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K–12 teaching and learning · from the UNC School of Education

Phi: The divine proportion

The "divine ratio" is valued by designers, artists, and architects because of its interesting and and unique properties. In this lesson for grade six, students learn about this ratio and use it to create a work of art.

An activity for grade 6 Mathematics

By Kim Abrams, Mike McDowell, and Barbara Strange

Provided by CareerStart

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CareerStart lessons: Grade six
This collection of lessons aligns the sixth grade curriculum in math, science, English language arts, and social studies with potential career opportunities.
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The “divine ratio” — a ratio of 1.6180339… — is usually denoted by the Greek letter phi. Designers, artists, and architects often use this ratio when creating rectangular objects. Easy examples include credit cards, light switch plates, and KitKat chocolate bars. With each of these objects, dividing the length by the width results in an answer of 1.6180339… In this lesson, students learn about the unique and interesting properties of the divine ratio.

Learning outcomes

Students will use the basic math operations with decimals as they relate to art and the idea of beauty (phi).

Teacher planning

Materials needed

Time required for lesson

1-2 class periods and homework time

Procedure

  1. Have students read their copy of “The Divine Proportion: Measuring Activity”
  2. Explain the scenario from the reading
  3. Walk around the classroom, school, or campus to answer question #1.
  4. Work on question #3 in class.
  5. Assign question #2 as homework.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 6

  • Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
    • Objective 1.04: Develop fluency in addition, subtraction, multiplication, and division of non-negative rational numbers.
      • Analyze computational strategies.
      • Describe the effect of operations on size.
      • Estimate the results of computations.
      • Judge the reasonableness of solutions.
  • Goal 2: Measurement - The learner will select and use appropriate tools to measure two- and three-dimensional figures.
    • Objective 2.01: Estimate and measure length, perimeter, area, angles, weight, and mass of two- and three-dimensional figures, using appropriate tools.
    • Objective 2.02: Solve problems involving perimeter/circumference and area of plane figures.