Unit+Plan+-+Carl+Peahota

Unit Title: ** The Mathematics of the Human Body
 * ​Carl Peahota - Unit Plan **
 * I. Subject Area:** Mathematics ** Grade level: ** 10


 * II. Estimated Time: ** This unit will take place over the course of three- 45 minute lessons. Lessons will occur on a daily basis with overlap in Biology, Chemistry, Mathematics, Anatomy, and Physics.

**III. Student Population:** 10th through 12th grade males/females from diverse educational and social backgrounds.


 * Stage 1 – Desired Results **


 * IV. Standards:** //Identify the national, state, or district standards for this lesson//

A. Model and compare values of irrational and complex numbers. B. Use factoring to create equivalent forms of polynomials. D. Use exponential, scientific, and calculator notation to represent any rational number. E. Apply the concepts of prime and composite polynomials to determine GCFs (Greatest Common Factor) and LCMs (Least Common Multiple) of polynomials. F. Understand the concepts of exponential and logarithmic forms and use the inverse relationships between exponential and logarithmic expression to determine unknown quantities in equations. C. Evaluate numerical expressions that include the four basic operations and operations of powers and roots, reciprocals, opposites, and absolute values. C. Use properties of geometric figures and measurement formulas to solve for a missing quantity (e.g., the measure of a specific angle created by parallel lines and a transversal). E. Describe how a change in the value of one variable in a formula affects the value of the measurement. A. Write formal proofs (direct proofs, indirect proofs/proofs by contradiction, use of counter-examples, truth tables, etc.) to validate conjectures or arguments. B. Use statements, converses, inverses and contrapositives to construct valid arguments or to validate arguments. A. Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts. B. Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas, and results. A. Design and conduct an experiment using random sampling. C. Select or calculate the appropriate measure of central tendency, calculate and apply the interquartile range for one-variable data, and construct a line of best fit and calculate its equation for two-variable data. E. Make predictions based on lines of best fit or draw conclusions on the value of a variable in a population based on the results of a sample. ** 2.7.10. Probability and Predictions ** A. Use probability to predict the likelihood of an outcome in an experiment. C. Compare odds and probability. E. Use probability to make judgments about the likelihood of various outcomes.
 * 2.1.10. Numbers, Number Systems, and Number Relationships **
 * 2.2.10. Computation and Estimation **
 * 2.3.10. Measurement and Estiation **
 * 2.4.10. Mathematical Reasoning and Connections **
 * 2.5.10. Mathematical Problem Solving and Communication **
 * 2.6.10. Statistics and Data Analysis **

**V. Understanding(s):** //1.)// //Identify the “big idea(s)” of the unit:// · The human body is one of the most complex machines ever created. To even begin to understand those complexities requires general knowledge of the sciences; and the sciences use the language of mathematics as a means of universal understanding and communication.

// 2.) Identify specific understandings about the “big idea(s)”: // // What questions will foster inquiry, understanding, and transfer of learning? //
 * ** Thermodynamics **
 * Discuss the processes in the human body which regulate temperature.
 * Identify which Laws of Thermodynamics take place in the human body.
 * ** Kinematics **
 * Discuss how Newton's 2nd and 3rd Laws apply to everyday experiences the human body encounters.
 * Explain how the concepts of "fulcrum", "torque", and "center of gravity" apply to the himan body.
 * VI. Essential Question(s):**


 * 1) What would happen to the human body if the processes that regulate temperature did not function correctly?
 * 2) How do the processes that regulate the human body function under adverse conditions (extreme hot/cold)?
 * 3) Why is the concept of a fulcrum so fundamentally important in the human body?
 * 4) Are the center of masses in males and females the same? Explain?
 * 5) What are the advantages/disadvantages to a center of mass that was displaced higher/lower in the human body?

**VII. Attitude(s) and Value(s):** // What positive attitudes and democratic values will students develop? //
 * Appreciate the necessity for mathematics in the understanding of how the human body functions.
 * Appreciation for the different scientific disciplines needed to understand how the human body works.
 * Develop an understanding of the complextities of the human body and the methods that are used to quantify those complexities.

1.) //What skills related to acquiring, organizing// //and using information will students// //develop?//
 * VIII. Skill(s): **

//2.) What technological skills will students develop?// //3.) What interpersonal skills will students develop?//
 * //identify and use content specific vocabulary//
 * //distinguish fact from misconceptions//
 * //identify cause and effect relationships//
 * //construct charts and graphs of collected data//
 * //derive conclusions from empiracal data//
 * //formulate/hypothesize data collections//
 * //develop a deeper understanding of how to apply mathematics to the human body//
 * //with the aid of a calulator,// //students will learn to plot data to be interpreted.//
 * //students will use Microsoft Excel as a means to further analize statistical data//
 * //students will use computers and graphing software to plot data for interpretation//
 * //students will use a group Wiki to share their ideas//
 * //students will learn to collaborate and cooperate in order to achieve their goals//
 * //students will develop problem-solving skills//
 * //leadership skills will be developed through cooperative learning//


 * Stage 2 – Assessment Evidence**

// Through what authentic performance task(s) will students demonstrate the desired understandings, attitudes, and/or skills? //
 * ** IX. Performance Task(s): **

// By what criteria will the evidence be assessed? // || ** Other Evidence: ** // Through what other evidence (e.g., quizzes, tests, observations, homework, journals, etc.), will students demonstrate achievement of the desired results? //

