POLYA'S PROBLEM-SOLVING STRATEGY (PART 1)

Summary

This tutorial introduces George Pólya's problem-solving strategy, focusing on a mathematical problem involving an airline with flights from Manila to Davao via Cebu. The strategy involves understanding the problem, devising a plan, and carrying out the plan. The tutorial demonstrates how to set up equations based on the given data and solve for the number of passengers who disembarked in Cebu. The process includes defining variables, creating equations, and substituting values to find the solution, which is then checked for accuracy.

Takeaways

• 📚 The tutorial focuses on George Pólya's problem-solving strategy.
• 🔍 Step one in Pólya's strategy is to understand the problem thoroughly.
• 📈 Step two involves devising a plan, which includes writing equations and guessing possible answers.
• 🛫 The example problem involves calculating passenger numbers for an airline with flights from Manila to Davao via Cebu.
• 💼 The airline charges different fares for different legs of the journey: Manila to Cebu and Manila to Davao.
• 🎟️ A total of 180 passengers board the plane in Manila, and the total collected fare is 494,000 pesos.
• 🧮 The tutorial demonstrates setting up algebraic equations based on the given information to find the unknowns.
• 🔢 The solution process involves substituting values into equations and solving for the unknown variables.
• 💡 The tutorial suggests using a scientific calculator to find the value of x, which represents the number of passengers who got off in Cebu.
• 🔄 The final step is to review the answers to check for errors and ensure the solution is valid.

Q & A

What is the main topic of the tutorial?

The main topic of the tutorial is George Polya's problem-solving strategy.

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

The first step in Polya's problem-solving strategy is to understand the problem.

What should you do after understanding the problem according to Polya?

After understanding the problem, you should devise a plan which includes writing an equation and guessing possible answers.

How many steps are there in Polya's problem-solving strategy as mentioned in the script?

There are three steps in Polya's problem-solving strategy as mentioned in the script.

What is the sample problem used in the tutorial to illustrate Polya's strategy?

The sample problem is about calculating the number of passengers who got off a plane in Cebu on a flight from Manila to Davao with a stopover in Cebu.

What are the fares mentioned in the sample problem for different routes?

The fare from Manila to Cebu is 1800 pesos, and from Manila to Davao is 3500 pesos.

How many passengers boarded the plane in Manila according to the sample problem?

180 passengers boarded the plane in Manila.

What is the total fare collected from the passengers in the sample problem?

The total fare collected is 494 thousand pesos.

What variable is used to represent the number of passengers who got off in Cebu in the sample problem?

The variable 'x' is used to represent the number of passengers who got off the plane in Cebu.

What is the equation used to solve for 'x' in the sample problem?

The equation used to solve for 'x' is 1800x + 3500(180 - x) = 494000.

How many passengers got off the plane in Cebu according to the solution of the sample problem?

80 passengers got off the plane in Cebu according to the solution.

Outlines

00:00

🔍 Introduction to Polya's Problem-Solving Strategy

The video begins with an introduction to a tutorial focused on Polya's problem-solving strategy. The presenter outlines the four-step strategy: understanding the problem, devising a plan, carrying out the plan, and reviewing the solution. The tutorial aims to apply this strategy to a mathematical problem involving an airline's fares and passenger counts. The problem presented is about an airline that flies from Manila to Davao with a stopover in Cebu, with given fares and total revenue, and the task is to determine how many passengers got off the plane in Cebu.

05:26

📘 Applying Step One: Understanding the Problem

In this segment, the presenter applies the first step of Polya's strategy by defining the problem. The problem involves calculating the number of passengers who disembarked in Cebu based on the total fare collected and the fares from Manila to Cebu and Manila to Davao. The presenter sets up the variables, with 'x' representing the number of passengers who got off in Cebu and 'y' for those who continued to Davao. The goal is to use the given information to form equations that can be solved.

10:59

🧮 Step Two: Devising a Plan with Equations

The presenter moves on to the second step of Polya's strategy, which involves devising a plan. This involves setting up equations based on the problem's conditions. The equations are formed using the variables 'x' and 'y' to represent the number of passengers getting off in Cebu and continuing to Davao, respectively. The presenter writes an equation that represents the total fare collected from the passengers, which is then used to find the values of 'x' and 'y'.

16:08

🛫 Carrying Out the Plan: Solving the Equations

In this part, the presenter carries out the plan by solving the equations. The process involves substituting and simplifying the equations to find the values of 'x' and 'y'. The presenter uses the total number of passengers and the total fare collected to derive the number of passengers who got off in Cebu. The calculations are shown step by step, leading to the solution of the problem.

21:56

🔄 Reviewing the Solution

The final part of the video script focuses on the last step of Polya's strategy: reviewing the solution. The presenter checks the solution by plugging the values of 'x' and 'y' back into the equations to ensure they are consistent with the problem's conditions. The presenter also encourages the use of a calculator for accuracy and emphasizes the importance of reviewing the answers to check for errors.

Keywords

💡Polio's Problem-Solving Strategy

Polio's Problem-Solving Strategy refers to a systematic approach to tackling mathematical problems, named after the mathematician George Pólya. The strategy involves four steps: understanding the problem, devising a plan, carrying out the plan, and looking back. In the video, this strategy is applied to a real-world problem involving airline fares and passenger counts, demonstrating how it can be used to structure and solve complex problems.

💡Understand the Problem

This is the first step in Pólya's problem-solving strategy, which emphasizes the importance of fully comprehending the problem before attempting to find a solution. In the context of the video, understanding the problem involves recognizing the relationships between different pieces of information, such as the fares for different legs of a flight and the total number of passengers.

