# Healthcare Math: Calculating Dosage

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1 Healthcare Math: Calculating Dosage Industry: Healthcare Content Area: Mathematics Core Topics: Applying medical abbreviations to math problems, using formulas, solving algebraic equations Objective: Students will be able to accurately calculate the dosage of medication in the correct form to fill a doctor s prescription Materials included: Instructor s notes Scenario: Pharmacy Technician Student worksheets Handouts Quiz Answer Keys Industry Overview: According to the U.S. Department of Labor, the healthcare industry is expected to generate over 20% of all new jobs created in the U.S. economy between 2012 and 2022.* The healthcare industry is comprised of a vast array of jobs, ranging from nursing assistants to physicians. Mathematics and literacy skills are essential for students who plan to pursue a career in this field. Healthcare professionals, including pharmacy technicians, need to understand medical terms, abbreviations, and metric measurements. They must also have the ability to use formulas to calculate the correct dosage of medication for patients. * Source: 1

2 Instructor s notes: The purpose of this module is to help students develop and apply math skills in a healthcare workplace setting. The learning activities were designed to be incorporated throughout multiple instructional periods as math concepts are taught in a healthcare context. After completing the module, students should be able to: o Interpret the essential information contained on a prescription o Apply medical abbreviations to solve mathematical problems o Use a formula to calculate the correct dosage of medication to fill prescriptions Setting the stage: Provide students with background information about the typical responsibilities of a pharmacy technician. You may want to have students use the occupational outlook handbook, O*NET and/or other relevant websites to research the job responsibilities, educational/training requirements, salary, etc. for this position. In addition, you could have students view YouTube videos depicting the typical responsibilities of a pharmacy technician. (See links below) Bureau of Labor Statistics Occupational Outlook Handbook: Occupational Information Network (O*NET) Pharmacy Technician videos: For Activity 1: Prescription Abbreviations Have students work individually, or in pairs, to review and study common prescription abbreviations listed in the scenario. You may want students to make flash cards to quiz each other on the terms. Have students complete Worksheet 1. For Activity 2: Decoding Prescriptions As a class, review the sample prescription and decode the information. Using copies of Worksheet 2, have students practice translating the information on several prescriptions. Handouts 2A, 2B, & 2C have some sample prescriptions, or you may want to use others of your own choosing. For Activity 3: Calculating Dosage Explain the dosage formula to students. As a class, practice putting the information into the formula and calculating the dosage. One example is contained in the scenario. You may want to provide additional examples for students. Have students complete Worksheet 3A and Worksheet 3B. Assessment: Quiz - Calculating Dosage 2

3 Workplace Scenario: Pharmacy Technician Maria is a pharmacy technician at a local pharmacy. Working under the supervision of a pharmacist, she fills a variety of prescriptions for customers each day. Currently, you are a pharmacy technician student receiving on-the-job training from Maria. Activity 1: Prescription Abbreviations Maria tells you that filling prescriptions accurately is extremely important, even one small error could cause great harm, or even death to a patient. The first step in filling any prescription is to understand all the information contained on the prescription form, including the medical abbreviations. Maria gives you the following chart to help you learn some common abbreviations used on prescriptions. She then asks you to complete Worksheet 1. Some common abbreviations found on prescriptions Abbreviation ac bid cap d Exlir. g gr gt h hs IM mg ml po pc pil prn q q2h qd qh Sig qid Supp. Ṫ tab tid U Meaning before meals twice a day capsule day (24 hours) liquid or syrup gram dry measure used in tablets grains dry weight of medication drop hour at bedtime Intramuscular milligram dry weight measure milliliter liquid volume measure by mouth after meals pill as needed every every 2 hours every day every hour patient instructions 4 times a day medications inserted rectally One tablet tablet 3 times a day Unit 3

4 Worksheet 1: Prescription Abbreviations Name Directions: Put the letter of the definition next to the correct medication abbreviation 1. qid A. by mouth or orally 2. hs B. liquid or syrup 3. bid C. every day 4. g D. three times a day 5. mg E. medication inserted rectally 6. po F. milligram 7. qd G. four times a day 8. gr H. every 6 hours 9. U I. milliliters 10. tid J. as needed 11. Elix. K. grain 12. Supp. L. Unit 13. q6h M. at the hour of sleep; bedtime 14. ml N. gram 15. prn O. twice a day 4

