Problem-Solving Strategies and Applications

This video tutorial introduces George Polya's four-step problem-solving strategy: understanding the problem, devising a plan, carrying out the plan, and reviewing the solution. The tutorial provides detailed explanations and examples to illustrate each step, helping learners apply these strategies to various problems effectively.

Which of the following is NOT a strategy for devising a plan?

• Look for a pattern

• Make a list of known information

• Draw a diagram

• Ignore extraneous information

What is the first step in Polya's problem-solving strategy?

• Review the solution

• Carry out the plan

• Understand the problem

• Devise a plan

Why is it important to keep an accurate record of your attempts?

• To avoid solving the problem

• To impress others with your work

• To make the process longer

• To ensure you don't repeat mistakes

Which step involves reflecting on what worked and what didn't in the problem-solving process?

• Devise a plan

• Understand the problem

• Review the solution

• Carry out the plan

In the baseball team example, how many different orders can the team have two wins and two losses?

• Seven

• Six

• Five

• Four

How many league games will be played in a basketball league with 10 teams, each playing the others three times?

• 165

• 150

• 120

• 135

What is the product of the ages of three teenagers if their ages are 15, 17, and 18?

• 4320

• 4590

• 5000

• 4800

If a hat and a jacket together cost $100, and the jacket costs $90 more than the hat, what is the cost of the hat?

• $5

• $10

• $20

• $15

In the example of finding two numbers, if one number is 7 more than the other, and twice the larger is equal to four times the smaller decreased by two, what are the numbers?

• 7 and 14

• 9 and 16

• 6 and 13

• 8 and 15

What is the 100th digit to the right of the decimal point in the decimal representation of 7 divided by 27?

• 5

• 9

• 7

• 2