Student worksheet
Downloadable versions of this activity are available in the following formats: (RTF format,PDF format)
Note: Teachers, see Teacher’s lesson plan
Leonardo da Vinci (14521519) was a scientist and an artist, one of the greatest painters of the Italian Renaissance. He left only a handful of completed paintings, one of which is the Mona Lisa. He was so secretive that he wrote backwards to disguise his ideas.
In 1492, Leonardo drew a picture of a man standing inside a circle and a square. This is known as the ‘Vitruvian Man’. It was a study of the proportions of the human body as described by Vitruvius, a Roman architect from the first century B.C. Based on his observations of European people of his day, Leonardo believed that arm span was equal to height in a perfectly proportioned body.
Why do you think he was interested in working out body proportions?
Do you think the Vitruvian theory illustrated by Leonardo would work today?
Problem
Is the Vitruvian theory that height is equal to arm span true for Canadian students today?
Plan
Before you begin your investigation, what answer do you predict? Why?
Now test your prediction using data from your class.
Data
Enter the data for 10 students from your class in this table.
How will you select the students for your sample?
Do not simplify the fraction for the arm span / height ratio.
Student  Gender  Arm span  Height  Ratio: arm span / height 

M or F  cm  fraction  decimal  
Student A  
Student B  
Student C  
Student D  
Student E  
Student F  
Student G  
Student H  
Student I  
Student J 
Analysis
1. Have a look at the table of data. What does each row represent? What do you notice about the data?
2. Which students most closely fit Leonardo’s theory?
3. How do you know that a student fits this theory?
4. Graph the information from the table, using graph paper. You might have to draw different kinds of graphs to show all the information.
5. Look at the graphs you have drawn. What words could you use to describe the shapes, range and spread of the information?
6. Not everybody has an arm span / height ratio that is equal to 1. Why do you think this is?
Conclusion
You are now ready to answer the question we asked at the beginning of the worksheet:
Is the Vitruvian theory that height is equal to arm span true for Canadian students today?
Using some of the words below, give reasons based on what you found in your investigation:
analysis  gradient  ratio 
arm span  height  row 
biased  investigate  sample 
bivariate  justify  scatterplot 
cluster  measure  selection 
conclusion  middle  skew 
data  outlier  slope 
distribution  predict  spread 
equal  problem  systematic 
frequent  random  table 
Adapted and reproduced with permission from CensusAtSchool New Zealand.