Leonardo da Vinci Activity
Art, Nature, Ratios,
adapted from a plan by Suzanne
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).
- The learner will collect, organize, and interpret data with
- The learner will begin to develop an appreciation of the
Leonardo da Vinci and an understanding of mathematical proportion in
- 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
- 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
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
- Graph paper for each student
- Straight edges (rulers) for graphs
- Begin by showing students a picture of the Mona Lisa. Ask
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
V. Lesson Procedure
- Using whatever method you prefer, divide the class into
groups of 2-4 students, depending upon class size.
- Tell the students what they will be doing: working together
to try to provide or disprove one of da Vinci's ideas
- Tell students to look at the picture at the top of their
page and ask them:
4. Gather data: Ask the
class to work within their groups to:
- 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?
- measure the both the height and arm span of their group
- cut the ____ color string to equal their height, and the
____ color string to equal their arm span
Work with students to encourage
accuracy as possible and to keep them on task. Ask if they notice
anything about their strings.
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.
- 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
other's work) with height along the x-axis and and arm span along the
While they are working, move
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:
do that for their graphs and find the slope of their line by choosing
two points on their line of best fit
- What does this line represent? An approximation of the graph of the
linear equation that represents our data.
students record their slope on the board
- What does the slope mean here? It's the ratio of arm span to height for
- If Leonardo's drawing was correct, what would we expect it
- 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
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?
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
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
- Allow students to use classroom computers to explore the
web sites referenced on their worksheets.
(after the lesson)