MATH IN THE MODERN WORLD - PROBLEM SOLVING.pptx

What is
problem
solving?
Problem solving is the act
of defining a problem;
determining the cause of
the problem; identifying,
prioritizing, and selecting
alternatives for a
solution; and
implementing a solution.

You are working
on something in
class and it is
very difficult.
You begin to
feel frustrated.
1.What is the problem?
2.What are the three
possible solutions to your
problem?
3.Which solution is the best?
4.What will happen
afterward?

3. Four students measure their
heights. Nikko was taller than
Ken, but not as tall as Toni. Gab
was taller than Toni. Write
down their names in order of
their heights , from shortest to
tallest.

4. Elisse has a watering schedule for
her plants. Her cacti get watered
every 10 days while her begonias get
watered every 3 days. If she watered
both sets of plants today, in how
many days will be the next time she
has to water BOTH sets?

2. A spider is climbing up a
32m building. Each day, it
climbs five meters and slide
back one meter. How many
days will it take to reach the
top?

1. Meg’s farm had chickens and
goats . There were 19 animal
heads on the farm and 60 legs.
How many were chickens and
how many were goats ?

Problem solving
is an artistic
science! There
is no single
approach in
problem solving
that works all
the time.
Each problem is slightly
different. George Polya,
known as the father of
problem solving did
extensive studies and
wrote paper and books
about problem solving.

POLYA’S FOUR STEPS
IN PROBLEM
SOLVING

01
UNDERSTAND
THE PROBLEM
PREPARATION

Consider
the terminology
and notation used
in the problem
Write down
specific examples
of the conditions
given in the
problem.
Learn the
necessary
underlying
mathematical
concepts
Rephrase the
problem in your
own words.

02
DEVISE A
PLAN
THINKING TIME

a.You must start somewhere to start something. How are you going to
attack the problem?
You must start somewhere to start something. How are you going to attack the
problem?
Once you understand what the problem is, if you are stumped or
stuck, set the problem aside for a while. Your subconscious
mind may keep working on it.
Possible strategies: (reach into your bag of tricks
Moving on to think about other things may help you stay
relaxed, flexible and creative rather than becoming tense,
frustrated, and forced in your efforts to solve the problem.

Once you have an idea for a new approach, jot it down
immediately. When you have time, try it out and see if
it leads to a solution.
The key is to keep trying until something works.
Once you have thought about a problem or returned to it enough
times, you will often have a flash of insight: a new idea to try or a new
perspective on how to approach solving the problem.
If the plan does not seem to be working, then start over
and try another approach.

a.Once you have a
potential solution,
check to see if it works.
b.If you find that your solution does not work, there may be only a
single mistake. Try to fix or modify your current attempt before
scrapping it. Remember what you tried- it is likely that at least part
of it will end up being useful.
c.Is there another way of
doing the problem which
may be simpler? (You need
to become flexible in your
thinking There usually is
not one right way)
d.Can the problem or method be generalized so as to be useful for
future problem?

POLYA’S FOUR STEPS
Understand the
problem
1
Devise a plan
2
Carry out the plan
3
Look back
4

GUESS AND CHECK
is a classic technique . While it may not be very
efficient or reliable, sometimes its all one has to
work with. One nice thing about this technique is
the low level of effort it requires. Guess and check
is one of the simplest strategies . Anyone can
guess and answer. If they can also check that the
guess fits the condition of the problem, then they
have mastered guess and check.

LIST/TABULATE
creating a systematic list and organizing tables
helps discover some hidden hints towards
solutions of some problems. To help solve logic
problems, tables with ticks and crosses are often
used. Tables can also be an efficient way of
finding number patterns.

ACT IT OUT
is an effective strategy for demonstration
purposes and to have a better grip of the problem
on hand. Devices use to act out the problem are
considered equipment. Act-It-Out strategy has
limited application.

DRAW
this includes drawing pictures, Venn diagram,
sketches, maps and other representations to help
solve mathematical problem, as well as problems
in mechanics.

1.In an apartment complex, there are five
windows in each apartment, and 9 apartments in
each floor. How many windows are there on 8
floors?

2.The sum of three consecutive numbers is 48.
What are these numbers?

“It’s not that I’m too smart.
It’s just that, I stay with
problems longer” - Albert Einstein

MATH IN THE MODERN WORLD - PROBLEM SOLVING.pptx

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