Problem Solving using Polya's 4 step method|Tano, Arjyll B.

Summary

In this video, the speaker demonstrates how to apply Polya's four-step method to solve two types of problems. First, they tackle an age-related problem involving three boys with different age relationships, showing how to represent ages algebraically and solve the equation. Then, they solve a geometric problem involving a triangle's angles, using the method to find the degree measures of the angles. Throughout, the video emphasizes understanding the problem, devising a plan, executing it, and checking the solution, providing a clear and practical example of how to use Polya's method in problem-solving.

Takeaways

• 😀 Polya's four-step method is a structured approach for solving problems, consisting of understanding the problem, devising a plan, carrying out the plan, and reviewing the solution.
• 😀 Step 1: Understand the problem by defining variables and forming relationships between them based on the given conditions.
• 😀 Step 2: Devise a plan by setting up equations or expressions that reflect the relationships and solve for unknowns.
• 😀 Step 3: Carry out the plan by performing calculations, simplifying expressions, and solving the equation.
• 😀 Step 4: Look back and check by substituting the values back into the original problem to verify the solution.
• 😀 The method is applied to real-world problems, such as determining the ages of three people given their relationships and a sum of their ages.
• 😀 In the first example, the solution to the problem of finding the ages of Neil, Del, and Jill is achieved by setting up an equation and solving it step by step.
• 😀 Jill's age is represented by 'x', Del's age by '2x - 4', and Neil's age by '2x - 4 + 3', with their total age summing to 35.
• 😀 After solving the equation, we find that Jill is 8, Del is 12, and Neil is 15 years old, and their ages add up to 35, confirming the solution.
• 😀 In the second example, the problem is about determining the angles of a triangle given certain relationships between the angles.
• 😀 The angles of the triangle are expressed as x (for the first angle), x - 20 (for the second angle), and 2x (for the third angle), with their sum equaling 180 degrees.
• 😀 Solving for x, we find that the first angle is 50 degrees, the second angle is 30 degrees, and the third angle is 100 degrees, confirming that the sum is 180 degrees.

Q & A

What is Polya's four-step method for solving problems?

Polya's four-step method consists of the following steps: 1) Understand the problem, 2) Devise a plan, 3) Carry out the plan, and 4) Look back or check the solution.

What is the first step in Polya's four-step method?

The first step is to understand the problem. This involves identifying the given information and what is being asked.

How do we represent Jill's age in the first problem using Polya's method?

In the first problem, Jill's age is represented by the variable 'x'.

What is Del's age represented as in the first problem?

Del's age is represented as '2x - 4' because he is 4 years younger than twice Jill's age.

How is Neil's age represented in the first problem?

Neil's age is represented as '2x - 4 + 3', which accounts for being 3 years older than Del.

What equation do we create in the second step of the first problem?

In the second step, we create the equation '2x - 4 + 3 + 2x - 4 + x = 35' to represent the sum of the ages of the three boys equaling 35.

How do we solve for 'x' in the first problem?

To solve for 'x', we combine like terms to get '5x - 5 = 35'. Then, we isolate 'x' by adding 5 to both sides and dividing by 5 to find that 'x = 8'.

What is the final solution for the ages of the three boys in the first problem?

The final solution for the ages is: Jill is 8 years old, Del is 12 years old, and Neil is 15 years old.

What is the sum of the three boys' ages in the first problem, and why is it important?

The sum of their ages is 35, and it is important because it confirms that the solution is correct, as it matches the total given in the problem.

What is the key equation in the second problem about the angles of a triangle?

The key equation in the second problem is 'x + (x - 20) + 2x = 180', where 'x' represents the first angle, 'x - 20' represents the second angle, and '2x' represents the third angle.

How do you solve for 'x' in the second problem about triangle angles?

To solve for 'x', we combine like terms to get '4x - 20 = 180', then isolate 'x' by adding 20 to both sides and dividing by 4 to find that 'x = 50'.

What are the final angles of the triangle in the second problem?

The final angles are: the first angle is 50 degrees, the second angle is 30 degrees, and the third angle is 100 degrees.

How does Polya's method ensure the solution is correct in the second problem about triangle angles?

Polya's method ensures correctness by checking the solution. After solving for 'x', substituting the value of 'x' into the original equation gives a total of 180 degrees, confirming the solution.