills. Include "find a pattern" on your strategies bulletin board and praise children when they use it to find a solution to a problem.

34 Arithmetic Teacher

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January 1985 35

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