5 Activity 2: Decoding Prescriptions Maria wants you to learn how to accurately interpret the information contained on a typical prescription. This includes the name of the medication, the dosage and form of the medication, the amount to be taken, the method of administration, and the frequency and duration the medication will be taken. As a pharmacy technician, you need to read the prescription very carefully. Many medications have similar names or come in more than one form. For example, an older adult may take the capsule or tablet form of a medication, while a young child might be prescribed an elixir, the liquid form of a medication. She gives you the following sample prescription and asks, How would you translate this information? Maria explains: The first part of a prescription is the name of the drug; it can be a brand name or generic. On this prescription, the drug name is Amoxicillin. The next part 250 mg denotes the strength of the drug. In this case, it's 250 milligrams in the form of tablets. ṪṪ stands for two tablets. The po means the medication is taken by mouth tid or three times a day. The x indicates this prescription is to be taken for a period of 7 days. Two tablets x 3 times a day for 7 days = 42, the total number of tablets to be dispensed. Maria gives you several prescriptions and asks you to complete all the information on Worksheet 2 for each prescription. 5

6 Worksheet 2: Decoding Prescriptions Name: Directions: On your own paper, record the following information for each prescription your instructor gives you. The patient s full name The date The drug name in manufacturer or generic format The doctor s order for dosage amount (how much medication) The administration route (by mouth, IV, injection) The frequency with which the patient is to take the medication The duration, the number of days that the patient is to take the medication The total quantity or amount that the pharmacist is to dispense A check-off or box allowing a generic substitute (if provided) The physician s name The physician s DEA number 6

7 Handout 2A: Sample Prescriptions Phone DEA# Patty Street, MD Pediatrician Pt. name Tim Jones Age 10 Date Aug. 30, 2014 Address: 2 Joyce Road, Anyway, IL R X Ceclor 10 ml bid x 10 d Refill: 0 X Generic and/or equivalent allowed Physician s Signature Pediatric Center 123 Abbey Road Anyway, IL PStreet Phone DEA# Sarah Jean, MD Pt. name Mary Brown Age 47 Date Sept. 20, 2014 Address: 789 6th Street, R X Darvon 1 g tab. p.o. q4h for 3 days Refill Ø Generic and/or equivalent allowed Physician s Signature S Jean SJMedical Associates 23South Street Anytown, IL

8 Handout 2B: Sample Prescriptions Phone DEA# Sarah James, MD Pt. name Jeff Howard Age 53 Date Sept. 20, 2014 Address: th Street, R X Ampicillin 250mg po qid x 10 days Refill Ø Generic and/or equivalent allowed Physician s Signature S James SJMedical Associates 23South Street Anytown, IL

9 Handout 2C: Sample Prescriptions 9

10 Activity 3: Calculating Dosage Maria says you are now ready to learn the dosage formula used to calculate the amount of medication needed to fill a prescription. Dosage Formula: Doctor s Order (D) Supply on Hand (H) x quantity(q) = individual dosage to be administered Short version: D x Q = one dose H The formula can be read as: The doctor s order (the numerator) divided by the supply on hand (the denominator), multiplied by the quantity equals the amount of one dose of medication. Understanding the parts of the Dosage Formula Doctor s Order (D) is the name and amount of the medicine prescribed by the doctor Supply on Hand (H) is the amount per item of the medication that is available in the pharmacy Quantity (Q) is the form of the medication, such as tablet, capsule, or milliliter. Dosage is the amount of medication to be given in one dose Important: The doctor s order and the supply on hand must be in the same unit of measure, such as grams (g), milligrams (mg), and milliliters (ml). Answers must include the correct unit notation. Maria gives you the following example: Dr. Smith has prescribed 30 mg of medicine for her patient. The drug label on the medicine indicates that the medicine is supplied in 60 mg per tablet. We will use the dosage formula to calculate the correct amount of medication for one dose. (D) 30 mg x (Q) 1 tablet = 0.5 mg. Therefore, one dose will be one half (1/2) tablet (H) 60 mg Important: In the medical field, any decimal number that is not greater than 1 should have a 0 in front of the decimal point. Thus, the correct form for the dosage in this example is 0.5 mg, not.5 mg 10

