Forensic Science in the Middle School Math Classroom

By Patricia Roberto
Rogers Middle School

 

 

Overview

This unit plan on forensic science was written for a middle school math classroom. However, it could easily be adapted for a science class or, idealistically, an integrated math/science program. Students will be introduced to forensic science, which is a branch of science that focuses on criminal investigation to provide physical evidence to solve criminal cases. Students will learn a brief history of the subject, discuss the many occupations related to this study, practice the Bertillon system of identification of criminals, experience the exactness of fingerprinting, and develop an understanding of the emerging importance of DNA testing. Finally, the students will use algebraic equations to determine the height of a person using only the length of certain bones. The unit could easily fit into a communications or literature class with the use of an abridged version of Mary Shelley’s Frankenstein or Sir Arthur Conan Doyle’s Sherlock Holmes as a prequel to the unit and the evaluation sheet at the end of the unit.

Rationale

As I began the Pittsburgh Teachers Institute course entitled The Math Connection, I knew that there would be so many avenues that I could explore to bridge my math curriculum with a science extension. The Pittsburgh Public School District encourages interdisciplinary lessons, and the administrator in my building emphasizes this train of thought. I currently teach in a building which helps the students discover and enrich their artistic abilities, whether it be visual art, instrumental and vocal music, creative writing, stagecraft, costume, dance, multi-media, or drama. We, as academic teachers, are encouraged to work with the arts teachers as much as possible. Unfortunately, the academic teachers do not often collaborate with each other due to curriculum restraints, time limitations, and scheduling conflicts. I truly believe that we are doing our students a disservice by not collaborating with each other as much as possible. This unit is written in the belief that the more we teachers relate common concepts, the better our students will retain and use them again.

I enrolled in this course with the thought that our students are constantly introduced to and use math concepts in the science classroom. These topics range from weights and measures to categorizing and graphing tables of information. However, science does not often enter our math classes. I wanted to try to create a unit in which both math and science instructors would benefit, and where the students would see the reasoning behind many of the abstract math concepts to which they are introduced throughout the school year, such as solving equations for an unknown variable. The lessons in this unit are intended for pre-algebra and Algebra I students.

The idea for this unit came from one of the books in the eighth grade Connected Math series, which is the adopted program used in the Pittsburgh Public School system. Students are introduced to a lesson called "Analyzing Bones", where they are given several algebraic equations and the measurement of certain bones. With these pieces of information, the students can then calculate the height of a person. Each time I have introduced this lesson, the students have been intrigued. They also see a real-world use and application for the algebraic concepts they have been learning. At first, I thought that expanding on this idea of forensics might be too gruesome for some of my students. But after discussing the topic with Professor Richard Holman, the leader of the seminar, and the other Fellows in my group, I decided to go ahead and make the math/science connection.

Many of the middle school students in my classes are technologically advanced. They are very adept at using graphing calculators, which can create tables and graphs in an instant; desktop and laptop computers, with e-mail, search engines, and personal web sites; Smart Board and Power Point presentations; and using technology to assist in their arts studies, such as editing decks and computer- generated music. I feel it is important for them to be exposed to some professions that also use technology to advance their fields. State troopers can send a driver to a hospital for a gas chromatography test to check on the blood-alcohol level; police laboratories might use a scanning electron microscope to detect minute gunpowder particles; ultraviolet and infrared lights can show fingerprints and blood stains.

My ultimate hope is that by relating algebra with real-life, my students will retain the science and math concepts better and longer than if the concepts had been presented solely from a textbook.

 

Objectives

Prior to this unit, students should be able to solve a single variable equation for the unknown, such as 56 + 19a = 265. For this unit of study, the students will be introduced to a brief history of forensic science. We will also discuss several occupations related to this field of scientific study. Students will also learn of different ways that criminals have been identified throughout history, from the Bertillon system of identification to fingerprinting to DNA testing. The students will be expected to apply algebraic concepts to solve the real world problems of forensic science, in particular forensic anthropometry, which is the study of human body measurements. Students will come out of this having improved their group and organizational skills, deductive reasoning, and equation solving skills.