// How will students reflect upon and self-assess their learning? // ||
 * * Working in groups of three, students will create various spreadsheets used to collect data from experiments done on the human body in the areas of thermodynamics and kinematics.
 * Graphing calculators will be used in conjunction with the spreadsheets to help compute and analyze data; students will also use computer software to validate analyses.
 * Oral presentations of finding and analyses will be presented to the class. || * throughout the unit, students will utilize marble notebooks to document and track all conjectures and hypotheses
 * students will complete a self assessment of note taking techniques (marble notebooks) and data analysis techniques; in particular, the accuracey of their findings. ||

**Stage 3 – Learning Plan **

**X. Learning Activities (3 lessons)** **Lesson # 1: Title:** //Kinematics of the Human Body - Introduction to Kinematics Applied to the Human Body// **Time Estimation:** Three 45 minute periods 1. Analyze how the equations of torque and rotational motion apply to the human body 2. Explain the concept of a fulcrum and relate it to part 1, above. 3. Demonstrate knowledge of torque, rotational motion and fulcrum via experimentation.
 * Objective(s):**
 * __Description__:** Ask students to conduct an experiment using concepts of torque, rotational motion, and fulcrum. Tell students that they are going to devise an experiment regarding aforementioned topics. Explain to students that each group member will add their knowledge and observations to the results of the experiment.

**Time Estimation:** Three 45 minute periods 1. Review eqauations of rotational motion and torque. 2. Analyze how the equations of thermodynamics and entropy apply to the human body 3. Demonstrate knowledge of thermodynamic properties and entropy via, experimentation.
 * Lesson # 2: Title:** //Kinematics Review and Introduction to Thermodynamics Applied to the Human Body//
 * Objective(s):**
 * __Description__:** Ask students to conduct an experiment using concepts of thermodynamics and entropy. Tell students that they are going to devise an experiment regarding aforementioned topics. Explain to students that each group member will add their knowledge and observations to the results of the experiment.

**Time Estimation:** Three 45 minute periods 1. Review the equations of thermodynamics and how it is applied to the human body 2. Review the concept of entropy and how it is applied to the human body. 3. Demonstrate knowledge of torque, rotational motion and fulcrum via experimentation.
 * Lesson # 3: Title:** //Thermodynamics Review//
 * Objective(s):**
 * __Description__:** Ask students to conduct an experiment using concepts of torque, rotational motion, fulcrum, thermodyanmics, and entropy. Tell students that they are going to devise an experiment regarding aforementioned topics. Explain to students that each group member will add their knowledge and observations to the results of the experiment.

1) Body Worlds 2 (n.d.). //Gunther Von Higgens Body World 2 Exhibition//. Retrieved March 2, 2010, from []
 * XI. References: **

2) Wikipedia (n.d.). //Wikipedia: Plastination//. Retrieved March 5, 2010, from []

// If this is a “taught” unit, please include a reflection that addresses the following: what was the reaction of the students to the unit? What understandings, attitudes, and skills did students gain as a result of this unit? Were there any surprises? What would you change, if anything, in the future? What did you learn as a result of teaching this unit? //
 * XII. Reflection: **

** STUDENT TEACHING JOURNAL **
 * Format A **

1. **Topic**: Kinematics/Thermodynamics of the Human Body

2. **Sequence of events** //-// Students were attentive to lesson at hand. I found particular areas for concern in:


 * equation manipulation of rotational motion and entropy
 * grasp of general ideas regarding entropy
 * inability to use more advanced mathematical tools (calculus, differential equations) for the puposes of understanding more advanced topics

3. **Highlights of one or two notable events** - (//Describe in detail what happened, including what you wanted students to learn and the extent to which you were successful in helping __all__ students)//

My goal in this unit was to get all of my students to comprehend the most general concepts of kinematics and thermodynamics. Despite a few setbacks with some of the more complex math that was involved, I believe that all of my students understood the basic concepts. My belief is based upon several well-designed rubrics that scored the students on basic understanding and experimental concepts. It is my opinion that utilizing the "Visible Human" models helped in the students' understanding. I am confident their comprehension and I feel that, in a short amount of time, I will be able to incorporate higher mathematics that will aid in a better sense of kinematics and theromdynamics.

4. **Analysis of the event(s)** - //(Include thoughts and feelings, questions that were raised, and// // what you learned) //

I feel very charged and eager in teaching the concepts of kinematics and dynamics as it relates to the human body. I can see that the students are genuinely interested and motivated. I attempted to introduce, too quickly, the more complex math that would be need to understand these concpts in a much broader light. It was something that will not be repeated again.

I feel that these concepts could be related to the lower grade levels and so, I ask, how can that be accomplished in a way that is comensurate with the learning that younger grades receive. It is something I plan to investigate with my collegues from the lower grades.

I have learned that students have the ability to absorb a great deal of information. The key to help them accomplish this is to present the material in a way that they find interesting and even useful, if possible. I feel that this trip to Body Worlds has certainly peaked their curiosity.


 * __ Resources for Body World Unit __**


 * __ Rating Scale __**
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 * [[image:4stars.jpg]] ||  ||< **= 4 sta​rs** ||


 * [[image:3stars.jpg]] ||  ||< ** = 3 stars ** ||


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1) [] This is an excellent resource package for students. It includes a FAQ section, an interview with Dr. Gunther von Hagens, classroom activities, and more. This serves as an excellent “jumping-off” point in helping the student understand the Plastination process. 2) [] This website has a really cool scavenger hunt that integrates fun and learning. Students are asked math question related to the human body and are asked to hunt for the answers. Links are provided for the students to help them hunt for the answers. 3) [] This si​te has a plethora of educational videos. Several videos about anatomy, math, and physics may be particularly interesting. 4) [] Here is a facinating YouTube video of Dr. von Hagens work. Here, you can get a "behind-the-sceens" look at what goes on in one of his labs.

5) [] To educate the student in the science of plastination, this Wiki defines the process and supplies several references and materials to inform the reader.