CensusAtSchool home page > Maths - C@S Projects
 CaSMa04 - Could the footprint belong to the person in the image?
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1. Subject Area
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Mathematics |
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2. Suggested Level
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Years 8-12 |
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3. Key Statistical Literacy Competencies Addressed | |
- Data awareness
- The ability to understand statistical concepts
- The ability to analyse, interpret and evaluate statistical information
- Communicating statistical information and understandings
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4. Overview |
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In this classroom activity you are to prepare a report for Belinda, the manager of a forensic science unit. Your report may be used as evidence by those investigating the crime so it must be clear and easy to understand. A part image of a person from a security camera and a footprint are the two key pieces of evidence from the crime scene. Are they from the same person? |
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5. Requirements | |
- Computer with internet connection
- Spreadsheet software
- Calculator
- Pens and paper
- Student Worksheet
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6. Instructions | |
You, Dan and Lucy work in a forensic science unit lead by Belinda. The unit is asked to investigate whether a footprint, found at a crime scene, belongs to the person whose partial image is captured by a security camera at the scene.
Figure 1:Security camera image.
The footprint was measured to be 24 cm in length.
Belinda wants to know if both belong to the same person.
Task 1. Dan’s first thoughts
Dan suggests that if they can determine the real-life length of something on the image from the security camera they may be able to make some progress.
After some investigation Dan identifies the brand and style of the board shorts being worn by the person. He also finds that they are made as a "one size fits all" with a length of 56 cm. Could this be used to find the real-life belly button height?
1. With a partner, list as many ways as you can to find the real-life belly button height of the person in the image.
2. Choose one way and use it to find the real-life belly button height of the person in the image. Include any rules, tables or graphs you used.
Task 2. Lucy poses a question.
Is it possible to estimate the height of a person from their ‘belly button’ height?
Height and belly button height are measured in the CensusAtSchool questionnaire. This data could be used to investigate Lucy's question.
3. Brainstorm ideas of how you can investigate Lucy's question using the CensusAtSchool data.
4. Choose one way and use it to estimate the height of the person in the image. Don't forget to include any rules, tables or graphs you used.
You can use the random sample in the Excel spreadsheet attachment at the bottom of the page or you can go to the CensusAtSchool website and use
the Random Sampler to obtain a sample.
Reference year Select Year
Select questions All
Sample size 200
Task 3. Another thought
Can the sample be used to estimate the height of a person from the length of their foot? If you can, is it the same as the height from the belly button estimation?
5. Brainstorm ideas of how you could investigate if it is possible to estimate the height of a person from the length of their foot.
6. Choose one way and use it to estimate the height of the person who left the footprint. Don't forget to include any rules, tables or graphs you used.
Task 4. Could the footprint belong to the person in the image?
7. From your investigations, prepare a report to the manager of the forensic science unit. You will need to clearly state your conclusion about the question "Could the foot print belong to the person in the image?" You must provide evidence to support your conclusion. |
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7. Extension | |
The Vitruvian Man and Golden Ratio
There are many relationships in nature similar to the one above. Arm span and height is another relationship that can be investigated using CensusAtSchool data.
The Vitruvian Man is one example that intrigues students of all ages. Who is he? Who made him? When? How is he connected to your earlier work?
Similarly, the golden ratio occurs in a wealth of situations natural and man made.
This topic is investigated in greater depth in CaSMa12: The Golden Ratio. |
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8. For the Teacher | |
One way to proceed with this investigation would be to:
- develop estimates for the height of the person in the image based on the belly button height
- develop estimates of the height of the person based on the footprint length
- compare the two sets of estimates.
To find the belly button height of the person in the image measure the length of the shorts and the belly button height in the image. Then use ratio to find the real belly button height of the person if the shorts are 56 cm long.
Belly button height in photograph = Belly button height in real life
length of shorts in photograph 56
We can find the belly button height in real life:
Belly button height in photograph x 56 = Belly button height in real life
length of shorts in photograph
To investigate Lucy's question students could:
Draw an xy scatter plot of the two variables (height and belly button height) to determine the relationship. Excel can be used to draw a line of best fit and find its equation, if required.
Or
Find the height divided by the belly button height for each row of data and average these.
You can expect this division to approximate to 1.6. (Height = 1.6 x Belly button height).
In assessing student’s work on this task, consideration of how well (if at all) the following points were included may be useful in differentiating between the levels of work presented.
Did the student :
- check the reliability of each of the data points in their sample?
- consider sampling variation by averaging the results from a number of like samples (this should be considered a high order inclusion)
- consider gender effects
- consider age effects
- choose the most appropriate sample
The activity could be broadened by changing Dan's first thought to:
"One of the team members, Dan, suggests that if they can determine the real-life length of something in the image from the security camera they may be able to make some progress.
After some investigation he identifies the brand and style of the board shorts being worn by the person. He also finds that they are made only in the following lengths 44 cm, 50 cm and 56 cm." |
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Download the Activity
To provide any feedback regarding this activity, please contact ABS Education Services on 1800 623 273 or email education@abs.gov.au.
Back to activities list for Maths - C@S Projects |
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This page last updated 17 March 2011 | 
