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 .

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Problam >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

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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

в, 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

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January 1986 39

■ Tip Board

1 /74 У*/ Щ Students in grades 7-9 might be en- 1 1 v*Aw x 1 Ш couraged to try this one. When the ■ 1 1 ^s^ / x I ■ digits in the factors in this multiplica- ■

lg 1 ^Чч^У/^ ' Щ tion are reversed> the answer is the ■

1 Same board ' xJL 1 I same! I 1 for Blockade '. /^ ^4. l Щ 36 reverse the digits 63 ■ 1

for l 'S ^4^4 Ш x 42 reverse the digits x 24 ■

1 /V_ " - ^2) I 1512 1512 I I '2/

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on e each of cells A and В. Щ Can you find other multiplications ■

Piover 1 places a marker on on

cells e Q The piay- Щ where this procedure works? Do you ■ Piover

Se 1 2 places places markers on cells ^ m

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