Problem Solving The Ralph Way :

1
Problem Solving The Ralph Way )

• The following is a power point that has been
  designed to help you work through an alternative
  method to solving story problems.
• We have condensed the steps down to 7 step. The
  next few pages are step up to show you the steps
  then to talk you through each of the steps
  similar to what would be presented in a lecture.
  The steps will then be used to help you solve
  several problems to help ingrain the process.

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Problem Solving The Ralph Way )

• 1. Read the whole problem
• 2. Read the problem carefully for facts.
• a. What is known
• b. What are you trying to find, What units is
  it in?
• c. What could be known.
• d. Other info.

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• 3. Select which number to start with
• 4. Put units in formula
• 5. Cancel units, top L -gt R, Bot L -gt R, Using
  Dimensional Analysis
• 6. use Calculator
• 7 Write down answer (with units), Determine Sig.
  Figs., Recheck Calculations

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• 1. Read the whole problem
• You want to read the problem without worrying
  about numbers. You are doing this to work on the
  flow of the question and story. It is often
  useful to just skip the numbers or say number.
• 2. Read the problem carefully for facts.
• This time you are reading the problem to look at
  the numbers and the information you will need to
  complete the problem.
• a. What is known
• What are the numbers given in the problem. Write
  them down with their units.

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• 2 b. What are you trying to find, What units is
  it in?
• This is where you are looking at what number you
  are solving for. I.E. Why are you even doing
  this problem. Try to figure out what type of
  number you are looking for. Make sure to include
  units.
• c. What could be known.
• What conversions could you look up, or do you
  know? I try to think about what conversions I
  may need to solve the problem.
• d. Other info.
• This is if there is some other piece of
  information you want to note like temperature or
  date or etc.

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• 3. Select which number to start with
• 4. Put units in formula
• 5. Cancel units, top L -gt R, Bot L -gt R, Using
  Dimensional Analysis
• 6. use Calculator
• 7 Write down answer (with units), Determine Sig.
  Figs., Recheck Calculations

7

• 3. Select which number to start with
• This is often the hardest part. Often times you
  will be presented with many numbers in a problem
  to pick from. So which number do you pick?
  First ask yourself, is there any conversions in
  the problem? Like 5 dogs equal a cat, this is
  a ratio or a conversion. So write it as such 5
  dogs , if it is not a ratio write it normal 5 mL.
• 1 cat
• The easiest number to start with is one that
  contains similar units to what you are solving
  for. If your answer needs a volume for instance
  pick a number that has volume in it. Even if
  the units do not match, you can always convert
  units.
• So if you are solving for cats you would want to
  start with the 5 dogs/1 cat instead of the 5ml.
• You should then place this number at the start of
  the problem.
• Be mindful of the units and the numbers. If you
  want cats on top for the answer you will need
  cats on top for the problem also so 1/5
• 4. Put units in formula
• Now you need to include units with your number.
  Always write out the units as well as the numbers
  they can be a great cross check of your answer
  later so 1 cat
• 5 dogs

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• 5. Cancel units, top L -gt R, Bot L -gt R, Using
  Dimensional Analysis
• See the next slide for the dimensional analysis
  steps
• I always like to work very systematically when
  doing my canceling of units. I will work across
  the top row from left to right of the problem
  canceling units as I go. When I get an unit that
  I need for the answer I often circle it to tell
  me that I do not need to cancel it. After I have
  canceled all the top row units I then work from
  left to right across the bottom row.
• Some times in the solving of a problem you place
  a unit from your problem that does not have a
  conversion on the other side of the equation.
  You can place a one on the other side of the
  problem if that helps you feel better about the
  problem. This is because one (1) times or
  divided into anything does not change the
  numbers.
• Here is an example of a complex problem, (Dont
  Panic this is just an example)

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Dimensional Analysis

• What unit are you canceling?
• Place that unit on the opposite side of the line.
• Place the other unit.
• Determine which unit is bigger
• Place a 1 in front of that unit
• Place conversion number in front of other unit.

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• 6. use Calculator
• Now that all the units are canceled you are ready
  to use the calculator.
• The easiest way to do this without brackets and
  to much calculator error is to use the Times (x)
  Key for everything above the horizontal line and
  use the divide key for everything below the line.
  
• You do not want to press the equals key till the
  very end! This is because calculators introduce
  rounding errors when the equal key is pressed.
  Another common error is when students try to
  times the top, write it down, then times the
  bottom, right it down then try to put them back
  in the calculator to do the divide. You have
  added to many steps and to many errors to get a
  good anwser.
• Using the old Example back two pages
• 45 x 4.5 / 1000 / 4.184 0.0483987
• 7 Write down answer (with units), Determine Sig.
  Figs., Recheck Calculations
• This is where you finish the problem off. Write
  down the answer, add the units, figure out the
  significant figures and then redo the calculator
  one time to make sure the answer is right
• Example 0.048/39 0.048 kg/J

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If a Recipe calls for 600. g of chocolate chips,
how many pounds of chips do you need?

