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Forensics and Mathematics Ricky Pedersen De La Salle College

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Newton’s Law of Cooling

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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 & 2.2 Curriculum 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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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, 3.1 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

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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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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, 1.11 Curriculum levels 4-6 Learning Outcomes: Substitution with variables Measuring and managing sources of variation Using an explanatory variable to predict a response variable

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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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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 & 1.4 Curriculum 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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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 & 3.6 Curriculum 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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Achievement Standard 1.6 & 1.7 Curriculum 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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Teachers Desk

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Copyright © Cengage Learning. All rights reserved. 12 Further Applications of the Derivative.

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