Car board game.

CareerStart lessons: Grade six

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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


  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.


Optional resources for more information on the topics covered in this lesson Arts Careers
This website lists and briefly describes careers in the arts, linking to more detailed information for each career on the Bureau of Labor Statistics website.
Mr. Narain’s Golden Ratio Website
This website introduces students to the golden, or divine, ratio and hosts eight activities about the use of the divine ratio in everyday objects, architecture, art, nature, and more.
Golden Rectangle
After reading the instructions, students can use this activity to plot spirals within the golden rectangle.
A Golden Ratio Activity: A Golden Greek Face
This website shows students how to calculate facial proportions using the divine ratio.
The Golden Ratio
This online lesson has students find and build golden rectangles and then confirm the ratio using algebra.

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.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 6

        • Ratios & Proportional Relationships
          • 6.RPR.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For...
      • Grade 7

        • The Number System
          • 7.NS.3Solve real-world and mathematical problems involving the four operations with rational numbers.1