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Problem Solving: Tips For TeachersAuthor(s): Phares G. O'DafferSource: The Arithmetic Teacher, Vol. 32, No. 8 (April 1985), pp. 34-35Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192628 .
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Problam totoing Tip> For T<zachar>
By Phares G. O'Daffer, Illinois State University, Normal, IL 61761
H 4 ACH iQEJj 4AAA
Mi 1985
3 / Strategy Spotlight | I Work Backward
An example of the work-backward strategy was given in conjunction with the draw-a-picture strategy in the October 1984 Tips section. Consider the following problem to see another situation in which this strategy might be used:
Problem: Sue counted the amount of money she had earned during the week and wrote it on a slip of paper. Then she bought some postcards for $0.56 and a pen that cost $2.80. After her shopping she had $6.89 left, but she had lost the slip of paper. What was the amount written on the paper?
This problem can be viewed as follows:
Beginning _*05ß *056 ^ _$2fiO *2'80 -»» Fjnal amount? f*]
_*05ß *056 |^| ^ _$2fiO *2'80
|^| -»»
amount: $6.89
To find the beginning amount, we use the idea that addition and subtraction are inverse operations and think about reversing the "flowchart" above.
Using the work-backward strategy, we begin with the final amount and reverse the operations to arrive at the first amount. It may help some children actually to make a "flowchart" like the one shown and reverse it to solve the problem.
Problems that can be solved using a work-backward strategy can often also be solved by writing and solving an equation. For the previous problem we could write the following:
A - 0.56 - 2.80 = 6.89 A - 3.36 = 6.89
A = 10.25
Early experience in solving problems using a work- backward strategy can help children begin to develop an understanding of the process- of translating verbal descriptions into equations, as well as of the technique of using inverse operations to solve equations.
Include the work-backward strategy on your classroom Problem-solving Strategies poster or bulletin board, encourage students to use it when appropriate, and compliment them when they use it effectively in a solution to a problem.
34 Arithmetic Teacher
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D Tip Board
_ | Classroom Climate ■ / Problem Corner "~~~
1
Find ways to help children experi- I I this one. A SÛT 4~6 m/9hi 'ite GSvSU I_J enee problem-solving situations that ■ / might he/n <5 öackward strateav Wr-MV are rufefe; I quart and'nTqZ he/n <5
ÏÏ *"" strateav
a 3 IdQaUI *-* • Groups of adults often work to- ■ I Use marWngs on either paJS
W'íh W
no »Of irV§
■j ™ greffier in solving problems and com- ■ I Use íh^se pa¡/s to qet p W Can youf Hi M ™ municate with each other about their ■ / quaris of water ¡n the
qet il p V 4 I II II rn work. Let students do this! ■f^ ^ J &0% ^^ gesi Pa«? II ■I
• Adults regularly i/se calculators to If o^^ ^
^v 0 ^^ _ ml '% ■ aid in solving problems. Find similar If ^ ^?^%^ ^^^W
_ V '^ V
opportunities for students! ■ ^^M^^^^J¡^^^^J^^^'Í 'y 'i I • Adults often have to search for W ml (n"fo¿JJL ^7 C 1 1 'y A ■ data to use in solving problems. Give W& ■!/• rT^il^^^^ ^^!^5* w3^ m m students problems that require realis- I 0' tffiu inl^ lpl f^- "^^y 11
m 'l ■
m
tic and interesting data-search expe- I J/rft Atff' Ivi, |L^j_ 'm 11 I] II M
• Adults are sometimes asked to fcS¿^^> ^7L»J^^=> *-^'Jy)i m write a description of their solution to 1^51 ( 'JPS^kV <=:~i r >/^J m
a problem, so that others can under- f^S^]*^11**^! (
E^^^m * ** J I ̂ ^^^^M stand their thinking. Ask children to ^^^lL_^* Vp^^^lv **
l^^^^Êm r record their work and write about ^ - lmr==:^ r ^^ their solutions! E^^^g^pS?^ Problem- | -solving I ■ • Adults sometimes make progress ^MÍ^^Í^H ■§ Developing Problem- -solving ■
toward a solution to a problem by B^^^^^ ™ Skills ■
■ solving only part of the problem. I 1 n develop skill in problem ■ ■ Others work on other parts, and their ■ 1 studf
solving n
b y acquiring abilities to un- ■ m solutions are combined to arrive at ■ 1 solving b y blem ancf question, m
the final solution. Can we arrange I ^f^i °® with data, to plan what todo, ■ ■
experiences like these for children? ■ 1 t0 °® J' ffte
with ansWer, and to checK^o
■
■ jb ̂ pajisap agi je aAUJB 01 ui jbmi I o¿ ** „ tQ get 28.) ■ ■ jnod pue ned 'b-£ agi ||i) 3m uaqi jb 1. agi u| 1
1 by subtracting
parts. ■ ■ jnod pue |ied jb-8 aqi Ajdoia a/w mon 'l^d jb 1 # Qreak 3 nU
find e'j 34 ^A -T 28 by add- ■
■ -e aqj uj 'b Bj^xa 1. mum m&' 8jb a/w 'ijBd jb-8 I ,por example, find 34 ^A 28
90 ¿u = 50 " I I aqj ojuni 6uunod puB S3LUU e |iBd jb-e aqi 1 .
in^ 4 + ß = I2to30 + 90 ¿u 62.)
= " ■ ■
I ■ ßuinu Ag jBLjv ¿ib 1 'q6 8m ubo mom mg jb e I in^ 4 +
IS 50 + 12, or 62.) ■ ■ pub 'b 1 6ujuaß Aq ib t^ laß ubo ay'A ||Bd I The answ IS
J ■ jb-g 9MJ ui ;b t7 jnoqe ßu^uiqj Aq )jb)S a/'A 1 ^^^^^^^^^^^^^^^^^^B I :((j3ujoo ui9|qoJd„ ̂ Ml oi uoijri|os ^
Part of the Tip Board is reserved for techniques that you've found useful in teaching problem solving in your class. Send your ideas to the editor of the section.
April 1985 35
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