Problem Solving: Tips For TeachersAuthor(s): Phares G. O'Daffer and Randall I. CharlesSource: The Arithmetic Teacher, Vol. 33, No. 8 (April 1986), pp. 34-35Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194168 .

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Problem >oh>lng Tip) For Tacichao

Edited by Phares G. O'Daffer, Illinois State University, Normal, IL 61761

Prepared by Randall I. Charles, Illinois State University, Normal, IL 61761

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f if |_^ ■ Your parents will give you all the water, ice, and I

Ф Ik Strategy Spotlight fL K.:- You have t0 buy "" rest ot I I '1И-7р^^^^^^^^^^^^^^^^^^^Л I ■ Paper cups are 12 for $0.39. I

^' n ̂Щ^^^^^^^^^^^^^^^^^^^^ Щ Ш Paper cups hold 8 ounces. I n Solvi no Add I ¡Gel I ■Lemonsare2í°r$o-35'andsu9ar;sabout$o-25 1 ProbIfìinS I " You need 4 lemons and 1 CUP of sugar for each ■

L^^^JJJJ^^^^^^^^^^^B pitcher of lemonade. ■ ^^^НННШ^ННННННН^ВНН! ■ Your pitchers hold 8 cups each. I

Students need experience in solving a variety of ■ You estimate that you will have between 50 and ■ problems fully to develop their problem-solving 75 customers for each game. ■ abilities. Applied problems are an important type of A valuable characteristic of applied problems is ■ problem that should be included at all grade levels. their connection with situations that are realistic to ■ Applied problems are realistic situations that require students. However, the solutions to most applied ■ students to collect and analyze data to make a problems involve several computational steps that ■ decision. Here's an example of an applied problem can quickly become "messy" unless a calculator is ■ appropriate for the intermediate grades: used. So that all students can work realistically with ■

applied problems, consider allowing the use of а Щ Problem: Your house is across the street from the calculator at all times. For the applied problem given I playing field of a semiprofessional baseball team. earHer> here are some of the subproblems (that I You and a friend think you can earn money selling ¡nv0|ve computations) that would have to be solved. I lemonade before and after the games. How much ■ will you charge for each glass of lemonade? ■ How many pitchers should you make? ■

■ How many lemons will you need? What will they ■ The solution to an applied problem is similar to, yet cost? ■

different from, the procedures we typically use to B What ¡s the cost of each cup? ■ solve story problems. The following phases are a What win the tota, cost be t0 you for each g|ass of ■ involved in the solution of an applied problem: lemonade? ^^^^ма^^вв^^^^^ I 1. Understand the problem. ^ ~^' M 2. Identify the conditions to be satisfied, the ^^^ ^^ Д ■ M

assumptions you will make, and the needed data. f^^^^^^l Jr*" ^^ж Л 11 3. Select or collect the needed data. | lr^ ^^ж

^*^L III 4. Identify and solve subproblems. ' W О 'i M I 5. Check your work. iT^^Tm

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The second and third phases are crucial in the j^^^^^nM II ' ' ' щ^ I solution of applied problems. To solve the applied fn' 7 [Arm ' I V v4 ш I problem given, students might proceed according to iHj Ì II '/А M l^4^

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the following assumptions and collect the following '¿^^^O^f ^^ È ^ ~^£

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34 Arithmetic Teacher

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given amounts as different as $0.15 and $1.25, but each answer has "made sense" given the conditions

they set for the situation. Finally, helping students deal with an applied problem,

like other problems, is not complete until the students reflect on their work for the purpose of improving their skills in solving applied problems in the future.

The "Applied Problem-Solving Guide" on the Tip Board shows some tasks that will help students work through the procedures of solving an applied problem and evaluating their work.

With students who have had little experience with applied problems, you might provide a list of things to consider and a list of some questions to answer to help them get started. Then, as they gain experience, they will be able to generate these types of questions on their own.

Good applied problems do not have only one correct answer. Many answers may be correct, depending on the assumptions and information with which the students started. For the applied problem given here, students in the same classroom have

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Щ Take a Look H ^^^^^^^^^^^^^^^^Я I These books have useful ideas to help H I you create some applied problems that H i i Part o* the т^ Board- 1 are appropriate for your students. ■ ■ Developing Skills for Solving U is reserved for I

■ Applied Problems ■ «»*"К^««« I _. „.. , _, . . ,_ _, . ^m ■ you've found useful I Sharron, _.

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Щ sources SUCh as the following: э ■ !^Г »eciion. I i Solving. This teacher s resource guide was ^Ш . .. . . . э ■ »eciion. i developed as part of a National Science ■ tables,

. .. Charts, . .

graphs, .

maps, ■ I Foundation Honors Teachers Project at Illinois ^m reference books, menus, ■ I State University. (Contact Carol Thornton, ■ advertisements, product labels, ■ Mathematics Department, Illinois State University, ^Ш . x ' , . • •_ ■ H I Normal, il 61761.) H experiments,

. x catalogs,

, checkbooks, . • •_ ■ ■ I

Д and newspapers. I I

April 1986 35

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