6th Grade Math Textbook, Fundamentals

(Marvins-Underground-K-12) #1
 &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
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