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Forensics and Mathematics
Ricky PedersenDe La Salle College
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Newton’s Law of Cooling
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Newton’s Law of Cooling
• You may wish to choose a volunteer to “play dead”
• Police tape is a bonus!
• Fake blood
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Newton’s Law of Cooling
Achievement Standards 3.7 & 2.2Curriculum Levels 7 - 8
Learning Outcomes:
• Solve Logarithmic equations for an unknown
• Graph Logarithmic equations
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Newton’s Law of Cooling
Things to watch out for:
Students may not know that k is specific to the body
They may also assume that the cooling rate of bodies is linear
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Suspect Radius
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Suspect Radius
Who could have done it?!?!?!
• Time of Death established with Newtons Law of Cooling – hopefully between classes
• Teacher must have walked to and from class in the transition time
(2 minutes)
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Suspect Radius
Achievement Standards 2.2, 2.14, 3.1Curriculum levels 5-8
Learning Outcomes:• Graphing the equation of a circle or
ellipse and finding the equation• Determine whether a point lies in
the interior or exterior of a circle/ellipse based on the equation
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Suspect Radius
Students will need to
• Decide on a suitable stride and speed at which a teacher would walk
• Using a map they can mark out possible suspects and rule out teachers who are not in the radius
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Suspect Radius
Guide the students
• Even though it is 2 minutes between classes, the circle radius would have to be halved
• The maximum distance can be found using the distance equation
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Suspect Radius
Extension
• Use buildings with multiple levels
• Add in extra information – “Mr Pedersen was seen arguing with Ms Yang in the morning”
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Suspect Height
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Suspect Height
Time to identify the suspect!
• You will need a shoe print…preferably not a high heel
• Discussion for students - what use is this shoe print to us?
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Suspect Height
Achievement Standards 1.4, 1.6, 1.11Curriculum levels 4-6
Learning Outcomes:• Substitution with variables • Measuring and managing sources of
variation• Using an explanatory variable to
predict a response variable
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Suspect Height
• Useful tools – iNZight or censusatschools database
• Provide an equation if you’re lazy • Good opportunity to do hands on
practical measuring!
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Bone Lengths and Height
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Bone Lengths and Height
These bones can be used to identify the height of a person
• Femur (thigh)• Humerus (arm)• Tibia (shin)• Radius (forearm)
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Bone Lengths and Height
Achievement Standards 1.2 & 1.4Curriculum levels 4 - 6
Learning Outcomes:
• Substitution with variables• Rearranging and using formulae • Linear graphing
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Bone Lengths and Height
Male measurements
Height = 69.089 + 2.238 F Height = 81.688 + 2.392 T Height = 73.570 + 2.970 H Height = 80.405 + 3.650 R
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Bone Lengths and Height
Female measurements
Height = 61.412 + 2.317 F Height = 72.572 + 2.533 T Height = 64.977 + 3.144 H Height = 73.502 + 3.876 R
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Bone Lengths and Height
• How tall is a male if his femur is 46.2cm long?
• If a female is 152cm tall, how long is her humerus?
• In order to ride a rollercoaster, your tibia should be at least 30cm’s. How tall does a male need to be?
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Bone Lengths and Height
• Graph the equation for a male and female radius on the same grid.
• What length radius will produce a male and female of the same height?
• What does the x and y intercepts mean in this context?
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Blood Spill
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Blood Spill
Other activities using blood….
• Let’s have a look at the blood spill (hopefully not stain)
• You can either use liquid or cut out paper
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Blood Spill
Achievement Standard 1.6 & 3.6Curriculum levels 4-6 and 7-8
Learning Outcomes:
• Calculate the area of compound shapes
• Calculate rates of change
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Blood Spill
• Draw up a unique blood spill which is non uniform in shape
• Students to calculate the area of this spill.
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Blood Spill
• Draw up several uniform blood spills
• Get students to measure the radius of the circles (as best they can)
• Calculate the rate of change of the area for different values of dr/dt
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Blood Spatter Analysis
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Blood Spatter Analysis
Achievement Standard 1.6 & 1.7Curriculum levels 4 – 6
Learning Outcome:
• Calculate unknown angles and sides of right angled triangles
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Blood Spatter Analysis
• When blood drops hit the ground, they stretch depending on the angle
• Students can simulate this using an eye dropper and beetroot juice
• Angle the paper, not the dropper!
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Blood Spatter Analysis
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Blood Spatter Analysis
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