# CRIME : Criminal Investigation through Mathematical Examination (Student)

### Author: Published by COMAP, Inc. in conjunction with DIMACS, Rutgers University.

**What is the BioMath Connection (BMC) Project?**

BMC was a pioneering project linking biology and mathematics in the high schools. It provided an opportunity for high school teachers, writers, researchers, and others to get in on the ground floor of developing innovative classroom materials. The materials consist of 20 modules that can be flexibly adapted for use in a variety of courses at a variety of grade levels in both biology and mathematics. The project was run by DIMACS at Rutgers University in collaboration with the Consortium for Mathematics and its Applications (COMAP) and Colorado State University (CSU).

Welcome to our unit on the mathematical examination of fingerprints! This unit provides a possible method to identify individuals in a species. Tracking individuals can be an important step in learning more about the species as a whole. This unit concentrates on human fingerprints. To accomplish this, we use a fictitious crime case to explore a mathematical procedure to examine and compare fingerprints. The unit consists of multiple activities to investigate the characteristics of a fingerprint and the biology behind why everyone's fingerprints differ. **TopicsBiology:** The biology of this unit involves skin anatomy, fingerprints, and the genetics associated with individuality, at least in the form of an expressed phenotype. The genetics include the concepts of penetrance, expressivity and epigenetics. Biological diversity is an important issue in evolution and sexual reproduction allows for the creation of individuals who are different from their parents and from any other individuals previously born. The unit also allows a convenient opportunity for the teacher to explore the physiology of the skin in more detail, if they wish. Teachers may add their own material for that purpose.

**Mathematics:**The mathematics of this unit is primarily the mathematics of graph theory. In graph theory, a primary concern is the connections (edges) between given vertices (points). This unit introduces basic graph theoretic concepts (networks, vertex, edge, connectedness). The process of formulating questions and answering those questions is introduced through data collection and organization, useful in identifying biological patterns of behavior within species. Constructing ordered pairs to label specific characteristics of the data provides easy-to-make and easy-to-interpret displays for the dataset. Matrices (rectangular arrays of numbers) are introduced to provide a more mathematically efficient representation of the graphs.

**Prerequisites**

Biology:Students should be familiar with basic genetics (e.g. DNA, genes, alleles).

Biology:

**Mathematics:**The mathematics of this unit includes introductions to sets (databases), collection and organization of data, basic graph theory, and matrices. Students should be familiar with representing quantities as ordered pairs, ratio and proportion, percent, sets and subsets.

**Length**

This unit consists of 4 lessons and will take 4-6 class periods (45 -minutes each) if the majority of the work is done during class.

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