A2A CSI Module Unit Plan
Mathematics Theme
CTE Theme
Time Expectation
Investigation of Applications in Linear, Quadratic, Exponential,
Logarithmic Functions
Health Science; Law and Public Safety; STEM
17 55-minute class periods
Identify Desired Results
Understandings
This module demonstrates how mathematical data is used in many occupations. Exponential growth, decay, linear
growth, and quadratic applications are found in law enforcement and health science careers.
Mathematics Essential Questions
How does a mathematical model help us solve real-world problems?
How can we use data to create mathematical models and draw conclusions?
How can we use exponential decay models to determine time of death?
How can we use quadratic models to determine speed of a vehicle given stopping distance?
How can we use linear and/or exponential models to determine the Blood Alcohol Content (BAC) of a driver at a given
time?
Concepts:
The students will know…
data can be modeled using linear, quadratic, exponential, and logarithmic functions.
the application of mathematics as related to dead bodies, auto accidents and BAC.
the application of mathematics as related to Law and Public Safety and Health Services Clusters.
Knowledge:
The students will know…
how to calculate time of death given ambient temperature and local physical conditions.
how to calculate speed of a vehicle given required stopping distance.
how to determine the BAC of an individual at a given time.
Skills:
the students will be able to…
1. graph and identify linear, quadratic, exponential and logarithmic data.
2. solve linear, quadratic, exponential, and logarithmic equations.
3. use a graphing calculator to determine best model and regression equation.
3. justify the model chosen for a specific situation.
4. identify specific career pathways given a particular mathematical application.
5. demonstrate leadership through varied roles in small group work.
Standards Addressed
A2.1.A Select and justify functions and equations to model and solve problems.
A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities.
A2.1.D Solve problems that can be represented by exponential and logarithmic functions and equations.
A2.3.C Solve quadratic equations and inequalities, including equations with complex roots.
A2.4.A Know and use basic properties of exponential and logarithmic functions and the inverse relationship between
them.
A2.4.B Graph an exponential function of the form f(x) = abx and its inverse logarithmic function.
A2.4.C Solve exponential and logarithmic equations.
A2.6.E Determine if a bivariate data set can be better modeled with an exponential or a quadratic function and use the
model to make predictions.
A2.8.A Analyze a problem situation and represent it mathematically.
A2.8.B Select and apply strategies to solve problems.
A2.8.C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original
problem.
A2.8.D Generalize a solution strategy for a single problem to a class of related problems and apply a strategy for a class
of related problems to solve specific problems.
A2.8.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of
mathematics.
A2.8.F Summarize mathematical ideas with precision and efficiency for a given audience and purpose.
CTE Exploratory Courses
3.1
Demonstrate knowledge of career options within the related pathway.
4.1
Demonstrate leadership skills and employability skills.
Presenting Theme Problem:
Students will explore linear, quadratic, exponential and logarithmic functions as they investigate the death of a
pedestrian. Three anchor activities will address the time of death, the speed of the car and the BAC of the driver at the
time of the accident.
Presenting Theme Problem: Students will be given a crime scene summary, including a diagram with skid marks and
body location. Data will be given regarding length of skid marks, road conditions, ambient temperature, body
temperature. As a suspect appears, the students will be given data about Blood Alcohol Content (BAC) and condition of
the driver at a given time.
Students will create a report to the prosecutor addressing their findings about the accident to include: the time of the
accident, the speed of the car, the BAC of the suspect at the time of the accident, and any other findings regarding the
condition of the victim. The report will include a 2 page summary and relevant graphs to mathematically prove their
claims.
Formative Assessment:
Students will be assessed through out the module. Upon completion of anchor activities, students will be assessed on
the Algebra 2 standards embedded in each activity.
Summative Assessment:
The assessment will be two parts, to include a performance assessment and skills test.
1. The performance assessment will consist of a presentation and/or written report summarizing their conclusions of
the accident scene.
2. Paper and pencil test assessing mastery of algebra 2 standards.
Necessary Prior Knowledge and Skills:
1. Create a scatterplot and determine equation for line of best fit. (8th grade PE)
2. Solve multi-step linear and quadratic equations. (8th grade and Algebra 1 PE)
Scope and Sequence of Instructional Activities
Presentation of Components of the Accident Scene
Anchor Activities:
Linear Application: Blood Alcohol Content
Quadratic Application: Stopping Distance of Car
Exponential Application: Newton’s Law of Cooling
1. Use BAC tables and generate equation or relationship
2. Collect bivariate data tables from text books, media, etc. and practice graphing the data, identifying the differences
between linear, power, exponential, and logarithmic functions
3. Use graphing calculators to determine “best” regression equations
4. Use Stopping Distance Data to determine a model and equation for stopping distance
5. Apply Newton’s Law of Cooling to determine time of death
6. Return to accident and begin data analysis and processing report
Necessary Materials:
Graphing Calculator
CBL and temperature probe or thermometer
Water and three different containers (thermos, cake pan, Styrofoam cup, etc.)
Graph paper
Printed Resources:
Sketch of Crime Scene
Activities worksheets
Electronic resources:
Other
(speakers,
field trips,
etc.):
http://www.jmu.edu/safetyplan/vehicle/generaldriver/stoppingdistance.shtml
http://hyperphysics.phy-astr.gsu.edu/HBASE/crstp.html
www.wolfram.com
http://education.ti.com/educationportal/activityexchange/activity_detail.do?cid=us&activityid=6380
Forensic
scientist,
coroner, state
patrol