11 Worksheet 3A: Calculating Dosage Name Maria gives you several prescriptions for you to practice using the formula to calculate the dosage. Make sure you include the correct form (g, mg, ml, etc.) when making your calculations. The first one has been set up for you. Note: If the quantity (Q) is larger than 1, you may want to simplify (cancel) before multiplying. Dosage formula: D x Q = one dose H 1. Order: 500 mg (D) 500 mg x (Q) 1 tablet = Supply on hand: 250 mg per tablet (H) 250 mg 2. Order: 1 g Supply on hand: 0.5 g per capsule 3. Order: 50 mg Supply on hand: 25 mg per 5 ml 4. Order: 1000 mg Supply on hand: 2000 mg per scored tablet 5. Order: 500 mg Supply on hand: 125 mg per caplet 6. Order: 250 mg Supply on hand: 125 mg per capsule 7. Order: 25 mg Supply on hand: 100 mg per 20 ml 8. Order: 75 mg Supply on hand: 5 mg per 20 ml 9. Order: 5 mg Supply on hand: 32 mg per 8 ml 10. Order: 500 mg Supply on hand: 50 mg per 2 ml 11

12 Worksheet 3B: Filling Complete Prescriptions Name Maria now wants you to calculate the individual dose, the daily dose, and the total amount needed to fill the complete prescription for several patients. Refer to your abbreviations list to help you decode the prescription information, if needed. Remember to write the form of medication in your answer. Prescription Single dose Daily dose Complete prescription Ampicillin 500 mg po qid x 5 d On hand: 250 mg capsules Digoxin elixir 150 mcg po tid x 10 d On hand: 50 mcg/ml Codeine sulfate 60 mg po q4h x 7 d On hand: 30 mg tablets Clondine 0.4 mg po bid x 3 d On hand: 0.1 mg tablets Amoxicillin 250 mg po qid x 10 d On hand: 125 mg capsules Lasix 40 mg po qd x 30 d On hand: 20 mg tablets Ampicillintrihydrate 250 mg po qid x 10 d On hand: 125 mg per 5 ml 12

13 Quiz: Calculating Dosage Name For each of the following doctor s orders, calculate the individual dose of medication. 1. Dr. Jones prescribed Plendil 7.5 mg. The drug label reads: Plendil 2.5 mg tab. 2. The doctor ordered Dilaudid 1.5 mg IM from a vial that is labeled 0.6 mg per ml 3. Dr. Sam prescribed 20 mg of a medication. You have 10 mg per 5 ml. 4. The physician ordered Procardia XL 60 mg. The drug on hand is Procardia XL 30 mg tablets. 5. Dr. Garza prescribed 30 mg of Phenobarbital. The pharmacy has 15 mg capsules available. For each of the following prescriptions, calculate the individual dose, the daily dose, and the total amount needed to fill the complete prescription. Single dose Daily dose Total amount 6. Amoxicillin 500 mg capsule po tid x 10 d On hand: 500 mg/1 capsule 7. Prednisone 40 mg po bid x 3 d On hand: 10 mg tablet 8. Ciprofloxin 750 mg po qd x 10 d On hand: 500 mg scored tablet 9. PenVK 250 mg po qid x 10 d On hand: PenVK 250 mg/1 tsp 10. Acetaminophen 500 mg tab po q4h x 5 d On hand: 250 mg/1 tablet 13

14 Worksheet 1: Prescription Abbreviations Answer Key 1. qid G A. by mouth or orally 2. hs M B. liquid or syrup 3. bid O C. every day 4. g N D. three times a day 5. mg F E. medication inserted rectally 6. po A F. milligram 7. qd C G. four times a day 8. gr K H. every 6 hours 9. U L I. milliliters 10. tid D J. as needed 11. Elix. B K. grain 12. Supp. E L. Unit 13. q6h H M. at the hour of sleep; bedtime 14. ml I N. gram 15. prn J O. twice a day 14

