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Problem Solving: Tips For TeachersAuthor(s): Phares G. O'Daffer and Oscar SchaafSource: The Arithmetic Teacher, Vol. 33, No. 5 (January 1986), pp. 38-39Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194142 .Accessed: 15/06/2014 01:15Your 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 support@jstor.org. .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 185.44.79.179 on Sun, 15 Jun 2014 01:15:12 AMAll use subject to JSTOR Terms and Conditionshttp://www.jstor.org/action/showPublisher?publisherCode=nctmhttp://www.jstor.org/stable/41194142?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jspProblam >otoing Tip> For Taachar} Edited by Phares G. O'Daffer, Illinois State University, Normal, IL 6176I Prepared by Oscar Schaaf, University of Oregon, Eugene, OR 97403 1QQ9 I www io Arithmetic Teacher I Strategy Spotlight | Computational Problems - Choosing Strategy Sequences Problem-solving strategies were spotlighted one at a time in past issues of the Arithmetic Teacher, This issue and the March 1986 issue will provide prob- lems that can be solved using a variety of strategies. One problem solver might use a certain sequence of strategies, whereas another would choose a different sequence. These problems are designed to afford a challenging context for a review of computational skills. The following suggests a way in which an in- teresting computation-oriented problem might be pre- sented to students, including some directions that might be given and some questions that might be asked. The Wonderful Wonders of 6174 What are these wonders? Let us do some exploring. Write the largest possible number using the digits , 1,7, and 4. e Subtract from ft the smallest 7 6 4 1 mmtm you cen write - 1 4,6 7 using these digits. | ill I The answer is 6174. Do you think some other four- digit numbers behave in this way? e Try these: (a) 5317 (b) 2864 (c) 9731 e Now try some of your own. e Record separately those that do and do not work. From here on you may choose to continue exploring I the wonders of 6174 by "doing mathematics" in your I I own way. You might consider these strategies as you I I form your own strategy sequences for your own re- I I search "expedition." I I e List again those numbers that do work by ordering I I the digits from largest to smallest. I I e Look for patterns. I I e Make a prediction. I e Search for numbers that contradict your prediction. I e When you tire of using paper and pencil, use a I calculator. E e Revise your prediction (if necessary). I e Discuss your efforts with classmates. I Write about your conclusions and the strategies E and thinking processes you used. I An Extension of the Search (for those who want I more!) I In exercise (c) 9731 did not work: I 9731 8532 I -1379 Butnowuse8352 -2358 I 8352 as your four-digit number: 6174 I 9731 works the second time around! Use your "do | not work" list. Find other numbers that do work the I second time around. Search for patterns, draw con- E elusions, and test. Pose other extensions to chai- I lenge your parente, teachers, and friends. I HJ H aiqjssod are suoijnios ' puncxre pu | -09S ' pilQ Sj J9/WSUB 'S = - Q pue fr = p - I j mum jequinu i;6jp-jnoj e u| :uo;suepo joj uoijnios I p pue ' lq 'e joj 's'xq | jo sjes juaje^ip j ;1 = - q pue 9 = p - 'sjeqtunu iioip-jnoi I 40ns u| p '| pue ' *' ' (q 'puooes'eMJ ' E ''6'p isju 4S8||BLus o' 'seje' tuojj jaqiunu }i!P-jno| I " eg ; syip ' jspjQ :punoje sj^ ' io E This content downloaded from 185.44.79.179 on Sun, 15 Jun 2014 01:15:12 AMAll use subject to JSTOR Terms and Conditionshttp://www.jstor.org/page/info/about/policies/terms.jspJanuary 1986 39 Tip Board 1 /74 */ Students in grades 7-9 might be en- 1 1 v*Aw x 1 couraged to try this one. When the 1 1 ^s^ / x I digits in the factors in this multiplica- lg 1 ^^/^ ' tion are reversed> the answer is the 1 Same board ' xJL 1 I same! I 1 for Blockade '. /^ ^4. l 36 reverse the digits 63 1 for l 'S ^4^4 x 42 reverse the digits x 24 1 /V_ " - ^2) I 1512 1512 I I '2/ " on e each of cells A and . Can you find other multiplications Piover 1 places a marker on on cells e Q The piay- where this procedure works? Do you Piover Se 1 2 places places markers on cells ^ m | ^ a ? | ForaddttlonaUdeasando Mathemat- 1 CS;nCTM PP 69-77. Reston, Va. : T^ ^^^ Handbook pQ = |Bnbe eq . spnpojd asagi 1 rl Stephen PP an ^%R^f MS.: Allyn & So/wng, Bon. ^^ PP oe^peo^Qooi^pQOO !>~~|jom ejnpeoojd sjm *-~-^^^^^^^^^ I :j9ujoq uj9|qojd ; Part of the Tip oard is reserved for techniques that you'^ found useful ih bachino This content downloaded from 185.44.79.179 on Sun, 15 Jun 2014 01:15:12 AMAll use subject to JSTOR Terms and Conditionshttp://www.jstor.org/page/info/about/policies/terms.jspArticle Contentsp. 38p. 39Issue Table of ContentsThe Arithmetic Teacher, Vol. 33, No. 5 (January 1986), pp. 1-59Front MatterOne Point of View: Let the Learning Disabled Learn [pp. 2-2]Readers' Dialogue [pp. 4, 43]Mathematics for the Learning Disabled Child in the Regular Classroom [pp. 5-11]The Value of Informal Approaches to Mathematics Instruction and Remediation [pp. 14-18]The Low Achiever in Mathematics: Readings from the "Arithmetic Teacher" [pp. 20-23]The Number Namer: An Aid to Understanding Place Value [pp. 24-28]Research ReportThe Process of Counting [pp. 29-29]How Our Decimal Money Began [pp. 30-33]Children's Conceptual Understanding of Situations Involving Multiplication [pp. 34-37]Problem Solving: Tips For Teachers [pp. 38-39]More Patterns with Square Numbers [pp. 40-42]Y Is for Yacht Race: A Game of Angles [pp. 44-48]Mathematics Attitudes of Elementary Education Majors [pp. 50-51]Computer Corner [pp. 52-54]Reviewing and ViewingComputer MaterialsReview: untitled [pp. 55-55]Review: untitled [pp. 55-56]Review: untitled [pp. 56-56]Review: untitled [pp. 57-57]Review: untitled [pp. 57-57]New Books for PupilsReview: untitled [pp. 57-57]Review: untitled [pp. 57-57]Review: untitled [pp. 57-57]New Books for TeachersReview: untitled [pp. 58-58]Review: untitled [pp. 58-59]From the File [pp. 58-58]Reviewing and ViewingEtceteraReview: untitled [pp. 59-59]Back Matter