💡Devise a Plan

The second step in Pólya's strategy, 'devise a plan,' involves creating a strategy to address the problem. This could include setting up equations or making educated guesses about possible solutions. In the video, the plan involves setting up equations based on the fares and the number of passengers to determine how many passengers disembarked at a stopover.

💡Carry Out the Plan

This step is about executing the strategy or plan devised in the previous step. It involves applying mathematical operations and logical reasoning to work towards a solution. In the video, carrying out the plan means solving the equations that were set up to find the number of passengers who got off the plane at Cebu.

💡Looking Back

The final step in Pólya's strategy, 'looking back,' is about reviewing the solution and the process to ensure accuracy and to learn from the experience. This step is crucial for understanding where errors might have occurred and for improving problem-solving skills over time. In the video, looking back would involve verifying the calculations and the logic used to solve the problem.

💡Equation

An equation is a mathematical statement that asserts the equality of two expressions. In the video, equations are used as a tool in Pólya's strategy to represent the relationships between the number of passengers and the fares collected. The equations help to model the problem and find the unknowns, such as the number of passengers who got off in Cebu.

💡Fare

In the context of the video, 'fare' refers to the cost charged by an airline for transporting passengers from one location to another. The script discusses different fares for different legs of a journey, which are crucial pieces of information for setting up the equations needed to solve the problem.

💡Passengers

Passengers are the individuals traveling on the airline. The video's problem involves determining the number of passengers who got off the plane at a stopover. The term 'passengers' is central to the problem as the goal is to calculate the number of passengers at different stages of the flight.

💡Manila, Cebu, Davao

These are geographical locations in the Philippines and are key to the problem presented in the video. Manila, Cebu, and Davao represent the starting point, stopover, and final destination of the flight, respectively. The problem involves calculating the number of passengers who disembarked at Cebu, which is a central part of understanding the flight's passenger dynamics.

💡Total Fare

The 'total fare' refers to the overall amount of money collected from all passengers for a particular flight. In the video, the total fare is given as 494,000 pesos, and this figure is used to set up an equation that helps determine the number of passengers who got off at Cebu.

💡Calculator

A calculator is a device used for performing mathematical calculations. In the video, a calculator is mentioned as a tool that could be used to solve the equations set up to find the number of passengers who got off at Cebu. It illustrates the practical application of technology in problem-solving.

Highlights

Introduction to Polya's problem-solving strategy.

Step one: Understand the problem.

Step two: Devise a plan to solve the problem.

Step three: Carry out the plan.

Example problem involving an airline's fares and passengers.

Defining variables for the number of passengers.

Setting up equations based on the problem's data.

Using the total fare collected to form an equation.

Solving the equation to find the number of passengers who got off in Cebu.

Calculating the total fare for passengers who continued to Davao.

Final calculation to determine the number of passengers who got off in Cebu.

Verification of the solution by checking the total number of passengers.

Using a calculator to confirm the calculated values.

Reviewing the answer for errors and ensuring accuracy.

Conclusion of the tutorial with a summary of the problem-solving process.

Transcripts

so welcome to another tutorial our topic

for today is about polio's problem

solving strategy

you know what strategy george poglia

for step number one

strategy so number one is understand the

problem

so you don't understand the problem so

say some

mathematical problems

and then what information or data can be

extracted or annoying the event now for

number two

you should devise a plan according to

polya so devising a plan

strategies to

is to write an equation

on how to deal with the mathematical

problems

now you can also guess possible answer

then check it later

if the result is valid now for number

three you can carry out the plans

for example equation

equation

so let's have a sample problem using the

polya solving

strategies for our problem number one

given uh an airline flies from manila to

davao

with a stop over in cebu

it charges a fare of 1800

pesos from manila to cebu

is 1800 pesos and a fair of 3500 pesos

from manila to davao so in one flight

a total of 180 passengers boarded the

plane

in manila and the collected fair total

494 thousand so

young flight night from manila

so how many passengers got off the plane

in cebu

so

[Music]

[Music]

from manila to davao now on total

passengers

collected which is

494 thousand pesos how many passengers

got off the plane in cebu

so you knew unknown

unknown unknown then the number

of passengers shortcut and passengers

got off

plane in cebu

[Music]

let x be the number of passengers

got off the plane in cebu so you see my

number

the number of passengers

um number of passengers

who got off the plane in

from manila

then the same airplane on the same

airline

x and y so put it on problem

x

letters to

[Music]

total fair

for example y is 100 so y times 100

times 3-5

equations

[Music]

which

you x debugging times

x and then plus

three thousand five hundred pesos times

y the beginning

equals

[Music]

to 180 minus x making negative inertia

so ethanol ion i consider nothing

equation

one so again my value now my volume

i know why all those

[Music]

[Music]

times y nayeon volume and y is 180 minus

x so yellow again i think substituting

that indeed starting equation two

and equals to 494 thousand

eta substitute in the equation from

is

times negative x or minus x omega0 is 1

1 hundred x plus

three thousand five hundred times one

eighty is six

hundred thirty thousand minus

three thousand five times x minus nine

because negative na

and then

x equals to

6 630 000 minus 494 thousand

answer i 136 000

pesos

[Music]

[Music]

[Music]

there are 80 passengers

who got off

the plane

but let's try to solve

180

80 and then 3 500 times 100 then union

total non-passengers

each destination from from manila to

cebu and then manila to davao

now if you answer your final answer now

i think number one problem

transpose and then divide nanaman and

then to find just to find the value of x

calculator scientific calculator

579

and then plus three five three thousand

five hundred times

180 diva 180 minus

x

unknown calculator input unknown

calculator i

now equals to 494 thousand

yen equation

normally

and then y is 100

you should review your answers to check

for errors