Chapter 2C SBM Approaches to Problem Solving

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Chapter 2C SBMApproaches to Problem Solving

• Problem-Solving Guidelines
• and Hints

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Problem Solving Hints

• Using a 4-step process will help you become
  better organized in solving problems.
• The best way to learn to problem solve is by
  learning these 4 steps and through guided
  practice.
• Try to develop an attitude about problem solving
  instead of a technique!

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The 4-Step Process

• Step 1 Understand the Problem
• Step 2 Devise a strategy for solving the
  problem.
• Step 3 Carry out your strategy and revise it
  if necessary.
• Step 4 Look back to check, interpret, and
  explain your result.

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Step 1

• Think about the context of the problem to gain
  insight into its purpose.
• Make a list/table of specific information given
  in the problem.
• Draw a picture/diagram to help you make sense of
  the problem.
• Restate the problem in different ways to clarify
  its question(s).
• Make a mental or written model of the solution to
  allow you to fill in details as you work through
  the problem.

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Step 2

• Obtain needed information that is not provided in
  the problem statement, using recall, estimation,
  or research.
• Make a list of possible strategies and hints that
  will help you select your overall strategy.
• Map out your strategy with a flow chart or
  diagram.

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Step 3

• Keep an organized, neat, and written record of
  your work, which will be helpful if you later
  need to review your solution.
• Double-check each step so that you do not risk
  carrying errors through to the end of your
  solution.
• Constantly reevaluate your strategy as you work
  if you find a flaw in your strategy, return to
  Step 2 and recreate a revised strategy.

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Step 4

• Be sure that your result makes sense (ie.
  expected units or values).
• Once you are sure that your result is reasonable,
  recheck your calculations.
• Identify and understand potential sources of
  uncertainty in your result.
• Write your solution clearly and concisely.
• Consider and discuss any pertinent implications
  of your result.

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8 Hints to Problem-Solving

• Hint 1 There may be more than one answer?
• Hint 2 There may be more than one strategy?
• Hint 3 Use appropriate tools?
• Hint 4 Consider simpler and similar
  problems?

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Problem-Solving Hints (cont)

• Hint 5 Consider equivalent (equal) problems
  with simpler solutions?
• Hint 6 Approximations can be useful?
• Hint 7 Try alternative patterns of thought?
• Hint 8 Do not spin your wheels????

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A Little more.

• Please refer to all seven examples in the lesson
  before you attempt the homework?
• Also, refer to the handout on Zenos
  paradox. (see web)
• And, most of all, use your brain to think things
  out- dont spin your wheels?

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Example(solution to 18 pg. 128)

• Suppose 10 large barrels are filled with golf
  balls that all look alike (each barrel holds
  1000s of golf balls).
• The golf balls in 9 of the barrels weigh 1 ounce
  each and the golf balls in 1 of the barrels weigh
  2 ounces each.
• With only one weighing on one scale with a
  capacity of 100 ounces, how can you determine
  which barrel contains the 2 ounce golf balls?
• See the next slide for the solution

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• Since the barrel with the 2-oz. Golf balls weighs
  more, we must find out which barrel weighs more
• So, pick a sequence of golf balls from each
  barrel. (ie. 1 from barrel 1, 2 from barrel 2,
  and so on)
• Therefore, 1 2 3 10 55 ounces.
• Since 60 55 5 ounces. Hence, 5 golf balls
  are weigh 2 oz.
• Maybe, you get 60 ounces, therefore the 5th
  barrel is the heaviest. And, it holds to 2-oz
  golf balls.

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Homework

• 2C I 2b, 3 5, 7, 10
• 2C II 6, 8, 11 19, 21