Leonardo da Vinci Activity

Art, Nature, Ratios, and Graphing

adapted from a plan by Suzanne Alejandre

Teacher Lesson Plan

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This activity is appropriate for a beginning Algebra course in either middle or high school. It aligns with NCTM Standards for Measurement, Connections, and Algebra for grades 9-12. In the North Carolina SCOS, it directly addresses a goal for all students that they develop: "Connections within mathematics and with other disciplines." It aligns with the following goals and objectives in grades 9-12: Introductory Math (3.01, 3.02, 4.01, 4.02), Algebra (3.03).

I.    Goals:
  • The learner will collect, organize, and interpret data with linear models
  • The learner will begin to develop an appreciation of the works of Leonardo da Vinci and an understanding of mathematical proportion in nature

II.   Objectives:
  • Students will gather data
  • Students will represent that data in a table, a graph, a function, and verbal description
  • Students will attempt to find the line of best fit and explain the significance of the slope of the line
  • Students will be encouraged to further explore the life and work of Leonardo da Vinci

III.   Materials
  • Each team of students (2-4, depending on class size) will need a measuring tape and/or yardstick
  • String (2 colors)
  • Scissors to cut string (you can precut the string into 6 foot lengths -- each student will need one string of each color)
  • Additional library materials on Leonardo da Vinci
  • Student Page for this activity (if you don't supply the student page, be sure to make a copy(ies) of da Vinci's Vitruvian Man available for viewing)
  • Graph paper for each student
  • Straight edges (rulers) for graphs
IV.   Motivation
  • Begin by showing students a picture of the Mona Lisa. Ask if they have ever seen it before and if they know who painted it. Pass out any collected books or materials on da Vinci for students to look at while you supply some background information. Then pass out student pages.
  • Tell the students that:
    • Leonardo da Vinci lived in Italy in the 1400s
    • He was a great painter, sculpture, engineer , scientist, inventor, singer, and also a mathematician
Transition: Today we are going to consider some of his mathematics ideas and try to find out if he was actually right!

V.   Lesson Procedure
  1. Using whatever method you prefer, divide the class into groups of 2-4 students, depending upon class size.
  2. Tell the students what they will be doing: working together to try to provide or disprove one of da Vinci's ideas
  3. Tell students to look at the picture at the top of their page and ask them:
  • What is the man inside of?
  • What does this drawing imply about the man in the picture?
  • Do you think this is true ... should we believe a drawing?
       4.   Gather data: Ask the class to work within their groups to:
  • measure the both the height and arm span of their group members*
  • cut the ____ color string to equal their height, and the ____ color string to equal their arm span

Work with students to encourage as much accuracy as possible and to keep them on task. Ask if they notice anything about their strings.

*if possible, you could save time by preparing 1-2 "measuring spots" on the wall of the room so they could just stand against it and measure height more quickly.

        5.    Direct students to:
  • return to their desks and convert their measurements into centimeters and calculate the ratio between their arm span and height.
  • write the results for their group on the chart on the board
  • copy down all the data from the class
  • construct a graph (individually, so the group can check each other's work) with height along the x-axis and and arm span along the y-axis.
While they are working, move around the room, answering questions and guiding efforts. Question them about anything they are noticing as they graph their points.

        6.    Draw and example on the board and talk with students about finding the "line of best fit."  Ask:
  • What does this line represent? An approximation of the graph of the linear equation that represents our data.
        7.    Ask them to do that for their graphs and find the slope of their line by choosing two points on their line of best fit
        8.    Have students record their slope on the board
        9.    Ask:
  • What does the slope mean here? It's the ratio of arm span to height for our class.
  • If Leonardo's drawing was correct, what would we expect it to be?*
  • Why possible sources of error were there in our project?
  • Could this ratio have changed over time? Would it be different for different age people?
* (if you have had the opportunity to enter data points into a calculator and actually compute the slope of the line of best fit with the students)

VI.   Closure
We began today looking at a picture of one of the greatest works of art, created by a brilliant man. Though Leonardo studied many things, he studied math to further his art. Tonight in your journal, I want you to answer three questions:
  • Why was an artist interested in this ratio?
  • Who else might need to understand the usual proportions of the human body?
  • Can you think of any other examples in nature of ratios?
VII.    Extension:
If there is time:
  • Have students attempt to line up all their strings for height and all their strings for arm span separately and  neatly along a length of masking tape in descending order of size. This can serve as a visual reminder of the measurements and displayed to remind them of the work they've done.
  • Allow students to use classroom computers to explore the web sites referenced on their worksheets.

VIII.   Reflections (after the lesson)

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Other resources

How not to think like Leonardo --
Timeline of Leonardo's math work --
The Anatomical Drawings of Leonardo da Vinci --
Exploring Leonardo --
Standard Visual Human Body Proportions --
Leonardo da Vinci: A Man of Both Worlds --