Math in Medicine: A Real-World Application
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.In what ways can mathematical principles, such as half-life, Newton's Law of Cooling, and unit conversions, be integrated with the interpretation of vital signs to optimize medical treatments and ensure accuracy in medical decision-making?Essential Questions
Supporting questions that break down major concepts.- How can mathematical models be used to describe and predict changes in medical contexts?
- How do different units of measurement impact calculations and interpretations in medicine?
- How does the half-life formula relate to medical treatments and drug dosages?
- How can Newton's Law of Cooling be applied to understanding changes in body temperature?
- How do significant figures affect the accuracy and reliability of medical calculations?
- How are vital signs measured, interpreted, and used in medical decision-making?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Apply the half-life formula to calculate drug dosages and predict medication concentrations over time.
- Apply Newton's Law of Cooling to model changes in body temperature in medical scenarios.
- Perform unit conversions accurately to ensure consistency and precision in medical calculations.
- Apply the rules of significant figures to ensure accuracy and reliability in medical data and calculations.
- Interpret and convert vital signs (e.g., temperature, pulse rate, blood pressure) to inform medical decisions.
Entry Events
Events that will be used to introduce the project to studentsVital Signs Forensics
Students are presented with a fictional crime scene scenario where the victim's vital signs were recorded at the time of death. Using Newton's Law of Cooling, half-life of potential toxins, and accurate unit conversions, students must work backward to estimate the time of death and identify potential causes, blending forensic science with mathematical modeling.Contaminated Cooling System Challenge
The school's cooling system has been contaminated with a radioactive substance. Students receive data on the substance's half-life, contamination levels, and the system's cooling rate. They must use math and science principles to determine the risk and devise a decontamination plan, connecting math to a relevant and timely issue.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Vital Signs Conversion Station
Students will begin by mastering the essential skill of converting vital signs between different units of measurement. This foundational activity ensures students can accurately interpret and utilize vital signs data in various medical contexts.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA completed worksheet demonstrating accurate conversions of vital signs between different units of measurement.Alignment
How this activity aligns with the learning objectives & standardsAddresses the learning goal: Perform unit conversions accurately to ensure consistency and precision in medical calculations.Significant Figures in Medical Data
This activity focuses on the application of significant figures in medical measurements and calculations. Students will learn how to determine the number of significant figures in a measurement and how to apply this knowledge in calculations to maintain accuracy and reliability.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA set of correctly calculated medical data, with all answers rounded to the appropriate number of significant figures.Alignment
How this activity aligns with the learning objectives & standardsAddresses the learning goal: Apply the rules of significant figures to ensure accuracy and reliability in medical data and calculations.Half-Life Dosage Calculations
Students will apply the half-life formula to calculate drug dosages and predict medication concentrations over time. This activity will help students understand how medications decay in the body and how to determine appropriate dosing intervals.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA set of solved problems demonstrating the correct application of the half-life formula in drug dosage calculations.Alignment
How this activity aligns with the learning objectives & standardsAddresses the learning goal: Apply the half-life formula to calculate drug dosages and predict medication concentrations over time.Newton's Law of Cooling and Body Temperature
This activity explores Newton's Law of Cooling and its applications in medical scenarios, particularly in estimating time of death or monitoring patient temperature changes. Students will use mathematical models to understand how body temperature changes over time.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA written analysis of body temperature problems using Newton's Law of Cooling, including calculations and a discussion of the law's limitations.Alignment
How this activity aligns with the learning objectives & standardsAddresses the learning goal: Apply Newton's Law of Cooling to model changes in body temperature in medical scenarios.Integrating Math in Medical Scenarios
In this final activity, students will integrate all the mathematical principles learned (unit conversions, significant figures, half-life formula, and Newton's Law of Cooling) to solve comprehensive medical scenarios. This activity aims to enhance their problem-solving skills and deepen their understanding of the interdisciplinary nature of math and medicine.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA detailed written report of the analysis of the medical scenarios, including all calculations, reasoning, and assumptions.Alignment
How this activity aligns with the learning objectives & standardsAddresses all learning goals: Apply the half-life formula, Apply Newton's Law of Cooling, Perform unit conversions accurately, Apply the rules of significant figures, and Interpret and convert vital signs.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioMath in Medicine Portfolio Rubric
Unit Conversions
Accuracy and proficiency in converting between different units of measurement for vital signs and other medical data.Conversion Accuracy
The degree to which unit conversions are performed correctly and consistently.
Exemplary
4 PointsAll unit conversions are performed accurately and efficiently, demonstrating a deep understanding of unit relationships.
Proficient
3 PointsMost unit conversions are performed accurately, with only minor errors or inconsistencies.
Developing
2 PointsSome unit conversions are performed accurately, but there are noticeable errors and inconsistencies.
Beginning
1 PointsUnit conversions are largely inaccurate or incomplete, indicating a limited understanding of unit relationships.
Problem-Solving Application
Effectiveness in applying unit conversions to solve practical medical problems.
Exemplary
4 PointsDemonstrates sophisticated problem-solving skills by accurately applying unit conversions to complex medical scenarios.
Proficient
3 PointsEffectively applies unit conversions to solve most medical problems, with a clear understanding of the context.
Developing
2 PointsApplies unit conversions to solve some medical problems, but struggles with more complex scenarios.
Beginning
1 PointsStruggles to apply unit conversions to solve medical problems, indicating a lack of understanding of the practical application.
