HELP! professor going to fail me on final

Okay,
Im in a transitional program Lpn to Rn at a CC and its my first semester (end of) a 4 semester program. Im taking a nursing class mixed with a pharmacology class. The pharm class is a 1 credit 3 test class + a final. We just today took our final and havnt had a test since october. My professor stressed to us that if we didnt use dimensional analysis, even if we got a correct answer the answer was WRONG. she said this at the beginning of the semester.
I have a B in the class and am okay at DA. I took final today and she gave me a 30 % on the final because my dosage calculations were correct they wernt according to her standards "dimensional analysis"
what she says is we set up the problem as 1. what we have on hand then 2. what is ordered or conversion then 3. what is ordered is conversion was used in step 2. She said to me today the reason she marked me so low was i "inverted my fractions" and put the have as say for a problem of doc orders 500 mg of A and on hand is 250 mg of tablets of a . we should state as : 1 tab/250 mg X 500 mg /dose WITH TABS BEING AS NUMERATOR.
i utilized format 250 mg/ 1 tab X dose/500 mg with tabs being as denominator I was able to calculate appropriately using method of desired/have. and i have failed the course now cannot move on to clinicals because we need to have a 75 % to pass. i have two days to file an appeal before we break for 6 weeks for winter break and i need to have representation that what i did on all my problems utilizing this method is indeed dimensional analysis. I have found documents online that argue for both tabs on top and tabs on bottom.
Please help me acquire some ammunition when i go to talk to the grievance department tomorrow and again on friday. 

Dec 10, '15This is an interesting dilemma. In many facilities, you actually have to write out the dose in mg/ml for instance, as (and I hope to be clear, as I am not sure I can explain) say that you have on hand both 325mg and 500mg of acetaminophen. The dose is 650mg (or even 975) the confusion can come in if you say "2 tabs" and those 2 tabs can mean different things to different nurses. (Even so much as "eh, 975, 1000 what's the difference?) Which then gets into max 24 hour dose for acetaminophen.....
So I would question the whole "tabs" thing. I could see the answer being __mg/tabs/caps/whatever med unit, being based on what's on hand.
If one is cross multiplying and dividing, again not sure why numerator/denominator is such a huge issueand very dependent on someone's understanding of math concepts in the past....ESPECIALLY if the answer is correct, and you figure out the answer but due to having to "show your work" invert the fraction
And yes, my mathmetician kid would tell me that numerator and denominator is a process by which you divide one thing (the denominator) by the numerator. And by not setting it up that way, you were not dividing in the correct format. But is the goal math or is it the correct answer in a pharmacology class? Bottom line you got every answer correct. Is the goal math, or is the goal safe and correct medication administration?
We had an ultra strict pharmacy, and "tabs" wasn't even used, as in fact not everything comes in tabs but in other units of medication. Orders were to be clarified "Acetamnophen, 325 mg, 975mg PO q 8 hours PRN pain. Dose not to exceed 4000mg q 24 hours" that kind of thing. Tabs is subjective, and not always on hand as a unit of medication. Hence why the mg on hand and mg to give were all in mg.
However, since your professor insisted you use "tabs", and what happened when you had liquid (ml's) and you could not use "tabs"....
I would argue that this is not a math class, but a pharmacology class. That you set up your problems as to how you best understand how to divide appropriately. The goal is patient safety and correct dose. That whenever an order requires some sort of alternate than what is on hand, another nurse checks math and dose calculation for safety. You would know your resources and how to use them.
Best wishes, and please let us know how it goes!Last edit by jadelpn on Dec 10, '15 
Dec 10, '15If the question was "how many tablets per dose," then I agree with the instructor.
The way you set up the equation, your answer would have been 1/2 dose per tablet.
The way the instructor set up the equation, the answer would have been 2 tablets per dose.
It really helps when doing a problem like this to show your work with the numerator written on 1 line. Then draw a straight line under it. Then write the denominator under the line. (I tried to show the work that way here, but I can't get the formatting to work for me.)
When you write the number as numerator followed by a slash followed by the denominator it is easy to subconsciously fix it in your head.Last edit by Anonymous865 on Dec 10, '15 
Dec 10, '15in this case it is intuitively obvious that if there is 1/2dose per tablet, that 2 tablets would make a full dose. Your equation does not account for something that is intuitively obvious in this example.
The next question might come up with something like 3/5 dose per tablet but in that case it won't be intuitively obvious what you need to do to get a full dose. That's why your equation must account for each step required to get the answer in # tablets / dose. 
Dec 10, '15When faced with a question like this, the easiest way to apprach it is to ask what kind of result do you want.
Do you want an answer in number of tablets per dose? Then you need to start with tablets as a numerator and dose as the denominator. (e.g. tablets / dose)
If you want the final answer to be dose size per 1 tablet, then you need to start with dose as a numerator and tablet as denominator (eg dose / tablet)
Most of the time you are going to want the number of tablets in a dose, or tablets/dose. That tells you that you have to have tablets in the numerator.
Now ask how you can create a valid equation where tablets is the numerator. What do you know about tablets. You know that 1 tablets is 250mg. You could either write this as 1 tablet / 250 mg or 250 mg / 1 tablet. We've already decided that we want the answer in number of tablets per dose, so I'm going to start the equation as
1 tablet / 250mg
Now I have to take dose into account. I could write 1 dose / 500 mg. I could also say that 500mg is 1 dose We've already decided that the final answer must be tablets per dose, so I want dose to be in the denominator in the final answer. It will be easier to get it into the denominator if I start it in the denominator. I'm going to use 500mg / 1 dose
So far then my equation will be
1 tablet / 250mg x 500 mg / 1 dose
since "mg" is in the denominator in the first part and the numerator in the 2nd part of the equation, you can get rid of the mg leaving an equation of
1 tablet /250 x 500/1 dose
This can be rewritten
1 tablet x 500

250 x 1 dose
That can be simplified to
1 tablet x 2 / 1 dose 
Dec 10, '15Just because you had the right answers does not mean your math was right. It sounds like after reading the end of your equation, you had to flip your answer to have the correct answer format. That means your math was incorrect, and you were relying on "intuitive" reasoning. That reliance can lead to some of the most subtle mistakes in your math as there is no track of it.
To start every DA problem off on the right foot, before even writing any numbers, use lined paper (if possible). Read the question, and ask "what is it they are looking for, and what units do they want that in?". If the answer is tablet/dose, then write tablet above the line and dose below, followed by a colon. THEN go ahead and set up the rest of your problem. Setting the goal unit (mg/mL, gtt/min, mL/hr, etc) ensures you start off on the correct units and prevents much of the unit flipping that happens with freeform dosage math.
DA is an excellent, standardized calculation format for dosage math. I would agree with your teacher that refusing/being unable to utilize it consistently and efficiently puts a nurse at higher risk of dosage error.
I am sorry. I can't imagine how frustrated and angry you must be, and how hard it is to see your entire semester go down in flames. Your professor warned you about the importance of DA though, and it sounds like you don't fully grasp it. Use your repeat class to master DA.
Didn't you take Chemistry for a prerequisite? This is exactly like the equations they utilize, if that helps.
If I may, I recommend the book Dimensional Analysis for Meds by Anna Curren. Excellent resource, problems are clear and direct, and it builds on prior skills.