Polya’s 4-steps in Problem Solving.pptx

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Polya’s 4-steps in
Problem Solving
Kenth Harold R. Endocal

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PROBLEM
 A statement requiring a
solution, usually by means of a
mathematical
operation/geometric
construction.

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PROBLEM SOLVING
 A mathematical task that has the potential to
provide intellectual challenges for enhancing
students’ mathematical understanding. It is
about resolving problems. It is finding
solutions and not just answers to problems. It
is an important skill not only in dealing with
Mathematics, but also in making decisions in
life.

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METHOD
 The ways or techniques used
to get an answer which will
usually involve one or more
problem solving strategies.

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ANSWER
 A number, quantity or some
other entity that the
problem is asking for.

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SOLUTION
 The whole process of solving
a problem, including the
method of obtaining an
answer and the answer itself.

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GEORGE POLYA
 One of the mathematicians to
make a study of problem solving.
He is a Hungarian mathematician.
He describes the methods of
Problem Solving. Polya’s four
steps are deceptively simple.

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1. Understand the Problem
 You must have a clear understanding of
the problem. You must have a full
grasp of what are known and not
known. Then solve as required by the
problem.
Polya’s 4 Steps in Problem-Solving

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2. Devise a Plan
 Try using strategies that could help you solve the problem. Here are some frequently used procedures:
Identifying a subgoal.
Make a table or a chart.
Make an organized list that shows all the possibilities. (Tree diagram, Venn Diagram)
Draw a diagram.
Eliminating possibilities.
Make an illustration/drawing.
Work backwards.
Write an equation. If necessary, define what each variable represents.
Perform an experiment.
Guess at a solution and then check your result. Trial and error.

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3. Carry Out the Plan
 Once you devised a plan, you must carry it out. As soon as you
have an idea for the solution of the problem, write it down
instantly then carry out your plan of the solution. Keep trying until
something works.
Work carefully.
Keep an accurate and neat record of all your attempts.
Realize that some of your initial plans will not work and
that you may have to devise another plan or modify your
existing plan.

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4. Review the Solution
 Take time to reflect, examine, and look back at what you have
done – think of what worked and what did not; doing this will
enable you to predict what strategy to use to solve future
problems.
Ensure that the solution is consistent with the facts of
the problem.
Interpret the solution in the context of the problem.
Ask yourself whether there are generalizations of the
solution that could apply to other problems.

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STATEGY: ELIMINATING POSSIBILITIES
Wally asked Joy how old she was. Joy said to him that she
would give him three clues and see if he could guess her age.
Joy wrote down the clues and let Wally make a guess.
 My age is between 18 and 35.
 My age is a multiple of 3.
 My age is an odd number.
 The digits of my age are repeated.
How old is Joy?

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1. Understand the Problem
 The problem is telling us that Wally
has to guess Joy’s age and to be able to
guess her age he needs to use the
different conditions given.

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2. Devise a Plan
 The strategy “Eliminating possibilities”
will be used because it is the most suitable
strategy and it can be used together with
the making a table or making an organized
list strategy.

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 We need to use the four different clues to solve
the problem.
Clue 1: Joy’s age is between 18 and 35. (When
we say “between” in math, we mean the
numbers excluding the boundaries.)

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 Clue 2: This clue says that Joy’s age is a
multiple of 3. Hence we need to remove from
the list all those that are not multiples of 3. So
we have,
19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34
❌ ❌ ❌ ❌ ❌ ❌
❌ ❌ ❌ ❌ ❌

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 Clue 3: Joy’s age is an odd number.
Among the five numbers left,
19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34
❌ ❌ ❌ ❌ ❌ ❌
❌ ❌ ❌ ❌ ❌
❌
❌

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 Clue 4: The digits of my age are
repeated.
19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34
❌ ❌ ❌ ❌ ❌ ❌
❌ ❌ ❌ ❌ ❌
❌
❌
❌
❌

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 Clue 4: The digits of my age are
repeated.
Therefore, the age of Joy is 33.
19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34
❌ ❌ ❌ ❌ ❌ ❌
❌ ❌ ❌ ❌ ❌
❌
❌
❌
❌

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4. Review the Solution
 Our answer is correct because 33 satisfy all the
given conditions in the problem.
✓ Clue 1: 33 is between 18 and 35.
✓ Clue 2: 33 is a multiple of 3.
✓ Clue 3: 33 is an odd number.
✓ Clue 4: The digits of 33 are repeating.

Polya’s 4-steps in Problem Solving.pptx

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