Leonardo da Vinci Activity

## Teacher Lesson Plan

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This activity is aligned to NCTM Standards - Grades 6-8: Algebra, Measurement, Problem Solving, Communication, and Reasoning and Proof

Vitruvius, a Roman engineer of the first century B.C., influenced Leonardo da Vinci's work in architecture and also his drawing of the human figure. One of Leonardo's drawings is called the Vitruvian Man. It is based on a model of ideal proportions which Vitruvius established.

The drawing shows a square inscribed inside a circle. There is a man with outstretched arms and legs, in fact two pairs of each, which touch both the circumference of the circle and the vertices of the square. Upon viewing the drawing the conclusion can be made that the length of a man's arm span is equal to the height of the man. In other words the ratio of the Vitruvian Man's arm span to his height equals 1.

How can we trust a drawing? The following activity will investigate if this is true or not. After data have been gathered from all of the students in the class, students will be asked:
1. Explain the conclusion to the question - Is your arm span equal to your height?
2. Do men (boys) of the 1900's and 2000's have the same proportions as the Vitruvian Man?
3. Do women (girls) of the 1900's and 2000's have the same proportions as the Vitruvian Man?
4. Are taller men (boys) more likely to have Vitruvian Man proportions than shorter men (boys)?
5. Are taller women (girls) more likely to have Vitruvian Man proportions than shorter women (girls)?
6. Generalize for all of the students in the class using the class data.
7. Explain what your graphs showed.
Question: Is the ratio of our arm span to our height really equal to 1?

 Gathering the Data
1. Pass out the following materials for each group of four students:
• 2 measuring tapes and/or yardsticks and/or rulers
• string
2. Instruct the students to work in pairs and measure both their height and their arm span. As they measure they should cut a piece of string equal to the two measurements. This can be accomplished by measuring first and then measuring out the string OR by using the string as the measuring device, cut it and then find the length of the string. Either method should result in two pieces of string per person and noted measurements per person.

Note: Another method in the interest of time is to create a measuring area in the room. Tape up some yard sticks and have students use that prepared area to measure their height. Once that measurement is quickly taken they can return to their groups to measure their arm spans.

3. Have the students note the difference between the lengths of string even as they note the exact linear measurements that they find. As they work with the data and calculate the ratios, remind them of the two string lengths as a physical reminder of the numerical data.

 Processing the Data

Collect the student data by recording on the overhead, chalkboard or poster paper. One column should list the height, a second column should list the arm span and a third column will be the ratio of the two.

Once the data have been entered into columns one and two, have the students calculate the ratios for the third column. This could be completed several ways:
1. each student completing the calculation and then reporting, coming to consensus and recording for all the class to see.
2. each group taking several to calculate and then reporting and recording for all the class to see.
3. as a homework assignment.

Method 1 -- Graph Paper
Using the class data instruct students to graph the two columns of data using either the given grid or standard graph paper. Here is a sample to display.

Using the class data instruct students to graph the third column of data using either the given grid or standard graph paper.
Using the class data instruct students to graph the two columns of data using a spreadsheet program.

Using the class data instruct students to graph the third column of data using a spreadsheet program
Discussion Questions:
• Do men (boys) of the 1900's and 2000's have the same proportions as the Vitruvian Man?
• Do women (girls) of the 1900's and 2000's have the same proportions as the Vitruvian Man?
• Are taller men (boys) more likely to have Vitruvian Man proportions than shorter men (boys)?
• Are taller women (girls) more likely to have Vitruvian Man proportions than shorter women (girls)?
• Does the arm span increase linearly with height, i.e. is there a sort of best-fit line through the data points or does the taller you are mean the wider your arm span is?
 Processing the Data

Instruct students to respond to the following journal prompts:
• Explain the conclusion to the question - Is your arm span equal to your height?
• Generalize for all of the students in the class using the class data
• Explain what your graphs showed.
 Extensions/Resources

Leonardo da Vinci Resources