Significant Figures
Proper application of significant figures in medical measurements and calculations.Identification and Application
Correctly identifies and applies the rules of significant figures in medical data and calculations.
Exemplary
4 PointsConsistently and accurately identifies and applies the rules of significant figures in all medical data and calculations, demonstrating a comprehensive understanding.
Proficient
3 PointsIdentifies and applies the rules of significant figures correctly in most medical data and calculations, with only minor errors.
Developing
2 PointsShows some understanding of significant figures but makes errors in identification or application in medical data and calculations.
Beginning
1 PointsStruggles to identify and apply the rules of significant figures in medical data and calculations, indicating a limited understanding.
Accuracy in Calculations
Maintains accuracy in calculations by correctly rounding answers based on significant figures.
Exemplary
4 PointsMaintains exceptional accuracy in calculations by consistently rounding answers to the appropriate number of significant figures.
Proficient
3 PointsMaintains accuracy in most calculations by rounding answers to the appropriate number of significant figures, with only minor inconsistencies.
Developing
2 PointsShows some accuracy in calculations but makes errors in rounding answers based on significant figures.
Beginning
1 PointsStruggles to maintain accuracy in calculations due to errors in rounding answers based on significant figures.
Half-Life Dosage
Accurate application of the half-life formula to calculate drug dosages and predict medication concentrations.Formula Application
Correctly applies the half-life formula to solve problems related to drug dosages and medication concentrations.
Exemplary
4 PointsConsistently and accurately applies the half-life formula to solve complex problems, demonstrating a thorough understanding of drug metabolism.
Proficient
3 PointsApplies the half-life formula correctly to solve most problems related to drug dosages and medication concentrations, with only minor errors.
Developing
2 PointsShows some understanding of the half-life formula but makes errors in application or calculations.
Beginning
1 PointsStruggles to apply the half-life formula, indicating a limited understanding of its use in drug dosage calculations.
Dosage Calculation Accuracy
Calculates drug dosages accurately using the half-life formula and relevant medical information.
Exemplary
4 PointsCalculates drug dosages with exceptional accuracy, demonstrating a clear understanding of the factors influencing medication concentrations.
Proficient
3 PointsCalculates drug dosages accurately in most cases, with only minor discrepancies or errors.
Developing
2 PointsShows some accuracy in dosage calculations but makes errors that could impact patient safety.
Beginning
1 PointsStruggles to calculate drug dosages accurately, indicating a significant lack of understanding of the relevant factors.
Newton's Law of Cooling
Application of Newton's Law of Cooling to model changes in body temperature in medical scenarios.Formula Comprehension
Understands and correctly applies Newton's Law of Cooling in medical contexts.
Exemplary
4 PointsDemonstrates a comprehensive understanding of Newton's Law of Cooling and its applications, including its limitations in real-world scenarios.
Proficient
3 PointsApplies Newton's Law of Cooling correctly in most medical scenarios, with a clear understanding of the formula and its components.
Developing
2 PointsShows some understanding of Newton's Law of Cooling but struggles with application or interpretation.
Beginning
1 PointsDemonstrates a limited understanding of Newton's Law of Cooling and its relevance in medical contexts.
Problem Analysis
Effectively analyzes problems and provides accurate solutions using Newton's Law of Cooling.
Exemplary
4 PointsProvides insightful analysis and accurate solutions to complex problems using Newton's Law of Cooling, demonstrating a strong grasp of the underlying principles.
Proficient
3 PointsAnalyzes problems effectively and provides accurate solutions using Newton's Law of Cooling in most cases.
Developing
2 PointsAttempts to analyze problems using Newton's Law of Cooling but struggles to provide accurate solutions.
Beginning
1 PointsStruggles to analyze problems or provide solutions using Newton's Law of Cooling, indicating a limited understanding.
Integration and Application
Ability to integrate multiple mathematical principles to solve complex medical scenarios.Problem-Solving
Effectively integrates unit conversions, significant figures, half-life, and Newton's Law of Cooling to solve complex medical scenarios.
Exemplary
4 PointsDemonstrates exceptional problem-solving skills by seamlessly integrating all mathematical principles to provide comprehensive and accurate solutions to complex medical scenarios.
Proficient
3 PointsIntegrates most mathematical principles effectively to solve medical scenarios, with a clear and logical approach.
Developing
2 PointsShows some ability to integrate mathematical principles but struggles with complex medical scenarios.
Beginning
1 PointsStruggles to integrate mathematical principles to solve medical scenarios, indicating a limited understanding of the interdisciplinary nature of the problems.
Reasoning and Assumptions
Provides clear reasoning and justifies assumptions made in solving medical scenarios.
Exemplary
4 PointsProvides clear, logical reasoning and thoroughly justifies all assumptions made in solving medical scenarios, demonstrating a sophisticated understanding of the underlying principles.
Proficient
3 PointsProvides clear reasoning and justifies most assumptions made in solving medical scenarios.
Developing
2 PointsShows some reasoning but struggles to justify assumptions or provide clear explanations.
Beginning
1 PointsStruggles to provide reasoning or justify assumptions made in solving medical scenarios, indicating a limited understanding of the problem-solving process.