Organs and Artificial Organs

CONTENTS OF CURRICULUM UNIT 11.07.10

  1. Unit Guide
  1. Rationale and Introduction
  2. Content Objectives
  3. Overview of the Circulatory System
  4. Dimensional Analysis Calculation Demonstrating Heart Reliability
  5. Introduction to Units of Measure
  6. Dimensional Analysis of Graphical Data: Ventricular Pressure vs. Volume Graph
  7. Dimensional Analysis for Evaluating Potential Power Sources for an Artificial Heart
  8. Dimensional Analysis does Problem Analysis
  9. Student Background and Challenges
  10. Strategies
  11. Classroom Activities and Lesson Plans
  12. Standards Alignment
  13. Teacher and Student Resources
  14. Endnotes
  15. Bibliography

Dimensional Analysis: A Mathematics Tool to Dissect the Circulatory System

Richard Cordia Taylor

Published September 2011

Tools for this Unit:

Classroom Activities and Lesson Plans

Lesson Plan 1: Your Pulse Rate

Materials

Wall clock and graph paper.

Objectives

After this lesson, students will be able to take their pulse and see where their pulse rate falls in the range of other students' pulse rates. Students will be able to use conversion factors to extrapolate the data measured to tell how many heartbeats they will have in a day, a month or a year. Students will be able to state quantitatively differences in pulse rate due to differences in physical activity.

Activity

I will show students how to take their pulse. After doing so, members of the class will take their pulse for 1 minute, counting their heartbeats while watching the classroom clock. I will pass around a piece of graph paper where each student will color a square in a grid based on his pulse rate in beats per minute, thus eventually forming a bar graph with the distribution of pulse rates vs. number of students with that pulse rate. I will use this graph to discuss measures of central tendency (mean, median, and mode) and measures of dispersion (range and, qualitatively, standard deviation). I will then repeat this experiment with the students after having them run in place for a minute. I will use this new set of data to explain the adjustments that the heart must make during physical exertion. I will use the differences in the graphs from the two trials to illustrate the range of performance that the heart must accommodate. I will then instruct students on how to calculate the number of beats for a variety of time periods using conversion factors.

Lesson Plan 2: Dimensional Analysis and Conversion Factor Flashcards

Materials

Index Cards or Printouts of Flashcards and scissors to cut them out.

Objectives

After this lesson, students will be able to combine units appropriately to construct other units representing important quantities. Students will also be able to use conversion factors appropriately to convert from one unit of measure to another.

Activity Part 1

Students will make flashcards with the basic and derived units as shown in the samples below. Students will place the flashcards side by side, indicating multiplication and from this, simplify to find the units of the result. Students will write down the operation shown with units for the quantities used and the resulting units for their answer. When I give students a list of final units, they will find appropriate flashcards to combine to create those units and will record the calculations and the results.

Base and Derived Units Sample Flash Cards

image 11.07.10.14

Activity Part 2

Students will create flashcards of conversion factors similar to those shown below. I will give them a beginning quantity and unit of measure, for example 13 feet and I will ask them to arrange the flashcards appropriately to convert to a target measure, for example, meters. Students will then use a calculator to finish the conversion. Students will write down their calculations including units and the result of their conversion.

Conversion Factor Sample Flashcards

image 11.07.10.15

Lesson Plan 3: Reading and Interpreting Slope from a Graph

Materials

A graph of Volume vs. Pressure for a heart chamber or a blood vessel. A straight edge.

Objective

After this lesson, the students will be able to explain what compliance means using appropriate units and will be able to calculate the compliance of a heart chamber or a blood vessel from a Volume vs. Pressure graph (or a Pressure vs. Volume graph). The student will also be able to explain why compliance is an important feature to consider in the development of artificial arteries.

Activity

After discussing with students why compliance is an important feature of blood vessels, I will use a Volume vs. Pressure graph to demonstrate how to calculate the slope of a secant line using the correct units shown on the graph. I will then demonstrate how to use a straight edge to estimate the location and the slope of a tangent line to the curve. I will then ask students to calculate the slopes of secant lines and tangent lines from the graph at different points. Students will then use conversion factors to convert their slopes into SI units.

Lesson Plan 4: Student Project

Materials

Internet and Library access

Objectives

Students will find an area of interest related to the topic of organs or artificial organ development where they can apply dimensional analysis in analyzing data.

Activity

Students will have a great deal of latitude in coming up with their topic for their project. The one characteristic that all of the projects must include is at least three calculations involving dimensional analysis or the use of a conversion factor to interpret data.

Student groups will present their projects both in written form and to the class as a whole orally and visually, and will be graded with a combination of peer grading and my grading with input from the co-teacher. Logistically, several two person groups will form larger super-groups for the purpose of presentation. This organization will save time and provide an additional opportunity for peer teaching within the group structure. I anticipate that A group students will do the bulk of the written work since that is one area where I cannot directly control group members' input. Ideally, however, with the differential evaluation points given that favor B group response, B group students should do the bulk of the oral and visual presentation to provide students with the highest group grade.

Comments:

Add a Comment

Characters Left: 500

Unit Survey

Feedback