There are several standards of learning which will be addressed in this unit. In Mathematics, the students will be working on four standards, which will improve their equation solving skills in theoretical and practical situations, computation skills, problem solving abilities, and general knowledge of algebraic concepts. For the Science standards, students will meet three standards, including explaining scientific relationships to technology and society in general, developing their skills of observation, data collection, and pattern recognition, and understanding how the scientific principles of forensic science have developed and how they relate to real-world situations. For the Communications standards, the students will work on developing their oral response skills and promoting effective group communication. The students will also be working on Citizenship standards by cooperating and working effectively with others. (See Appendix A for detailed descriptions of the Student Learning Standards in the Pittsburgh Public School District)

 

Classroom Activities

DAY ONE

As you begin this unit of study, you will want to explain to your students the reasoning behind combining math and science topics. In life, it is very rare that a math problem such as 12/4 comes along. However, it could very easily come into play if you applied an everyday situation, such as separating a dozen doughnuts among four friends. Explain to the students that math is a natural extension of science. Begin the first day with brief excerpts from the movie Frankenstein (the older versions of the movie are usually better) or any of the Sherlock Holmes or Hercule Poirot series that can be found on the public broadcasting stations. After that, introduce the topic of forensic science, which is the study of science as it applies to criminal investigations. Ask the students when this type of science might be used (a lively discussion will more than likely ensue). Then ask the students if they can think of what occupation might often use forensics. Hopefully, someone will come up with a coroner. Historically, coroners were not medical personnel. It was an appointed office. However, during the late 1800’s when many immigrants came to the United States, living conditions were extremely poor, especially in the crowded manufacturing sections of cities. Crime also took an uphill spiral. Physicians were then called in to identify victims’ causes of death and testify in criminal court cases when homicide was involved. From these origins, the office of Medical Examiner was created. Other professions that are connected to forensic science include: odontologists (who examine and characterize the teeth of unidentified bodies), anthropologists (who determine the sex, height, weight, and ethnic group of a dead person from an incomplete body), pathologists (examine the body tissues and organs), toxicologists (study poisons, including drugs), psychiatrists, biologists, physicists, and chemists. Finish the day with a brief excerpt from the TV show C.S.I., which depicts the use of forensic science at different types of crime scenes. (See Appendix B for vocabulary sheet for students)

DAY TWO

Introduce the history of classifying criminals. In 1879, a Frenchmen named Alphonse Bertillon (bair-tee-awn) created a system of criminal identification which involved taking a series of precise body measurements of the head, left arm and left foot. A series of photographs was also taken. At this point, ask 3-4 students to come up to the front of the room. Try to choose students who are physically similar in size. Use the Bertillon system to measure and compare. The students will summize that the system has some flaws. Take the case of Will West and William West, who were both prisoners at Leavenworth Prison in 1903. They had almost the same name, the same appearance, and the same Bertillon measurements. Fingerprints of the two men turned out to be different. Although they denied it, the men were, in fact, identical twins. Although the measurements are no longer used, the photograph part of the system is still used today.

DAYS THREE AND FOUR

Today the students will discover the exactness and uniqueness of fingerprints. Start off the class reminding them of the West twins from yesterday’s discussion. Although the men were identical twins, their fingerprints were different. Experts have come to believe that each person’s fingerprints are unique. Explain to the students that police and the F.B.I. group fingerprints patterns into three basic categories: whorls, which go in circles or swirls; loops, which have a single hairpin or upside-down U shape; and arches, shaped like a hill or a pointed tent. These three categories are then divided into eight types: plain whorl, central pocket loop, double loop, accidental whorl, ulnar loop, radial loop, plain arch, and tented arch (see Appendix C for attached visual, which can copied onto overhead film or enlarged into a poster). You can purchase a simple fingerprint kit for less than $10.00 or you can use products you probably already have at your disposal. To leave finger prints, be sure to have the students touch a surface that is hard, smooth, and shiny. Touch the surface firmly for a second or two, then lift finger directly up, so as not to smudge the print. If the fingerprint is on a dark-colored surface, use talcum powder. If on a light-colored surface, carefully use graphite powder. Shake a small amount of powder (an amount about the size of your thumb nail) onto the print and lightly brush the powder back and forth with a feather. Brush softly until every detail of the print is clear. Then lightly blow across the print to remove the excess powder. To lift the print, use a piece of clear adhesive tape. Carefully cover the print with the tape and gently lift the tape and place onto a piece of dark-colored paper for talcum powder or light-colored paper for graphite powder. Be sure to display students’ finished prints for all to see. Tally and make a bar graph for the three categories of prints. After all students have been printed, ask the class if they can think of any other ways of identification that might be even more precise than fingerprinting. Hopefully, someone will come up with DNA testing. Explain that DNA stands for deoxyribonucleic acid (you may want to write this on the chalkboard), which is the genetic material found within the cell nuclei of all living things. A DNA sample can be taken from body tissue or fluid, such as hair, blood, or saliva. The strands of DNA are grouped into structures known as chromosomes. Your students should recognize chromosomes from science class. This leads to a lively discussion of genetics and what characteristics we get from our parents. Most courts now accept the results of DNA testing. FOX television has even done a special program on inmates who are waiting to see if their DNA testing could possibly set them free. Unlike fingerprints, identical twins have the same DNA. DNA testing can also be used for animals. Take the case of a grizzly bear attack in Glacier National Park. Human DNA was found in bear droppings. Scientists were able to match bear hair found at the scene to hair samples taken the year before. The female grizzly and her two cubs were captured and destroyed. Because DNA testing is a relatively new field (1985), there are still some areas of uncertainty, such as the accuracy of the results (human error in the lab could be a problem), the cost of the testing, and the case of identical twins. All things considered, DNA testing continues to be an emerging field for evidence in criminology.

