ProblemSolving Strategies

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Enduring Understandings
Math Strategies How to Take on Word
Problems--and Win!
Bonne Ecole Elementary Retreat Stephanie Purser
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Problem-Solving Strategies
Definition of a problem
To truly be a problem, a mathematical question
must contain some effort or thought on the part
of the solver.
--As teachers, we need to understand that what
constitutes a problem for some students, may
not be for others.
--Good problems include modifications that may be
made for students of varying abilities.
(differentiated instruction)
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The Five-Step Model
Many teachers use or are familiar with the
following four-step model

• Understand
• Plan (Strategy)
• Solve
• Check

The five-step model is the same process. The
only difference is that the first step is broken
down into 2 more specific steps.
1. What is the problem asking? (What kind of
answer) 2. What are the key facts? 3. Choose a
strategy 4. Solve 5. Does it make sense?
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Points to Consider
--Teachers need a plan for introducing
strategies it is not feasible to focus on them
all at once. --While act it out may be
appropriate for lower elementary, it may not be
for middle grades. --It is rare that a problem
can be solved only with one strategy. For this
reason, a repertoire of strategies is useful.
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What Problem-Solving Strategies Should Be Taught?
1. Act It Out (K-5)

• Stress that other objects may be used in place of
  the real thing.
• Students will see the value of this strategy as
  problems become more challenging.

Sample If I have 16 cookies and there are 4
children to share the cookies, how many cookies
will each child get?
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What Problem-Solving Strategies Should Be Taught?
2. Draw a picture (K-5)

• Remind students that there is no need to draw
  detailed illustrations. Only draw what is
  necessary to solve the problem.

Sample Laura had 3 green chips, 4 blue chips and
1 red chip in her bag. What fractional part of
the bag of chips is green?
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What Problem-Solving Strategies Should Be Taught?
3. Find a Pattern (K-5)

• Students will identify a pattern and predict what
  will come next.
• Students familiar with tables will often
  construct one to aid them in finding a pattern.

Sample Carol has written a number pattern that
begins with 1, 3, 6, 10, 15. If she continues
this pattern, what are the next four numbers in
her pattern?
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What Problem-Solving Strategies Should Be Taught?
4. Make a Table or Organized List (2-5)

• Students can use tables or lists to organize
  large amounts of data.
• An organized list is also helpful with listing
  combinations.

Sample You save 3 on Monday. Each day after
that you save twice as much as the day before. If
this pattern continues, how much would you save
on Friday?
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What Problem-Solving Strategies Should Be Taught?
5. Guess and Check (3-5)

• Many times a large number is given, and the
  student is asked to break it down into parts.
• Students use information from the problem to make
  EDUCATED guesses.
• The check part of this strategy is essential!
• Using a table is very helpful when using this
  strategy.
• Use information from each guess to modify
  subsequent guesses.

Sample Amy and Judy sold 12 show tickets
altogether. Amy sold 2 more tickets than Judy.
How many tickets did each girl sell?
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What Problem-Solving Strategies Should Be Taught?
6. Work Backward (3-5)

• Some problems are written in such a way that
  students are given the end result, and asked
  about something that occurred earlier. (Think
  about rewind on the VCR)

Sample I have 6 marbles left. I gave 3 to a
friend, and I lost 5 on the way home. How many
did I start with?
Step 1 Write a number sentence
(start) - 3 - 5 6

Step 2 Work the number sentence backward, using
opposite operation
6 5 3 (start)
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What Problem-Solving Strategies Should Be Taught?
7. Logical Reasoning (4-5)

• Some problems are written in such a way that
  students are given the end result, and asked
  about something that occurred earlier.

Sample Four children built snowmen. Kareems
snowman is next to Sarahs. Brents is on the far
left. Ebonys is on the far right and is next to
Kareems. Whose snowman is where?

• Act it Out and Draw a Picture lend themselves
  to
• this type of problem.

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What Problem-Solving Strategies Should Be Taught?
8. Solve a Simpler Problem (4-5)

• Some problems are written in such a way that
  students are given the end result, and asked
  about
• something that occurred earlier.

Sample We are having a party and are putting
square tables together in a long row for the
party. We can put two chairs on each side of a
table. The tables are all the same size. If we
put together ten tables in a row, how many people
can sit down?
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Quiz Time!
Sir Miss-a-lot, known all over the kingdom for
his bad aim, is practicing his archery skills. He
shot 3 arrows at the target shown. To his
amazement, all 3 arrows hit the target. How many
possible point totals could Sir Miss-a-lot have
scored?
Answer organized list
3
7
10
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Quiz Time!
Together, Jamie and Jan spent 8.00 on snacks at
the theater. Jamie spent 2.00 more than Jan.
How much did Jan spend?
Answer Guess and Check (also make a table)
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Quiz Time!
Antonio sells t-shirts that have his restaurants
name printed on them. On Saturday, Antonio sold
one t-shirt. He sold 3 t-shirts on Sunday, 6 on
Monday, 10 on Tuesday, and 15 on Wednesday. If
sales continue in this way, how many
t-shirts will Antonio sell on Friday?
Answer find a pattern, make a table, solve
simpler problem
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Quiz Time!
Trevor left his campsite and hiked 6 miles south
to the river. He then hiked 4 miles west to a
cave. Then he turned north and hiked 3 miles to
an old cabin. After he rests a while, Trevor
plans to hike east to pick up the first trail.
When he leaves the cabin, how far does Trevor
have to hike to reach the campsite?
Answer Draw a picture
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Quiz Time!
Greg, Mike, Sally, Ann and Jason are lining up at
the starting line waiting for a race to begin.
Mike is standing directly to the left of Ann.
Sally is between Ann and Jason. Greg is in lane
1. Ann is not in lane 5. In what order are the
runners lined up?
Answer Logical reasoning, make a table, act it
out, draw a picture
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Quiz Time!
The Newsy Comic Book Company published a new
comic book. They sold 200 copies of the book in
the first week after it was published. They sold
700 copies in the second week, 1,700 in the
third week, and 3,200 copies in the fourth week.
At this rate, how many copies will they sell in
the eighth week?
Answer find a pattern, make a table, solve a
simpler problem
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Quiz Time!
Hannah collects marbles. On Thursday, she used
her allowance to buy 12 marbles. On Friday, she
lost 6 marbles in a tournament. If Hannah now
has 120 marbles in her collection, how many did
she have on Wednesday?
Answer work backwards