6th Grade Math Textbook, Fundamentals

 &KDSWHU

14-11

Problem-Solving Strategies

1.Guess and Test

2.Organize Data

3.Find a Pattern

4.Make a Drawing

5.Solve a Simpler Problem

6.Reason Logically

7.Adopt a Different Point of View

8.Account for All Possibilities

9.Work Backward

10.Consider Extreme Cases

Problem Solving: Review of Strategies

Objective To solve problems using a variety of strategies

Problem:Fred and Phil wish to open a business together, so they
pool their resources. When they combine their money, they have a
total of $4000. If the amount Phil contributed is subtracted from the
amount Fred contributed, the result is $680. How much money did
each contribute to their $4000 pool of funds?

Read to understand what is being asked.

List the facts and restate the question.

Facts: Fred and Phil contributed a total of $4000.

Fred contributed $680 more than Phil.

Question:How much money did Fred contribute?

How much did Phil contribute?

Select a strategy.

There are many ways to solve this problem.

You can use the Make a Drawingstrategy to help

you understand the relationships. You could also

use the Guess and Teststrategy.

Apply the strategy.

Method 1: Make a Drawing

Let Frepresent the amount Fred contributed,

and let Prepresent the amount Phil contributed.

• Draw rectanglesFandP, as shown in the figure below,
  withFlonger than Pbecause Fis greater than P.
  The total is $4000.


• Make a copy of rectangleP, and place it so its right
  end is exactly on top of the right end of length F.
  The uncovered portion of Fhas length FP.

FP

$4000

F  P PP

$4000