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```					Riverside Unified School District
Instructional Services
Dawn Smith, K-6 Math Specialist

PROBLEM SOLVING
WITH BAR DIAGRAMS
l_________________?_________________l
What’s the Issue???
Why do so many students continue to find story
problems so difficult?

Is it figuring out what is being asked?

Is it deciding which operation(s) to use?
The issue with regard to story problems
is that too many students continue to
be unsuccessful at solving them!
One thing we know for sure is….

Practice alone does not help
students improve their problem
solving skills!

Students need help to learn
new strategies!
Common Strategies Used

 Key Words (Such as “in all”, “less”, “total”…)

Strategy doesn’t always   work and can be misleading!

Real life problems are not perfectly set up
with key words!
Key Word approach

 John had 7 apples. He gave 4 apples to Mary.
How may apples did John have left?

 Here’s the algorithm.

 John had 7 apples. He gave 4 apples to Mary.
How may apples did John have left?
7–4=3

 John had 7 apples. He left the room to get
another 4 apples. How many apples does John
have?

 Mr. Left had 7 apples…

You can guess what happens!
 Problem Solving “Steps”
(such as Understand, Plan, Solve, Look
Back)

Steps” implies that a set of actions, if followed in order
(such as an algorithm) will lead to the correct solution…like
teaching a skill

“Steps” implies that one moves off one step and onto another.

Most get stuck at “Understand”
Following “steps” is a strategy that
can help students approach a
problem in a systematic way, but it
does NOT guarantee success!
What may have seemed
straightforward:

 Made a model or diagram

 Write the number sentence or equation (after
determining correct operation)

 Solve

 Check
   Show the Problem
   Draw a Picture
   Make an Organized List        o Multiply
   Make a Table                  o Divide

x
   Make a Graph                  o Add
   Act It Out/Use Objects        o Subtract
   Look for a Pattern            o Two-part
   Try, Check, Revise
o Missing Information
   Write an Equation
   Use Reasoning
   Work Backwards
   Solve a Simpler Problem
Actually turns out pretty complicated!
Make                   Approach the
sense of               situation with a                     BBuild a
the                     productive                        situation
context                 mathematical                          model
disposition

Decide
Infer
information
the                     character of       Employ
is relevant
problem                  solution from      the right
the wording         meta-
Decide                                                      knowledge
which        Decide how to
Build a diagram
quantities     represent the
or other
get            relevant
appropriate             Derive
represented       quantities
representation         operation or
Select the                                                equations
appropriate                                                 from the
Solve the
conceptual    Check that the                               diagram/
relevant
model       solution makes                               situations
equation
sense
#1 Problem Solving Strategy:

I don’t get it!!
The reason so many teachers have used a key
word or a steps approach to teaching
problem solving is that they have not had
any alternative instructional strategies!
The challenge in solving story problems is often
not to identify the known and unknown
quantities.

Rather, the challenge is to:
Identify statements in the problem that
express relationships between quantities,

To understand those relationships,

And to choose an appropriate operation(s)
to show those relationships.
Let’s use some bar diagrams!
Joining Problem 1
Kim has 23 antique dolls. Her father gives her
18 more antique dolls. Now how many antique
dolls does she have?

_____________?____________

23                   18
Joining Problem 2

Debbie has saved \$57.00 How much more
money does she need in order to have \$112.00?

l___________112____________l

57                   ?
Joining Problem 3

Tom had some money in his savings account. He
then deposited \$45 into the same account. Then he
had \$92 in all. How much money was in his
account in the beginning?

_____________92____________

?                    45
Separating Problem 1

Steven has 122 jelly beans. He eats 71 of them
in one weekend. How many jelly beans are
left?

_____________122____________

71                    ?
Separating Problem 2

Carrie had 45 CDs. She gave some to Jo. Then
Carrie had 27 left. How many did she give to
Jo?

l____________45____________

?                   27
Separating Problem 3

Alan had some marbles. He lost 12 of them.
Then he had 32 left. How many did he have
before he lost some?

l_____________?____________l

12                  32
Part-Part-Whole Problem 1

Fourteen cats and 16 dogs are in the kennel.
How many dogs and cats are in the kennel?

l____________?_____________l

14                   16
Part-Part-Whole Problem 2

Some adults and 12 children were on a bus.
There are 31 people in all on the bus. How
many adults were on the bus?

_____________31___________

?                   12
Part-Part-Whole Problem 3

Forty-nine people went on a hike. Six were
adults and the rest were children. How many
children went on the hike?

l____________49____________l

6                   ?
Comparison Problem 1

Alex has 47 toy cars. Keisha has 12 cars. How
many more cars does Alex have?

l___________47____________l

12                   ?
Comparison Problem 2

Fran spent \$84 which was \$26 more than Alice
spent. How much did Alice spend?

l____________84___________l

?                  26
Comparison Problem 3

Barney has 23 old coins. Steve has 16 more old
coins than Barney. How many old coins does
Steve have?

____________?____________

23                    16
Bar Diagrams for
Multiplication and Division
Joining Equal Groups Problem 1
Kim has 4 photo albums. Each album has 85
pictures. How many photos are in her 4
albums?

_______?_______

85    85    85     85
Joining Equal Groups Problem 2

Pam had 4 bags and put the same number of
apples into each bag. She had 52 apples to
place in the bags. How many apples did she
put into each bag?

_______52_______

?     ?      ?     ?
Joining Equal Groups Problem 3

Fred bought some books that each cost \$16.
He spent \$80 altogether. How many books

_______80_______

16                     ?
Separating Equal Groups
Problem 1
Byron has 45 pigeons. He keeps them in 5
pens with the same number of pigeons in
each. How many pigeons are in each pen?

_______45_______

?   ?    ?    ?    ?
Separating Equal Groups
Problem 2
A total of 108 students signed up for soccer.
How many 18-person teams can be made?

_______108_______

18                       ?
Separating Equal Groups
Problem 3
Kim had some cards. She put them in piles
of 35 and was able to make 4 piles. How
many cards did she have to start?

________?_______

35     35    35    35
Comparison Problem 1

Alex has 17 toy cars. Keisha has 3 times as
many. How many cars does Keisha have?

________?_______
Keisha       17       17       17

Alex        17
Comparison Problem 2

Barney has 24 old coins. This is 3 times more
coins than Steve has. How many old coins
does Steve have?

________24_______
Barney
?        ?        ?

Steve       ?
Now that you are the
experts…

It’s time to do some grade level
specific examples!

```
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 views: 49 posted: 8/17/2010 language: English pages: 36