Forensics and Mathematics
Ricky Pedersen
De La Salle College
Newton’s Law of Cooling
Newton’s Law of Cooling
• You may wish to choose a volunteer
to “play dead”
• Police tape is a bonus!
• Fake blood
Newton’s Law of Cooling
Achievement Standards 3.7 & 2.2
Curriculum Levels 7 - 8
Learning Outcomes:
• Solve Logarithmic equations for an
unknown
• Graph Logarithmic equations
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
Suspect Radius
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)
Suspect Radius
Achievement Standards 2.2, 2.14, 3.1
Curriculum 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
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
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
Suspect Radius
Extension
• Use buildings with multiple levels
• Add in extra information – “Mr
Pedersen was seen arguing with Ms
Yang in the morning”
Suspect Height
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?
Suspect Height
Achievement Standards 1.4, 1.6, 1.11
Curriculum levels 4-6
Learning Outcomes:
• Substitution with variables
• Measuring and managing sources of
variation
• Using an explanatory variable to
predict a response variable
Suspect Height
• Useful tools – iNZight or
censusatschools database
• Provide an equation if you’re lazy
• Good opportunity to do hands on
practical measuring!
Bone Lengths and Height
Bone Lengths and Height
These bones can be used to identify
the height of a person
•
•
•
•
Femur (thigh)
Humerus (arm)
Tibia (shin)
Radius (forearm)
Bone Lengths and Height
Achievement Standards 1.2 & 1.4
Curriculum levels 4 - 6
Learning Outcomes:
• Substitution with variables
• Rearranging and using formulae
• Linear graphing
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
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
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?
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?
Blood Spill
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
Blood Spill
Achievement Standard 1.6 & 3.6
Curriculum levels 4-6 and 7-8
Learning Outcomes:
• Calculate the area of compound
shapes
• Calculate rates of change
Blood Spill
• Draw up a unique blood spill which
is non uniform in shape
• Students to calculate the area of
this spill.
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
Blood Spatter Analysis
Blood Spatter Analysis
Achievement Standard 1.6 & 1.7
Curriculum levels 4 – 6
Learning Outcome:
• Calculate unknown angles and sides
of right angled triangles
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!
Blood Spatter Analysis
Blood Spatter Analysis
Teachers
Desk