sanity check on this method of problem solving (quantitative science problems)

[serendipitous journey]

I'd be very grateful for feedback on this method of teaching formal science problem-solving, which is given in the Centripetal Press / Novare "Accelerated Studies in Physics and Chemistry" we are using. 

My child really would benefit from explicit requirements for writing his work out.  So that bit seems good.  I'm not sure about the MKS (meter/kilogram/second) requirement.  The Centripetal Press / Novare method has the student follow these steps:

1. Write down the given information in a column on the left side of your page.
2. Perform needed unit conversions to convert to MKS (meter/kilogram/second) units, writing conversion factors to the right of the given quantities you wrote in the previous step.
3. Write the equation to be used in its standard form.
4. Perform the algebra necessary to isolate the unknown you are solving for. 
5. Using only values in MKS units, insert values and compute the result.
6. Convert to non-MKS units, if required in the problem.
7. Write the result with correct significant digits and units of measure.
8. Check over your work, looking for errors.
9. Make sure your result is reasonable.  First, check to see if your result makes sense.  Second, if possible, estimate the answer from the given information and compare your estimate to your result. 

Thanks for perspective on this!

[regentrude]

This sounds very good advice. 
Especially solving algebraically for the unknown BEFORE putting in numbers!  This step is really, really important. We have a hard time teaching our college students to do that because most of them are not taught properly in their high school science classes and put the numbers in way too early.

If you are looking for a method that always works, your student should absolutely convert to SI (i.e. kg-m-s) units, because then the answer will come out in SI units as well. 
In some cases it would be safe to leave non-SI units, but it takes a lot of expertise to know when that would be ok, and the student is typically not in that position.
While this is probably meant here, I would explicitly add to convert all prefixes (nano, kilo, etc) into powers of 10; it's very easy to lose orders of magnitude otherwise.

I would also add that it is important to put the numbers with their units into the equation to make sure the units cancel properly and the result has the correct dimension. That is an important check to for mistakes. And it's yet another thing many high school students are not taught to do - they just put the numbers. No, no no.

 

Edited April 30, 2020 by regentrude

[serendipitous journey]

Regentrude, thanks so much for your thoughtful feedback & the explicit extensions of converting prefixes into powers of 10 + plugging units into the equation to ensure the dimensions are correct. 

Quick question @regentrude: I'd have thought to use grams as the base unit of mass and not kilograms because that keeps prefixes clean, ie a milligram would be gram/10^3 just as a millimeter is meter/10^3, but the milligram would be kg/10^6 ; if you have any thoughts about this, I'd be glad to know them. 

ETA: in case it wasn't clear to folks, the kilogram question arises because the kilogram (and not the gram) is the base unit of mass in the metric system, and I'm wondering how that translates to working problems as cleanly as possible. 

Edited May 1, 2020 by serendipitous journey

[regentrude]

5 hours ago, serendipitous journey said:

Regentrude, thanks so much for your thoughtful feedback & the explicit extensions of converting prefixes into powers of 10 + plugging units into the equation to ensure the dimensions are correct. 

Quick question @regentrude: I'd have thought to use grams as the base unit of mass and not kilograms because that keeps prefixes clean, ie a milligram would be gram/10^3 just as a millimeter is meter/10^3, but the milligram would be kg/10^6 ; if you have any thoughts about this, I'd be glad to know them. 

ETA: in case it wasn't clear to folks, the kilogram question arises because the kilogram (and not the gram) is the base unit of mass in the metric system, and I'm wondering how that translates to working problems as cleanly as possible. 

Please do not use grams, but kilograms. Yes, it is not logical that the kg should be the base unit, but the definition is that it is. To give a good example why that is important: Newton's first law is F=ma. Force is mass times acceleration. If you put the mass in kg and the acceleration in m/s^2, the force comes out in the SI unit which is the Newton (N). 1N=1kg m/s^2. If the student were using grams for the mass, it would screw up the units because g m/s^2= milli-Newton!  So, even though it looks as if there shouldn't be a prefix, there would be. 

It's like this with all units that are derived from kg, m and s. Joule. Watt. All the electrical ones. 
Please make sure your student internalizes that the kilogram is the SI unit.

[serendipitous journey]

11 hours ago, regentrude said:

... To give a good example why that is important: Newton's first law is F=ma. Force is mass times acceleration. If you put the mass in kg and the acceleration in m/s^2, the force comes out in the SI unit which is the Newton (N). 1N=1kg m/s^2. If the student were using grams for the mass, it would screw up the units because g m/s^2= milli-Newton!  ..

Regentrude, thanks so much for your kind but firm guidance on this!  I'm embarrassed I'd not thought of that consequence. 

Your example is a great one and will make it clear to my child, too.  Again: thanks!

[regentrude]

10 minutes ago, serendipitous journey said:

Regentrude, thanks so much for your kind but firm guidance on this!  I'm embarrassed I'd not thought of that consequence. 

Your example is a great one and will make it clear to my child, too.  Again: thanks!

There is NO need to be embarrassed. It is absolutely not obvious. (And I've been doing this for a living for almost 20 years.)

[Dicentra]

A small addition to the discussion... 🙂

If your student is also doing chemistry calculations, they will want to leave the mass units as grams. 🙂  I'm not sure why chemists have stuck with grams over the SI unit of kg - maybe we're just a contrary bunch. 😉  The only introductory chemistry calculation that I can think of that involves kg is the calculation for molality (a type of concentration unit for aqueous solutions with the units of moles/kg).  All other chemistry calculations that involve mass will use grams. 🙂

[serendipitous journey]

2 hours ago, Dicentra said:

A small addition to the discussion... 🙂

If your student is also doing chemistry calculations, they will want to leave the mass units as grams. 🙂  I'm not sure why chemists have stuck with grams over the SI unit of kg - maybe we're just a contrary bunch. 😉  The only introductory chemistry calculation that I can think of that involves kg is the calculation for molality (a type of concentration unit for aqueous solutions with the units of moles/kg).  All other chemistry calculations that involve mass will use grams. 🙂

Thank you for this. 

[Dicentra]

2 hours ago, Dicentra said:

A small addition to the discussion... 🙂

If your student is also doing chemistry calculations, they will want to leave the mass units as grams. 🙂  I'm not sure why chemists have stuck with grams over the SI unit of kg - maybe we're just a contrary bunch. 😉  The only introductory chemistry calculation that I can think of that involves kg is the calculation for molality (a type of concentration unit for aqueous solutions with the units of moles/kg).  All other chemistry calculations that involve mass will use grams. 🙂

Quoting myself as I kept thinking on this. 🙂  The SI unit for molar mass is actually kg/mol but in practice, chemists will virtually always use g/mol.

From Wikipedia:

"In the International System of Units (SI), the base unit of molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol. "

Many, many chemical calculations will be based off of conversions using molar mass - that's why I suggested keeping the mass unit as grams for chemical calculations.

Which just goes to reinforce how odd and stubborn chemists can be. 😉 😄