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Polya"s Problem

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This content outlines George Pólya's four-step problem-solving process (Understand, Plan, Solve, Review) and introduces various strategies for tackling mathematical problems, emphasizing logical deduction and systematic approaches.

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updated my lecture is nothing

okay so for today we're going to discuss

and says george poglia he was a teacher

and a mathematician

and lived from 1887 to 1985.

he published a book in 1949 which is how

to solve it

explaining that people could learn

to become a better problem solvers

of problem solving first we have to understand

understand

so what do i notice what do i wonder

how can i estimate and what questions

can i ask and then after that you have

to plan

so what are the strategies you should i use

use

what steps will take to solve the problems

problems

and then after that you have to review

does my answer make sense

did i check my work and then

could someone see how i found my answer

and then solve the problem and then how

do i apply my strategy

have i shown all the all the uh

my work is my voice loud

or four is of problem solving

we have to understand the problem then

first you have to understand the problem

and then you have to look for the

unknown and what are the data

and then the conditions and then it

is it possible to satisfy the condition

is the condition

sufficient to determine the unknown

or it's insufficient remember

figure introduce suitable notation

and then after that separate the various

parts of the

and then after that that we have to

devise a

plan second find the connection between

the data and the unknown

you may be obliged to consider the auxiliary

auxiliary

problems if an an immediate connection

cannot be

found you should obtain them into

eventually a plan

of the solution so have you seen it before

before families

and then do you know a related problem

do you know a charm that could be useful yeah

and then is a problem related to your to

yours and so before

could you see it could you use its

results could you use its method

and then should you introduce some auxiliary

auxiliary

element in order to make the to make its

use possible can you restate the problem

could you restate it still differently

and go back to the

definitions and then if you cannot solve

the problem

or propose problem try to solve for some

related problems a more general problem

and then a more special problem

an analogous problems or could you solve

a part of the problem keep only a part

of the conditions or drop the other part

how far is the unknown that determine

how can it

vary could you there are

derive something useful from the data

could you think of other data appropriately

appropriately

determine the unknown and then could you

change the unknown or a data or both

if necessary so that the

new unknown and new data are nearer to

so did you use all the data

this is data not date data and data this

is date

data and data the end date

did you see use the whole condition so

how have you

have you taken but it didn't go on money caller

okay did you use the whole condition

have you taken into account all excuse me

essential notations involved in the problems

problems

so after that

so third carry out the other card so

carrying out your plan

of the solution so check each step

so can you see clearly that the step is correct

correct

and then looking back examine the

can you check this result or can you

check the argument so you have to check that

that

and then can you derive the solution

differently or can you see it

at a glance can you use the result or

the method for the

some other problems yeah

okay so you you know apatna uh

pays nippolius for solving problems

so try nothing committed so this is a

sample problems middle school students populations

populations

so we have the name of school yeah

lincoln mason and washington so they

have different

numbers of female students and then male students

students

so lincoln we have 980 862 for the mail

and then for the mission

or amazon reason seven one two eight

nine four

and then five six eight for the

washington and then seven six one

so until nito how many more students are

at lincoln middle school

than washington middle school so you

have to compare

so target nothing in lincoln washington

so after that so you have to look for

the difference

so the quality of the 513 so

that there were 513 more students

in lincoln compared in washington

so that's not nothing problem because

we're looking for the

how many more students are at lincoln

compared to washington middle school so

i'll find the sum of the first 100

natural numbers

is what it's still 101 per yen diva okay

so now

okay so now that i think jenna how many

players are drawing from one to another

so we have 50 5050 and final answer nothing

nothing

going so check in later and remember

questions and then still

a total of 100 chickens and caramels are

in the farm

so if the total number it

so 70 times 4 is 280 30 times 360. 340.

okay probably solving strategies

according to

hall.org.uk so we have to create a diagram

diagram

so draw a picture have the people play roles

roles

or use manipulatives to act the problem

out manipulate your materials to find

deep solution

to the problem remember different pictures

pictures

might all lead to correct solution

so label the steps as your as you work

out the problem so next

we have to guess and check you know

attica now think of the answer

that you might that might work and then

test your guess

if your guess isn't right think about

how you

can change it to get closer to your

answer or to the answer

so write down your guesses right

so you can start seeing patterns and use

the information

to make the to make

revised guesses okay repeat until you

and next we have to use a table or make

a list

so decide what information need to go to

or in your chart

and then list all the possible in a

table or

chart to make sure pieces of the problem don't

don't

get lost so organize and record the

information so it makes sense

and then draw pictures diagrams sketches

maps and other presentations or representations

representations

so drawing helps solve mathematical

problems so we have the precise measures

measurements and careful drawings

lead to accurate solutions

so we have the logical reasoning remember

remember

so we have to organize your information examine

examine

relationships and think about your

answer to

from to form a logical answer and then

we have to generalize each cell

relationship to each to reach a logical conclusion

conclusion

so find the pattern so list deformation

you know and identify the information

you need to may find

so make an organized list of tables so

examine your release

for a recognized pattern use the pattern

to find the missing information

so working backgrounds start with the

end of a problem

and work step by step toward the

beginning to get a solution

so write down what you need don't know

and what

do you know so write down each step

as you go get closer to your answer

or to the answer so the last step will verify

verify

that the solution works

some similar but simpler problems so

divide the

problems to smaller and easiest steps

so rewarding the problem if you need talaga

talaga

so using smaller numbers say use the

algebraic expressions

or use mathematical theorems or use

of equations and formulas

so it is an effective strategy for demonstrations

demonstrations

purposes and to help a better grief of

the problem on hand

devices used to act out the problem and

consider equipment

so we have to record uh you can

recreational mathematics

involves problems riddles puzzle brains

brain tracers

and games carried out for recreation or leisure

leisure

it employs creative problem solving logical

logical

reasoning approaches reflective thinking and

and

so if you like sudoku there's a good

chance you'll like

love ken ken if you'll hate sadoku

there's a good chance that you love

ken ken invented invented by a japanese

mathematic teacher with statue

miyamoto in 2004 so ken ken is an

elegant and rich logic puzzle

which with a few easy to understand

rules which helps explain why new york

times buzzer editor wheels

shorts call it the most addictive

then straight forward are

straightforward so fill in each square

cell in the puzzle with the number between

between

one and the size of the grid

for example in a four by four grid use

the numbers one two four because

four yeah and then use each number

exactly once in a row

so the number in each case indicated by

must combine in any order to produce the cage

cage

target number using the indicated math operation

operation

operation so numbers may be repeated

with the cage as long as

okay number four no guessing is required

so each puzzle can be solved completely

using only logical deduction so harder puzzles

puzzles

that's all you need to know the rest is

just logical deduction derived from the rules

rules

okay so try national solve so an item

you add

divided into division or divide

seven plus four negative two

two minus four times three minus

and four so pakpina got me the one three

check that in four

chaka three and four and three

a magic square of order n is an

arrangement of numbers in square such

that the

sum of n numbers in each row column and

diagonal is

the same number okay so for example

parameters

so one two three four five six seven

eight nine 10 11

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YouTube Transcript:Polya"s Problem