DAY FIVE

Prior to the start of class, secretly choose one student who will represent the thief. You will need to have that student leave fingerprints around the "crime scene". Give the class the following scenario:

"Yesterday after your class left my room, I noticed that something was wrong. Someone had taken all the rulers that usually sit in this jar on my desk. The class’s task for today will be to figure out which of your classmates wants to "rule" the world! Remember that we must have physical evidence. "Hunches" won’t work here! Using our forensic science training, where should we begin?"

As the teacher, your job is to listen and give leading questions when necessary. You might also have to help the students organize their thoughts and data. When there are 5-10 minutes left until the end of class, have a class spokesperson summarize what the class has learned and who they believe is the culprit.

DAY SIX

Start the class by bringing in (clean) large and small animal bones. You can probably get some at a local butcher shop or a grocery store meat department. Discuss the obvious differences and similarities. Ask the students if they can tell what kind of animals the bones are from. Using the attached sheets (Appendices D & E), which were created by George Knill, give the students an introduction, such as:

Two hunters were hiking up a mountain when they discovered a gruesome find.

A pile of human bones was located under a large oak tree. They reported the find to the local authorities, who in turn notified the medical examiner’s office. Using certain algebraic equations, the medical examiners were able to determine the height of the victim.

The students’ job is to use the given equations to find the appropriate height of each person on the worksheet.

DAY SEVEN (optional)

Bring in 4-5 sets of the game Clue. After separating the students in to groups, have them use their deductive reasoning skills to solve the mystery. If time permits, have the winners of each table play to determine a Grand Champion, who can be given the Sherlock Holmes Award.

 

DAY EIGHT (optional)

Contact your local forensic science branch of the police department or the coroner’s office and check to see if they would be willing to come into your classroom for a question and answer session.

DAY NINE

You can use the attached evaluation sheet (Appendix F) as an informal assessment and to get some feedback from your students. If possible, check with the communications / language arts teacher to see if this essay could be used in both classes for a grade.

Appendix A

Abriged Version of the Student Learning Standards of the Pittsburgh Public School District addressed in this unit of study.

Mathematics

1. All students use numbers, number systems, and equivalent form (including numbers, word objects and graphics) to represent theoretical and practical situations.

2. All students compute, measure, and estimate to solve theoretical and practical problems, using appropriate tools, including modern technology such as calculators and computers.

4. All students formulate and solve problems and communicate the mathematical processes used and the reasons for using them.

5. All students understand and apply basic concepts of algebra, geometry, probability and statistics to solve theoretical and practical problems.

Science and Technology

1. All students explain how scientific principles of chemical, physical and biological phenomena have developed and relate them to real-world situations.

4. All students explain the relationships among science, technology, and society.

6. All students develop and apply skills of observation, data collection, analysis, pattern recognition, prediction and scientific reasoning in designing and conducting experiments and solving technological problems.

Communications

3. All students respond orally and in writing to information and ideas gained by reading narrative and informational texts and use the information and ideas to make decisions and solve problems.

6. All students exchange information orally, including understanding and giving spoken instructions, asking and answering quesions appropriately, and promoting effective group communications.

