The website is designed to walk students through a forensic investigation and help them develop the mathematical skills involved in data and statistics, probability, algebra and rational number. It is designed for a year 12 mathematics general one class. All information on the website including missing persons and suspects are fabricated for the purposes of the task.
Before I begin using the website with my students I will be showing them an episode of Bones to give them some context. After the episode we will engage a discussion surrounding the following questions:
What mathematics did they use to help them solve the crime?
What other mathematics could they have used? Why?
Possible Answers:
Probability
Measurement
Data and statistics
Ratios
Angles
Volume
Rates (decomposition, speed)
Equations
Modelling
Home Page/ Research and Background Information
Allow approximately one lesson to complete the home page activity and research and background information activity. As a class, we conducted a brainstorm for the first task, before students independently completed the next task.
The Crime Scene
The crime scene activity will take approximately 20 minutes. You can have students calculate the dimensions of each room using the scale located on the side before you have them answer the questions. For this task I had my students work in a small group, approximately 6 students.
Content/Topics:
Ratios and scales
Measurement
Literacy
Time of Death
Firstly, students need to analyse the evidence and the evidence bags presented. In one bag there is a watch - the time is stopped on this watch at 3.02. They need to use this evidence to hypothesis when the victim may have died. Also, marked on each evidence bag is the time the evidence was collected. I had most students hypothesis that the time of death would have been either at 3.02am on the day the body was found or 3.02pm the day before.
Secondly, they now need to complete activity 2 which requires them to calculate the time of death using algebra. The worksheet itself bases itself on the linear relationship between body temperature and cooling time. For the purposes of this task the body has not reached ambient temperature - so what happens after it does reach ambient temperature was not considered. I found it would have been best to run an algebra skills workshop before this task, as a number of students were not familiar with how to write expressions using algebraic terms.
Content/Topics:
Generate a table of values
Graph linear functions for all values of x with pencil and paper and graphing software
Algebra and modelling
Solve for a linear term in an equation following substitution into a mathematical formula
More on the Crime Scene
This section looks at the distance the murderer has travelled after the crime was committed. For question 2, students need to calculate the average distance travelled first. Once they have done that, have them draw a dot on a piece of paper and mark the radius. They may use a compass to draw a circle. Have students mark the radius and the diameter and then use the circle area formula to calculate the area. Content/Topics:
Area
Rates
Statistics - Mean, median, mode and range
Literacy
The Body Part I: Blood Loss
For the blood loss topic - students might require some assistance. When calculating the area - student's can either estimate by using rectangles that encompass each area of blood, or use circles, or they could apply Simpsons rule. Student's could work in small groups and one group could look at rectangles, another circles and the other Simpsons rule, and then they could compare their results and decide which might be a more accurate way to calculate area.
When calculating the blood loss volume, I will have my students assume that the depth of the blood into the carpet is 1.5cm.
Content/Topics:
Convert Units from cm^3 to Litres
Area of a circle
Area of composite figures
Calculate the volume of a cylinder
Estimate and check to determine if results are reasonable
Algebra and modelling
The Body Part II: Bullet Trajectory
Before students complete the activity in class, have them model it using a skeleton. A 'bullet' will be placed in the ribcage between the 9th and 10th ribs, and students can move the skeleton around to estimate where the assailant may have been if the victim was standing or laying. Students can then use this to help them sketch their two scenarios.
Content/Topics:
Pythagoras Theorem
Trigonometry
The Body Part III: The Bones
Students will use the bones print outs to help them decide who our victim is and how to identify them. They will input lengths into equations to calculate height, use scales to calculate the length of the real bones. If you want to include probability students can calculate the probability the victim is male or female, the probability that it is any of the four victims or they could draw a tree diagram examining the combination of the four victims with the two suspects and therefore calculate the probability of each combination.
Content/Topics:
Probability
Tree Diagrams (4 victims, 2 suspects)
Equations
Ratios
Measurement
The Body Part IV: Gender
Students need to use the bone sets from The Body Part III: The Bones to compare the pelvis' of each victim. One victim is male and one is female. Our victim (bone set 4) is female. Students can then identify using the height and gender which one of the missing persons is the likely victim.
Content/Topics:
Number
Measurement
The Murderer
This section focuses on the use of fingerprints as a form of identification. Students will examine their own fingerprints first and identify if their fingerprints contain loops, whorls or arches. They will then calculate the class totals of loops, whorls and arches and convert them to percentages before using graphing software to graph a column graph comparing them.
Finally students will examine each suspects fingerprints and compare them to the ones at the crime scene. They will count the number of ridges and loops, whorls and arches to help them identify if there are any matches.
Content/Topics:
Literacy
Number
Data and statistics
Percentages
Activity 2 Solutions Suspect two has some matches, as per below. From gun = Left Thumb From the glass entry way = No Match From Hammer = Right Thumb From Bedroom Door Handle = Left Pinkie From Hallway Door = Left 3rd Finger