__Societal impact:__

- May prolong life of those living with chronic disease
- Provide pain relief
- Improve quality of life
- Improve body vital body functions

**Engineering Design Process (EDP)**

1. Problem is to design a schedule for administration of the drug that will get the concentration level to an effective and safe level

2. Identify Criteria & Constraints

- Drugs must be administered intravenously (single Rapid injection , IV infusion, single rapid Injection Followed by IV infusion only)
- Research and investigate. Each group will research at least 10 drugs (at least 2 drugs per student)
- Use Internet FDA website http://www.accessdata.fda.gov/scripts/cder/drugsatfda/index.cfm

3. Brainstorm Possible Solutions

- Student will brainstorm in group about what makes a schedule easy to understand easy to use in Administrating drug

4. & 5. Generate Ideas/Explore Possibilities

- Each group will develop two or three ideas that a layperson will be able to understand
- Discuss developed ideas with team members

6. Select an Approach

- Now it is time to select the best solution for further development ( Pro/Cons of each design) and Why the team selected the final design

7. Build a Model or Prototype of the Solution

8. Revise and Refine the Solution

Use peer feedback, to make sure your design meets all the constraints:

Drug schedule that will:

- Get the concentration to an effective level as soon as possible
- Keep the concentration below a known safe maximum level
- Keep the concentration above a known effective level

##### Unit Academic Standard

The College Board state that:

- Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation, and should be able to use derivatives to solve a variety of problems.
- Students should be able to communicate mathematics and explain solutions to problems both verbally and in written sentences.
- Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral.
- Students should be able to use technology to help solve problems, experiment, interpret results, and support conclusions.
- Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

##### Where the CBL and EDP appear in the Unit

Lesson 1: investigation

- Activity 2: Pharmacokinetics Data (
**EDP)**
- Activity 3: Analyzing Pharmacokinetics Data (
**CBL, EDP)**

Lesson 2

- Activity 4: Modeling (
**CBL, EDP)**

##### Misconceptions

The mathematics behind medicinal drug administration is more than how many pills or what is the dose of the medication.

##### Additional Resources

Here are 5 YouTube video that will help put pharmacokinetics into perspective

##### Pre-Unit Assessment Instrument

##### Post-Unit Assessment Instrument

##### How to Make This a Hierarchical Unit

Determining the Relationship of Insulin to Diabetes

The 7^{th} Grade math standards focus on such things as:

- ratios and proportions
- solving real-life and mathematical problems using numerical and algebraic expressions and equations

The 8^{th} grade math standards focus on such things as:

- modeling an association in bivariate data with a linear equation
- solving linear equations
- understanding the Pythagorean Theorem

This unit could be changed to investigate linear relationships in medicine such as the relationship between blood sugar level and time (https://www.bced.gov.bc.ca/irp/resdocs/math9res/projectb.pdf). Students might still prepare a brochure or presentation to illustrate a drug regimen that would be effective in controlling a disease such as diabetes.

##### Reflection

One of my biggest concerns was that the subject matter of Pharmacokinetics would be challenging for my 10^{th} graders. Covering a large amount of material in my AP Calculus block is already very difficult for this group of students, but luckily I have the students for two consecutive periods which in small part removes some of the obstacles of having to find time to cover all of my planned lessons. So I was able to do the unit in 5 lessons and it was very successful. My students showed genuine interest in the units and were excited to discuss the different possibilities of more efficient ways to deliver medicine to patients.

Dr Giovanni Pauletti Director of the graduate program in Pharmaceutical Sciences was instrumental in getting my students getting and holding the students’ interest with his introductory lesson introducing the concepts in the unit. He was recommended by the dean of the College of Pharmacy at the University of Cincinnati. The best way to make the material accessible to students is to get the assistance from the professionals who are working in the field. They know how to best present the work that they do so that students are interested. The proof of the effectiveness of Dr. Pauletti is that the students were talking about pharmacokinetics with other teachers. What a triumph!

Covering this unit was successful because the students covered math problems in the context of pharmacokinetics.

Students used equations in a context to find the minimum and maximum concentration.

Students used scenarios to communicate their understanding of medications.

The next time I will divide this units into 3 units because it will be more beneficial for student’s to start with basic drug administration to give them a more comprehensive approach to pharmacokinetics. My divisions will be as followed:

**Unit 1: **Oral Administration vs Rapid Infusion; Rate of Change

**Unit 2: **One Compartment Drug; Area Under Curve (AUC)

**Unit 3: **Two Compartment Drug; Second Order of Differential Equations

What I would do differently:

- Break the project into manageable sections
- Set concrete deadlines for each part of the project in order to have student be responsible for turning in completed work.
- Do a better job at clearly defining requirements for each part of the project
- When taking videos of student presentations, I would use a camera with a tripod so that you do not get “jittery” videos
- During the unit, I will make sure that students understand where they are at in the engineering design process.