Angle of Impact

Blood splatter analysis is a powerful forensic tool.  Spatter patterns allow investigators to reconstruct what happened at a crime scene.  The blood spatter pattern "tells a story" of the crime and help the investigators determine if eyewitness accounts are consistent with the evidence.  To study impact angle, you will need to use trigonometry math skills.

Use trigonometric functions to determine if the impact angle for any given blood droplet.

By accurately measuring the length and width of a bloodstain, you can calculate the impact angle using the following sine formula:

c=opposite/hypotenuse=width(a-b)/length(b-c).

To determine the angle of impact, take the inverse sine to get degrees.

Lesson: Angle of Impact Lab

Objective: For students to learn and use trig functions in the real world.  Students should be able to solve for angles in a right triangle.

Standards: Apply content to real-world scenarios.

Time: 45 minute class.

Set-up: 10 minutes before class.

Procedure:

• As students enter the classroom, students will begin work on the daily question.
• After two students go up to the board to work out the daily question, go over the correct answer with them.
• Spend 5 minutes going over any missed or confusing questions the students had on the assignment.
• Before the start of the angle of impact lab share with them a quick way of determining the blood splatter pattern. It should look like the image to the right.
• Have students spend 20-30 minutes working on the angle of impact lab.  Worksheet is attached.  Students should be in groups of 2 or 3.
• When students are finished with the angle of impact lab, students are to complete the final part of the lab with a poster.  Students should spend the remainder of the classroom working on the poster and putting their finishing touches on the assignment.
• 2-3 minutes before the bell rings students should fill out their exit slip, for an informal assessment.

Goals: Students should be able to use their knowledge to real-world scenarios.  Students should be able to use the angle of impact formula and know how it is derived.  Students should be creative and put their math knowledge to the test to apply the concepts provided. 

Forensics in Math

I have been looking for ways to get students to use math that we learn outside of the classroom and I know that some of my students love mystery books and crime scene investigation shows.  So I have obtained some extra activities for my students to do that includes some forensics work.  Here are some ways you can include forensics in math.

• Probability is the chance of something occurring.  It is calculated by dividing the number of favorable outcomes by the number of possible outcomes.  The theoretical probability of how a coin will land after being tossed 100 times is half. 50/50, if you actually flip a coin a 100 times, you will find the experimental probability, which may be 60 heads and 40 tails, whatever your result.
• Ask students to define probability.  How high does the probability occur for a conviction to occur?
• Regardless of their specialty, scientists use mathematics to help describe the world around them.  Forensic investigations use average growth rates of various structures in the human body, such as hair and fingernails, to decode clues left at a crime scene.  When using average growth rates, it is important to pay close attention to the units of measurement being used.
• To illustrate how blood types are inherited, show a cross between a mother who has blood type O and father who has type AB.  The mother can contribute either an A or a B allele.  So this couple could have children of either blood type A or B.  Point out that the child would have a probability of 1 in 2 of having type A blood.
• Explain how the laws of probability are used in determining the probability that a particular person's blood will match the blood found at a crime scene. 

There will be more activities included in the future.  Right now these are just a few questions to have your students use forensics in these questions.

How could you incorporate this in to your classroom?