Problem Solving The Ralph Way :): 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.
Problem Solving The Ralph Way :): 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.
Slide3: 3. Select which number to start with
4. Put units in formula
5. Cancel units, top L -> R, Bot L -> R, Using Dimensional Analysis
6. use Calculator
7 Write down answer (with units), Determine Sig. Figs., Recheck Calculations
Slide4: 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.
Slide5: 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.
Slide6: 3. Select which number to start with
4. Put units in formula
5. Cancel units, top L -> R, Bot L -> R, Using Dimensional Analysis
6. use Calculator
7 Write down answer (with units), Determine Sig. Figs., Recheck Calculations
Slide7: 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
Slide8: 5. Cancel units, top L -> R, Bot L -> 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, (Don’t Panic this is just an example)
Dimensional Analysis: 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.
Slide10: 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
If a Recipe calls for 600. g of chocolate chips, how many pounds of chips do you need? : 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
If a Recipe calls for 600. g of chocolate chips, how many pounds of chips do you need?: If a Recipe calls for 600. g of chocolate chips, how many pounds of chips do you need? 5. Cancel units, topL-> R, Bot L-> 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
You want to change oil on your car, it need 4.0L, how many quarts is that?: 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
You want to change oil on your car, it need 4.0L, how many quarts is that?: You want to change oil on your car, it need 4.0L, how many quarts is that? 5. Cancel units, top L->R, Bot L->R
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
A Board is 27.0in long, It weights 1.2kg. Can it be used to connect a 0.56m opening?: 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
A Board is 27.0in long, It weights 1.2kg. Can it be used to connect a 0.56m opening?: 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-> R, Bot. L->R
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
Slide17: 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.
Slide18: 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 => $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 => 6.00e3 g
1 1 apple
Slide19: 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 => 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 => 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 => 1.7e3 cm3 = ml So 200ml will fit
Slide20: 7. If the temperature outside is 25oC how hot is that in oF? In K?
(1.8 x 25oC)+32= 77oF
25oC + 273.15 = 298.15=> 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 = 4.44444=> 4.4g/ml
Water has a density of 1.0g/ml so the substance is more dense than water so it will sink.
Slide21: 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 = 16.66666=> 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 => 4.5 g
ml 1