6th Grade Math Textbook, Fundamentals

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

 &KDSWHU

Problem-Solving Strategy:

Consider Extreme Cases

Objective To solve problems using the strategy Consider Extreme Cases

Problem 1:After taking six tests worth 100 points each,

Jacqueline’s test average is 88. What is the lowest possible

test result Jacqueline could have received?

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Read to understand what is being asked.

List the facts and restate the question.

Facts: Jacqueline’s average on six 100-point

tests is 88.

Question:What is the lowest test score Jacqueline

could have received?

Select a strategy.

You can use the strategy Consider Extreme Cases.

Is it possible that Jacqueline could have received

a 0 on one test?

Apply the strategy.

Suppose Jacqueline had received a 0 on one of

the tests.

Let a, b, c, d, and erepresent Jacqueline’s scores on

the other five exams. Then the average of the scores

would be:

 88

Multiplying both sides by 6 gives abcde 0 528,

or equivalently, abcde528. However, this is impossible

because even if she had received 100 on each of the other five tests,

the total score would be only 500, which is 28 short of 528. This

reasoning leads to the answer.

The lowest possible score Jacqueline could have received is 28, not 0.

That is, had Jacqueline scored 100 on five of her tests, she would have

had to score exactly 28 on the sixth test to have an average of 88.

So 28 is the lowest possible test result Jacqueline could have received.

abcde 0

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Check to make sure your answer makes sense.

Suppose that Jacqueline’s scores were 100, 100, 100, 100, 100, and 28.

Her average score would then be

88.

So the answer checks.

100  100  100  100  100  28

6

528

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