8.9: Quantway Core 3.7 Workforce (Health Care) - Student Lesson

INTRODUCTION

Lucas Fuel Treatment is formulated for both gasoline and diesel engines. It gives your fuel system what it really needs – a blend of super slick oils and additives with a high detergent action that allows the engine to operate at maximum efficiency. Also, it cleans and lubricates the carburetor and injectors and causes the fuel to burn more thoroughly for increased power and less fuel consumption.

In your group, use the information from the image to answer the following two questions:

• What is the recommended dosage of Fuel Treatment per 50 gallons of fuel?
• What is the recommended dosage of Fuel Treatment per 37 gallons of fuel?

Completing the CaS Chart

You can use the Comprehension and Synthesis (CaS) Chart in this collaboration. Remember, using the CaS Chart will help you have a deeper understanding of the problem situation. CaS Charts help you understand the main issue(s) that need(s) to be resolved, and will help you to recognize the quantitative information that is available in the problem situation that can help you to solve the problem. You will use CaS Charts in some of the Quantway lessons to “unpack” problem situations and support problem-solving.

Read through the steps for completing the CaS Chart below. As you read the problem situation, complete the CaS Chart. You may wish to return to these steps as you complete the CaS Chart.

Read through the problem situation below, Problem Situation: Medical Dosages in Hospitals. As you are reading:

• Complete Column A. Hint: What issues in the problem situation do you need to understand in order to solve the problem? Is there contextual information that you need to know in order to understand the problem situation?
• Complete Column B. Hint: What quantitative information is provided in the problem situation that will help you solve the problem? Hint: Quantitative information is often a number, but also could be a number word, like “two”.
• Complete Column C. Hint: It is not necessary to solve the problem or use calculations right now. In this column, brainstorm ways you might address the issues presented in the problem situation (Column A) using the quantitative information in Column B. There are no wrong answers.

SPECIFIC OBJECTIVES

By the end of this collaboration, you should understand that

• proportional relationships are based on a constant ratio.
• rules for solving equations can be applied in unfamiliar situations.

By the end of this collaboration, you should be able to

• set up a proportion based on a contextual situation.
• solve a proportion with algebraic methods.

SPECIFIC LANGUAGE AND LITERACY OBJECTIVES

By the end of this collaboration, you should be able to

• read and comprehend the problem situation about medical dosages.
• complete the Comprehension and Synthesis (CaS) Chart with contextual and quantitative information from the problem situation about medical dosages.
• demonstrate an understanding of mathematics by writing complete and correct responses to questions.
• demonstrate the ability to interpret, predict, analyze, and revise answers about the medical dosages.
• use appropriate quantitative and health care vocabulary to discuss mathematics in this collaboration.

PROBLEM SITUATION 1: MEDICAL DOSAGES IN HOSPITALS

Michael is a night nurse at Central County Hospital. He is responsible for administering medicines to three patients. This is his first night on the job. He wants to be very careful about the medicine he administers, because of a new study.

This study has shown that medical errors in hospitals are the third leading cause of the death in the U.S. As many as 440,000 people in the U.S. die from medical errors each year.¹ If there is a medication error, it is most commonly the result of calculation errors by the nurse or doctor.²

Nurses must work with many different types of medicines. Drugs are generally measured according to:

• weight of the drug (for example, grams or milligrams),
• volume of the drug (for example, liters or milliliters), or
• strength of the drug when dissolved in liquid, for example, milligrams per milliliter (also called concentration).

Often the doctor prescribes a medicine using one type of measurement, but the medicine is available to nurses in a different measurement.

Michael’s first patient, Viola, has been diagnosed with pneumonia and prescribed amoxicillin. Aiyana, his second patient, has tonsillitis and was prescribed penicillin. His third patient, Thomas, was prescribed colchicine to treat the gout in his hands.

Below are the prescriptions and availability of medicine for Michael’s first three patients. How can Michael calculate the correct dosage for each patient?

