POLYA'S PROBLEM-SOLVING STRATEGY (PART 1)
Summary
TLDRThis 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
🔍 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.
📘 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.
🧮 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'.
🛫 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.
🔄 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.
Mindmap
Keywords
💡Polio's Problem-Solving Strategy
💡Understand the Problem
💡Devise a Plan
💡Carry Out the Plan
💡Looking Back
💡Equation
💡Fare
💡Passengers
💡Manila, Cebu, Davao
💡Total Fare
💡Calculator
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
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