15 Worksheet 2: Decoding Prescriptions Answer Key Answers will vary depending on the prescriptions used for this activity The patient s full name The date The drug name in manufacturer or generic format The doctor s order for dosage amount (how much medication) The administration route (by mouth, IV, injection) The frequency with which the patient is to take the medication The duration, the number of days that the patient is to take the medication The total quantity or amount that the pharmacist is to dispense A check-off or box allowing a generic substitute (if provided) The physician s name The physician s DEA number 15

16 Worksheet 3A: Calculating Dosage Answer Key Dosage Formula: D x Q = drug dose H 1. Order: 500 mg Supply on hand: 250 mg per tablet 2 tablets 2. Order: 1 g Supply on hand: 0.5 g per capsule 2 capsules 3. Order: 50 mg Supply on hand: 25 mg per 5 ml 10 ml 4. Order: 1000 mg Supply on hand: 2000 mg per scored tablet ½ tablet 5. Order: 500 mg Supply on hand: 125 mg per caplet 4 caplets 6. Order: 250 mg Supply on hand: 125 mg per capsule 2 capsules 7. Order: 25mg Supply on hand: 100 mg per 20 ml 5 ml 8. Order: 75 mg Supply on hand: 5 mg per 20 ml 300 ml 9. Order: 5 mg Supply on hand: 32 mg per 8 ml 1.25 ml 10. Order: 500 mg Supply on hand: 50 mg per 2 ml 20 ml 16

17 Worksheet 3B: Filling Complete Prescriptions Answer Key Prescription Single dose Daily dose Complete prescription Ampicillin 500 mg po qid x 5 d On hand: 250 mg capsules 2 capsules 8 capsules 40 capsules Digoxin elixir 150 mcg po tid x 10 d On hand: 50 mcg/ml 3 ml 9 ml 90 ml Codeine sulfate 60 mg po q4h x 7 d On hand: 30 mg tablets 2 tab 12 tab 84 tab Clondine 0.4 mg po bid x 3 d On hand: 0.1 mg tablets 4 tab 8 tab 24 tab Amoxicillin 250 mg po qid x 10 d On hand: 125 mg capsules 2 tab 8 tab 80 tab Lasix 40 mg po qd x 30 d On hand: 20 mg tablets 2 tab 2 tab 60 tab Ampicillintrihydrate 250 mg po qid x 10 d On hand: 125 mg per 5 ml 10 ml 40 ml 400 ml 17

18 Quiz: Calculating Dosage Answer Key For each of the following doctor s orders, calculate the individual dose of medication: 1. Dr. Jones prescribed Plendil 7.5 mg. The drug label reads: Plendil 2.5 mg tab. 3 tab 2. The doctor ordered Dilaudid 1.5 mg IM from a vial that is labeled 0.6 mg per ml 2.5 ml 3. Dr. Sam prescribed 20 mg of a medication. You have 10 mg per 5 ml. 10 ml 4. The physician ordered Procardia XL 60 mg. The drug on hand is Procardia XL 30 mg tablets. 2 tab 5. Dr. Garza prescribed 30 mg of Phenobarbital. The pharmacy has 15 mg capsules available. 2 capsules For each of the following prescriptions, calculate the individual dose, the daily dose, and the total amount needed to fill the complete prescription. Single dose Daily dose Total amount 6. Amoxicillin 500 mg capsule po tid x 10 d On hand: 500 mg/1 capsule 1 capsule 3 capsules 30 capsules 7. Prednisone 40 mg po bid x 3 d On hand: 10 mg tablet 4 tabs 8 tabs 24 tabs 8. Ciprofloxin 750 mg po qd x 10 d On hand: 500 mg scored tablet 1 ½ tabs 1 ½ tabs 15 tabs 9. PenVK 250 mg po qid x 10 d On hand: PenVK 250 mg/1 tsp 1 tsp 4 tsp 40 tsp 10. Acetaminophen 500 mg tab po q4h x 5 d On hand: 250 mg/1 tablet 2 tabs 12 tabs 60 tabs 18

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