	Patient Name: Viola Shore Prescription: 80 mg Amoxicillin		The vial of medicine at Central County Hospital is labeled 100 mg/mL.
	Patient Name: Aiyana Jones Prescription: 100,000 units penicillin.		The label for the penicillin on hand is 250,000 units/mL.
	Patient Name: Thomas Grady Prescription: 0.6 mg colchicine		The colchicine in the hospital medicine room is labeled 250 mcg/mL.
	* 1 mg= 1,000 mcg

(1) What is the correct dosage for each patient?

(a) Patient One (Viola):

(b) Patient Two (Aiyana):

(c) Patient Three (Thomas):

(2) These three examples show how proportions are useful in assigning correct dosages to patients. In each case, the problem required knowing the concentration of the drug. Why is it necessary to know the concentration of a drug before you can prescribe the drug’s dosage? Explain your reasoning in two or three complete sentences.

PROBLEM SITUATION 2: YOLANDA, THE PEDIATRIC NURSE

In the same hospital, one floor above, Yolanda is a pediatric nurse. Pediatric nurses work with infants and children. It is essential that the pediatric nurses calculate the correct dosage of medicine, because children and infants weigh much less than adults. If children or infants are given the wrong dose of medicine, it could result in severe illness or even death. Medications for infants and children are commonly prescribed by body weight to ensure that patients are receiving the exact dose for their size.

Medicines are often prescribed in milligrams (mg) or micrograms (mcg) per kilogram (kg) of body weight. This is different from the U.S. common measurement of weight (i.e., pounds). At Central County hospital, patients are weighed using scales that measure in pounds. So, Yolanda must first convert the patient’s weight in pounds to kilograms before calculating patient dosage. Here is the conversion rate for 1 kg:

1 kg = 2.2 lbs

(3) A 20-pound child is given the following prescription: Solu-Medrol 1.5 mg/kg. Solu-Medrol is one drug prescribed as a treatment for leukemia. How much Solu-Medrol should the child receive? (Hint: Remember, you must first convert kg to lbs.)

(4) Anthony is a 5-year-old boy who weighs 40 lbs. He is in the hospital with meningitis. The doctor prescribed 100 mg/kg/day of ceftriaxone administered through an IV once daily. The drug is already pre-diluted in a concentration of 40 mg/mL. How many mL of ceftriaxone should Anthony receive each day?

(5) In this collaboration, you have learned about the importance of proportions in helping nurses make decisions about how much medicine an infant, child or adult patient should receive.

(a) In your own words, first explain why there is often a mismatch between the amount of medicine that doctors prescribe and the amount of medicine that nurses give to patients.

(b) Now explain why knowing how to do dimensional analysis calculations helps nurses give patients the correct dosages of medicine.

FURTHER APPLICATIONS

Nurses are required to determine whether children’s prescribed dosages are in the safe range. This “safe range” change ensures that the doctor prescribes the appropriate dosage, and that the nurse makes the correct calculations to administer the correct dose. This requirement is important because administering the wrong dose to an infant or small child could result in long-term damage or death.

(6) Determine whether a dosage of 400 mg of Phenytoin is safe for a 55 lb child. The “safe range” is 15-20 mg/kg.

(7) Sometimes there is a 24-hour safe range for a medicine. In this case, the nurse must also determine how many doses of the medicine it is safe to give a patient within a 24-hour period.

For an infant who weighs 11 lbs, a doctor ordered 18 mg/kg every 6 hours. The maximum daily dose for this medicine is 40 mg/kg/day. Does the doctor’s prescription exceed the maximum daily dose? Why or why not?

MAKING CONNECTIONS

Record the important mathematical ideas from the discussion.

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¹ http://www.npr.org/blogs/health/2013/09/20/224507654/how-many-die-from-medical-mistakes-in-u-s-hospitals

² http://www.nursingtimes.net/how-to-ensure-patient-safety-in-drug-dose-calculation/5050561.article