MAT 156 Mathematics for Elementary School Teachers

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MAT 156Mathematics for Elementary School Teachers

• Problem Solving

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• The Problem-Solving Process
• Understanding the problem
• Devising a plan
• Carrying out the plan
• Looking back

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• The Problem-Solving Process
• Understand the problem
• Can you state the problem in your own words?
• What are you trying to find or do?
• What are the unknowns?
• What information do you obtain from the problem?
• What information (if any) is missing or not
  needed?
• Avoid Mind Sets

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Spell the word spot three times out loud What
do you do when you come to a green light?
Go Back
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• The Problem-Solving Process
• Devise a plan
• Here are some useful strategies
• Look for a pattern
• Examine related problems
• Examine a simpler or special case
• Make a table or list
• Make a diagram
• Write an equation
• Guess and Check
• Work Backward
• Identify a subgoal

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• The Problem-Solving Process
• 3. Carry out the plan plan
• Implement the strategy in step 2 and perform any
  necessary computations
• Check each step of the plan as you proceed. This
  may be intuitive checking or a formal proof of
  each step.
• Keep an accurate record of your work

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• The Problem-Solving Process
• 4. Looking Back
• Check your results in the original problem
• Interpret your solution in terms of the original
  problem. Does your answer make sense? Is it
  reasonable? Does it answer the question that was
  asked?
• Determine whether there is another method for
  finding the solution
• If possible, determine other related or more
  general problems for which the techniques will
  work

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Example Consider the following problem A
shepherd had 36 sheep. All but 10 died. How
many lived?
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Look for a Pattern Gausss Problem When Carl
Gauss was a child, the teacher asked the students
to find the sum of the first 100 natural numbers.
The teacher expected this problem to keep the
class occupied for some time. Gauss gave the
answer almost immediately. Can you?
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Examine a Related Problem Find the sum of the
even natural numbers less than or equal to 100.
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Identify a Subgoal A Magic Square Arrange the
numbers 1 through 9 into a square subdivided into
9 smaller squares like the one below so that the
sum of every row, column, and main diagonal is
the same