Problem Solving Techniques

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Problem Solving Techniques

• FIRST HALF

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1. Find a Pattern
If a pattern can be established, it becomes
fairly simple to predict what comes next. Once a
pattern is checked for accuracy, it can be used
at any stage of the problem.
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Example to work through

• ant, butterfly, caterpillar, _____, _____, ____
• 1, 3, 5, 7, 9, _____, _____, _____
• 1000, 520, 280, 160, ____, ____, ____

Step 1 Look at the information you have been
given. Step 2 Try to see if the information is
alike. Step 3 Try to see if the information is
different. Step 4 Using the information,
determine if there is a pattern and
if it can be continued.
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Example to work through

• ant, butterfly, caterpillar, _____, _____, ____
• (all in Animal Kingdom alphabetical order)
• 1, 3, 5, 7, 9, ___, ___, ____
• (add 2 to all to get next number)
• 1000, 520, 280, 160, ____, ____, ____
• (divide by 2 and add 20 to each)

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2. Make a Table or Chart
Set out the information given in an orderly
chart, graph, or table. Fill in the missing
information.
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Example to work through
In training for the Pie Eating Contest, Bill
eats five pies the first day, ten the next, and
so on, adding five more each day as he becomes
better trained. How many days would Bill train
until he used up all his 330 practice pies?
Step 1 Read the problem thoroughly. Step 2
Organize the information given into a grid to
show up any patterns. Step 3 If
possible, fill in the blanks.
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• In training for the Pie Eating Contest, Bill
  eats five pies the first day, ten the next, and
  so on, adding five more each day as he becomes
  better trained. How many days would Bill train
  until he used up all his 330 practice pies?

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3. Work Backwards
Problems that have a range of events that have
occurred can be solved using this technique.
Start at the end point and work backwards to find
the beginning point.
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Example to work through
At the ice cream factory, the quantities of each
of the six flavors are decided mathematically.
The total amount of chocolate, mint, and
butterscotch is always half of the days
production. They produce fifteen more tubs of
chocolate than mint and fifteen more tubs of mint
than butterscotch. Of the remaining ice cream,
half is honey, with the rest being split 1/3
2/3 between caramel and bubblegum. If there are
fifteen tubs of caramel ice cream, how many tubs
of each of the other flavors are made?
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Given Caramel 15 (represents 1/3)

(together represent ½ of remaining)
Bubblegum 30 (represents 2/3)
Honey 45 (represents the other ½ of
the remaining)
90 (represents total of this half of the ice
cream) 90
(represents total of the other half of the ice
cream) Butterscotch 15
Mint 30 (15 15) Chocolate
45 (30 15) 90


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4. Guess and Check(2 variables)
Guess a possible answer, check back to see if it
makes sense, and change the possible answer
according to the results of the check.
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Example to work through
Billy has 56 marbles in his collection. If he
had 14 more cats eyes than bullets, how many
of each marble did he have?
Step 1 Decide what you need to find out. Step
2 Read the question for clues. Step 3 Make
reasonable guesses and check for
accuracy.
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Billy has 56 marbles in his collection. If he
had 14 more cats eyes than bullets, how many
of each marble did he have?
Step 1 How many cats eyes does Billy
have? Step 2 14 more cats eyes than
bullets Step 3 half of 56 28 guess 1
30 cats eyes 14 16 30
16 46 (off by 10) guess 2 35 cats eyes
14 21 35 21 56
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Problem Solving Techniques

• SECOND HALF

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Guess and Check(3 variables)
Guess a possible answer, check back to see if it
makes sense, and change the possible answer
according to the results of the check. More
variables means more information needs to be
checked.
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Example to work through
At the zoo there are 90 animals, including birds,
reptiles, and marsupials. If there are eight
more reptiles than marsupials, but two more
marsupials than birds, how many of each are there?
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At the zoo there are 90 animals, including birds,
reptiles, and marsupials. If there are eight
more reptiles than marsupials, but two more
marsupials than birds, how many of each are
there?

• Reptiles Marsupials Birds Total
• 30 22 (8 less) 20 (2 less) 72
• 35 27 (8 less) 25 (2 less) 87
• 36 28 (8 less) 26 (2 less) 90

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Draw a Diagram or a Picture
There are two drawing techniques which can be
useful a) scalingwhere the information is
converted into a scale diagram, b) sketching
where the information is arranged visually to
produce a solution.
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Example to work through
Scaling
If this is 3 miles l-----l how long is this?
l-----l-----l-----l Answer 9 miles
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Example to work through
Sketching
A plot of land has been divided into 16 squares.
The land is to be equally divided among 4
children so that each children get a piece of
land the same shape and size. Can you find and
color five different ways to equally divide the
land?
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One way
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A second way
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A third way
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A fourth way
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A fifth way
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Make a List
This technique is used when there is much
information present. The information needs to be
set out to show the possibilities for solutions.
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Example to work through
When five friends meet, they each shake hands
with each other. How many handshakes are
exchanged?
1 with 2 2 with 3 3 with 4 4 with 5 1 with 3 2
with 4 3 with 5 1 with 4 2 with 5 1 with 5 10
handshakes
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Use Logical Reasoning
Statements or information can be used to create
the next part of the solution. Each piece of
information should confirm the one before.
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Example to work through

• Match the students with the sport, using the
  clues outlined below.
• Students James, Karen, Charles, Terry, Lee
• Sports Football, Basketball, Tennis, Softball,
  Baseball
• James likes to practice shooting, but kicking is
  not allowed in his sport.
• Passing and catching arent the only moves in the
  game that Charles plays.
• Lee often uses her own glove and can get out more
  than once each game.
• Karen finds it difficult to practice her sport
  without others.
• Terry has developed a great throw in his sport.

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Match the students with the sports.
Student Sport James __________________ Kare
n __________________ Charles ______________
____ Terry __________________ Lee ________
__________
Jamesshooting, no kickingbasketball Charlespass
ing and catching and running and
kickingfootball Leeown glove and more than one
outsoftball Karendifficult to practice without
otherstennis Terrygreat throwbaseball
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REVIEW

• Find a Pattern
• Make a Table or Chart
• Work Backwards
• Guess and Check (using 2 variables)

• Guess and Check (using 3 or more variables)
• Draw a Diagram or Picture
• Make a List
• Use Logical Reasoning