• 1. Read problem
• 2. read for facts
• a. what is known? 600.g
• b. what are we finding? ? in pounds
• c. What do we know?
• (from book) 1 lbs 454g
• d. other info? none
• 3. select which number to start with? You only
  have 600.g
• 4. put units formula
• 600 g
• 1

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If a Recipe calls for 600. g of chocolate chips,
how many pounds of chips do you need?

• 5. Cancel units, topL-gt R, Bot L-gt R
• 600 g 1 lbs
• 1 454 g
• 6. use calculator
• 600 /454
• 7. Write down answer,
• 1.3215859 lbs
• determine sig. figs
• 3
• 1.32 lbs
• recheck calculations

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You want to change oil on your car, it need 4.0L,
how many quarts is that?

• 1. Read problem
• 2. read for facts
• a. what is known? 4.0 L
• b. what are we finding? ? in Quarts
• c. What do we know? 1 qts 0.9463529 L
• d. other info? none
• 3. Select which number to start with
• 4.0 L
• 4. Put units in formula
• 4.0 L
• 1

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You want to change oil on your car, it need 4.0L,
how many quarts is that?

• 5. Cancel units, top L-gtR, Bot L-gtR
• 4.0 L 1 qts
• 1 0.9463529 L
• 6. use calculator
• 4.0 / 0.9463529
• 7. Write down answer
• 4.2267530 qts.
• determine sig. figs
• 2
• 4.2 qts.
• recheck calculations

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A Board is 27.0in long, It weights 1.2kg. Can
it be used to connect a 0.56m opening?

• 1. Read problem
• 2. Read for facts
• a. what is known?
• 27.0in B
• 1.2kg B
• Opening 0.56m
• b. what are we finding?
• ? m, will it fit?
• or ? in is it long enough?
• c. What do we know?
• 1 in 2.54 cm
• 1 m 100cm
• d. other info?
• 3. Select which number to start with
• 27.0 in or 0.56 m
• 4. put units in formula
• 27.0 in or 0.56 m
• 1 1

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A Board is 27.0in long, It weights 1.2kg. Can
it be used to connect a 0.56m opening?

• 5. Cancel units, top L-gt R, Bot. L-gtR
• 27.0 in 2.54 cm 1 m or 0.56
  m 100cm 1 in
• 1 1 in 100cm
  1 1 m 2.54cm
• 6. use calculator
• 7. Write down answer
• 0.6858 m 22.047in
• determine sig. figs
• 3 2
• 0.686 m 22 in
• recheck calculations
• Yes it Could

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• It is now time to see what you know?
• To aid you and give you more practice at solving
  story problems, on the next few pages, there are
  many examples of story problems. We would like
  you to try each problem on your own. Then you
  can click the screen and the complete formula
  with answers will show up so that you can check
  your work.
• Also check the Assignments for the week because
  there is additional worksheets to work through.

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• 1. If you have a 3498mL of a substance how many L
  is that? How many ML is it?
• 3498 mL 1L 3.498 L
• 1 1000mL
• and 3498 mL 1ML
  3.498e-6 ML
• 1 1,000,000 (or 1e6)
• 2. What is the cost of a Kg of sugar if it cost
  1.37 per 5 lb bag?
• 1.37 2.2 Lbs 0.6028 gt 0.60/Kg
• 5 Lbs 1Kg
• 3. You have a 10.12lb container which contains
  50 apples. Each apple weights 120. g. How much
  will the apples weight?
• 50 apples 120. g 6000 gt 6.00e3 g
• 1 1 apple

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• 4. If you have a car traveling at 30m/sec how
  many Km/hr would that be?
• 30 m 1 km 60 sec 60 min 108 gt
  1e2 km/hr
• 1 sec 1000 m 1 min 1 hr
• 5. A New drug has a dose of 2.3mL/kg body
  weight. If you have a patient who weights
  198lbs. How much drug should you give them?
• 2.3 mL 1 kg 198 lbs 207 gt
  2.1e2 mL
• 1 kg 2.2 lbs 1
• 6. If you have a 12cm square box. And you have
  200.mL of sand weighting 1000g, can you fit the
  sand in the box in one trip?
• 12 x 12 x 12 1728 cm3 gt 1.7e3 cm3 ml
  So 200ml will fit

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• 7. If the temperature outside is 25oC how hot is
  that in oF? In K?
• (1.8 x 25oC)32 77oF
• 25oC 273.15 298.15gt 298K
• 8. If you have 200.g of a substance and it takes
  up 45ml what is the density of the substance?
  Will it float on water?
• 200.g / 45ml 4.44444gt 4.4g/ml
• Water has a density of 1.0g/ml so the substance
  is more dense than water so it will sink.

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• 9. If you have a compound with the density of
  4.5g/ml and a mass of 75g what volume does it
  take up?
• 1ml 75g 16.66666gt 17ml
• 4.5g 1
• 10. If you have a compound that is 6.03 ml and
  has a density of 0.74g/ml what is its mass?
• 0.74 g 6.03ml 4.4622 gt 4.5 g
• ml 1