6th Grade Math Textbook, Fundamentals

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8-14

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

10 ft 10 ft

10 ft

10 ft

Problem Solving: Review of Strategies

Objective To solve problems using a variety of strategies

Problem 1:A park has two concentric square

walking paths with a 10-foot distance between them.

The inside path measures 240 feet per side. Sylvester

walked once around the outside path in 160 seconds.

At this rate, about how many seconds would it take

him to walk once around the inside path?

Read to understand what is being asked.

List the facts and restate the question.

Facts: Two square paths, one inside the other,

have a 10-foot gap between them.

The inside (shorter) path has 240-foot sides.

In 160 seconds, Sylvester walked once

around the outside path.

Question:If Sylvester walks at the same rate around

the inside path, about how many seconds

will it take him to complete one lap?

Select a strategy.

There are many ways to approach this problem.

Here are two possibilities:

• You could use the strategy Organize Datato
  try to analyze the problem situation.


• You could also try to ask a simpler question,
  using the strategy Solve a Simpler Problem.

Apply the strategy.

Method 1:Organize Data

First, make a sketch, labeling the information

you know. You do not need a scale drawing;

rather, you need a rough sketch that shows the

important information. The sketch at the right

makes it clear that each side of the outside path

is 20 feet longer than each side of the inside path.

Therefore, the outside path has sides of length

260 feet, and the perimeter of the outside path

is 4(260 feet), or 1040 feet. So Sylvester walked

1040 feet in 160 seconds.

The inside path has perimeter 4(240 feet), or

960 feet. To solve the problem, you must find

out how much time it would take Sylvester to

walk the inside path’s 960 feet.