NCDPI – AIG Instructional Resource: Background Information
Resource Title: Perfectly Proportioned
Subject Area/Grade Level (s): Mathematics/4
Time Frame: One-two days
Common Core Standard Addressed:
Number and Operations -Fractions
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording
the conclusion by the equation 5/4 = 5 × (1/4).
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a
visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to
represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party,
how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Mathematical Practice
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
Additional Standards Addressed:
4.V.3 Create art using a variety of tools, media, and processes, safely and appropriately.
4.V.3.3 Create art using the processes of drawing, painting, weaving, printing, stitchery, collage, mixed media, sculpture, ceramics, and current
technology.
4.CX.2 Understand the interdisciplinary connections and life applications of the visual arts.
4.CX.2.2 Apply skills and concepts learned in other disciplines, such as math, science, language arts, social studies, and other arts, in the visual arts.
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
Brief Description of Lesson/Task/Activity: Students will recognize the utility of mathematics in art. They will apply Leonardo Da Vinci’s rules of
proportion for the human body and will use these rules to compose self-portraits. In order to determine the measurements of specific body
parts, students will use multiple strategies, such as multiplying whole numbers by fractional parts. This activity also allows students to make
conversions between measurements, connections between linear measurement and fractions, and see the relationship between multiplication
of a fraction and division by a whole number.
Type of Differentiation for AIGs (include all that apply):
Adaptations for AIGs: Content
x Process
x Enrichment
x Extension
Acceleration
x Product
Explanation of How Resource is Appropriate for AIGs: In fourth grade, students multiply fractions by whole numbers using concrete
representations and models. This task requires students to apply fourth grade concepts to a more complex and abstract situation. As students
complete their self-portraits, they will continuously make connections between linear measurement and fraction concepts. Additionally,
students must contextualize fraction concepts as they work; they will need to self-monitor their strategies by ensuring that the mathematics is
accurate and their portraits are proportional.
Needed Resources/Materials
•
Rules of Proportion
•
Sample Portraits
•
computers with access to Microsoft Publisher
•
craft paper
•
markers
•
rulers
•
calculators
Sources: NA
TEACHER NOTES: NA
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
NCDPI AIG Curriculum Resource Outline
STAGE ONE: ENGAGE
One of the most difficult subjects to paint is the human body. Leonardo Da Vinci, a famous artist, realized that the use of mathematics is vital in
painting an accurately proportioned person. Therefore, he developed rules about the proportions of the human body. For example, a person’s
head should be one eighth of their total height. When painting or drawing, DaVinci followed these rules to ensure that the subject looked
realistic.
Show students Da Vinci’s Rules of Proportion. Show students Da Vinci’s painting of The Mona Lisa. Discuss how the rules may have been used to
create The Mona Lisa. Compare Da Vinci’s portrait to El Greco’s St. Jerome, cardinal. Discuss which painting more accurately depicts a real
person. Make observations.
STAGE TWO: ELABORATE
Preview Da Vinci’s Rules of Proportion. Provide students with craft paper or access to Microsoft Publisher, and challenge them to use Da Vinci’s
rules to create a self-portrait that is two feet tall. Before beginning, ask students to silently answer the following questions:
 What is the first thing you will need to do? Students may want to draw as they are finding each measure. However, it will be easier to start
by finding all measurements.
 What mathematics will you need to use to determine your measurements? Students will need to convert feet to inches. Then, they will need
to multiply 24” by each fraction to determine the various measurements.
 How will you organize your measurements? It may be necessary to suggest that students record all information in a chart or table before
beginning their self-portrait.
As students work, they will tend to think solely about the mathematics of the task. Make sure that students periodically contextualize their
mathematics by ensuring that their measurements accurately depict the proportions of the human body. If not, the student may need to revisit
their mathematics. Ask, “How can you prove that your measurements are accurate?”
Once all students have completed their self-portraits, have them share with the group. Ask the following questions, while encouraging students
to add on to each other’s thinking, and critic each other’s reasoning
 How did you organize your work? Draw attention to the use of charts and tables.
 What strategies did you use to solve this problem? For example, students should realize that they could find the measurement of the head by
multiplying 24 by 1/8. However, they should also realize that this is the same as dividing 24 by 8. Make connections between the two strategies.
 What tools were useful in determining the various measures? E.g., a ruler or number line
 What was the easiest part of this task? What was the most difficult?
 How did you monitor your work for accuracy? Was there a time when you realized something was incorrect? How did you know? How did
you fix your error?
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project
STAGE THREE: EVALUATE
The teacher should observe the mathematics used for determining the lengths of each body part. Students should accurately and precisely
explain how the measurements were found and justify their solutions. Assessment will also be based on the student’s ability to self-monitor
their work and check for accuracy of the mathematics throughout the process.
TEACHER NOTES:
 El Greco is known for purposely distorting and exaggerating proportions of the human body. Many of his paintings display examples of the
human form with exaggerated physical features.
 If students opt to use Microsoft Publisher, they will need to create a custom page size to fit a 24” portrait.
PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction
AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project