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Forensics and Mathematics

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

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Forensics and Mathematics

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  1. Forensics and Mathematics Ricky Pedersen De La Salle College

  2. Newton’s Law of Cooling

  3. Newton’s Law of Cooling • You may wish to choose a volunteer to “play dead” • Police tape is a bonus! • Fake blood

  4. 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

  5. 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

  6. Suspect Radius

  7. 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)

  8. 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

  9. 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

  10. 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

  11. Suspect Radius • Extension • Use buildings with multiple levels • Add in extra information – “Mr Pedersen was seen arguing with Ms Yang in the morning”

  12. Suspect Height

  13. 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?

  14. 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

  15. Suspect Height • Useful tools – iNZight or censusatschools database • Provide an equation if you’re lazy • Good opportunity to do hands on practical measuring!

  16. Bone Lengths and Height

  17. Bone Lengths and Height • These bones can be used to identify the height of a person • Femur (thigh) • Humerus (arm) • Tibia (shin) • Radius (forearm)

  18. 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

  19. 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

  20. 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

  21. 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?

  22. 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?

  23. Blood Spill

  24. 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

  25. 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

  26. Blood Spill • Draw up a unique blood spill which is non uniform in shape • Students to calculate the area of this spill.

  27. 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

  28. Blood Spatter Analysis

  29. Blood Spatter Analysis • Achievement Standard 1.6 & 1.7 • Curriculum levels 4 – 6 • Learning Outcome: • Calculate unknown angles and sides of right angled triangles

  30. 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!

  31. Blood Spatter Analysis

  32. Blood Spatter Analysis Teachers Desk

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