Secondary
The data you need to collect with your class is described on the Core Activities page.
Lead-up ideas
What measurements could you make about your foot? Is there a correlation between length and any of the other measurements you suggested?
Pose some questions or develop some hypotheses about the relationship (if any) between people's foot length and their height.
Find out what data are being collected in Reach for the Stars 2007. Will this help you to answer your questions? If you are able to conduct investigations involving other classes, what form will you want to collect the data in for comparison and analysis? (Is the “averaging” process being used in the national data collection sufficient for your investigation, or do you want to have a collection of paired height and foot length measurements for individuals? How will you manage this?)
Work with a pre-school or junior primary class to assist them with measuring and recording data – we are developing a “Measurement Mentors” sheet which will provide some guidance for working with young children on measurement tasks.
Construct a “Foot Size” measurement device which could be used by (or with) young students.
Discuss how you will record and group your collected data.
Find out about the relative proportions of the (male) human body according to Vitruvius (Try a Google search on “Vitruvian Man”). If these proportions are correct, how many “feet” should there be in a person’s height? How could you test this?
Collecting and recording the data
| Class data record sheets are available (as printable sheets or as an Excel workbook). |
Students could propose, discuss and decide on appropriate methods for measuring, recording and summarising the necessary information.
Conversions between millimetre (mm) and centimetre (cm) units could be discussed in the context of foot length measurements.
If some students have difficulty determining their "Foot Size" by comparing their foot length measurement with the Foot Size Scale table, then more concrete comparison methods could be used (see the suggestions on various pages targeted at younger age groups).
Record the data in a variety of tables and graphs (which might include cumulative frequency tables for some classes).
Investigating
Describe the data with appropriate statistical measures (e.g. mean, median, mode, range, maximum, minimum etc.).
Use a scatter plot to look at the possibility of a relationship between height and foot length. Is it reasonable to draw a line of best fit? If so, what is the slope and y-intercept of the line (using technology or a hand-drawn graph)? What is the real-life meaning of the "y-intercept" value? What does the equation of the line allow you to do? if you found a relationship, does this mean that the ration of height to foot length should be exactly the same for every person?
Can you use your data to construct an argument in support of Vitruvius’ statements about the proportions of the body? Can you use it to argue that Vitruvius was wrong? Can you do both? Hold a classroom debate.
Can you compare your data with data from other classes? What similarities and differences are there? Does age or stage of life influence your findings about any relationship between foot size and height (i.e. are adults different from children? Are babies different?)
Why do you think the national data were collected as grouped data (“Foot Sizes” and total heights) rather than individual measures of height and foot length? If you could determine how the national data would be collected, what would you do in order to best explore the questions you developed?
What limitations does the national data collection have? What kind of assumptions must have been made in calculating the returned information? Are any of these problematic?
Do some further research to discover whether others have found a “normal” ratio of height to foot length for humans. How does this relate to the slope of your graph? Does their data differ with gender, age, ethnicity etc.?
Some possible avenues for extension for senior students
- Function fitting to scatter plots of height and foot length data.
- Further appropriate statistical calculations, descriptions and representations (such as standard deviation, quartile calculations, box plots...)
- Comparisons of data separated by age, gender etc.
- What type of distribution describes height or foot length for students of a given age? What is the probability that the student who made a particular footprint is in Year 11?