LEARN NC

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

Golden ratio

http://illuminations.nctm.org/LessonDetail.aspx?ID=L658

A lesson plan for Grades 6–8 Mathematics

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
6–8
Subjects
mathematics (algebra)
Provider
National Council of Teachers of Mathematics

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Students explore the Fibonacci sequence, examine how the ratio of two consecutive Fibonnacci numbers creates the Golden Ratio, and identify real-life examples of the Golden Ratio. Illuminations provides an activity sheet, and overhead template, and detailed instructions for completing the lesson.

Students will:

  • Discover the Fibonacci Sequence with the rabbit problem.
  • Use a spreadsheet to examine the Fibonacci Sequence.
  • Graph the Fibonacci numbers in a scatterplot.
  • Examine similar rectangles.
  • Recognize the Golden Ratio in nature, architecture, and art.

NCTM Standards and Expectations:

  • Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
  • Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 6

  • Goal 5: Algebra - The learner will demonstrate an understanding of simple algebraic expressions.
    • Objective 5.03: Solve simple (one- and two-step) equations or inequalities.
    • Objective 5.04: Use graphs, tables, and symbols to model and solve problems involving rates of change and ratios.

Grade 7

  • Goal 5: Algebra - The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.
    • Objective 5.01: Identify, analyze, and create linear relations, sequences, and functions using symbols, graphs, tables, diagrams, and written descriptions.
    • Objective 5.03: Use and evaluate algebraic expressions, linear equations or inequalities to solve problems.

Grade 8

  • Goal 5: Algebra - The learner will understand and use linear relations and functions.
    • Objective 5.03: Solve problems using linear equations and inequalities; justify symbolically and graphically.