Citizenship

7. All students demonstrate their skills of communicating, negotiating and cooperating with others.

8. All students demonstrate that they can work effectively with others.

 

 

 

 

 

Appendix B - Vocabulary Sheet for Students

____________________________________________________________

Name__________________________ Period________

Define the following professions which relate to the study of forensics:

1. forensic scientist

 

2. coroner (medical examiner)

 

3. odontologist

 

4. anthropologist

 

5. pathologist

 

6. toxicologist

 

7. psychiatrist

 

8. biologist

 

9. physicist

 

10. chemist

 

 

 

Appendix C

plain arch tented arch

1. Plain Arch, shaped like a low, rounded hill.

2. Tented Arch,- shaped like a high, pointed hill.

 

 

 

 

u1nar loop radial loop

3. Ulnar Loop, a loop that slants toward the little finger side of the hand. Named after the ulna. the arm bone on that side of the arm.

4. Radial Loop, a loop that slants toward the thumb side of the hand. Named after the radius, the arm bone on the thumb side of the arm.

applications

MATHEMATICS IN FORENSIC SCIENCE

Knowing the exact physical dimensions of a victim of a crime is extremely useful in identifying the victim. When a skeleton is found, a forensic scientist uses the lengths of certain bones to calculate the height of the living person. The bones that are used are the femur (F), the tibia (T), the humerus (H), and the radius (R). See figure 1. When one of the following formulas is used to determine the height. All measurements are in centimeters.

After the age of thirty, the height of a person begins to decrease at the rate of approximately 0.06 cm per year. This shrinkage must be considered when the age of the victim is known.

1. The femur of a 25-year-old male measured 49.7 cm. What was the height of the person?

          2. The tibia of a 32-year-old female measured 33.5 cm. What was the height of the person?

3. Have students use the formulas to calculate the lengths of their femur, tibia, humerus, and radius.

4. Have students contact the forensic science branch of the police department to determine how mathematics is used in crime detection.

Answers. 1. 180.3 cm, 2. 157.3 cm.

Fig.1. Front view of a human skeleton

Forensic scientists can estimate a person's height by measuring the length of certain bones, including the femur, the tibia, the humerus, and the radius.  The table below gives equations for the relationships between the length of each bone and the height for males and females. These relationships were found by scientists after much study and data collection. 

In the table, F represents the length of the femur.
T the length of the tibia, H the length of the humerus,
R the length of the radius, and b the person's height.
All measurements are in centimeters.

Introduce the forensics information, and ask questions to make sure students understand what information each equation can give.

Have students work in groups on the problem.

Give groups transparencies or large sheets of paper for recording answers. (optional)

Ask groups who finish early to try to measure their own bone lengths and their heights to test the equations.

Have students do the follow up individually and then share answers in groups.

Have students share their work and thinking for each pan of the problem.

Ask several students to share their graph from the follow-up and explain what the x- and 1-intercepts mean.

A. h = 61.412 + 2.317(46.2) = 168.5 cm

B. h = 81.688 + 2.392(50.1) = 201.5 cm

C. See page 63h. D. See page 63h.

Graphs will vary. The x-intercept tells the value for x (femur, tibia, humerus, or radius length) when the height of the person is 0, and the y-intercept tells the value for y (the person's height) when the length of a bone is 0. These values do not make sense in the context of the problem.

ACE questions 9, 10, 14, 15, 17, and unassigned choices from earlier problems (17 is particularly difficult)

Appendix F - Evaluation Sheet

____________________________________________________________

Name ___________________________ Period __________

Over the past two weeks, we have been studying the mathematics involved in forensic science. Give a brief definition of forensic science. Then write about two of your favorite ideas / topics that you have learned and explain why you chose what you did. Finally, describe your feelings about doing this type of unit of study as opposed to a regular unit of study from the textbook.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Bibliography

 

Clark and Crawford. Legal Medicine in History. Cambridge University Press, Great Britain., 1994: 268-282.

Derr, Mark. "The Tale of Three Bad News Bears Who Became Killers,"

New York Times, New York. 8/18/98.

Doyle, Sir Arthur Conan. Sherlock Holmes.

Encarta Encyclopedia (computer version), 1999. "Forensic Science", "DNA Fingerprinting".

Grolier Interactive Encyclopedia, 1998. "Forensic Science", Anthropology", "Bertillon System", "Anthropometry".

Knill, George. "Mathematics in Forensic Science." Mathematics Teacher, Feb. 1981:125,149.

Lappan, Fey, Fitzgerald, Friel, and Phillips. Moving Straight Ahead,

Dale Seymour Publications, Michigan State University, 1998:57,63g,63h.

Minilabs Science Fingerprint Kit Instruction Book, Educational Design, Inc. New York, 1998.

Shelley, Mary. Frankenstein.